Stat.CLT.BerryEsseen.PrawitzLowRationalCertificate
This arithmetic leaf certifies every parameter cell, including the switch between the two discrepancy branches.
PrawitzLowRationalCertificate 1 core · 0 supporting This arithmetic leaf certifies every parameter cell, including the switch between the two discrepancy branches. ★ prawitz_low_rational_sum_certificate
Finite rational certificate for the normalized low Prawitz sum
This arithmetic leaf certifies every parameter cell, including the switch between the two discrepancy branches. It imports no admitted cutoff, integral allocation, smoothing comparison, or Berry--Esseen theorem. The sum includes the initial singularity enclosure and all adjacent cells; its normalization is 5/6 times the raw low integral, so its target is 1/4. Unreduced integer fractions avoid repeated normalization of large Taylor numerators; proved evaluation identities preserve the exact rounded cells.
theorem prawitz_low_rational_sum_certificate reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
On each of the explicit compact parameter cells, the complete outward-rounded rational low-frequency sum is at most one quarter.
Formal statement
Proof (Lean source)
theorem prawitz_low_rational_sum_certificate (j : Fin 270) :
prawitzRationalLowSum j.val ≤ (1 / 4 : ℚ) := by
/- Lowest open layer: EXACT finite rational sums only. Every cell is
rounded UP to a common denominator of 10^8, so the sum is an integer
comparison after multiplying by that denominator. Generate checked
upper integer bounds for blocks of cells if full reduction is expensive.
Reuse the defined polynomial; no exp/log/sqrt or integration is
needed in this file. Kernel-checked norm_num/decide certificates are
acceptable; native_decide and extra axioms are not. Exploratory DOUBLE
arithmetic reported a maximum about 0.247515 near rho=0.235 before
rounding (<=859 cells add less than 0.00000859). This is sanity guidance,
not a proof. Preserve every table, term, minimum, and rounding direction.
Later assembly: locate rho in one of the 270 contiguous parameter cells,
use the cutoff certificate to extend the nonnegative low integral to
B=K/200<=U, and split with sum_integral_adjacent_intervals. Apply
prawitz_low_compact_initial_integral_bound to [0,1/200] and
prawitz_low_compact_endpoint_cell_integral_bound thereafter. Replace
1/pi by 100000/314159, exp(-e/2) and exp(-e) by reciprocal Taylor
bounds, and each resulting rational by its outward rounding. This
leaf proves its numerical total; it is never an assumption on a law. -/
have hblocks (b : Fin 27) (l : Fin 10) :
(⌈100000000 * prawitzRationalLowInitial (10 * b.val + l.val)⌉ +
∑ i ∈ Ico 1 (prawitzLowCutoffIndex (10 * b.val + l.val)),
⌈100000000 * prawitzRationalLowCell (10 * b.val + l.val) i⌉ : ℤ) ≤ 25000000 := by
fin_cases b
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block00 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block01 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block02 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block03 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block04 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block05 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block06 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block07 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block08 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block09 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block10 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block11 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block12 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block13 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block14 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block15 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block16 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block17 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block18 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block19 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block20 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block21 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block22 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block23 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block24 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block25 l
· simpa only [lowIntPrefix_cutoff, lowCellInteger_eq] using lowInteger_block26 l
let b : Fin 27 := ⟨j.val / 10, by omega⟩
let l : Fin 10 := ⟨j.val % 10, Nat.mod_lt _ (by decide)⟩
have hj : 10 * b.val + l.val = j.val := by
dsimp [b, l]
omega
have h := hblocks b l
rw [hj] at h
have hc : ((⌈100000000 * prawitzRationalLowInitial (j.val)⌉ +
∑ i ∈ Ico 1 (prawitzLowCutoffIndex (j.val)),
⌈100000000 * prawitzRationalLowCell (j.val) i⌉ : ℤ) : ℚ) ≤ 25000000 := by
exact_mod_cast h
push_cast at hc
unfold prawitzRationalLowSum prawitzRoundUp
simp only [div_eq_mul_inv, ← Finset.sum_mul, ← add_mul]
linarith
Bounds 1 core · 0 supporting Assembles the ten-row tables into one lookup indexed by the parameter cell.
Low Prawitz certificate: selector for the candidate bound tables
Assembles the ten-row tables into one lookup indexed by the parameter cell.
def lowBounds reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The list of candidate integer upper bounds for parameter cell j: row j mod 10 of the ⌊j/10⌋-th of twenty-seven ten-row tables, and the empty list when j is out of range. The candidates are data; each is checked separately by the certificate.
Definition (Lean source)
parameters
j :
ℕ
def
given by
((#[lowBounds00, lowBounds01, lowBounds02, lowBounds03, lowBounds04, lowBounds05, lowBounds06, lowBounds07, lowBounds08, lowBounds09, lowBounds10, lowBounds11, lowBounds12, lowBounds13, lowBounds14, lowBounds15, lowBounds16, lowBounds17, lowBounds18, lowBounds19, lowBounds20, lowBounds21, lowBounds22, lowBounds23, lowBounds24, lowBounds25, lowBounds26].getD (j / 10) #[]).getD (j % 10) [])
Core 16 core · 0 supporting Unreduced integer-fraction arithmetic, the rounded low-cell integers, and the Boolean prefix checker with its soundness lemma.
Low Prawitz certificate: unreduced-fraction arithmetic and checker
Unreduced integer-fraction arithmetic, the rounded low-cell integers, and the Boolean prefix checker with its soundness lemma. The data tables and the kernel-checked blocks that consume them live in sibling modules.
def lowRawVal reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The rational value of an unreduced integer pair (numerator, denominator) is the numerator divided by the denominator; a zero denominator gives zero.
Definition (Lean source)
parameters
q :
ℤ × ℤ
def
lowRawVal q :
ℚ
given by
(q.1 : ℚ) / (q.2 : ℚ)
def lowRawRat reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The pair (numerator, denominator) of a rational number in lowest terms.
Definition (Lean source)
parameters
x :
ℚ
def
lowRawRat x :
ℤ × ℤ
given by
(x.num, x.den)
def lowRawMul reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Multiplication of unreduced fractions: numerators and denominators are multiplied separately, with no reduction to lowest terms.
Definition (Lean source)
parameters
q r :
ℤ × ℤ
def
lowRawMul q r :
ℤ × ℤ
given by
(q.1 * r.1, q.2 * r.2)
def lowRawDiv reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Division of unreduced fractions: (n₁, d₁) divided by (n₂, d₂) is (n₁·d₂, d₁·n₂), with no reduction to lowest terms.
Definition (Lean source)
parameters
q r :
ℤ × ℤ
def
lowRawDiv q r :
ℤ × ℤ
given by
(q.1 * r.2, q.2 * r.1)
def lowRawAdd reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Addition of unreduced fractions by cross-multiplication, (n₁·d₂ + n₂·d₁, d₁·d₂), except that when one summand has zero denominator (rational value zero) the other summand is returned unchanged.
Definition (Lean source)
parameters
q r :
ℤ × ℤ
def
lowRawAdd q r :
ℤ × ℤ
given by
if q.2 = 0 then r else if r.2 = 0 then q else (q.1 * r.2 + r.1 * q.2, q.2 * r.2)
def lowRawCeil reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The ceiling of the integer fraction with numerator n and denominator d, computed by integer division: −⌊−n/d⌋ when d ≥ 0 and −⌊n/(−d)⌋ when d < 0. A zero denominator gives zero.
Definition (Lean source)
parameters
q :
ℤ × ℤ
def
lowRawCeil q :
ℤ
given by
if 0 ≤ q.2 then -(-q.1 / q.2) else -(q.1 / -q.2)
def lowTaylorNum reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The integer Taylor numerator at integers n and d is the sum over k from 0 to 15 of (15!/k!)·nᵏ·d^(15−k), written in Horner form. For d ≠ 0 it equals 15!·d¹⁵ times the sixteen-term Taylor polynomial of the exponential at n/d.
Definition (Lean source)
parameters
n d :
ℤ
def
lowTaylorNum n d :
ℤ
given by
(1307674368000 * d ^ 15 + n * (1307674368000 * d ^ 14 + n * (653837184000 * d ^ 13 + n * (217945728000 * d ^ 12 + n * (54486432000 * d ^ 11 + n * (10897286400 * d ^ 10 + n * (1816214400 * d ^ 9 + n * (259459200 * d ^ 8 + n * (32432400 * d ^ 7 + n * (3603600 * d ^ 6 + n * (360360 * d ^ 5 + n * (32760 * d ^ 4 + n * (2730 * d ^ 3 + n * (210 * d ^ 2 + n * (15 * d ^ 1 + n * 1)))))))))))))))
def lowRawTaylor reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The sixteen-term Taylor polynomial of the exponential evaluated on an unreduced fraction (n, d), returned as the unreduced fraction whose numerator is the integer Taylor numerator at (n, d) and whose denominator is 15!·d¹⁵. For d = 0 (rational value zero) it returns (1, 1).
Definition (Lean source)
parameters
q :
ℤ × ℤ
def
lowRawTaylor q :
ℤ × ℤ
given by
if q.2 = 0 then (1, 1) else (lowTaylorNum q.1 q.2, 1307674368000 * q.2 ^ 15)
def lowRawPow reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The n-th power of an unreduced fraction: numerator and denominator are raised to the power separately.
Definition (Lean source)
parameters
q :
ℤ × ℤ
n :
ℕ
def
lowRawPow q n :
ℤ × ℤ
given by
(q.1 ^ n, q.2 ^ n)
def lowRawMin reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Of two unreduced fractions, the one with the smaller rational value (the first when they tie), returned in its given unreduced representation.
def lowCellBranches reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The two branches of the rational low cell bound for parameter cell j and frequency index i, each multiplied by one hundred million and kept as an unreduced integer fraction: first the Taylor branch, second the modulus-sum branch. Neither is rounded here.
Definition (Lean source)
parameters
j i :
ℕ
def
lowCellBranches j i :
(ℤ × ℤ) × (ℤ × ℤ)
given by
r :
s :
a :
(i, 200) (: ℤ × ℤ)
b :
(i + 1, 200) (: ℤ × ℤ)
neg :
(-1, 1) (: ℤ × ℤ)
e :
(lowRawMul c (lowRawDiv (lowRawAdd (lowRawDiv (lowRawPow b 3) (6, 1)) (lowRawDiv (lowRawMul s (lowRawPow b 4)) (8, 1))) (lowRawTaylor (lowRawDiv e (2, 1)))), lowRawMul c (lowRawDiv (lowRawAdd (lowRawDiv (1, 1) (lowRawTaylor e)) (lowRawDiv (1, 1) (lowRawTaylor (lowRawDiv (lowRawPow a 2) (2, 1))))) r))
def lowCellInteger reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The integer low-frequency cell for parameter cell j and frequency index i is the smaller of the ceilings of the two branch fractions. It equals the rational low cell bound multiplied by one hundred million and rounded up.
Definition (Lean source)
parameters
j i :
ℕ
def
lowCellInteger j i :
ℤ
given by
def lowIntPrefix reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The integer prefix sum for parameter cell j and length n is the sum of the integer low-frequency cells over frequency indices 1 through n; it is zero for n = 0.
Definition (Lean source)
parameters
j :
ℕ
def
lowIntPrefix j :
ℕ → ℤ
def lowBranchBound reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The Boolean test that an unreduced fraction (n, d) is at most an integer z, decided in integer arithmetic: it holds exactly when d > 0 and n ≤ z·d. When it holds, the ceiling of the fraction is at most z.
Definition (Lean source)
def lowCellBound reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The Boolean test that the integer low-frequency cell at (j, i) is at most an integer z: it holds when at least one of the two branch fractions passes the fraction test against z, which suffices because the cell is the smaller of the two rounded branches.
Definition (Lean source)
parameters
j i :
ℕ
z :
ℤ
def
given by
def lowCheckPrefix reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
The Boolean test that a list of integers bounds, entry by entry, the integer low-frequency cells of parameter cell j at frequency indices n, n − 1, …, 1 (the list is in decreasing index order): it holds exactly when the list has length n and every cell passes the cell test against its entry.
Definition (Lean source)
parameters
j :
ℕ
given by
clause 1
| 0, [] => true
clause 2
| n + 1, z :: zs => lowCellBound j (n + 1) z && lowCheckPrefix j n zs
clause 3
| _, _ => false
Tables00 9 core · 0 supporting Proposed integer upper bounds for the rounded low-frequency cells, ten parameter rows per table.
Low Prawitz certificate: candidate bound tables 0 through 8
Proposed integer upper bounds for the rounded low-frequency cells, ten parameter rows per table. They are data only; every entry is checked by the block theorems.
def lowBounds00 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 0 through 9.
Definition (Lean source)
given by
#[ [892, 911, 931, 952, 973, 994, 1016, 1038, 1061, 1084, 1108, 1132, 1157, 1182, 1207, 1234, 1261, 1288, 1316, 1344, 1374, 1403, 1434, 1465, 1496, 1528, 1561, 1595, 1629, 1664, 1700, 1737, 1774, 1812, 1851, 1890, 1931, 1972, 2014, 2057, 2101, 2146, 2191, 2238, 2285, 2334, 2383, 2434, 2485, 2538, 2591, 2646, 2702, 2758, 2816, 2876, 2936, 2998, 3060, 3125, 3190, 3257, 3324, 3394, 3465, 3537, 3610, 3685, 3762, 3840, 3919, 4000, 4083, 4167, 4253, 4341, 4430, 4521, 4614, 4709, 4806, 4904, 5005, 5107, 5211, 5317, 5426, 5536, 5649, 5764, 5881, 6000, 6122, 6245, 6372, 6500, 6631, 6765, 6901, 7040, 7181, 7326, 7472, 7622, 7774, 7930, 8088, 8249, 8414, 8581, 8751, 8925, 9102, 9282, 9466, 9653, 9844, 10038, 10236, 10437, 10642, 10851, 11064, 11281, 11501, 11726, 11955, 12188, 12426, 12667, 12914, 13164, 13420, 13680, 13944, 14214, 14488, 14768, 15052, 15342, 15598, 15690, 15782, 15874, 15967, 16060, 16153, 16246, 16340, 16434, 16528, 16623, 16718, 16813, 16908, 17004, 17100, 17196, 17293, 17390, 17487, 17584, 17681, 17779, 17877, 17976, 18074, 18173, 18272, 18371, 18471, 18571, 18671, 18771, 18871, 18972, 19073, 19174, 19276, 19377, 19479, 19581, 19683, 19786, 19888, 19991, 20094, 20198, 20301, 20405, 20509, 20613, 20717, 20822, 20926, 21031, 21136, 21241, 21346, 21452, 21558, 21663, 21769, 21875, 21982, 22088, 22195, 22301, 22408, 22515, 22622, 22730, 22837, 22945, 23052, 23160, 23268, 23376, 23484, 23592, 23700, 23809, 23917, 24026, 24134, 24243, 24352, 24461, 24570, 24679, 24788, 24897, 25006, 25115, 25225, 25334, 25443, 25553, 25662, 25771, 25881, 25990, 26100, 26209, 26319, 26428, 26538, 26647, 26757, 26866, 26976, 27085, 27195, 27304, 27413, 27523, 27632, 27741, 27850, 27959, 28068, 28177, 28286, 28395, 28503, 28612, 28720, 28829, 28937, 29045, 29153, 29261, 29369, 29477, 29585, 29692, 29799, 29906, 30013, 30120, 30227, 30333, 30440, 30546, 30652, 30758, 30863, 30969, 31074, 31179, 31284, 31388, 31493, 31597, 31701, 31804, 31908, 32011, 32114, 32216, 32318, 32421, 32522, 32624, 32725, 32826, 32927, 33027, 33127, 33227, 33326, 33425, 33524, 33622, 33720, 33818, 33915, 34012, 34109, 34205, 34301, 34396, 34491, 34586, 34680, 34774, 34868, 34961, 35053, 35145, 35237, 35329, 35419, 35510, 35600, 35689, 35778, 35867, 35955, 36043, 36130, 36216, 36303, 36388, 36473, 36558, 36642, 36726, 36809, 36891, 36973, 37054, 37135, 37215, 37295, 37374, 37453, 37531, 37608, 37685, 37761, 37836, 37911, 37986, 38059, 38132, 38205, 38277, 38348, 38418, 38488, 38557, 38626, 38694, 38761, 38827, 38893, 38958, 39023, 39086, 39149, 39212, 39273, 39334, 39394, 39453, 39512, 39570, 39627, 39683, 39739, 39794, 39848, 39901, 39954, 40005, 40056, 40106, 40156, 40204, 40252, 40299, 40345, 40390, 40435, 40478, 40521, 40563, 40604, 40645, 40684, 40722, 40760, 40797, 40833, 40868, 40902, 40935, 40968, 40999, 41030, 41060, 41088, 41116, 41143, 41169, 41194, 41219, 41242, 41264, 41286, 41306, 41326, 41344, 41362, 41379, 41394, 41409, 41423, 41436, 41448, 41459, 41469, 41477, 41485, 41492, 41498, 41503, 41507, 41510, 41513, 41514, 41514, 41513, 41511, 41508, 41504, 41499, 41493, 41485, 41477, 41468, 41458, 41447, 41435, 41422, 41407, 41392, 41376, 41358, 41340, 41321, 41300, 41279, 41256, 41232, 41208, 41182, 41155, 41128, 41099, 41069, 41038, 41006, 40973, 40939, 40903, 40867, 40830, 40792, 40752, 40712, 40670, 40628, 40584, 40540, 40494, 40447, 40399, 40350, 40300, 40249, 40197, 40144, 40090, 40035, 39979, 39922, 39863, 39804, 39743, 39682, 39619, 39556, 39491, 39426, 39359, 39291, 39223, 39153, 39082, 39010, 38938, 38864, 38789, 38713, 38636, 38558, 38479, 38399, 38318, 38236, 38154, 38070, 37985, 37899, 37812, 37724, 37635, 37545, 37454, 37363, 37270, 37176, 37082, 36986, 36889, 36792, 36693, 36594, 36494, 36392, 36290, 36187, 36083, 35978, 35872, 35765, 35658, 35549, 35440, 35329, 35218, 35106, 34993, 34879, 34765, 34649, 34533, 34416, 34298, 34179, 34059, 33939, 33817, 33695, 33572, 33448, 33324, 33199, 33073, 32946, 32818, 32690, 32561, 32431, 32300, 32169, 32037, 31904, 31771, 31636, 31502, 31366, 31230, 31093, 30955, 30817, 30678, 30539, 30399, 30258, 30116, 29974, 29832, 29688, 29545, 29400, 29255, 29110, 28964, 28817, 28670, 28522, 28374, 28225, 28076, 27926, 27776, 27625, 27474, 27323, 27171, 27018, 26865, 26712, 26558, 26404, 26249, 26094, 25939, 25783, 25627, 25470, 25314, 25156, 24999, 24841, 24683, 24525, 24366, 24207, 24048, 23888, 23729, 23569, 23409, 23248, 23088, 22927, 22766, 22605, 22443, 22282, 22120, 21958, 21796, 21634, 21472, 21310, 21148, 20985, 20823, 20660, 20498, 20335, 20172, 20010, 19847, 19684, 19522, 19359, 19197, 19034, 18872, 18709, 18547, 18385, 18223, 18061, 17899, 17737, 17575, 17414, 17253, 17091, 16930, 16770, 16609, 16449, 16289, 16129, 15969, 15810, 15651, 15492, 15333, 15175, 15017, 14860, 14702, 14545, 14389, 14233, 14077, 13921, 13766, 13611, 13457, 13303, 13150, 12997, 12845, 12693, 12541, 12390, 12239, 12089, 11940, 11791, 11642, 11494, 11347, 11200, 11054, 10908, 10763, 10619, 10475, 10332, 10189, 10047, 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2166, 2211, 2256, 2302, 2350, 2398, 2447, 2497, 2548, 2601, 2654, 2708, 2763, 2819, 2877, 2935, 2995, 3055, 3117, 3180, 3245, 3310, 3377, 3445, 3514, 3585, 3657, 3731, 3806, 3882, 3959, 4039, 4119, 4202, 4285, 4371, 4458, 4546, 4636, 4728, 4822, 4917, 5015, 5114, 5214, 5317, 5422, 5528, 5637, 5748, 5860, 5975, 6092, 6211, 6332, 6455, 6581, 6709, 6839, 6972, 7107, 7245, 7385, 7528, 7673, 7821, 7972, 8125, 8281, 8440, 8602, 8766, 8934, 9105, 9279, 9455, 9635, 9819, 10005, 10195, 10388, 10585, 10785, 10989, 11196, 11407, 11622, 11841, 12063, 12289, 12519, 12754, 12992, 13235, 13482, 13733, 13988, 14248, 14513, 14782, 15056, 15334, 15617, 15906, 16199, 16497, 16800, 17109, 17423, 17742, 18067, 18397, 18733, 19074, 19422, 19775, 20135, 20500, 20871, 21180, 21286, 21393, 21499, 21606, 21713, 21821, 21928, 22036, 22143, 22251, 22359, 22468, 22576, 22685, 22794, 22902, 23012, 23121, 23230, 23340, 23449, 23559, 23669, 23779, 23889, 23999, 24109, 24220, 24331, 24441, 24552, 24663, 24774, 24885, 24996, 25107, 25219, 25330, 25441, 25553, 25664, 25776, 25888, 26000, 26111, 26223, 26335, 26447, 26559, 26671, 26783, 26895, 27007, 27119, 27231, 27343, 27455, 27567, 27679, 27791, 27903, 28015, 28127, 28239, 28351, 28463, 28574, 28686, 28798, 28910, 29021, 29133, 29244, 29355, 29467, 29578, 29689, 29800, 29911, 30021, 30132, 30243, 30353, 30463, 30574, 30684, 30793, 30903, 31013, 31122, 31232, 31341, 31450, 31558, 31667, 31775, 31884, 31992, 32099, 32207, 32314, 32421, 32528, 32635, 32742, 32848, 32954, 33060, 33165, 33270, 33375, 33480, 33584, 33689, 33792, 33896, 33999, 34102, 34205, 34307, 34409, 34511, 34612, 34713, 34814, 34914, 35014, 35114, 35213, 35312, 35410, 35509, 35606, 35704, 35801, 35897, 35993, 36089, 36184, 36279, 36374, 36468, 36561, 36654, 36747, 36839, 36931, 37022, 37113, 37203, 37293, 37382, 37471, 37560, 37647, 37735, 37821, 37908, 37993, 38078, 38163, 38247, 38331, 38414, 38496, 38578, 38659, 38740, 38820, 38899, 38978, 39056, 39134, 39211, 39287, 39363, 39438, 39513, 39586, 39660, 39732, 39804, 39875, 39946, 40016, 40085, 40153, 40221, 40288, 40355, 40420, 40485, 40549, 40613, 40676, 40738, 40799, 40860, 40919, 40978, 41037, 41094, 41151, 41207, 41262, 41317, 41370, 41423, 41475, 41526, 41577, 41626, 41675, 41723, 41770, 41816, 41862, 41906, 41950, 41993, 42035, 42076, 42116, 42156, 42194, 42232, 42269, 42304, 42339, 42374, 42407, 42439, 42470, 42501, 42530, 42559, 42587, 42614, 42639, 42664, 42688, 42711, 42733, 42754, 42775, 42794, 42812, 42829, 42846, 42861, 42875, 42889, 42901, 42913, 42923, 42932, 42941, 42948, 42955, 42960, 42965, 42968, 42970, 42972, 42972, 42972, 42970, 42967, 42963, 42959, 42953, 42946, 42938, 42929, 42920, 42909, 42897, 42884, 42869, 42854, 42838, 42821, 42803, 42783, 42763, 42741, 42719, 42695, 42671, 42645, 42618, 42590, 42561, 42531, 42500, 42468, 42435, 42401, 42366, 42329, 42292, 42253, 42214, 42173, 42131, 42088, 42045, 42000, 41954, 41906, 41858, 41809, 41759, 41707, 41655, 41602, 41547, 41491, 41435, 41377, 41318, 41258, 41197, 41135, 41072, 41008, 40943, 40877, 40809, 40741, 40672, 40601, 40530, 40457, 40384, 40309, 40233, 40157, 40079, 40000, 39920, 39840, 39758, 39675, 39591, 39506, 39420, 39333, 39246, 39157, 39067, 38976, 38884, 38791, 38697, 38602, 38507, 38410, 38312, 38213, 38114, 38013, 37911, 37809, 37705, 37601, 37496, 37389, 37282, 37174, 37065, 36955, 36844, 36732, 36619, 36506, 36391, 36276, 36160, 36042, 35924, 35806, 35686, 35565, 35444, 35322, 35199, 35075, 34950, 34824, 34698, 34571, 34443, 34314, 34185, 34054, 33923, 33791, 33659, 33525, 33391, 33257, 33121, 32985, 32848, 32710, 32572, 32432, 32293, 32152, 32011, 31869, 31727, 31584, 31440, 31295, 31150, 31005, 30858, 30712, 30564, 30416, 30267, 30118, 29968, 29818, 29667, 29516, 29364, 29212, 29059, 28905, 28751, 28597, 28442, 28286, 28131, 27974, 27818, 27660, 27503, 27345, 27186, 27028, 26868, 26709, 26549, 26389, 26228, 26067, 25906, 25744, 25582, 25420, 25257, 25095, 24932, 24768, 24605, 24441, 24277, 24113, 23948, 23783, 23618, 23453, 23288, 23123, 22957, 22791, 22626, 22460, 22294, 22127, 21961, 21795, 21628, 21462, 21295, 21129, 20962, 20796, 20629, 20462, 20296, 20129, 19963, 19796, 19630, 19463, 19297, 19131, 18965, 18799, 18633, 18467, 18301, 18136, 17971, 17805, 17640, 17476, 17311, 17147, 16983, 16819, 16655, 16492, 16329, 16166, 16003, 15841, 15679, 15517, 15356, 15195, 15034, 14874, 14714, 14555, 14395, 14237, 14078, 13921, 13763, 13606, 13450, 13293, 13138, 12983, 12828, 12674, 12520, 12367, 12215, 12063, 11911, 11760, 11610, 11460, 11311, 11163, 11015, 10867, 10721, 10575, 10429, 10285, 10141, 9997, 9855, 9713, 9571, 9431, 9291, 9152, 9014, 8876, 8739, 8603, 8468, 8334, 8200, 8067, 7935, 7804, 7674, 7545, 7416, 7288, 7161, 7035, 6910, 6786, 6663, 6540, 6419, 6298, 6179, 6060, 5942, 5826, 5710, 5595, 5481, 5369, 5257, 5146, 5036, 4927, 4820, 4713, 4607, 4503, 4399, 4297, 4195, 4095, 3996, 3898, 3801, 3705, 3610, 3516, 3424, 3332, 3242, 3153, 3065, 2978, 2892, 2807, 2724, 2642, 2561, 2481, 2402, 2325, 2249, 2174, 2100, 2027, 1956, 1885, 1817, 1749, 1682, 1617, 1553, 1490, 1429, 1369, 1310, 1252, 1195, 1140, 1086, 1034, 982, 932, 884, 836, 790, 745, 701, 659, 618, 578, 540, 503, 467, 433, 399, 368, 337, 308, 280, 254, 228, 204, 182, 161, 141, 122, 105, 89, 74, 61, 49, 38, 29, 21, 15, 9, 6], [1831, 1869, 1908, 1947, 1987, 2028, 2070, 2112, 2156, 2200, 2245, 2291, 2338, 2386, 2435, 2484, 2535, 2587, 2639, 2693, 2747, 2803, 2860, 2918, 2977, 3037, 3098, 3161, 3225, 3290, 3356, 3423, 3492, 3562, 3633, 3706, 3780, 3855, 3932, 4011, 4090, 4172, 4255, 4339, 4425, 4513, 4602, 4693, 4785, 4880, 4976, 5074, 5173, 5275, 5378, 5484, 5591, 5700, 5812, 5925, 6040, 6158, 6278, 6399, 6524, 6650, 6779, 6910, 7043, 7179, 7317, 7458, 7602, 7748, 7896, 8048, 8202, 8359, 8518, 8681, 8846, 9014, 9186, 9360, 9538, 9719, 9902, 10090, 10280, 10474, 10671, 10872, 11077, 11285, 11496, 11712, 11931, 12154, 12380, 12611, 12846, 13085, 13328, 13576, 13827, 14083, 14344, 14609, 14878, 15152, 15431, 15715, 16003, 16297, 16595, 16899, 17208, 17522, 17841, 18166, 18497, 18833, 19174, 19522, 19875, 20235, 20600, 20971, 21349, 21733, 21937, 22045, 22153, 22261, 22369, 22478, 22586, 22695, 22804, 22913, 23022, 23132, 23241, 23351, 23461, 23571, 23681, 23791, 23902, 24012, 24123, 24233, 24344, 24455, 24566, 24677, 24789, 24900, 25011, 25123, 25234, 25346, 25458, 25570, 25681, 25793, 25905, 26017, 26130, 26242, 26354, 26466, 26578, 26691, 26803, 26915, 27028, 27140, 27253, 27365, 27477, 27590, 27702, 27815, 27927, 28039, 28152, 28264, 28376, 28489, 28601, 28713, 28825, 28937, 29049, 29161, 29273, 29385, 29496, 29608, 29720, 29831, 29942, 30054, 30165, 30276, 30387, 30497, 30608, 30719, 30829, 30939, 31049, 31159, 31269, 31379, 31488, 31598, 31707, 31816, 31925, 32033, 32141, 32250, 32358, 32465, 32573, 32680, 32787, 32894, 33001, 33107, 33213, 33319, 33425, 33530, 33635, 33740, 33845, 33949, 34053, 34156, 34260, 34363, 34465, 34568, 34670, 34772, 34873, 34974, 35075, 35175, 35275, 35375, 35474, 35573, 35671, 35770, 35867, 35965, 36062, 36158, 36254, 36350, 36445, 36540, 36634, 36728, 36822, 36915, 37007, 37099, 37191, 37282, 37373, 37463, 37553, 37642, 37731, 37819, 37907, 37994, 38080, 38166, 38252, 38337, 38421, 38505, 38589, 38671, 38754, 38835, 38916, 38997, 39077, 39156, 39234, 39312, 39390, 39467, 39543, 39618, 39693, 39767, 39841, 39914, 39986, 40058, 40129, 40199, 40268, 40337, 40405, 40473, 40540, 40606, 40671, 40736, 40800, 40863, 40925, 40987, 41048, 41108, 41167, 41226, 41284, 41341, 41397, 41453, 41508, 41562, 41615, 41667, 41719, 41770, 41820, 41869, 41917, 41965, 42011, 42057, 42102, 42146, 42189, 42232, 42273, 42314, 42354, 42393, 42431, 42468, 42504, 42539, 42574, 42607, 42640, 42672, 42703, 42733, 42762, 42790, 42817, 42843, 42868, 42893, 42916, 42938, 42960, 42980, 43000, 43019, 43036, 43053, 43069, 43083, 43097, 43110, 43122, 43132, 43142, 43151, 43159, 43165, 43171, 43176, 43180, 43182, 43184, 43185, 43185, 43183, 43181, 43178, 43173, 43168, 43161, 43154, 43145, 43136, 43125, 43113, 43101, 43087, 43072, 43056, 43039, 43021, 43002, 42982, 42961, 42939, 42915, 42891, 42866, 42839, 42812, 42783, 42753, 42723, 42691, 42658, 42624, 42589, 42553, 42516, 42477, 42438, 42398, 42356, 42314, 42270, 42225, 42180, 42133, 42085, 42036, 41986, 41935, 41883, 41829, 41775, 41720, 41663, 41606, 41547, 41487, 41427, 41365, 41302, 41238, 41173, 41107, 41040, 40972, 40903, 40832, 40761, 40689, 40615, 40541, 40466, 40389, 40312, 40233, 40153, 40073, 39991, 39908, 39825, 39740, 39654, 39567, 39480, 39391, 39301, 39210, 39119, 39026, 38932, 38837, 38742, 38645, 38547, 38449, 38349, 38249, 38147, 38045, 37941, 37837, 37732, 37625, 37518, 37410, 37301, 37191, 37080, 36968, 36856, 36742, 36628, 36512, 36396, 36279, 36161, 36042, 35923, 35802, 35681, 35558, 35435, 35311, 35186, 35061, 34935, 34807, 34679, 34551, 34421, 34291, 34159, 34027, 33895, 33761, 33627, 33492, 33357, 33220, 33083, 32945, 32807, 32667, 32528, 32387, 32246, 32104, 31961, 31818, 31674, 31529, 31384, 31238, 31092, 30945, 30797, 30649, 30500, 30351, 30201, 30050, 29899, 29747, 29595, 29443, 29289, 29136, 28981, 28827, 28672, 28516, 28360, 28203, 28046, 27889, 27731, 27572, 27414, 27255, 27095, 26935, 26775, 26614, 26453, 26292, 26130, 25968, 25806, 25643, 25480, 25317, 25154, 24990, 24826, 24662, 24497, 24333, 24168, 24002, 23837, 23672, 23506, 23340, 23174, 23008, 22841, 22675, 22508, 22342, 22175, 22008, 21841, 21674, 21507, 21340, 21173, 21006, 20838, 20671, 20504, 20337, 20170, 20003, 19835, 19669, 19502, 19335, 19168, 19001, 18835, 18668, 18502, 18336, 18170, 18004, 17838, 17673, 17508, 17343, 17178, 17013, 16849, 16685, 16521, 16357, 16194, 16031, 15868, 15706, 15544, 15382, 15220, 15059, 14899, 14738, 14578, 14419, 14260, 14101, 13943, 13785, 13627, 13470, 13314, 13158, 13002, 12847, 12693, 12539, 12386, 12233, 12080, 11928, 11777, 11627, 11476, 11327, 11178, 11030, 10882, 10735, 10589, 10443, 10298, 10154, 10010, 9867, 9725, 9584, 9443, 9303, 9163, 9025, 8887, 8750, 8614, 8478, 8344, 8210, 8077, 7945, 7813, 7683, 7553, 7424, 7296, 7169, 7043, 6918, 6793, 6670, 6547, 6425, 6305, 6185, 6066, 5948, 5831, 5715, 5600, 5487, 5374, 5262, 5151, 5041, 4932, 4824, 4717, 4611, 4507, 4403, 4300, 4199, 4098, 3999, 3901, 3804, 3708, 3613, 3519, 3426, 3335, 3244, 3155, 3067, 2980, 2894, 2809, 2726, 2644, 2562, 2483, 2404, 2326, 2250, 2175, 2101, 2028, 1957, 1887, 1817, 1750, 1683, 1618, 1554, 1491, 1429, 1369, 1310, 1252, 1196, 1141, 1087, 1034, 983, 933, 884, 836, 790, 745, 702, 659, 618, 578, 540, 503, 467, 433, 400, 368, 337, 308, 280, 254, 228, 204, 182, 161, 141, 122, 105, 89, 74, 61, 49, 38, 29, 21, 15, 9, 6], [1944, 1984, 2025, 2066, 2109, 2152, 2196, 2241, 2286, 2333, 2381, 2429, 2478, 2529, 2580, 2632, 2686, 2740, 2795, 2852, 2909, 2968, 3028, 3089, 3151, 3214, 3278, 3344, 3411, 3479, 3549, 3620, 3692, 3765, 3840, 3916, 3994, 4073, 4154, 4236, 4320, 4405, 4492, 4581, 4671, 4763, 4856, 4952, 5049, 5147, 5248, 5351, 5455, 5561, 5670, 5780, 5892, 6007, 6123, 6242, 6362, 6485, 6611, 6738, 6868, 7000, 7135, 7272, 7411, 7553, 7697, 7845, 7994, 8147, 8302, 8460, 8621, 8784, 8951, 9120, 9293, 9469, 9647, 9829, 10014, 10203, 10394, 10589, 10788, 10990, 11196, 11405, 11618, 11834, 12054, 12279, 12507, 12739, 12975, 13215, 13459, 13708, 13960, 14218, 14479, 14745, 15016, 15291, 15571, 15856, 16146, 16441, 16740, 17045, 17355, 17670, 17991, 18317, 18648, 18985, 19328, 19676, 20031, 20391, 20757, 21130, 21509, 21894, 22285, 22597, 22706, 22815, 22924, 23034, 23143, 23253, 23363, 23473, 23583, 23694, 23804, 23915, 24025, 24136, 24247, 24358, 24469, 24581, 24692, 24804, 24915, 25027, 25139, 25250, 25362, 25474, 25587, 25699, 25811, 25923, 26036, 26148, 26261, 26373, 26486, 26598, 26711, 26824, 26936, 27049, 27162, 27274, 27387, 27500, 27613, 27726, 27838, 27951, 28064, 28177, 28289, 28402, 28515, 28627, 28740, 28852, 28965, 29077, 29190, 29302, 29414, 29526, 29638, 29750, 29862, 29974, 30086, 30197, 30309, 30420, 30532, 30643, 30754, 30865, 30976, 31086, 31197, 31307, 31417, 31527, 31637, 31747, 31856, 31966, 32075, 32184, 32292, 32401, 32509, 32617, 32725, 32833, 32941, 33048, 33155, 33262, 33368, 33474, 33580, 33686, 33791, 33897, 34002, 34106, 34210, 34314, 34418, 34522, 34625, 34727, 34830, 34932, 35034, 35135, 35236, 35337, 35437, 35537, 35637, 35736, 35835, 35934, 36032, 36130, 36227, 36324, 36420, 36516, 36612, 36707, 36802, 36896, 36990, 37084, 37177, 37269, 37361, 37453, 37544, 37634, 37724, 37814, 37903, 37992, 38080, 38167, 38254, 38341, 38427, 38512, 38597, 38681, 38765, 38848, 38931, 39013, 39094, 39175, 39255, 39335, 39414, 39492, 39570, 39647, 39723, 39799, 39875, 39949, 40023, 40097, 40169, 40241, 40312, 40383, 40453, 40522, 40591, 40659, 40726, 40792, 40858, 40923, 40987, 41051, 41114, 41176, 41237, 41298, 41357, 41416, 41475, 41532, 41589, 41645, 41700, 41754, 41808, 41861, 41913, 41964, 42014, 42064, 42112, 42160, 42207, 42254, 42299, 42343, 42387, 42430, 42472, 42513, 42553, 42592, 42631, 42668, 42705, 42740, 42775, 42809, 42842, 42874, 42906, 42936, 42965, 42994, 43021, 43048, 43073, 43098, 43122, 43145, 43166, 43187, 43207, 43226, 43244, 43261, 43277, 43292, 43306, 43319, 43332, 43343, 43353, 43362, 43370, 43377, 43383, 43388, 43393, 43396, 43398, 43399, 43399, 43398, 43396, 43393, 43389, 43384, 43377, 43370, 43362, 43353, 43342, 43331, 43319, 43305, 43291, 43275, 43258, 43241, 43222, 43202, 43181, 43160, 43137, 43113, 43087, 43061, 43034, 43006, 42976, 42946, 42914, 42882, 42848, 42813, 42777, 42741, 42703, 42664, 42623, 42582, 42540, 42497, 42452, 42407, 42360, 42313, 42264, 42214, 42163, 42111, 42058, 42004, 41949, 41893, 41835, 41777, 41718, 41657, 41596, 41533, 41469, 41404, 41339, 41272, 41204, 41135, 41065, 40994, 40922, 40848, 40774, 40699, 40623, 40545, 40467, 40387, 40307, 40225, 40143, 40059, 39975, 39889, 39803, 39715, 39626, 39537, 39446, 39354, 39262, 39168, 39074, 38978, 38881, 38784, 38685, 38586, 38485, 38384, 38282, 38178, 38074, 37969, 37863, 37755, 37647, 37538, 37428, 37318, 37206, 37093, 36980, 36865, 36750, 36634, 36517, 36399, 36280, 36160, 36040, 35918, 35796, 35673, 35549, 35424, 35298, 35172, 35045, 34917, 34788, 34658, 34528, 34397, 34265, 34132, 33998, 33864, 33729, 33593, 33457, 33320, 33182, 33043, 32904, 32764, 32623, 32481, 32339, 32197, 32053, 31909, 31764, 31619, 31473, 31326, 31179, 31031, 30883, 30734, 30584, 30434, 30283, 30132, 29980, 29828, 29675, 29521, 29367, 29213, 29058, 28902, 28746, 28590, 28433, 28276, 28118, 27960, 27801, 27642, 27483, 27323, 27163, 27002, 26841, 26680, 26518, 26356, 26194, 26031, 25868, 25705, 25541, 25377, 25213, 25049, 24884, 24719, 24554, 24388, 24223, 24057, 23891, 23725, 23558, 23392, 23225, 23058, 22891, 22724, 22557, 22390, 22222, 22055, 21887, 21720, 21552, 21384, 21217, 21049, 20881, 20713, 20546, 20378, 20210, 20042, 19875, 19707, 19540, 19372, 19205, 19038, 18871, 18704, 18537, 18370, 18204, 18038, 17871, 17706, 17540, 17374, 17209, 17044, 16879, 16714, 16550, 16386, 16222, 16059, 15895, 15733, 15570, 15408, 15246, 15084, 14923, 14763, 14602, 14442, 14283, 14124, 13965, 13807, 13649, 13491, 13335, 13178, 13022, 12867, 12712, 12558, 12404, 12251, 12098, 11946, 11794, 11643, 11493, 11343, 11194, 11045, 10897, 10750, 10603, 10457, 10312, 10167, 10023, 9880, 9738, 9596, 9455, 9314, 9175, 9036, 8898, 8761, 8624, 8488, 8354, 8219, 8086, 7954, 7822, 7691, 7561, 7432, 7304, 7177, 7050, 6925, 6800, 6677, 6554, 6432, 6311, 6191, 6072, 5954, 5837, 5721, 5606, 5492, 5379, 5266, 5155, 5045, 4936, 4828, 4721, 4615, 4510, 4407, 4304, 4202, 4102, 4002, 3904, 3807, 3710, 3615, 3521, 3429, 3337, 3246, 3157, 3069, 2982, 2896, 2811, 2728, 2645, 2564, 2484, 2405, 2328, 2251, 2176, 2102, 2029, 1958, 1888, 1818, 1751, 1684, 1619, 1555, 1492, 1430, 1370, 1311, 1253, 1196, 1141, 1087, 1035, 983, 933, 884, 837, 790, 745, 702, 659, 618, 579, 540, 503, 467, 433, 400, 368, 337, 308, 280, 254, 228, 204, 182, 161, 141, 122, 105, 89, 74, 61, 49, 38, 29, 21, 15, 9, 6] ]
def lowBounds01 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 10 through 19.
Definition (Lean source)
given by
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29501, 29337, 29173, 29008, 28843, 28677, 28511, 28345, 28178, 28011, 27843, 27675, 27507, 27338, 27170, 27000, 26831, 26661, 26491, 26321, 26150, 25980, 25809, 25637, 25466, 25294, 25122, 24950, 24778, 24605, 24433, 24260, 24087, 23914, 23741, 23568, 23395, 23221, 23048, 22874, 22701, 22527, 22354, 22180, 22006, 21832, 21659, 21485, 21311, 21138, 20964, 20791, 20617, 20444, 20271, 20098, 19925, 19752, 19579, 19407, 19234, 19062, 18890, 18718, 18546, 18375, 18203, 18032, 17862, 17691, 17521, 17351, 17181, 17012, 16843, 16674, 16505, 16337, 16169, 16002, 15835, 15668, 15502, 15336, 15171, 15006, 14841, 14677, 14513, 14350, 14187, 14025, 13863, 13702, 13541, 13381, 13221, 13062, 12903, 12745, 12588, 12431, 12275, 12119, 11964, 11810, 11656, 11503, 11350, 11198, 11047, 10897, 10747, 10598, 10450, 10302, 10155, 10009, 9863, 9719, 9575, 9432, 9289, 9148, 9007, 8867, 8728, 8590, 8453, 8316, 8180, 8045, 7911, 7778, 7646, 7515, 7385, 7255, 7127, 6999, 6872, 6747, 6622, 6498, 6375, 6253, 6133, 6013, 5894, 5776, 5659, 5543, 5429, 5315, 5202, 5091, 4980, 4871, 4762, 4655, 4549, 4444, 4340, 4237, 4135, 4034, 3935, 3836, 3739, 3643, 3548, 3454, 3361, 3270, 3179, 3090, 3002, 2915, 2830, 2745, 2662, 2580, 2500, 2420, 2342, 2265, 2189, 2114, 2041, 1969, 1898, 1828, 1760, 1693, 1627, 1562, 1499, 1437, 1376, 1317, 1258, 1202, 1146, 1092, 1039, 987, 936, 887, 840, 793, 748, 704, 661, 620, 580, 542, 504, 469, 434, 401, 369, 338, 309, 281, 254, 229, 205, 182, 161, 141, 122, 105, 89, 74, 61, 49, 38, 29, 21, 15, 9, 6] ]
def lowBounds02 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 20 through 29.
Definition (Lean source)
given by
#[ [3512, 3580, 3649, 3719, 3790, 3863, 3937, 4012, 4088, 4167, 4246, 4327, 4409, 4493, 4578, 4665, 4753, 4843, 4935, 5028, 5123, 5220, 5318, 5418, 5520, 5623, 5728, 5836, 5945, 6056, 6169, 6284, 6401, 6520, 6641, 6764, 6890, 7017, 7147, 7279, 7413, 7550, 7689, 7830, 7974, 8120, 8269, 8421, 8575, 8731, 8890, 9052, 9217, 9385, 9555, 9729, 9905, 10084, 10266, 10452, 10640, 10832, 11027, 11225, 11427, 11632, 11840, 12052, 12267, 12486, 12709, 12935, 13165, 13399, 13637, 13878, 14124, 14374, 14627, 14885, 15148, 15414, 15685, 15961, 16240, 16525, 16814, 17108, 17406, 17710, 18018, 18331, 18649, 18973, 19302, 19636, 19975, 20320, 20670, 21026, 21387, 21755, 22128, 22507, 22892, 23284, 23681, 24085, 24495, 24912, 25335, 25765, 26202, 26645, 27095, 27553, 28017, 28489, 28969, 29455, 29636, 29753, 29870, 29987, 30103, 30220, 30337, 30453, 30570, 30686, 30803, 30919, 31036, 31152, 31268, 31384, 31500, 31616, 31732, 31848, 31963, 32079, 32194, 32310, 32425, 32540, 32655, 32770, 32884, 32999, 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29, 21, 15, 9, 6], [3705, 3776, 3848, 3922, 3997, 4073, 4150, 4229, 4310, 4391, 4475, 4559, 4646, 4733, 4823, 4914, 5006, 5100, 5196, 5294, 5393, 5494, 5597, 5701, 5808, 5916, 6026, 6138, 6253, 6369, 6487, 6607, 6729, 6854, 6980, 7109, 7240, 7373, 7509, 7646, 7787, 7929, 8074, 8222, 8372, 8525, 8680, 8838, 8999, 9162, 9328, 9497, 9669, 9844, 10021, 10202, 10386, 10572, 10762, 10956, 11152, 11352, 11555, 11761, 11971, 12184, 12401, 12622, 12846, 13074, 13305, 13541, 13780, 14023, 14270, 14522, 14777, 15037, 15301, 15569, 15842, 16119, 16400, 16686, 16977, 17272, 17573, 17878, 18188, 18503, 18823, 19148, 19479, 19814, 20155, 20502, 20854, 21212, 21575, 21944, 22319, 22700, 23087, 23480, 23880, 24285, 24697, 25116, 25541, 25972, 26411, 26856, 27308, 27768, 28234, 28708, 29189, 29677, 30137, 30254, 30371, 30488, 30605, 30722, 30839, 30956, 31073, 31190, 31306, 31423, 31539, 31656, 31772, 31888, 32004, 32120, 32236, 32352, 32468, 32583, 32699, 32814, 32929, 33044, 33159, 33274, 33388, 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15, 9, 6], [3838, 3911, 3986, 4061, 4138, 4217, 4297, 4378, 4461, 4545, 4631, 4718, 4807, 4897, 4989, 5083, 5178, 5275, 5373, 5474, 5576, 5680, 5786, 5893, 6003, 6114, 6227, 6343, 6460, 6579, 6701, 6824, 6950, 7078, 7208, 7340, 7475, 7612, 7751, 7892, 8036, 8183, 8332, 8483, 8638, 8794, 8954, 9116, 9281, 9448, 9619, 9792, 9968, 10148, 10330, 10515, 10704, 10895, 11090, 11288, 11489, 11694, 11902, 12114, 12329, 12547, 12769, 12995, 13225, 13458, 13696, 13937, 14182, 14431, 14684, 14941, 15203, 15469, 15739, 16013, 16292, 16576, 16864, 17156, 17454, 17756, 18063, 18375, 18692, 19014, 19342, 19674, 20012, 20355, 20704, 21058, 21418, 21783, 22154, 22531, 22915, 23304, 23699, 24100, 24508, 24922, 25343, 25770, 26204, 26645, 27092, 27547, 28008, 28477, 28952, 29436, 29926, 30425, 30758, 30876, 30993, 31110, 31227, 31344, 31462, 31578, 31695, 31812, 31929, 32045, 32162, 32278, 32395, 32511, 32627, 32743, 32859, 32974, 33090, 33205, 33320, 33435, 33550, 33665, 33780, 33894, 34008, 34122, 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46356, 46410, 46463, 46515, 46566, 46616, 46665, 46714, 46761, 46808, 46854, 46899, 46943, 46986, 47028, 47070, 47110, 47150, 47188, 47226, 47262, 47298, 47333, 47367, 47400, 47432, 47463, 47493, 47522, 47550, 47577, 47603, 47628, 47652, 47675, 47697, 47718, 47739, 47758, 47776, 47793, 47809, 47824, 47838, 47851, 47863, 47874, 47884, 47893, 47901, 47907, 47913, 47918, 47921, 47924, 47925, 47926, 47925, 47923, 47921, 47917, 47912, 47906, 47899, 47891, 47881, 47871, 47860, 47847, 47834, 47819, 47803, 47786, 47768, 47749, 47729, 47708, 47685, 47662, 47637, 47611, 47584, 47556, 47527, 47497, 47466, 47433, 47400, 47365, 47329, 47293, 47255, 47215, 47175, 47134, 47091, 47048, 47003, 46957, 46910, 46862, 46813, 46762, 46711, 46658, 46604, 46550, 46494, 46436, 46378, 46319, 46259, 46197, 46134, 46070, 46006, 45940, 45872, 45804, 45735, 45664, 45593, 45520, 45446, 45372, 45296, 45219, 45140, 45061, 44981, 44899, 44817, 44733, 44649, 44563, 44476, 44388, 44299, 44209, 44118, 44026, 43932, 43838, 43743, 43646, 43549, 43451, 43351, 43250, 43149, 43046, 42943, 42838, 42732, 42625, 42518, 42409, 42299, 42189, 42077, 41964, 41851, 41736, 41620, 41504, 41386, 41268, 41148, 41028, 40906, 40784, 40661, 40536, 40411, 40285, 40158, 40030, 39902, 39772, 39642, 39510, 39378, 39245, 39111, 38976, 38840, 38703, 38566, 38428, 38288, 38148, 38008, 37866, 37724, 37581, 37437, 37292, 37146, 37000, 36853, 36705, 36557, 36408, 36258, 36107, 35955, 35803, 35650, 35497, 35343, 35188, 35032, 34876, 34719, 34561, 34403, 34244, 34085, 33925, 33764, 33603, 33441, 33279, 33116, 32952, 32788, 32624, 32458, 32293, 32126, 31960, 31793, 31625, 31457, 31288, 31119, 30949, 30779, 30609, 30438, 30266, 30095, 29923, 29750, 29577, 29404, 29230, 29056, 28882, 28707, 28532, 28357, 28182, 28006, 27830, 27653, 27476, 27300, 27122, 26945, 26767, 26590, 26411, 26233, 26055, 25876, 25698, 25519, 25340, 25161, 24981, 24802, 24622, 24443, 24263, 24084, 23904, 23724, 23544, 23364, 23184, 23005, 22825, 22645, 22465, 22285, 22106, 21926, 21746, 21567, 21387, 21208, 21029, 20850, 20671, 20492, 20314, 20135, 19957, 19779, 19601, 19423, 19246, 19069, 18892, 18715, 18539, 18362, 18187, 18011, 17836, 17661, 17486, 17312, 17138, 16964, 16791, 16618, 16446, 16274, 16102, 15931, 15760, 15590, 15420, 15251, 15082, 14914, 14746, 14578, 14411, 14245, 14079, 13914, 13749, 13585, 13422, 13259, 13096, 12935, 12773, 12613, 12453, 12294, 12135, 11977, 11820, 11664, 11508, 11353, 11198, 11045, 10892, 10739, 10588, 10437, 10287, 10138, 9990, 9842, 9696, 9550, 9405, 9260, 9117, 8974, 8833, 8692, 8552, 8413, 8275, 8138, 8001, 7866, 7731, 7598, 7465, 7334, 7203, 7073, 6945, 6817, 6690, 6564, 6440, 6316, 6193, 6072, 5951, 5831, 5713, 5595, 5479, 5364, 5249, 5136, 5024, 4913, 4803, 4695, 4587, 4481, 4375, 4271, 4168, 4066, 3965, 3866, 3767, 3670, 3574, 3479, 3385, 3293, 3202, 3112, 3023, 2935, 2848, 2763, 2679, 2597, 2515, 2435, 2356, 2278, 2201, 2126, 2052, 1979, 1908, 1838, 1769, 1701, 1635, 1570, 1506, 1443, 1382, 1322, 1264, 1207, 1151, 1096, 1043, 991, 940, 891, 843, 796, 750, 706, 664, 622, 582, 543, 506, 470, 435, 402, 370, 339, 309, 281, 255, 229, 205, 182, 161, 141, 122, 105, 89, 74, 61, 49, 39, 29, 21, 15, 9, 6] ]
def lowBounds03 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 30 through 39.
Definition (Lean source)
given by
#[ [5272, 5369, 5467, 5567, 5668, 5771, 5876, 5983, 6092, 6202, 6315, 6429, 6545, 6663, 6783, 6906, 7030, 7156, 7285, 7415, 7548, 7683, 7820, 7960, 8102, 8246, 8393, 8542, 8694, 8848, 9005, 9164, 9326, 9491, 9658, 9828, 10001, 10177, 10355, 10537, 10722, 10909, 11100, 11293, 11490, 11690, 11894, 12100, 12310, 12524, 12740, 12961, 13185, 13412, 13643, 13878, 14116, 14359, 14605, 14855, 15109, 15368, 15630, 15896, 16167, 16442, 16721, 17005, 17293, 17586, 17883, 18185, 18492, 18804, 19120, 19441, 19768, 20099, 20436, 20778, 21125, 21477, 21835, 22198, 22567, 22942, 23323, 23709, 24101, 24499, 24904, 25314, 25731, 26154, 26583, 27019, 27462, 27911, 28367, 28830, 29300, 29777, 30262, 30753, 31252, 31758, 32272, 32793, 33322, 33860, 34405, 34958, 35243, 35360, 35478, 35594, 35711, 35828, 35944, 36060, 36176, 36292, 36407, 36522, 36637, 36752, 36867, 36981, 37095, 37209, 37322, 37435, 37548, 37661, 37773, 37885, 37997, 38108, 38219, 38330, 38441, 38551, 38661, 38770, 38879, 38988, 39097, 39205, 39312, 39420, 39527, 39633, 39739, 39845, 39950, 40055, 40160, 40264, 40368, 40471, 40574, 40676, 40778, 40880, 40981, 41081, 41182, 41281, 41380, 41479, 41577, 41675, 41772, 41869, 41965, 42060, 42156, 42250, 42344, 42438, 42531, 42623, 42715, 42806, 42897, 42987, 43076, 43165, 43254, 43341, 43428, 43515, 43601, 43686, 43771, 43855, 43938, 44021, 44103, 44184, 44265, 44345, 44424, 44503, 44581, 44658, 44735, 44811, 44886, 44961, 45034, 45107, 45180, 45251, 45322, 45392, 45462, 45530, 45598, 45665, 45731, 45797, 45862, 45926, 45989, 46051, 46113, 46173, 46233, 46292, 46351, 46408, 46465, 46521, 46575, 46630, 46683, 46735, 46787, 46837, 46887, 46936, 46984, 47031, 47077, 47123, 47167, 47210, 47253, 47295, 47335, 47375, 47414, 47452, 47489, 47525, 47560, 47595, 47628, 47660, 47692, 47722, 47751, 47780, 47807, 47834, 47859, 47884, 47907, 47929, 47951, 47971, 47991, 48009, 48027, 48043, 48059, 48073, 48086, 48099, 48110, 48120, 48129, 48138, 48145, 48151, 48156, 48160, 48163, 48164, 48165, 48165, 48163, 48161, 48157, 48153, 48147, 48140, 48133, 48124, 48114, 48103, 48090, 48077, 48063, 48047, 48031, 48013, 47994, 47974, 47953, 47931, 47908, 47883, 47858, 47831, 47804, 47775, 47745, 47714, 47682, 47649, 47614, 47579, 47542, 47504, 47465, 47425, 47384, 47342, 47299, 47254, 47209, 47162, 47114, 47065, 47015, 46964, 46911, 46858, 46803, 46747, 46690, 46632, 46573, 46513, 46452, 46389, 46326, 46261, 46195, 46128, 46060, 45991, 45921, 45849, 45777, 45703, 45629, 45553, 45476, 45398, 45319, 45239, 45158, 45075, 44992, 44907, 44822, 44735, 44647, 44558, 44468, 44377, 44285, 44192, 44098, 44003, 43907, 43809, 43711, 43611, 43511, 43409, 43307, 43203, 43099, 42993, 42886, 42779, 42670, 42561, 42450, 42338, 42226, 42112, 41997, 41882, 41765, 41648, 41529, 41410, 41289, 41168, 41045, 40922, 40798, 40673, 40547, 40420, 40292, 40163, 40034, 39903, 39771, 39639, 39506, 39372, 39237, 39101, 38964, 38827, 38688, 38549, 38409, 38268, 38127, 37984, 37841, 37697, 37552, 37406, 37260, 37113, 36965, 36816, 36667, 36517, 36366, 36214, 36062, 35909, 35755, 35601, 35445, 35290, 35133, 34976, 34818, 34660, 34501, 34341, 34181, 34020, 33859, 33697, 33534, 33371, 33207, 33042, 32877, 32712, 32546, 32379, 32212, 32045, 31877, 31708, 31539, 31370, 31200, 31029, 30859, 30687, 30516, 30344, 30171, 29998, 29825, 29651, 29477, 29303, 29128, 28953, 28778, 28602, 28426, 28250, 28073, 27896, 27719, 27541, 27364, 27186, 27008, 26829, 26651, 26472, 26293, 26114, 25935, 25755, 25576, 25396, 25216, 25036, 24856, 24676, 24496, 24316, 24135, 23955, 23775, 23594, 23414, 23233, 23053, 22872, 22692, 22511, 22331, 22151, 21970, 21790, 21610, 21430, 21250, 21070, 20891, 20711, 20532, 20353, 20174, 19995, 19816, 19638, 19460, 19282, 19104, 18926, 18749, 18572, 18396, 18219, 18043, 17867, 17692, 17517, 17342, 17168, 16994, 16820, 16647, 16474, 16301, 16129, 15958, 15786, 15616, 15445, 15276, 15106, 14937, 14769, 14601, 14434, 14267, 14101, 13935, 13770, 13606, 13442, 13278, 13116, 12953, 12792, 12631, 12471, 12311, 12152, 11994, 11837, 11680, 11524, 11368, 11213, 11059, 10906, 10754, 10602, 10451, 10301, 10151, 10003, 9855, 9708, 9562, 9416, 9272, 9128, 8985, 8843, 8702, 8562, 8423, 8284, 8147, 8010, 7875, 7740, 7606, 7473, 7342, 7211, 7081, 6952, 6824, 6697, 6571, 6446, 6322, 6199, 6077, 5957, 5837, 5718, 5601, 5484, 5369, 5254, 5141, 5029, 4918, 4808, 4699, 4591, 4484, 4379, 4275, 4171, 4069, 3968, 3869, 3770, 3673, 3577, 3482, 3388, 3295, 3204, 3114, 3025, 2937, 2850, 2765, 2681, 2598, 2517, 2436, 2357, 2279, 2203, 2127, 2053, 1980, 1909, 1839, 1770, 1702, 1636, 1570, 1507, 1444, 1383, 1323, 1264, 1207, 1151, 1096, 1043, 991, 940, 891, 843, 796, 751, 707, 664, 622, 582, 543, 506, 470, 435, 402, 370, 339, 309, 281, 255, 229, 205, 183, 161, 141, 122, 105, 89, 74, 61, 49, 39, 29, 21, 15, 9, 6], [5482, 5582, 5683, 5786, 5891, 5998, 6106, 6217, 6329, 6443, 6559, 6678, 6798, 6920, 7044, 7170, 7299, 7429, 7562, 7697, 7834, 7973, 8115, 8259, 8406, 8555, 8706, 8860, 9017, 9176, 9338, 9502, 9669, 9839, 10012, 10187, 10365, 10547, 10731, 10918, 11108, 11302, 11498, 11698, 11901, 12107, 12316, 12529, 12745, 12965, 13189, 13415, 13646, 13880, 14118, 14360, 14605, 14855, 15108, 15366, 15628, 15893, 16163, 16437, 16716, 16999, 17286, 17578, 17874, 18175, 18481, 18792, 19107, 19427, 19752, 20083, 20418, 20759, 21105, 21456, 21812, 22174, 22542, 22915, 23294, 23679, 24070, 24466, 24869, 25278, 25693, 26114, 26542, 26976, 27417, 27864, 28318, 28779, 29247, 29722, 30204, 30693, 31190, 31694, 32205, 32724, 33251, 33785, 34328, 34878, 35437, 35770, 35887, 36004, 36120, 36237, 36353, 36469, 36585, 36701, 36816, 36931, 37046, 37161, 37275, 37389, 37503, 37617, 37730, 37843, 37956, 38068, 38180, 38292, 38404, 38515, 38626, 38736, 38846, 38956, 39066, 39175, 39284, 39392, 39500, 39608, 39715, 39822, 39929, 40035, 40141, 40246, 40351, 40455, 40560, 40663, 40766, 40869, 40972, 41073, 41175, 41276, 41376, 41476, 41576, 41675, 41774, 41872, 41969, 42066, 42163, 42259, 42354, 42449, 42544, 42637, 42731, 42824, 42916, 43007, 43098, 43189, 43279, 43368, 43457, 43545, 43632, 43719, 43806, 43891, 43976, 44061, 44144, 44227, 44310, 44392, 44473, 44553, 44633, 44712, 44790, 44868, 44945, 45021, 45097, 45172, 45246, 45320, 45392, 45464, 45535, 45606, 45676, 45745, 45813, 45880, 45947, 46013, 46078, 46142, 46206, 46269, 46330, 46392, 46452, 46511, 46570, 46628, 46685, 46741, 46796, 46851, 46904, 46957, 47009, 47060, 47110, 47159, 47208, 47255, 47302, 47347, 47392, 47436, 47479, 47521, 47562, 47602, 47642, 47680, 47717, 47754, 47789, 47824, 47857, 47890, 47922, 47953, 47982, 48011, 48039, 48066, 48091, 48116, 48140, 48163, 48185, 48206, 48225, 48244, 48262, 48279, 48295, 48309, 48323, 48336, 48347, 48358, 48367, 48376, 48383, 48390, 48395, 48399, 48402, 48405, 48406, 48406, 48405, 48403, 48399, 48395, 48390, 48383, 48376, 48367, 48357, 48347, 48335, 48322, 48308, 48292, 48276, 48259, 48240, 48221, 48200, 48178, 48155, 48131, 48106, 48080, 48052, 48024, 47994, 47963, 47931, 47898, 47864, 47829, 47793, 47755, 47717, 47677, 47636, 47594, 47551, 47507, 47461, 47415, 47367, 47318, 47269, 47218, 47165, 47112, 47058, 47002, 46946, 46888, 46829, 46769, 46708, 46646, 46582, 46518, 46452, 46385, 46318, 46249, 46178, 46107, 46035, 45962, 45887, 45811, 45735, 45657, 45578, 45498, 45417, 45335, 45251, 45167, 45082, 44995, 44907, 44819, 44729, 44638, 44546, 44453, 44359, 44264, 44168, 44071, 43972, 43873, 43773, 43671, 43569, 43465, 43361, 43255, 43149, 43041, 42933, 42823, 42712, 42601, 42488, 42375, 42260, 42144, 42028, 41910, 41792, 41672, 41552, 41431, 41308, 41185, 41061, 40936, 40810, 40683, 40555, 40426, 40296, 40166, 40034, 39902, 39768, 39634, 39499, 39363, 39227, 39089, 38951, 38811, 38671, 38530, 38388, 38246, 38102, 37958, 37813, 37668, 37521, 37374, 37226, 37077, 36927, 36777, 36626, 36474, 36322, 36168, 36014, 35860, 35705, 35549, 35392, 35235, 35077, 34918, 34759, 34599, 34438, 34277, 34115, 33953, 33790, 33627, 33462, 33298, 33133, 32967, 32801, 32634, 32466, 32298, 32130, 31961, 31792, 31622, 31452, 31281, 31110, 30938, 30766, 30594, 30421, 30247, 30074, 29900, 29725, 29550, 29375, 29200, 29024, 28848, 28671, 28495, 28318, 28140, 27963, 27785, 27607, 27428, 27250, 27071, 26892, 26712, 26533, 26353, 26174, 25994, 25813, 25633, 25453, 25272, 25092, 24911, 24730, 24549, 24368, 24187, 24006, 23825, 23644, 23463, 23282, 23101, 22920, 22738, 22557, 22376, 22196, 22015, 21834, 21653, 21473, 21292, 21112, 20932, 20751, 20572, 20392, 20212, 20033, 19854, 19675, 19496, 19317, 19139, 18961, 18783, 18606, 18429, 18252, 18075, 17899, 17723, 17547, 17372, 17197, 17023, 16849, 16675, 16502, 16329, 16156, 15984, 15812, 15641, 15470, 15300, 15130, 14961, 14792, 14624, 14456, 14289, 14123, 13957, 13791, 13626, 13462, 13298, 13135, 12972, 12811, 12649, 12489, 12329, 12170, 12011, 11853, 11696, 11539, 11384, 11229, 11074, 10921, 10768, 10616, 10464, 10314, 10164, 10015, 9867, 9720, 9573, 9428, 9283, 9139, 8996, 8854, 8712, 8572, 8432, 8294, 8156, 8019, 7883, 7749, 7615, 7481, 7349, 7218, 7088, 6959, 6831, 6704, 6578, 6453, 6328, 6205, 6083, 5962, 5843, 5724, 5606, 5489, 5374, 5259, 5145, 5033, 4922, 4812, 4703, 4595, 4488, 4382, 4278, 4175, 4073, 3972, 3872, 3773, 3676, 3579, 3484, 3390, 3298, 3206, 3116, 3027, 2939, 2852, 2767, 2683, 2600, 2518, 2438, 2358, 2281, 2204, 2128, 2054, 1981, 1910, 1840, 1771, 1703, 1636, 1571, 1507, 1445, 1384, 1324, 1265, 1208, 1152, 1097, 1044, 991, 941, 891, 843, 796, 751, 707, 664, 623, 582, 544, 506, 470, 435, 402, 370, 339, 310, 281, 255, 229, 205, 183, 161, 141, 122, 105, 89, 74, 61, 49, 39, 29, 21, 15, 9, 6], [5599, 5701, 5804, 5909, 6016, 6124, 6235, 6347, 6461, 6577, 6695, 6816, 6938, 7062, 7188, 7316, 7447, 7579, 7714, 7851, 7991, 8133, 8277, 8423, 8572, 8723, 8877, 9034, 9192, 9354, 9518, 9685, 9855, 10027, 10203, 10381, 10562, 10746, 10933, 11123, 11316, 11512, 11711, 11914, 12120, 12329, 12541, 12757, 12977, 13199, 13426, 13656, 13890, 14127, 14368, 14614, 14863, 15115, 15372, 15633, 15898, 16168, 16441, 16719, 17001, 17288, 17579, 17874, 18175, 18480, 18789, 19104, 19423, 19747, 20077, 20411, 20751, 21095, 21446, 21801, 22162, 22528, 22901, 23278, 23662, 24051, 24446, 24848, 25255, 25669, 26088, 26515, 26947, 27386, 27832, 28284, 28743, 29210, 29683, 30163, 30650, 31144, 31646, 32156, 32672, 33197, 33729, 34269, 34817, 35373, 35938, 36298, 36415, 36532, 36648, 36764, 36880, 36996, 37112, 37227, 37342, 37457, 37571, 37685, 37799, 37913, 38026, 38139, 38252, 38365, 38477, 38589, 38700, 38812, 38923, 39033, 39143, 39253, 39363, 39472, 39581, 39689, 39797, 39905, 40013, 40119, 40226, 40332, 40438, 40543, 40648, 40753, 40857, 40960, 41063, 41166, 41268, 41370, 41472, 41572, 41673, 41773, 41872, 41971, 42070, 42168, 42265, 42362, 42458, 42554, 42650, 42744, 42839, 42932, 43025, 43118, 43210, 43301, 43392, 43483, 43572, 43661, 43750, 43838, 43925, 44012, 44098, 44183, 44268, 44352, 44435, 44518, 44600, 44682, 44763, 44843, 44922, 45001, 45079, 45157, 45233, 45309, 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47924, 47848, 47772, 47694, 47616, 47536, 47455, 47373, 47290, 47206, 47120, 47034, 46946, 46857, 46768, 46677, 46585, 46492, 46397, 46302, 46206, 46108, 46010, 45910, 45810, 45708, 45605, 45501, 45396, 45290, 45183, 45075, 44966, 44856, 44745, 44633, 44519, 44405, 44290, 44174, 44056, 43938, 43819, 43699, 43577, 43455, 43332, 43208, 43082, 42956, 42829, 42701, 42572, 42442, 42311, 42179, 42047, 41913, 41779, 41643, 41507, 41369, 41231, 41092, 40952, 40811, 40670, 40527, 40384, 40240, 40094, 39949, 39802, 39654, 39506, 39357, 39207, 39056, 38904, 38752, 38599, 38445, 38291, 38135, 37979, 37822, 37665, 37506, 37347, 37188, 37027, 36866, 36704, 36542, 36379, 36215, 36051, 35886, 35720, 35554, 35387, 35220, 35052, 34883, 34714, 34544, 34373, 34203, 34031, 33859, 33687, 33514, 33340, 33166, 32991, 32816, 32641, 32465, 32289, 32112, 31935, 31757, 31579, 31400, 31222, 31042, 30863, 30683, 30502, 30322, 30141, 29959, 29778, 29596, 29413, 29231, 29048, 28865, 28682, 28498, 28314, 28130, 27946, 27761, 27577, 27392, 27207, 27022, 26836, 26651, 26465, 26280, 26094, 25908, 25722, 25536, 25350, 25164, 24977, 24791, 24605, 24418, 24232, 24046, 23860, 23673, 23487, 23301, 23115, 22929, 22743, 22557, 22371, 22186, 22000, 21815, 21630, 21445, 21260, 21075, 20891, 20706, 20522, 20338, 20155, 19971, 19788, 19605, 19423, 19240, 19058, 18877, 18695, 18514, 18334, 18153, 17973, 17794, 17615, 17436, 17257, 17079, 16902, 16725, 16548, 16372, 16196, 16021, 15846, 15672, 15498, 15325, 15152, 14980, 14808, 14637, 14467, 14297, 14128, 13959, 13791, 13623, 13457, 13290, 13125, 12960, 12796, 12632, 12470, 12308, 12146, 11985, 11826, 11666, 11508, 11350, 11193, 11037, 10882, 10727, 10573, 10421, 10268, 10117, 9967, 9817, 9668, 9521, 9374, 9227, 9082, 8938, 8795, 8652, 8511, 8370, 8230, 8092, 7954, 7817, 7681, 7546, 7413, 7280, 7148, 7017, 6887, 6759, 6631, 6504, 6379, 6254, 6131, 6008, 5887, 5767, 5648, 5530, 5413, 5297, 5182, 5069, 4956, 4845, 4735, 4626, 4518, 4411, 4306, 4201, 4098, 3996, 3896, 3796, 3698, 3600, 3504, 3410, 3316, 3224, 3133, 3043, 2955, 2867, 2781, 2696, 2613, 2530, 2449, 2370, 2291, 2214, 2138, 2063, 1990, 1918, 1847, 1778, 1710, 1643, 1577, 1513, 1450, 1389, 1328, 1269, 1212, 1155, 1100, 1047, 994, 943, 894, 845, 799, 753, 709, 666, 624, 584, 545, 507, 471, 436, 403, 370, 340, 310, 282, 255, 230, 206, 183, 161, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6] ]
def lowBounds04 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 40 through 49.
Definition (Lean source)
given by
#[ [7194, 7320, 7448, 7578, 7711, 7845, 7981, 8120, 8261, 8404, 8550, 8698, 8848, 9001, 9156, 9314, 9475, 9637, 9803, 9971, 10142, 10316, 10492, 10671, 10853, 11038, 11226, 11417, 11611, 11808, 12008, 12211, 12417, 12627, 12840, 13056, 13276, 13499, 13725, 13956, 14189, 14427, 14668, 14913, 15161, 15414, 15670, 15930, 16195, 16463, 16736, 17012, 17293, 17579, 17868, 18162, 18461, 18764, 19072, 19384, 19701, 20023, 20350, 20682, 21019, 21361, 21708, 22060, 22417, 22780, 23148, 23522, 23901, 24286, 24677, 25074, 25476, 25884, 26299, 26719, 27146, 27579, 28019, 28464, 28917, 29376, 29842, 30314, 30794, 31280, 31773, 32274, 32782, 33297, 33820, 34350, 34888, 35434, 35987, 36549, 37118, 37696, 38282, 38876, 39479, 40090, 40462, 40575, 40689, 40802, 40914, 41027, 41139, 41250, 41361, 41472, 41582, 41692, 41802, 41911, 42020, 42128, 42236, 42344, 42451, 42558, 42664, 42770, 42875, 42980, 43084, 43188, 43292, 43395, 43497, 43599, 43701, 43802, 43902, 44002, 44102, 44200, 44299, 44397, 44494, 44591, 44687, 44783, 44878, 44972, 45066, 45159, 45252, 45344, 45436, 45527, 45617, 45707, 45796, 45884, 45972, 46059, 46146, 46232, 46317, 46401, 46485, 46568, 46651, 46733, 46814, 46894, 46974, 47053, 47131, 47209, 47286, 47362, 47437, 47512, 47586, 47659, 47731, 47803, 47873, 47943, 48013, 48081, 48149, 48216, 48282, 48347, 48412, 48475, 48538, 48600, 48661, 48722, 48781, 48840, 48898, 48954, 49010, 49066, 49120, 49173, 49226, 49278, 49328, 49378, 49427, 49475, 49522, 49569, 49614, 49658, 49702, 49744, 49786, 49827, 49866, 49905, 49943, 49980, 50015, 50050, 50084, 50117, 50149, 50180, 50210, 50239, 50267, 50294, 50320, 50345, 50369, 50392, 50414, 50434, 50454, 50473, 50491, 50508, 50523, 50538, 50552, 50564, 50576, 50586, 50595, 50604, 50611, 50617, 50622, 50626, 50629, 50631, 50632, 50631, 50630, 50627, 50624, 50619, 50613, 50606, 50598, 50589, 50579, 50568, 50555, 50542, 50527, 50511, 50494, 50476, 50457, 50437, 50415, 50393, 50369, 50344, 50318, 50291, 50263, 50233, 50203, 50171, 50138, 50104, 50069, 50033, 49995, 49957, 49917, 49876, 49834, 49791, 49747, 49702, 49655, 49607, 49558, 49508, 49457, 49405, 49352, 49297, 49241, 49184, 49126, 49067, 49007, 48945, 48882, 48819, 48754, 48688, 48621, 48552, 48483, 48412, 48340, 48267, 48193, 48118, 48042, 47965, 47886, 47806, 47726, 47644, 47561, 47477, 47391, 47305, 47218, 47129, 47039, 46949, 46857, 46764, 46670, 46574, 46478, 46381, 46282, 46183, 46082, 45981, 45878, 45774, 45670, 45564, 45457, 45349, 45240, 45130, 45019, 44906, 44793, 44679, 44564, 44448, 44330, 44212, 44093, 43973, 43851, 43729, 43606, 43482, 43356, 43230, 43103, 42975, 42846, 42716, 42585, 42453, 42321, 42187, 42052, 41917, 41780, 41643, 41505, 41366, 41225, 41085, 40943, 40800, 40657, 40512, 40367, 40221, 40074, 39927, 39778, 39629, 39479, 39328, 39176, 39024, 38870, 38716, 38562, 38406, 38250, 38093, 37935, 37776, 37617, 37457, 37297, 37135, 36973, 36811, 36648, 36484, 36319, 36154, 35988, 35821, 35654, 35486, 35318, 35149, 34979, 34809, 34639, 34467, 34296, 34123, 33951, 33777, 33603, 33429, 33254, 33079, 32903, 32727, 32550, 32373, 32195, 32017, 31838, 31659, 31480, 31301, 31120, 30940, 30759, 30578, 30397, 30215, 30033, 29850, 29667, 29484, 29301, 29118, 28934, 28750, 28565, 28381, 28196, 28011, 27826, 27640, 27455, 27269, 27083, 26897, 26711, 26525, 26338, 26152, 25965, 25779, 25592, 25405, 25218, 25031, 24844, 24657, 24470, 24283, 24096, 23909, 23723, 23536, 23349, 23162, 22976, 22789, 22602, 22416, 22230, 22044, 21858, 21672, 21486, 21301, 21116, 20931, 20746, 20561, 20377, 20192, 20008, 19825, 19641, 19458, 19275, 19093, 18911, 18729, 18547, 18366, 18185, 18005, 17825, 17645, 17466, 17287, 17108, 16930, 16753, 16576, 16399, 16223, 16047, 15872, 15697, 15523, 15349, 15176, 15004, 14831, 14660, 14489, 14319, 14149, 13980, 13812, 13644, 13477, 13310, 13144, 12979, 12814, 12650, 12487, 12325, 12163, 12002, 11842, 11682, 11523, 11365, 11208, 11052, 10896, 10741, 10587, 10434, 10281, 10130, 9979, 9829, 9680, 9532, 9385, 9239, 9093, 8949, 8805, 8662, 8520, 8380, 8240, 8101, 7963, 7826, 7690, 7555, 7421, 7288, 7156, 7025, 6895, 6766, 6638, 6511, 6385, 6260, 6137, 6014, 5893, 5772, 5653, 5535, 5418, 5302, 5187, 5073, 4960, 4849, 4739, 4630, 4522, 4415, 4309, 4205, 4101, 3999, 3899, 3799, 3700, 3603, 3507, 3412, 3319, 3226, 3135, 3045, 2957, 2869, 2783, 2698, 2614, 2532, 2451, 2371, 2293, 2215, 2139, 2065, 1991, 1919, 1848, 1779, 1711, 1644, 1578, 1514, 1451, 1389, 1329, 1270, 1212, 1156, 1101, 1047, 995, 944, 894, 846, 799, 753, 709, 666, 624, 584, 545, 507, 471, 436, 403, 370, 340, 310, 282, 255, 230, 206, 183, 161, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [7365, 7494, 7624, 7757, 7892, 8029, 8168, 8309, 8453, 8599, 8747, 8898, 9052, 9207, 9365, 9526, 9690, 9855, 10024, 10195, 10369, 10546, 10726, 10908, 11094, 11282, 11473, 11667, 11865, 12065, 12269, 12476, 12686, 12899, 13116, 13336, 13559, 13786, 14017, 14251, 14489, 14730, 14975, 15224, 15477, 15734, 15995, 16259, 16528, 16801, 17078, 17359, 17645, 17935, 18229, 18528, 18832, 19140, 19452, 19770, 20092, 20419, 20751, 21088, 21430, 21777, 22129, 22487, 22850, 23218, 23592, 23972, 24357, 24748, 25144, 25547, 25955, 26370, 26790, 27217, 27650, 28089, 28535, 28987, 29446, 29912, 30384, 30864, 31350, 31843, 32344, 32851, 33366, 33889, 34419, 34956, 35501, 36054, 36615, 37184, 37762, 38347, 38941, 39543, 40153, 40773, 41001, 41114, 41227, 41339, 41451, 41563, 41674, 41785, 41895, 42005, 42115, 42224, 42333, 42441, 42549, 42656, 42763, 42870, 42976, 43082, 43187, 43292, 43396, 43500, 43603, 43706, 43809, 43911, 44012, 44113, 44213, 44313, 44412, 44511, 44609, 44707, 44804, 44901, 44997, 45092, 45187, 45281, 45375, 45468, 45561, 45653, 45744, 45835, 45925, 46014, 46103, 46191, 46279, 46365, 46452, 46537, 46622, 46706, 46790, 46873, 46955, 47037, 47117, 47197, 47277, 47355, 47433, 47511, 47587, 47663, 47738, 47812, 47886, 47958, 48030, 48101, 48172, 48242, 48310, 48378, 48446, 48512, 48578, 48643, 48707, 48770, 48832, 48894, 48954, 49014, 49073, 49131, 49189, 49245, 49301, 49355, 49409, 49462, 49514, 49565, 49616, 49665, 49713, 49761, 49807, 49853, 49898, 49942, 49984, 50026, 50067, 50107, 50147, 50185, 50222, 50258, 50293, 50328, 50361, 50393, 50424, 50455, 50484, 50512, 50540, 50566, 50591, 50616, 50639, 50661, 50682, 50702, 50722, 50740, 50757, 50773, 50788, 50802, 50815, 50826, 50837, 50847, 50856, 50863, 50870, 50875, 50879, 50883, 50885, 50886, 50886, 50885, 50882, 50879, 50875, 50869, 50863, 50855, 50846, 50836, 50825, 50813, 50800, 50785, 50770, 50753, 50735, 50716, 50696, 50675, 50653, 50629, 50605, 50579, 50552, 50524, 50495, 50465, 50434, 50401, 50367, 50333, 50297, 50259, 50221, 50182, 50141, 50099, 50056, 50012, 49967, 49921, 49873, 49825, 49775, 49724, 49672, 49619, 49564, 49509, 49452, 49394, 49335, 49275, 49214, 49152, 49088, 49023, 48957, 48890, 48822, 48753, 48682, 48611, 48538, 48464, 48389, 48313, 48236, 48158, 48078, 47998, 47916, 47833, 47749, 47664, 47578, 47490, 47402, 47312, 47222, 47130, 47037, 46943, 46848, 46752, 46655, 46556, 46457, 46357, 46255, 46152, 46049, 45944, 45838, 45731, 45623, 45514, 45404, 45293, 45181, 45068, 44954, 44839, 44723, 44605, 44487, 44368, 44248, 44127, 44004, 43881, 43757, 43632, 43506, 43378, 43250, 43121, 42991, 42860, 42728, 42596, 42462, 42327, 42192, 42055, 41918, 41779, 41640, 41500, 41359, 41217, 41075, 40931, 40787, 40641, 40495, 40348, 40200, 40052, 39902, 39752, 39601, 39449, 39296, 39143, 38989, 38834, 38678, 38522, 38364, 38207, 38048, 37888, 37728, 37568, 37406, 37244, 37081, 36917, 36753, 36588, 36423, 36257, 36090, 35922, 35754, 35586, 35416, 35247, 35076, 34905, 34734, 34562, 34389, 34216, 34042, 33868, 33693, 33518, 33342, 33166, 32989, 32812, 32635, 32457, 32278, 32099, 31920, 31740, 31560, 31380, 31199, 31017, 30836, 30654, 30472, 30289, 30106, 29923, 29739, 29556, 29372, 29187, 29003, 28818, 28633, 28447, 28262, 28076, 27890, 27704, 27518, 27331, 27145, 26958, 26771, 26584, 26397, 26210, 26022, 25835, 25648, 25460, 25273, 25085, 24897, 24710, 24522, 24334, 24147, 23959, 23772, 23584, 23397, 23209, 23022, 22835, 22648, 22461, 22274, 22087, 21901, 21714, 21528, 21342, 21156, 20971, 20785, 20600, 20415, 20230, 20046, 19862, 19678, 19494, 19311, 19127, 18945, 18762, 18580, 18399, 18217, 18036, 17856, 17675, 17496, 17316, 17137, 16959, 16781, 16603, 16426, 16249, 16073, 15898, 15722, 15548, 15374, 15200, 15027, 14855, 14683, 14511, 14341, 14171, 14001, 13832, 13664, 13496, 13329, 13163, 12998, 12833, 12668, 12505, 12342, 12180, 12019, 11858, 11698, 11539, 11381, 11223, 11066, 10910, 10755, 10601, 10447, 10295, 10143, 9992, 9841, 9692, 9544, 9396, 9250, 9104, 8959, 8815, 8672, 8530, 8389, 8249, 8110, 7972, 7834, 7698, 7563, 7429, 7295, 7163, 7032, 6902, 6773, 6644, 6517, 6391, 6266, 6143, 6020, 5898, 5778, 5658, 5540, 5423, 5306, 5191, 5078, 4965, 4853, 4743, 4633, 4525, 4418, 4313, 4208, 4105, 4002, 3901, 3802, 3703, 3606, 3510, 3415, 3321, 3228, 3137, 3047, 2958, 2871, 2785, 2700, 2616, 2534, 2452, 2373, 2294, 2217, 2141, 2066, 1992, 1920, 1849, 1780, 1711, 1644, 1579, 1515, 1452, 1390, 1329, 1270, 1213, 1156, 1101, 1048, 995, 944, 894, 846, 799, 753, 709, 666, 624, 584, 545, 507, 471, 436, 403, 371, 340, 310, 282, 255, 230, 206, 183, 161, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [7673, 7806, 7941, 8079, 8218, 8360, 8505, 8651, 8800, 8951, 9105, 9261, 9420, 9581, 9745, 9911, 10080, 10252, 10427, 10604, 10784, 10967, 11153, 11342, 11533, 11728, 11926, 12127, 12331, 12538, 12749, 12963, 13180, 13400, 13624, 13852, 14083, 14317, 14556, 14798, 15043, 15293, 15546, 15803, 16064, 16329, 16599, 16872, 17149, 17431, 17717, 18007, 18302, 18601, 18905, 19214, 19527, 19844, 20167, 20494, 20827, 21164, 21506, 21854, 22206, 22564, 22928, 23296, 23670, 24050, 24435, 24826, 25223, 25626, 26035, 26449, 26870, 27297, 27730, 28169, 28615, 29068, 29526, 29992, 30465, 30944, 31430, 31923, 32424, 32931, 33446, 33968, 34498, 35035, 35580, 36133, 36694, 37263, 37840, 38425, 39018, 39620, 40230, 40849, 41429, 41542, 41654, 41766, 41877, 41988, 42099, 42210, 42320, 42429, 42538, 42647, 42755, 42863, 42971, 43078, 43184, 43290, 43396, 43501, 43606, 43710, 43814, 43917, 44020, 44122, 44224, 44325, 44426, 44526, 44626, 44725, 44823, 44921, 45019, 45116, 45212, 45308, 45403, 45498, 45592, 45686, 45778, 45871, 45962, 46053, 46144, 46234, 46323, 46412, 46499, 46587, 46673, 46759, 46845, 46929, 47013, 47096, 47179, 47261, 47342, 47422, 47502, 47581, 47659, 47737, 47814, 47890, 47965, 48040, 48114, 48187, 48259, 48331, 48402, 48472, 48541, 48609, 48677, 48744, 48810, 48875, 48939, 49003, 49066, 49128, 49189, 49249, 49308, 49367, 49424, 49481, 49537, 49592, 49646, 49700, 49752, 49804, 49854, 49904, 49953, 50000, 50047, 50093, 50139, 50183, 50226, 50268, 50310, 50350, 50389, 50428, 50465, 50502, 50538, 50572, 50606, 50638, 50670, 50701, 50730, 50759, 50787, 50813, 50839, 50864, 50887, 50910, 50931, 50952, 50971, 50990, 51007, 51024, 51039, 51053, 51066, 51079, 51090, 51100, 51109, 51116, 51123, 51129, 51134, 51137, 51140, 51141, 51141, 51141, 51139, 51136, 51132, 51126, 51120, 51113, 51104, 51095, 51084, 51072, 51059, 51045, 51030, 51013, 50996, 50977, 50957, 50937, 50915, 50891, 50867, 50842, 50815, 50787, 50759, 50729, 50697, 50665, 50632, 50597, 50561, 50525, 50487, 50447, 50407, 50366, 50323, 50279, 50234, 50188, 50141, 50092, 50043, 49992, 49940, 49887, 49833, 49778, 49721, 49664, 49605, 49545, 49484, 49422, 49358, 49294, 49228, 49161, 49093, 49024, 48954, 48883, 48810, 48737, 48662, 48586, 48509, 48431, 48351, 48271, 48189, 48106, 48023, 47938, 47852, 47764, 47676, 47587, 47496, 47405, 47312, 47218, 47123, 47027, 46930, 46832, 46732, 46632, 46531, 46428, 46324, 46220, 46114, 46007, 45899, 45791, 45681, 45570, 45458, 45345, 45230, 45115, 44999, 44882, 44764, 44645, 44524, 44403, 44281, 44158, 44033, 43908, 43782, 43655, 43527, 43398, 43268, 43137, 43005, 42872, 42738, 42604, 42468, 42331, 42194, 42055, 41916, 41776, 41635, 41493, 41350, 41206, 41062, 40917, 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47946, 47847, 47747, 47646, 47544, 47440, 47336, 47231, 47124, 47017, 46908, 46798, 46687, 46576, 46463, 46349, 46234, 46118, 46001, 45883, 45764, 45643, 45522, 45400, 45277, 45153, 45028, 44901, 44774, 44646, 44517, 44387, 44256, 44124, 43991, 43857, 43722, 43586, 43449, 43311, 43173, 43033, 42893, 42751, 42609, 42466, 42322, 42177, 42031, 41884, 41737, 41588, 41439, 41289, 41138, 40986, 40834, 40680, 40526, 40371, 40215, 40059, 39901, 39743, 39584, 39425, 39264, 39103, 38941, 38779, 38615, 38451, 38286, 38121, 37955, 37788, 37621, 37453, 37284, 37114, 36944, 36774, 36602, 36431, 36258, 36085, 35911, 35737, 35562, 35387, 35211, 35034, 34857, 34680, 34502, 34323, 34144, 33965, 33785, 33604, 33424, 33242, 33060, 32878, 32696, 32513, 32329, 32145, 31961, 31777, 31592, 31406, 31221, 31035, 30849, 30662, 30475, 30288, 30101, 29913, 29725, 29537, 29348, 29160, 28971, 28782, 28592, 28403, 28213, 28024, 27834, 27644, 27453, 27263, 27073, 26882, 26691, 26501, 26310, 26119, 25928, 25737, 25546, 25355, 25164, 24973, 24782, 24591, 24400, 24210, 24019, 23828, 23637, 23447, 23256, 23066, 22876, 22686, 22496, 22306, 22117, 21927, 21738, 21549, 21360, 21172, 20983, 20795, 20607, 20420, 20233, 20046, 19859, 19673, 19486, 19301, 19115, 18930, 18746, 18561, 18377, 18194, 18011, 17828, 17646, 17464, 17283, 17102, 16921, 16741, 16562, 16383, 16204, 16027, 15849, 15672, 15496, 15320, 15145, 14970, 14796, 14623, 14450, 14278, 14107, 13936, 13766, 13596, 13427, 13259, 13092, 12925, 12759, 12593, 12429, 12265, 12102, 11940, 11778, 11617, 11457, 11298, 11140, 10982, 10825, 10669, 10514, 10360, 10207, 10054, 9903, 9752, 9602, 9453, 9305, 9158, 9012, 8867, 8722, 8579, 8437, 8296, 8155, 8016, 7877, 7740, 7604, 7468, 7334, 7201, 7068, 6937, 6807, 6678, 6550, 6423, 6297, 6172, 6049, 5926, 5805, 5684, 5565, 5447, 5330, 5214, 5100, 4986, 4874, 4763, 4653, 4544, 4436, 4330, 4225, 4121, 4018, 3916, 3816, 3717, 3619, 3522, 3427, 3333, 3240, 3148, 3057, 2968, 2880, 2794, 2708, 2624, 2541, 2460, 2380, 2301, 2223, 2147, 2071, 1998, 1925, 1854, 1784, 1716, 1649, 1583, 1518, 1455, 1393, 1332, 1273, 1215, 1159, 1104, 1050, 997, 946, 896, 848, 800, 755, 710, 667, 625, 585, 546, 508, 472, 437, 403, 371, 340, 310, 282, 255, 230, 206, 183, 162, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [8656, 8804, 8953, 9105, 9260, 9416, 9576, 9737, 9902, 10069, 10238, 10411, 10586, 10763, 10944, 11127, 11313, 11502, 11694, 11889, 12087, 12288, 12493, 12700, 12911, 13124, 13342, 13562, 13786, 14013, 14244, 14478, 14716, 14958, 15203, 15452, 15705, 15961, 16222, 16486, 16755, 17027, 17304, 17584, 17869, 18159, 18452, 18750, 19053, 19360, 19671, 19987, 20308, 20634, 20964, 21300, 21640, 21985, 22336, 22692, 23052, 23419, 23790, 24167, 24550, 24938, 25332, 25731, 26136, 26548, 26965, 27388, 27817, 28253, 28695, 29143, 29598, 30059, 30527, 31001, 31482, 31971, 32466, 32968, 33477, 33994, 34518, 35049, 35588, 36134, 36688, 37250, 37820, 38398, 38984, 39578, 40180, 40791, 41410, 42038, 42675, 43320, 43919, 44028, 44137, 44245, 44353, 44461, 44568, 44675, 44781, 44886, 44991, 45096, 45200, 45304, 45407, 45510, 45612, 45713, 45814, 45915, 46015, 46114, 46213, 46311, 46409, 46506, 46603, 46699, 46794, 46889, 46983, 47076, 47169, 47262, 47353, 47444, 47535, 47625, 47714, 47802, 47890, 47977, 48064, 48150, 48235, 48319, 48403, 48486, 48568, 48650, 48731, 48811, 48890, 48969, 49047, 49124, 49201, 49276, 49351, 49426, 49499, 49572, 49643, 49714, 49785, 49854, 49923, 49991, 50058, 50124, 50189, 50254, 50318, 50381, 50443, 50504, 50564, 50624, 50682, 50740, 50797, 50853, 50908, 50962, 51015, 51068, 51119, 51170, 51219, 51268, 51316, 51363, 51409, 51454, 51498, 51541, 51583, 51624, 51665, 51704, 51742, 51779, 51816, 51851, 51885, 51919, 51951, 51983, 52013, 52042, 52071, 52098, 52124, 52150, 52174, 52197, 52219, 52241, 52261, 52280, 52298, 52315, 52331, 52345, 52359, 52372, 52384, 52394, 52404, 52412, 52419, 52426, 52431, 52435, 52438, 52440, 52441, 52440, 52439, 52436, 52433, 52428, 52422, 52415, 52407, 52397, 52387, 52376, 52363, 52349, 52334, 52318, 52301, 52283, 52263, 52243, 52221, 52198, 52174, 52149, 52122, 52095, 52066, 52037, 52006, 51973, 51940, 51906, 51870, 51833, 51796, 51756, 51716, 51675, 51632, 51589, 51544, 51498, 51450, 51402, 51352, 51302, 51250, 51197, 51143, 51087, 51031, 50973, 50914, 50854, 50793, 50730, 50667, 50602, 50536, 50469, 50401, 50332, 50261, 50190, 50117, 50043, 49968, 49892, 49814, 49736, 49656, 49575, 49493, 49410, 49326, 49241, 49154, 49067, 48978, 48888, 48797, 48705, 48612, 48517, 48422, 48325, 48228, 48129, 48029, 47928, 47826, 47723, 47618, 47513, 47407, 47299, 47191, 47081, 46970, 46858, 46746, 46632, 46517, 46401, 46284, 46166, 46047, 45926, 45805, 45683, 45560, 45436, 45311, 45184, 45057, 44929, 44800, 44670, 44539, 44407, 44274, 44140, 44005, 43869, 43732, 43594, 43455, 43316, 43175, 43034, 42891, 42748, 42604, 42459, 42313, 42166, 42018, 41870, 41721, 41570, 41419, 41267, 41115, 40961, 40807, 40651, 40496, 40339, 40181, 40023, 39864, 39704, 39543, 39382, 39220, 39057, 38894, 38729, 38564, 38399, 38232, 38065, 37898, 37729, 37560, 37390, 37220, 37049, 36878, 36705, 36533, 36359, 36185, 36011, 35836, 35660, 35484, 35307, 35129, 34952, 34773, 34594, 34415, 34235, 34055, 33874, 33692, 33511, 33329, 33146, 32963, 32779, 32596, 32411, 32227, 32042, 31856, 31671, 31484, 31298, 31111, 30924, 30737, 30549, 30361, 30173, 29985, 29796, 29607, 29418, 29228, 29039, 28849, 28659, 28469, 28278, 28088, 27897, 27706, 27515, 27324, 27133, 26942, 26750, 26559, 26367, 26176, 25984, 25793, 25601, 25409, 25218, 25026, 24834, 24643, 24451, 24260, 24068, 23877, 23686, 23494, 23303, 23112, 22922, 22731, 22540, 22350, 22160, 21970, 21780, 21591, 21401, 21212, 21023, 20834, 20646, 20458, 20270, 20082, 19895, 19708, 19522, 19335, 19150, 18964, 18779, 18594, 18410, 18225, 18042, 17859, 17676, 17494, 17312, 17130, 16949, 16769, 16589, 16410, 16231, 16052, 15875, 15697, 15520, 15344, 15169, 14994, 14819, 14646, 14472, 14300, 14128, 13957, 13786, 13616, 13447, 13278, 13110, 12943, 12777, 12611, 12446, 12282, 12119, 11956, 11794, 11633, 11472, 11313, 11154, 10996, 10839, 10683, 10528, 10373, 10219, 10067, 9915, 9764, 9614, 9465, 9316, 9169, 9023, 8877, 8733, 8589, 8446, 8305, 8164, 8025, 7886, 7748, 7612, 7476, 7342, 7208, 7076, 6944, 6814, 6685, 6556, 6429, 6303, 6178, 6054, 5932, 5810, 5690, 5570, 5452, 5335, 5219, 5104, 4991, 4878, 4767, 4657, 4548, 4440, 4334, 4228, 4124, 4021, 3919, 3819, 3720, 3622, 3525, 3429, 3335, 3242, 3150, 3060, 2970, 2882, 2796, 2710, 2626, 2543, 2461, 2381, 2302, 2224, 2148, 2073, 1999, 1926, 1855, 1785, 1717, 1649, 1583, 1519, 1456, 1394, 1333, 1274, 1216, 1159, 1104, 1050, 997, 946, 896, 848, 801, 755, 710, 667, 625, 585, 546, 508, 472, 437, 403, 371, 340, 311, 282, 255, 230, 206, 183, 162, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [9022, 9174, 9329, 9487, 9647, 9810, 9975, 10142, 10313, 10486, 10662, 10840, 11021, 11205, 11392, 11582, 11775, 11971, 12170, 12372, 12577, 12785, 12996, 13211, 13429, 13650, 13875, 14103, 14335, 14570, 14809, 15051, 15297, 15547, 15800, 16058, 16319, 16584, 16854, 17127, 17404, 17686, 17972, 18262, 18557, 18855, 19159, 19467, 19779, 20096, 20418, 20744, 21076, 21412, 21753, 22099, 22451, 22807, 23169, 23536, 23909, 24286, 24670, 25059, 25453, 25854, 26260, 26672, 27090, 27514, 27944, 28381, 28823, 29272, 29728, 30190, 30658, 31134, 31616, 32105, 32600, 33103, 33613, 34131, 34655, 35187, 35727, 36274, 36829, 37391, 37962, 38540, 39127, 39721, 40324, 40936, 41556, 42184, 42821, 43467, 44122, 44462, 44570, 44678, 44786, 44893, 44999, 45105, 45211, 45316, 45420, 45524, 45628, 45731, 45833, 45935, 46037, 46137, 46238, 46338, 46437, 46535, 46633, 46731, 46828, 46924, 47020, 47115, 47210, 47304, 47397, 47490, 47582, 47673, 47764, 47854, 47944, 48032, 48121, 48208, 48295, 48381, 48467, 48551, 48636, 48719, 48802, 48884, 48965, 49045, 49125, 49204, 49283, 49360, 49437, 49513, 49588, 49663, 49737, 49810, 49882, 49953, 50024, 50094, 50163, 50231, 50299, 50365, 50431, 50496, 50560, 50623, 50686, 50747, 50808, 50868, 50927, 50985, 51042, 51098, 51154, 51208, 51262, 51315, 51366, 51417, 51467, 51516, 51565, 51612, 51658, 51703, 51748, 51791, 51834, 51875, 51916, 51956, 51994, 52032, 52069, 52104, 52139, 52173, 52205, 52237, 52268, 52298, 52326, 52354, 52381, 52406, 52431, 52454, 52477, 52499, 52519, 52538, 52557, 52574, 52590, 52605, 52620, 52633, 52645, 52655, 52665, 52674, 52682, 52688, 52694, 52698, 52701, 52703, 52705, 52705, 52703, 52701, 52698, 52693, 52688, 52681, 52673, 52664, 52654, 52643, 52631, 52617, 52603, 52587, 52570, 52552, 52533, 52512, 52491, 52468, 52445, 52420, 52394, 52366, 52338, 52308, 52278, 52246, 52213, 52179, 52143, 52107, 52069, 52030, 51990, 51949, 51907, 51863, 51819, 51773, 51726, 51678, 51628, 51578, 51526, 51473, 51419, 51364, 51308, 51250, 51192, 51132, 51071, 51009, 50946, 50881, 50815, 50749, 50681, 50611, 50541, 50470, 50397, 50323, 50248, 50172, 50095, 50017, 49937, 49857, 49775, 49692, 49608, 49523, 49436, 49349, 49260, 49170, 49079, 48987, 48894, 48800, 48705, 48608, 48511, 48412, 48312, 48211, 48109, 48006, 47902, 47797, 47690, 47583, 47474, 47365, 47254, 47143, 47030, 46916, 46801, 46685, 46568, 46450, 46331, 46211, 46090, 45968, 45844, 45720, 45595, 45469, 45342, 45214, 45084, 44954, 44823, 44691, 44558, 44424, 44289, 44153, 44016, 43878, 43739, 43600, 43459, 43317, 43175, 43032, 42887, 42742, 42596, 42449, 42301, 42153, 42003, 41853, 41702, 41550, 41397, 41243, 41089, 40933, 40777, 40620, 40462, 40304, 40145, 39985, 39824, 39662, 39500, 39337, 39173, 39009, 38844, 38678, 38511, 38344, 38176, 38007, 37838, 37668, 37497, 37326, 37154, 36982, 36809, 36635, 36461, 36286, 36110, 35934, 35758, 35580, 35403, 35225, 35046, 34867, 34687, 34506, 34326, 34145, 33963, 33781, 33598, 33415, 33232, 33048, 32863, 32679, 32494, 32308, 32122, 31936, 31750, 31563, 31375, 31188, 31000, 30812, 30623, 30435, 30246, 30057, 29867, 29677, 29487, 29297, 29107, 28916, 28725, 28534, 28343, 28152, 27961, 27769, 27577, 27385, 27194, 27002, 26810, 26617, 26425, 26233, 26041, 25848, 25656, 25464, 25271, 25079, 24887, 24694, 24502, 24310, 24118, 23926, 23734, 23542, 23350, 23159, 22967, 22776, 22585, 22394, 22203, 22013, 21822, 21632, 21442, 21252, 21063, 20874, 20685, 20496, 20308, 20119, 19932, 19744, 19557, 19370, 19184, 18998, 18812, 18627, 18442, 18257, 18073, 17889, 17706, 17523, 17341, 17159, 16978, 16797, 16616, 16436, 16257, 16078, 15900, 15722, 15545, 15368, 15192, 15017, 14842, 14668, 14494, 14321, 14149, 13977, 13806, 13636, 13466, 13298, 13129, 12962, 12795, 12629, 12464, 12299, 12135, 11972, 11810, 11648, 11488, 11328, 11169, 11011, 10853, 10697, 10541, 10386, 10232, 10079, 9927, 9776, 9625, 9476, 9327, 9180, 9033, 8887, 8743, 8599, 8456, 8314, 8173, 8033, 7895, 7757, 7620, 7484, 7349, 7216, 7083, 6951, 6821, 6691, 6563, 6436, 6309, 6184, 6060, 5937, 5816, 5695, 5575, 5457, 5340, 5224, 5109, 4995, 4882, 4771, 4661, 4552, 4444, 4337, 4232, 4127, 4024, 3922, 3822, 3722, 3624, 3527, 3432, 3337, 3244, 3152, 3062, 2972, 2884, 2797, 2712, 2627, 2544, 2463, 2382, 2303, 2225, 2149, 2074, 2000, 1927, 1856, 1786, 1717, 1650, 1584, 1520, 1456, 1394, 1334, 1274, 1216, 1160, 1104, 1050, 998, 947, 897, 848, 801, 755, 711, 667, 626, 585, 546, 508, 472, 437, 403, 371, 340, 311, 282, 256, 230, 206, 183, 162, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [9246, 9402, 9560, 9721, 9884, 10050, 10219, 10390, 10564, 10740, 10920, 11102, 11287, 11475, 11665, 11859, 12056, 12255, 12458, 12664, 12873, 13085, 13301, 13520, 13742, 13967, 14197, 14429, 14665, 14905, 15148, 15395, 15646, 15900, 16159, 16421, 16687, 16957, 17232, 17510, 17793, 18079, 18370, 18666, 18966, 19270, 19579, 19892, 20210, 20533, 20860, 21193, 21530, 21872, 22219, 22572, 22929, 23292, 23660, 24033, 24412, 24796, 25186, 25582, 25983, 26390, 26803, 27222, 27647, 28078, 28515, 28959, 29409, 29865, 30328, 30798, 31274, 31757, 32247, 32743, 33247, 33758, 34276, 34802, 35335, 35875, 36423, 36978, 37542, 38113, 38692, 39280, 39875, 40479, 41091, 41712, 42341, 42979, 43625, 44281, 44897, 45005, 45112, 45219, 45326, 45431, 45537, 45642, 45746, 45850, 45953, 46056, 46159, 46260, 46362, 46462, 46562, 46662, 46761, 46859, 46957, 47055, 47151, 47247, 47343, 47438, 47532, 47626, 47719, 47811, 47903, 47994, 48085, 48175, 48264, 48353, 48440, 48528, 48614, 48700, 48785, 48870, 48953, 49037, 49119, 49201, 49281, 49362, 49441, 49520, 49598, 49675, 49751, 49827, 49902, 49976, 50050, 50122, 50194, 50265, 50335, 50404, 50473, 50541, 50608, 50674, 50739, 50804, 50867, 50930, 50992, 51053, 51113, 51172, 51231, 51288, 51345, 51401, 51456, 51510, 51563, 51615, 51666, 51717, 51766, 51815, 51862, 51909, 51955, 51999, 52043, 52086, 52128, 52169, 52209, 52248, 52286, 52323, 52359, 52394, 52428, 52461, 52493, 52524, 52554, 52583, 52611, 52638, 52664, 52689, 52713, 52736, 52758, 52779, 52798, 52817, 52835, 52851, 52867, 52881, 52895, 52907, 52918, 52928, 52937, 52945, 52952, 52958, 52963, 52966, 52969, 52970, 52970, 52969, 52968, 52964, 52960, 52955, 52949, 52941, 52932, 52923, 52912, 52900, 52886, 52872, 52857, 52840, 52822, 52803, 52783, 52762, 52740, 52716, 52692, 52666, 52639, 52611, 52582, 52551, 52520, 52487, 52453, 52418, 52382, 52344, 52306, 52266, 52225, 52183, 52140, 52095, 52050, 52003, 51955, 51906, 51856, 51804, 51752, 51698, 51643, 51587, 51529, 51471, 51411, 51351, 51289, 51225, 51161, 51096, 51029, 50961, 50892, 50822, 50751, 50678, 50605, 50530, 50454, 50377, 50299, 50220, 50139, 50057, 49975, 49891, 49806, 49719, 49632, 49544, 49454, 49363, 49271, 49178, 49084, 48989, 48893, 48795, 48697, 48597, 48496, 48394, 48291, 48187, 48082, 47976, 47868, 47760, 47650, 47540, 47428, 47315, 47201, 47087, 46971, 46854, 46736, 46617, 46497, 46376, 46253, 46130, 46006, 45881, 45755, 45627, 45499, 45370, 45240, 45109, 44977, 44843, 44709, 44574, 44438, 44301, 44163, 44025, 43885, 43744, 43603, 43460, 43317, 43172, 43027, 42881, 42734, 42586, 42437, 42287, 42137, 41986, 41833, 41680, 41527, 41372, 41216, 41060, 40903, 40745, 40586, 40427, 40267, 40106, 39944, 39781, 39618, 39454, 39290, 39124, 38958, 38791, 38624, 38455, 38286, 38117, 37947, 37776, 37604, 37432, 37259, 37086, 36912, 36737, 36562, 36386, 36210, 36033, 35856, 35677, 35499, 35320, 35140, 34960, 34779, 34598, 34417, 34235, 34052, 33869, 33686, 33502, 33317, 33133, 32948, 32762, 32576, 32390, 32203, 32016, 31829, 31641, 31453, 31265, 31076, 30887, 30698, 30508, 30318, 30128, 29938, 29748, 29557, 29366, 29175, 28983, 28792, 28600, 28408, 28216, 28024, 27832, 27639, 27447, 27254, 27062, 26869, 26676, 26483, 26290, 26097, 25904, 25711, 25518, 25325, 25132, 24939, 24746, 24553, 24360, 24168, 23975, 23782, 23590, 23398, 23205, 23013, 22821, 22630, 22438, 22247, 22055, 21864, 21674, 21483, 21293, 21103, 20913, 20723, 20534, 20345, 20156, 19968, 19780, 19592, 19405, 19218, 19031, 18845, 18659, 18474, 18289, 18104, 17920, 17736, 17553, 17370, 17188, 17006, 16824, 16644, 16463, 16283, 16104, 15925, 15747, 15570, 15393, 15216, 15040, 14865, 14690, 14516, 14343, 14170, 13998, 13827, 13656, 13486, 13317, 13148, 12980, 12813, 12647, 12481, 12316, 12152, 11989, 11826, 11664, 11503, 11343, 11184, 11025, 10867, 10711, 10555, 10399, 10245, 10092, 9939, 9788, 9637, 9487, 9339, 9191, 9044, 8898, 8753, 8609, 8466, 8324, 8182, 8042, 7903, 7765, 7628, 7492, 7357, 7223, 7090, 6958, 6828, 6698, 6569, 6442, 6316, 6190, 6066, 5943, 5821, 5700, 5580, 5462, 5344, 5228, 5113, 4999, 4886, 4775, 4664, 4555, 4447, 4340, 4235, 4131, 4027, 3925, 3825, 3725, 3627, 3530, 3434, 3340, 3246, 3154, 3064, 2974, 2886, 2799, 2713, 2629, 2546, 2464, 2384, 2305, 2227, 2150, 2075, 2001, 1928, 1857, 1787, 1718, 1651, 1585, 1520, 1457, 1395, 1334, 1275, 1217, 1160, 1105, 1051, 998, 947, 897, 848, 801, 755, 711, 668, 626, 585, 546, 509, 472, 437, 404, 371, 340, 311, 282, 256, 230, 206, 183, 162, 141, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6] ]
def lowBounds05 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 50 through 59.
Definition (Lean source)
given by
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40227, 40054, 39880, 39706, 39531, 39355, 39178, 39001, 38824, 38645, 38466, 38287, 38107, 37926, 37744, 37562, 37380, 37197, 37013, 36829, 36644, 36459, 36273, 36087, 35900, 35713, 35525, 35337, 35149, 34960, 34770, 34580, 34390, 34199, 34008, 33816, 33624, 33432, 33239, 33046, 32853, 32660, 32466, 32271, 32077, 31882, 31687, 31491, 31296, 31100, 30904, 30707, 30511, 30314, 30117, 29920, 29722, 29525, 29327, 29129, 28932, 28733, 28535, 28337, 28139, 27940, 27742, 27543, 27345, 27146, 26948, 26749, 26550, 26352, 26153, 25955, 25756, 25558, 25359, 25161, 24963, 24765, 24567, 24369, 24171, 23974, 23776, 23579, 23382, 23185, 22988, 22791, 22595, 22399, 22203, 22008, 21812, 21617, 21423, 21228, 21034, 20840, 20647, 20454, 20261, 20068, 19876, 19685, 19493, 19302, 19112, 18922, 18732, 18543, 18354, 18166, 17978, 17791, 17604, 17418, 17232, 17047, 16863, 16679, 16495, 16312, 16130, 15948, 15767, 15586, 15406, 15227, 15048, 14870, 14693, 14516, 14340, 14165, 13991, 13817, 13644, 13471, 13300, 13129, 12959, 12789, 12621, 12453, 12286, 12120, 11954, 11790, 11626, 11463, 11301, 11140, 10980, 10821, 10662, 10505, 10348, 10192, 10038, 9884, 9731, 9579, 9428, 9278, 9129, 8981, 8834, 8688, 8543, 8398, 8255, 8113, 7972, 7833, 7694, 7556, 7419, 7284, 7149, 7015, 6883, 6752, 6622, 6493, 6365, 6238, 6112, 5988, 5864, 5742, 5621, 5501, 5383, 5265, 5149, 5034, 4920, 4807, 4696, 4585, 4476, 4368, 4262, 4156, 4052, 3949, 3848, 3747, 3648, 3550, 3454, 3358, 3264, 3172, 3080, 2990, 2901, 2813, 2727, 2642, 2559, 2476, 2395, 2315, 2237, 2160, 2084, 2010, 1937, 1865, 1794, 1725, 1657, 1591, 1526, 1462, 1400, 1339, 1279, 1221, 1164, 1108, 1054, 1001, 950, 900, 851, 803, 757, 713, 669, 627, 587, 548, 510, 473, 438, 404, 372, 341, 311, 283, 256, 230, 206, 183, 162, 142, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [11391, 11577, 11766, 11957, 12151, 12348, 12549, 12752, 12958, 13167, 13380, 13596, 13815, 14037, 14262, 14491, 14724, 14959, 15199, 15442, 15688, 15938, 16192, 16450, 16711, 16976, 17245, 17518, 17796, 18077, 18362, 18651, 18945, 19243, 19546, 19852, 20163, 20479, 20799, 21124, 21454, 21788, 22127, 22472, 22821, 23175, 23534, 23898, 24267, 24642, 25022, 25408, 25799, 26195, 26597, 27005, 27419, 27838, 28263, 28695, 29132, 29575, 30025, 30481, 30944, 31412, 31888, 32370, 32859, 33354, 33856, 34366, 34882, 35405, 35936, 36474, 37019, 37572, 38133, 38701, 39277, 39860, 40452, 41052, 41659, 42276, 42900, 43533, 44174, 44824, 45483, 46151, 46827, 47513, 48208, 48912, 49266, 49365, 49464, 49562, 49660, 49757, 49853, 49949, 50044, 50138, 50232, 50325, 50418, 50510, 50601, 50691, 50781, 50870, 50959, 51046, 51133, 51220, 51305, 51390, 51474, 51558, 51641, 51722, 51804, 51884, 51964, 52043, 52121, 52198, 52275, 52351, 52426, 52500, 52573, 52646, 52718, 52789, 52859, 52928, 52997, 53064, 53131, 53197, 53262, 53326, 53390, 53452, 53514, 53575, 53634, 53693, 53751, 53809, 53865, 53920, 53975, 54028, 54081, 54132, 54183, 54233, 54282, 54329, 54376, 54422, 54467, 54511, 54554, 54596, 54637, 54677, 54717, 54755, 54792, 54828, 54863, 54897, 54930, 54962, 54993, 55023, 55052, 55080, 55107, 55132, 55157, 55181, 55203, 55225, 55246, 55265, 55283, 55301, 55317, 55332, 55346, 55359, 55371, 55382, 55391, 55400, 55407, 55414, 55419, 55423, 55426, 55428, 55429, 55428, 55427, 55424, 55420, 55416, 55410, 55402, 55394, 55385, 55374, 55362, 55349, 55335, 55320, 55304, 55286, 55267, 55247, 55226, 55204, 55181, 55156, 55130, 55103, 55075, 55046, 55016, 54984, 54951, 54917, 54882, 54846, 54808, 54769, 54729, 54688, 54646, 54602, 54558, 54512, 54465, 54417, 54367, 54316, 54265, 54212, 54157, 54102, 54045, 53987, 53929, 53868, 53807, 53744, 53681, 53616, 53550, 53482, 53414, 53344, 53273, 53201, 53128, 53053, 52978, 52901, 52823, 52744, 52664, 52582, 52499, 52416, 52331, 52245, 52157, 52069, 51979, 51888, 51796, 51703, 51609, 51514, 51417, 51319, 51220, 51120, 51019, 50917, 50814, 50709, 50604, 50497, 50389, 50280, 50170, 50059, 49947, 49833, 49719, 49603, 49486, 49369, 49250, 49130, 49009, 48887, 48764, 48640, 48515, 48388, 48261, 48133, 48004, 47873, 47742, 47609, 47476, 47341, 47206, 47070, 46932, 46794, 46654, 46514, 46373, 46230, 46087, 45943, 45798, 45651, 45504, 45356, 45207, 45058, 44907, 44755, 44603, 44449, 44295, 44140, 43984, 43827, 43669, 43510, 43351, 43191, 43030, 42868, 42705, 42541, 42377, 42212, 42046, 41879, 41712, 41543, 41374, 41205, 41034, 40863, 40691, 40518, 40345, 40171, 39996, 39821, 39645, 39468, 39291, 39113, 38934, 38755, 38575, 38394, 38213, 38031, 37849, 37666, 37483, 37299, 37114, 36929, 36744, 36557, 36371, 36184, 35996, 35808, 35619, 35430, 35241, 35051, 34860, 34670, 34478, 34287, 34095, 33902, 33710, 33516, 33323, 33129, 32935, 32740, 32546, 32351, 32155, 31959, 31763, 31567, 31371, 31174, 30977, 30780, 30583, 30385, 30187, 29989, 29791, 29593, 29394, 29196, 28997, 28798, 28600, 28401, 28202, 28002, 27803, 27604, 27405, 27205, 27006, 26807, 26607, 26408, 26209, 26010, 25810, 25611, 25412, 25213, 25014, 24816, 24617, 24418, 24220, 24022, 23824, 23626, 23428, 23230, 23033, 22836, 22639, 22442, 22246, 22050, 21854, 21658, 21463, 21268, 21073, 20879, 20685, 20491, 20297, 20104, 19912, 19720, 19528, 19336, 19145, 18955, 18765, 18575, 18386, 18197, 18009, 17821, 17634, 17447, 17261, 17075, 16890, 16706, 16522, 16338, 16155, 15973, 15792, 15611, 15430, 15250, 15071, 14893, 14715, 14538, 14362, 14186, 14011, 13837, 13663, 13491, 13319, 13147, 12977, 12807, 12638, 12470, 12303, 12136, 11971, 11806, 11642, 11479, 11316, 11155, 10994, 10835, 10676, 10518, 10361, 10205, 10050, 9896, 9743, 9590, 9439, 9289, 9139, 8991, 8844, 8697, 8552, 8408, 8265, 8122, 7981, 7841, 7702, 7564, 7427, 7291, 7156, 7023, 6890, 6759, 6628, 6499, 6371, 6244, 6118, 5993, 5870, 5748, 5626, 5506, 5387, 5270, 5153, 5038, 4924, 4811, 4699, 4589, 4480, 4372, 4265, 4160, 4055, 3952, 3851, 3750, 3651, 3553, 3456, 3361, 3267, 3174, 3082, 2992, 2903, 2815, 2729, 2644, 2560, 2478, 2397, 2317, 2238, 2161, 2085, 2011, 1938, 1866, 1795, 1726, 1658, 1592, 1527, 1463, 1401, 1339, 1280, 1221, 1164, 1109, 1055, 1002, 950, 900, 851, 804, 758, 713, 670, 628, 587, 548, 510, 473, 438, 404, 372, 341, 311, 283, 256, 230, 206, 183, 162, 142, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [11497, 11684, 11873, 12066, 12261, 12460, 12661, 12866, 13073, 13284, 13498, 13715, 13935, 14158, 14385, 14615, 14849, 15086, 15327, 15571, 15819, 16071, 16326, 16585, 16848, 17114, 17385, 17659, 17938, 18221, 18508, 18798, 19094, 19393, 19697, 20005, 20318, 20635, 20957, 21284, 21615, 21951, 22292, 22637, 22988, 23344, 23704, 24070, 24441, 24818, 25200, 25587, 25979, 26378, 26781, 27191, 27606, 28027, 28455, 28888, 29327, 29772, 30224, 30681, 31146, 31616, 32093, 32577, 33068, 33565, 34069, 34580, 35099, 35624, 36156, 36696, 37244, 37798, 38361, 38931, 39508, 40094, 40687, 41289, 41899, 42517, 43143, 43778, 44421, 45073, 45734, 46404, 47082, 47770, 48466, 49173, 49707, 49806, 49904, 50001, 50098, 50194, 50290, 50384, 50479, 50572, 50665, 50757, 50849, 50940, 51030, 51119, 51208, 51296, 51384, 51470, 51556, 51641, 51726, 51810, 51893, 51975, 52057, 52138, 52218, 52297, 52375, 52453, 52530, 52606, 52682, 52756, 52830, 52903, 52975, 53046, 53117, 53187, 53255, 53323, 53391, 53457, 53522, 53587, 53651, 53713, 53775, 53836, 53897, 53956, 54014, 54072, 54128, 54184, 54239, 54293, 54345, 54397, 54448, 54499, 54548, 54596, 54643, 54689, 54735, 54779, 54822, 54865, 54906, 54947, 54986, 55024, 55062, 55098, 55134, 55168, 55201, 55234, 55265, 55295, 55325, 55353, 55380, 55406, 55431, 55455, 55478, 55500, 55521, 55541, 55559, 55577, 55593, 55609, 55623, 55637, 55649, 55660, 55670, 55679, 55686, 55693, 55699, 55703, 55706, 55708, 55710, 55709, 55708, 55706, 55702, 55698, 55692, 55685, 55677, 55668, 55658, 55646, 55633, 55620, 55605, 55589, 55571, 55553, 55533, 55512, 55490, 55467, 55443, 55417, 55391, 55363, 55334, 55304, 55272, 55240, 55206, 55171, 55135, 55098, 55059, 55019, 54979, 54936, 54893, 54849, 54803, 54756, 54708, 54659, 54609, 54557, 54504, 54450, 54395, 54338, 54281, 54222, 54162, 54101, 54039, 53975, 53910, 53844, 53777, 53709, 53639, 53569, 53497, 53424, 53349, 53274, 53197, 53119, 53040, 52960, 52879, 52796, 52713, 52628, 52542, 52455, 52366, 52277, 52186, 52094, 52001, 51907, 51812, 51715, 51618, 51519, 51419, 51318, 51216, 51113, 51008, 50903, 50796, 50688, 50579, 50469, 50358, 50246, 50133, 50018, 49903, 49786, 49668, 49550, 49430, 49309, 49187, 49064, 48940, 48814, 48688, 48561, 48432, 48303, 48173, 48041, 47909, 47775, 47641, 47505, 47369, 47231, 47093, 46953, 46813, 46672, 46529, 46386, 46242, 46096, 45950, 45803, 45655, 45506, 45356, 45205, 45053, 44901, 44747, 44593, 44437, 44281, 44124, 43966, 43807, 43648, 43487, 43326, 43164, 43001, 42837, 42672, 42507, 42341, 42174, 42006, 41838, 41669, 41499, 41328, 41156, 40984, 40811, 40638, 40463, 40288, 40113, 39936, 39759, 39582, 39403, 39224, 39045, 38864, 38684, 38502, 38320, 38137, 37954, 37770, 37586, 37401, 37216, 37030, 36843, 36656, 36468, 36280, 36092, 35903, 35713, 35523, 35333, 35142, 34951, 34759, 34567, 34375, 34182, 33988, 33795, 33601, 33406, 33212, 33017, 32821, 32626, 32430, 32234, 32037, 31840, 31643, 31446, 31248, 31051, 30853, 30655, 30456, 30258, 30059, 29860, 29661, 29462, 29263, 29063, 28864, 28664, 28464, 28264, 28065, 27865, 27665, 27465, 27265, 27065, 26864, 26664, 26464, 26264, 26065, 25865, 25665, 25465, 25265, 25066, 24866, 24667, 24468, 24269, 24070, 23871, 23673, 23474, 23276, 23078, 22880, 22683, 22485, 22288, 22092, 21895, 21699, 21503, 21307, 21112, 20917, 20722, 20528, 20334, 20141, 19948, 19755, 19562, 19370, 19179, 18988, 18797, 18607, 18417, 18228, 18039, 17851, 17663, 17476, 17289, 17103, 16918, 16733, 16548, 16364, 16181, 15998, 15816, 15635, 15454, 15274, 15094, 14916, 14737, 14560, 14383, 14207, 14032, 13857, 13683, 13510, 13338, 13166, 12995, 12825, 12656, 12487, 12320, 12153, 11987, 11821, 11657, 11494, 11331, 11169, 11008, 10848, 10689, 10531, 10374, 10218, 10062, 9908, 9754, 9602, 9450, 9300, 9150, 9002, 8854, 8707, 8562, 8417, 8274, 8131, 7990, 7849, 7710, 7572, 7435, 7299, 7164, 7030, 6897, 6765, 6635, 6505, 6377, 6250, 6124, 5999, 5875, 5753, 5631, 5511, 5392, 5274, 5158, 5042, 4928, 4815, 4703, 4593, 4483, 4375, 4269, 4163, 4058, 3955, 3853, 3753, 3654, 3555, 3459, 3363, 3269, 3176, 3084, 2994, 2905, 2817, 2731, 2645, 2562, 2479, 2398, 2318, 2239, 2162, 2086, 2012, 1939, 1867, 1796, 1727, 1659, 1593, 1527, 1464, 1401, 1340, 1280, 1222, 1165, 1109, 1055, 1002, 950, 900, 851, 804, 758, 713, 670, 628, 587, 548, 510, 473, 438, 404, 372, 341, 311, 283, 256, 230, 206, 183, 162, 142, 123, 105, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6] ]
def lowBounds06 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 60 through 69.
Definition (Lean source)
given by
#[ [11793, 11984, 12177, 12374, 12574, 12776, 12982, 13191, 13403, 13618, 13836, 14058, 14283, 14511, 14743, 14978, 15216, 15458, 15704, 15953, 16206, 16463, 16724, 16988, 17256, 17528, 17804, 18084, 18368, 18657, 18949, 19246, 19547, 19853, 20163, 20477, 20796, 21119, 21447, 21780, 22118, 22460, 22808, 23160, 23517, 23880, 24247, 24620, 24998, 25382, 25771, 26165, 26565, 26971, 27382, 27799, 28222, 28651, 29086, 29527, 29974, 30428, 30887, 31353, 31826, 32305, 32791, 33283, 33782, 34289, 34802, 35322, 35849, 36383, 36925, 37475, 38031, 38596, 39167, 39747, 40335, 40930, 41534, 42146, 42766, 43394, 44031, 44676, 45330, 45993, 46665, 47345, 48035, 48734, 49442, 50150, 50248, 50345, 50441, 50537, 50632, 50727, 50821, 50914, 51006, 51098, 51190, 51280, 51370, 51459, 51548, 51635, 51722, 51809, 51894, 51979, 52063, 52147, 52229, 52311, 52392, 52473, 52553, 52631, 52709, 52787, 52863, 52939, 53014, 53088, 53161, 53234, 53306, 53376, 53446, 53516, 53584, 53651, 53718, 53784, 53849, 53913, 53976, 54038, 54100, 54160, 54220, 54279, 54336, 54393, 54449, 54504, 54559, 54612, 54664, 54716, 54766, 54815, 54864, 54912, 54958, 55004, 55048, 55092, 55135, 55177, 55217, 55257, 55296, 55334, 55370, 55406, 55441, 55474, 55507, 55539, 55569, 55599, 55627, 55655, 55681, 55707, 55731, 55754, 55777, 55798, 55818, 55837, 55855, 55872, 55887, 55902, 55916, 55928, 55939, 55950, 55959, 55967, 55974, 55980, 55984, 55988, 55990, 55992, 55992, 55991, 55989, 55986, 55982, 55976, 55970, 55962, 55953, 55943, 55932, 55919, 55906, 55891, 55875, 55858, 55840, 55821, 55800, 55778, 55755, 55731, 55706, 55680, 55652, 55623, 55593, 55562, 55530, 55496, 55462, 55426, 55389, 55350, 55311, 55270, 55229, 55185, 55141, 55096, 55049, 55001, 54952, 54902, 54851, 54798, 54744, 54689, 54633, 54576, 54517, 54457, 54396, 54334, 54271, 54206, 54140, 54073, 54005, 53936, 53865, 53794, 53721, 53647, 53571, 53495, 53417, 53338, 53258, 53177, 53095, 53011, 52926, 52841, 52754, 52665, 52576, 52485, 52394, 52301, 52207, 52111, 52015, 51918, 51819, 51719, 51618, 51516, 51413, 51309, 51203, 51097, 50989, 50880, 50770, 50659, 50547, 50433, 50319, 50204, 50087, 49969, 49851, 49731, 49610, 49488, 49365, 49241, 49115, 48989, 48862, 48734, 48604, 48474, 48342, 48210, 48076, 47942, 47806, 47670, 47532, 47394, 47254, 47114, 46972, 46830, 46686, 46542, 46396, 46250, 46103, 45955, 45806, 45655, 45504, 45353, 45200, 45046, 44892, 44736, 44580, 44423, 44264, 44105, 43946, 43785, 43624, 43461, 43298, 43134, 42969, 42804, 42637, 42470, 42302, 42134, 41964, 41794, 41623, 41451, 41279, 41106, 40932, 40757, 40582, 40406, 40229, 40052, 39874, 39695, 39516, 39336, 39155, 38974, 38792, 38610, 38427, 38243, 38059, 37874, 37689, 37503, 37317, 37130, 36943, 36755, 36566, 36377, 36188, 35998, 35807, 35617, 35425, 35234, 35041, 34849, 34656, 34463, 34269, 34075, 33880, 33685, 33490, 33295, 33099, 32903, 32706, 32509, 32312, 32115, 31917, 31719, 31521, 31323, 31124, 30926, 30727, 30528, 30328, 30129, 29929, 29729, 29529, 29329, 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49286, 49142, 48996, 48850, 48703, 48555, 48406, 48256, 48105, 47953, 47800, 47647, 47492, 47336, 47180, 47022, 46864, 46704, 46544, 46383, 46221, 46058, 45894, 45729, 45564, 45397, 45230, 45062, 44893, 44723, 44553, 44382, 44209, 44037, 43863, 43688, 43513, 43337, 43160, 42983, 42804, 42625, 42446, 42265, 42084, 41902, 41720, 41537, 41353, 41168, 40983, 40797, 40611, 40424, 40236, 40048, 39859, 39670, 39480, 39289, 39098, 38906, 38714, 38521, 38328, 38134, 37939, 37745, 37549, 37353, 37157, 36960, 36763, 36566, 36367, 36169, 35970, 35771, 35571, 35371, 35171, 34970, 34769, 34567, 34366, 34164, 33961, 33759, 33556, 33352, 33149, 32945, 32741, 32537, 32332, 32128, 31923, 31718, 31513, 31307, 31102, 30896, 30690, 30484, 30278, 30072, 29866, 29659, 29453, 29246, 29040, 28833, 28627, 28420, 28213, 28007, 27800, 27594, 27387, 27181, 26974, 26768, 26562, 26356, 26149, 25944, 25738, 25532, 25327, 25121, 24916, 24711, 24506, 24302, 24097, 23893, 23689, 23486, 23282, 23079, 22876, 22674, 22471, 22269, 22068, 21867, 21666, 21465, 21265, 21065, 20866, 20667, 20468, 20270, 20072, 19875, 19678, 19482, 19286, 19091, 18896, 18701, 18508, 18314, 18121, 17929, 17738, 17547, 17356, 17166, 16977, 16788, 16600, 16413, 16226, 16040, 15854, 15670, 15486, 15302, 15120, 14938, 14757, 14576, 14396, 14217, 14039, 13862, 13685, 13509, 13334, 13160, 12987, 12814, 12642, 12471, 12301, 12132, 11964, 11797, 11630, 11465, 11300, 11136, 10973, 10811, 10651, 10491, 10332, 10174, 10017, 9861, 9705, 9551, 9398, 9246, 9095, 8945, 8797, 8649, 8502, 8356, 8212, 8068, 7926, 7784, 7644, 7505, 7367, 7230, 7094, 6960, 6826, 6694, 6563, 6433, 6304, 6176, 6050, 5925, 5800, 5678, 5556, 5435, 5316, 5198, 5081, 4966, 4852, 4739, 4627, 4516, 4407, 4299, 4192, 4087, 3982, 3880, 3778, 3678, 3579, 3481, 3384, 3289, 3195, 3103, 3012, 2922, 2833, 2746, 2660, 2576, 2493, 2411, 2330, 2251, 2173, 2097, 2022, 1948, 1875, 1804, 1735, 1666, 1599, 1534, 1470, 1407, 1345, 1285, 1227, 1169, 1113, 1059, 1005, 954, 903, 854, 806, 760, 715, 672, 629, 589, 549, 511, 475, 439, 405, 373, 342, 312, 283, 256, 231, 207, 184, 162, 142, 123, 106, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [14157, 14379, 14604, 14833, 15065, 15300, 15539, 15781, 16027, 16276, 16529, 16786, 17046, 17310, 17578, 17849, 18125, 18404, 18688, 18975, 19267, 19563, 19863, 20167, 20475, 20788, 21106, 21428, 21754, 22085, 22421, 22761, 23106, 23456, 23811, 24171, 24536, 24906, 25281, 25661, 26047, 26438, 26834, 27236, 27643, 28056, 28475, 28900, 29330, 29766, 30208, 30657, 31111, 31572, 32038, 32512, 32991, 33477, 33970, 34469, 34975, 35488, 36008, 36535, 37069, 37610, 38158, 38714, 39277, 39847, 40426, 41011, 41605, 42207, 42816, 43433, 44059, 44693, 45335, 45986, 46645, 47313, 47990, 48675, 49369, 50073, 50785, 51507, 52238, 52979, 53729, 54335, 54422, 54508, 54594, 54679, 54764, 54847, 54930, 55012, 55093, 55173, 55253, 55332, 55410, 55487, 55563, 55639, 55714, 55788, 55861, 55933, 56004, 56075, 56144, 56213, 56281, 56348, 56414, 56480, 56544, 56608, 56670, 56732, 56793, 56853, 56912, 56970, 57027, 57083, 57139, 57193, 57246, 57299, 57350, 57401, 57450, 57499, 57546, 57593, 57639, 57683, 57727, 57770, 57811, 57852, 57891, 57930, 57968, 58004, 58040, 58074, 58108, 58140, 58171, 58202, 58231, 58259, 58286, 58312, 58337, 58361, 58384, 58406, 58426, 58446, 58464, 58482, 58498, 58513, 58527, 58540, 58552, 58563, 58572, 58581, 58588, 58594, 58599, 58603, 58606, 58607, 58608, 58607, 58605, 58603, 58598, 58593, 58587, 58579, 58570, 58560, 58549, 58537, 58523, 58509, 58493, 58476, 58458, 58438, 58418, 58396, 58373, 58349, 58323, 58297, 58269, 58240, 58210, 58179, 58146, 58112, 58077, 58041, 58004, 57965, 57925, 57884, 57842, 57798, 57754, 57708, 57661, 57612, 57563, 57512, 57460, 57407, 57352, 57297, 57240, 57182, 57122, 57062, 57000, 56937, 56873, 56807, 56741, 56673, 56604, 56534, 56462, 56389, 56316, 56240, 56164, 56087, 56008, 55928, 55847, 55764, 55681, 55596, 55510, 55423, 55335, 55245, 55154, 55062, 54969, 54875, 54780, 54683, 54585, 54486, 54386, 54285, 54182, 54078, 53974, 53868, 53760, 53652, 53543, 53432, 53320, 53207, 53093, 52978, 52862, 52744, 52626, 52506, 52385, 52264, 52141, 52016, 51891, 51765, 51638, 51509, 51380, 51249, 51117, 50984, 50851, 50716, 50580, 50443, 50305, 50166, 50026, 49885, 49742, 49599, 49455, 49310, 49164, 49017, 48868, 48719, 48569, 48418, 48266, 48113, 47959, 47804, 47648, 47492, 47334, 47175, 47016, 46855, 46694, 46532, 46369, 46205, 46040, 45874, 45708, 45540, 45372, 45203, 45033, 44862, 44691, 44518, 44345, 44171, 43996, 43821, 43644, 43467, 43290, 43111, 42932, 42752, 42571, 42390, 42208, 42025, 41841, 41657, 41472, 41287, 41101, 40914, 40726, 40538, 40350, 40160, 39970, 39780, 39589, 39397, 39205, 39013, 38819, 38626, 38431, 38237, 38041, 37845, 37649, 37452, 37255, 37058, 36859, 36661, 36462, 36263, 36063, 35863, 35662, 35461, 35260, 35058, 34856, 34654, 34451, 34248, 34045, 33842, 33638, 33434, 33229, 33025, 32820, 32615, 32409, 32204, 31998, 31792, 31586, 31380, 31174, 30967, 30761, 30554, 30347, 30140, 29933, 29726, 29519, 29311, 29104, 28897, 28689, 28482, 28275, 28067, 27860, 27653, 27446, 27238, 27031, 26824, 26617, 26410, 26204, 25997, 25790, 25584, 25378, 25172, 24966, 24760, 24555, 24350, 24145, 23940, 23735, 23531, 23327, 23123, 22920, 22717, 22514, 22311, 22109, 21907, 21706, 21505, 21304, 21103, 20903, 20704, 20505, 20306, 20108, 19910, 19713, 19516, 19319, 19123, 18928, 18733, 18539, 18345, 18152, 17959, 17767, 17575, 17384, 17194, 17004, 16815, 16626, 16439, 16251, 16065, 15879, 15694, 15509, 15326, 15142, 14960, 14778, 14598, 14417, 14238, 14059, 13882, 13705, 13528, 13353, 13178, 13005, 12832, 12660, 12488, 12318, 12148, 11980, 11812, 11645, 11479, 11314, 11150, 10987, 10825, 10664, 10504, 10344, 10186, 10029, 9872, 9717, 9563, 9409, 9257, 9106, 8956, 8807, 8658, 8511, 8366, 8221, 8077, 7934, 7793, 7652, 7513, 7375, 7237, 7101, 6967, 6833, 6700, 6569, 6439, 6310, 6182, 6055, 5930, 5806, 5683, 5561, 5440, 5321, 5203, 5086, 4970, 4856, 4742, 4631, 4520, 4410, 4302, 4195, 4090, 3985, 3882, 3781, 3680, 3581, 3483, 3387, 3291, 3198, 3105, 3014, 2924, 2835, 2748, 2662, 2577, 2494, 2412, 2332, 2252, 2174, 2098, 2023, 1949, 1876, 1805, 1736, 1667, 1600, 1535, 1470, 1407, 1346, 1286, 1227, 1170, 1114, 1059, 1006, 954, 904, 854, 807, 760, 715, 672, 630, 589, 549, 511, 475, 439, 405, 373, 342, 312, 284, 257, 231, 207, 184, 162, 142, 123, 106, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6] ]
def lowBounds07 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 70 through 79.
Definition (Lean source)
given by
#[ [14525, 14752, 14982, 15216, 15453, 15693, 15937, 16185, 16436, 16690, 16949, 17211, 17477, 17746, 18020, 18297, 18578, 18864, 19153, 19447, 19745, 20046, 20353, 20663, 20978, 21298, 21622, 21950, 22283, 22621, 22963, 23311, 23663, 24020, 24382, 24749, 25121, 25498, 25881, 26269, 26662, 27061, 27465, 27875, 28290, 28711, 29138, 29571, 30009, 30454, 30905, 31362, 31825, 32294, 32770, 33252, 33740, 34236, 34738, 35246, 35762, 36284, 36814, 37350, 37894, 38445, 39003, 39569, 40142, 40723, 41312, 41908, 42513, 43125, 43745, 44374, 45010, 45656, 46309, 46971, 47642, 48322, 49010, 49707, 50414, 51129, 51854, 52588, 53332, 54085, 54780, 54866, 54951, 55036, 55120, 55203, 55285, 55367, 55447, 55527, 55606, 55685, 55762, 55839, 55915, 55990, 56064, 56138, 56210, 56282, 56353, 56423, 56492, 56560, 56628, 56694, 56760, 56824, 56888, 56951, 57013, 57075, 57135, 57194, 57252, 57310, 57366, 57422, 57477, 57530, 57583, 57635, 57686, 57736, 57785, 57832, 57879, 57925, 57970, 58014, 58057, 58099, 58140, 58180, 58219, 58257, 58294, 58329, 58364, 58398, 58431, 58462, 58493, 58522, 58551, 58578, 58605, 58630, 58654, 58677, 58699, 58720, 58740, 58759, 58776, 58793, 58808, 58823, 58836, 58848, 58859, 58869, 58878, 58885, 58892, 58897, 58901, 58904, 58906, 58907, 58907, 58905, 58902, 58899, 58893, 58887, 58880, 58871, 58862, 58851, 58839, 58826, 58811, 58796, 58779, 58761, 58742, 58721, 58700, 58677, 58653, 58628, 58602, 58574, 58545, 58516, 58484, 58452, 58418, 58384, 58348, 58311, 58272, 58232, 58192, 58150, 58106, 58062, 58016, 57969, 57921, 57872, 57821, 57769, 57716, 57662, 57607, 57550, 57492, 57433, 57372, 57311, 57248, 57184, 57119, 57052, 56985, 56916, 56846, 56774, 56702, 56628, 56553, 56477, 56400, 56321, 56241, 56160, 56078, 55995, 55910, 55824, 55737, 55649, 55559, 55469, 55377, 55284, 55190, 55094, 54998, 54900, 54801, 54701, 54600, 54497, 54394, 54289, 54183, 54076, 53968, 53858, 53748, 53636, 53523, 53409, 53294, 53178, 53060, 52942, 52822, 52701, 52579, 52456, 52332, 52207, 52081, 51953, 51825, 51695, 51565, 51433, 51300, 51166, 51032, 50896, 50759, 50620, 50481, 50341, 50200, 50058, 49915, 49770, 49625, 49479, 49332, 49183, 49034, 48884, 48733, 48580, 48427, 48273, 48118, 47962, 47805, 47648, 47489, 47329, 47168, 47007, 46845, 46681, 46517, 46352, 46186, 46019, 45852, 45683, 45514, 45344, 45173, 45001, 44828, 44655, 44481, 44306, 44130, 43953, 43776, 43598, 43419, 43240, 43059, 42878, 42697, 42514, 42331, 42147, 41963, 41777, 41592, 41405, 41218, 41030, 40842, 40653, 40463, 40273, 40082, 39891, 39699, 39506, 39313, 39119, 38925, 38730, 38535, 38339, 38143, 37947, 37749, 37552, 37353, 37155, 36956, 36756, 36557, 36356, 36156, 35955, 35753, 35551, 35349, 35147, 34944, 34740, 34537, 34333, 34129, 33925, 33720, 33515, 33310, 33104, 32899, 32693, 32487, 32280, 32074, 31867, 31660, 31453, 31246, 31039, 30831, 30624, 30416, 30208, 30001, 29793, 29585, 29377, 29169, 28960, 28752, 28544, 28336, 28128, 27920, 27712, 27504, 27296, 27088, 26880, 26673, 26465, 26258, 26050, 25843, 25636, 25429, 25223, 25016, 24810, 24604, 24398, 24192, 23987, 23782, 23577, 23372, 23168, 22963, 22760, 22556, 22353, 22150, 21948, 21746, 21544, 21343, 21142, 20941, 20741, 20541, 20342, 20143, 19945, 19747, 19549, 19353, 19156, 18960, 18765, 18570, 18376, 18182, 17989, 17796, 17604, 17412, 17222, 17031, 16842, 16653, 16465, 16277, 16090, 15904, 15718, 15533, 15349, 15165, 14982, 14800, 14619, 14439, 14259, 14080, 13902, 13724, 13548, 13372, 13197, 13023, 12849, 12677, 12505, 12335, 12165, 11996, 11828, 11661, 11494, 11329, 11165, 11001, 10839, 10677, 10517, 10357, 10198, 10041, 9884, 9729, 9574, 9420, 9268, 9116, 8966, 8817, 8668, 8521, 8375, 8230, 8086, 7943, 7801, 7660, 7521, 7382, 7245, 7109, 6974, 6840, 6707, 6575, 6445, 6316, 6188, 6061, 5935, 5811, 5688, 5566, 5445, 5326, 5207, 5090, 4974, 4860, 4746, 4634, 4523, 4414, 4306, 4199, 4093, 3988, 3885, 3783, 3683, 3584, 3486, 3389, 3294, 3200, 3107, 3016, 2926, 2837, 2750, 2664, 2579, 2496, 2414, 2333, 2254, 2176, 2099, 2024, 1950, 1877, 1806, 1736, 1668, 1601, 1535, 1471, 1408, 1347, 1286, 1228, 1170, 1114, 1060, 1006, 954, 904, 855, 807, 761, 716, 672, 630, 589, 550, 511, 475, 439, 406, 373, 342, 312, 284, 257, 231, 207, 184, 162, 142, 123, 106, 89, 75, 61, 49, 39, 29, 21, 15, 9, 6], [14673, 14902, 15134, 15369, 15608, 15850, 16096, 16345, 16598, 16855, 17115, 17379, 17646, 17918, 18193, 18473, 18756, 19043, 19335, 19630, 19930, 20234, 20542, 20855, 21172, 21493, 21819, 22150, 22485, 22825, 23170, 23519, 23873, 24233, 24597, 24966, 25341, 25720, 26105, 26495, 26891, 27292, 27698, 28111, 28528, 28952, 29381, 29816, 30257, 30705, 31158, 31617, 32083, 32555, 33033, 33518, 34009, 34507, 35011, 35523, 36041, 36566, 37098, 37637, 38184, 38738, 39299, 39867, 40443, 41027, 41619, 42218, 42825, 43440, 44063, 44695, 45335, 45983, 46639, 47304, 47978, 48661, 49352, 50052, 50762, 51481, 52208, 52946, 53693, 54449, 55215, 55310, 55394, 55477, 55560, 55642, 55723, 55803, 55883, 55961, 56039, 56116, 56193, 56268, 56342, 56416, 56489, 56561, 56632, 56703, 56772, 56841, 56909, 56975, 57041, 57106, 57171, 57234, 57296, 57358, 57418, 57478, 57537, 57594, 57651, 57707, 57762, 57816, 57869, 57921, 57973, 58023, 58072, 58120, 58167, 58214, 58259, 58303, 58346, 58389, 58430, 58470, 58509, 58548, 58585, 58621, 58656, 58690, 58723, 58755, 58786, 58816, 58844, 58872, 58899, 58924, 58949, 58972, 58995, 59016, 59036, 59055, 59073, 59090, 59105, 59120, 59134, 59146, 59157, 59167, 59176, 59184, 59191, 59197, 59201, 59204, 59207, 59208, 59208, 59206, 59204, 59200, 59196, 59190, 59183, 59174, 59165, 59154, 59142, 59129, 59115, 59100, 59083, 59066, 59047, 59027, 59005, 58983, 58959, 58934, 58908, 58881, 58852, 58823, 58792, 58760, 58726, 58692, 58656, 58619, 58581, 58542, 58501, 58459, 58416, 58372, 58326, 58279, 58232, 58182, 58132, 58080, 58028, 57973, 57918, 57862, 57804, 57745, 57685, 57623, 57561, 57497, 57432, 57366, 57298, 57229, 57159, 57088, 57016, 56942, 56867, 56791, 56714, 56636, 56556, 56475, 56393, 56310, 56225, 56139, 56053, 55964, 55875, 55785, 55693, 55600, 55506, 55411, 55314, 55216, 55118, 55018, 54916, 54814, 54711, 54606, 54500, 54393, 54285, 54175, 54065, 53953, 53840, 53726, 53611, 53495, 53378, 53259, 53140, 53019, 52897, 52774, 52650, 52525, 52398, 52271, 52142, 52013, 51882, 51750, 51618, 51484, 51349, 51213, 51076, 50938, 50798, 50658, 50517, 50375, 50231, 50087, 49942, 49795, 49648, 49500, 49350, 49200, 49049, 48896, 48743, 48589, 48434, 48278, 48121, 47963, 47804, 47644, 47483, 47321, 47159, 46995, 46831, 46666, 46500, 46333, 46165, 45996, 45827, 45656, 45485, 45313, 45140, 44966, 44792, 44617, 44441, 44264, 44086, 43908, 43729, 43549, 43368, 43187, 43005, 42822, 42639, 42455, 42270, 42084, 41898, 41711, 41524, 41336, 41147, 40957, 40767, 40577, 40386, 40194, 40001, 39808, 39615, 39421, 39226, 39031, 38835, 38639, 38443, 38245, 38048, 37850, 37651, 37452, 37252, 37052, 36852, 36651, 36450, 36249, 36047, 35844, 35641, 35438, 35235, 35031, 34827, 34623, 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28677, 28462, 28248, 28033, 27819, 27604, 27390, 27176, 26962, 26748, 26535, 26321, 26108, 25895, 25682, 25469, 25257, 25045, 24833, 24622, 24410, 24199, 23989, 23778, 23568, 23358, 23149, 22940, 22731, 22523, 22315, 22108, 21901, 21694, 21488, 21282, 21077, 20872, 20668, 20464, 20260, 20058, 19855, 19654, 19452, 19252, 19052, 18852, 18653, 18455, 18257, 18060, 17863, 17668, 17472, 17278, 17084, 16891, 16698, 16507, 16315, 16125, 15935, 15747, 15558, 15371, 15184, 14999, 14814, 14629, 14446, 14263, 14082, 13901, 13720, 13541, 13363, 13185, 13009, 12833, 12658, 12484, 12311, 12139, 11968, 11798, 11629, 11461, 11293, 11127, 10962, 10797, 10634, 10472, 10310, 10150, 9991, 9833, 9676, 9520, 9365, 9211, 9058, 8906, 8756, 8606, 8458, 8311, 8164, 8019, 7875, 7733, 7591, 7451, 7312, 7173, 7037, 6901, 6766, 6633, 6501, 6370, 6241, 6112, 5985, 5859, 5734, 5611, 5488, 5367, 5248, 5129, 5012, 4896, 4782, 4668, 4556, 4446, 4336, 4228, 4121, 4016, 3911, 3809, 3707, 3607, 3508, 3410, 3314, 3219, 3126, 3034, 2943, 2853, 2765, 2678, 2593, 2509, 2426, 2345, 2265, 2187, 2109, 2034, 1959, 1886, 1815, 1744, 1675, 1608, 1542, 1477, 1414, 1352, 1291, 1232, 1175, 1118, 1063, 1010, 958, 907, 857, 809, 763, 718, 674, 632, 591, 551, 513, 476, 440, 406, 374, 342, 313, 284, 257, 231, 207, 184, 162, 142, 123, 106, 90, 75, 61, 49, 39, 29, 21, 15, 9, 6] ]
def lowBounds08 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 80 through 89.
Definition (Lean source)
given by
#[ [17397, 17660, 17927, 18197, 18472, 18750, 19032, 19318, 19608, 19902, 20200, 20503, 20809, 21120, 21435, 21754, 22078, 22406, 22739, 23076, 23418, 23765, 24116, 24473, 24834, 25200, 25571, 25947, 26328, 26714, 27106, 27503, 27905, 28313, 28726, 29144, 29569, 29999, 30435, 30876, 31324, 31777, 32237, 32702, 33174, 33652, 34137, 34628, 35125, 35629, 36140, 36657, 37181, 37712, 38250, 38795, 39347, 39906, 40473, 41047, 41628, 42217, 42814, 43418, 44030, 44651, 45279, 45915, 46559, 47212, 47873, 48542, 49220, 49906, 50602, 51306, 52019, 52741, 53473, 54213, 54963, 55722, 56491, 57270, 58058, 58856, 59307, 59379, 59451, 59521, 59591, 59660, 59727, 59794, 59861, 59926, 59990, 60053, 60116, 60177, 60238, 60298, 60356, 60414, 60471, 60527, 60581, 60635, 60688, 60740, 60791, 60841, 60890, 60938, 60985, 61031, 61076, 61120, 61163, 61204, 61245, 61285, 61324, 61362, 61398, 61434, 61469, 61502, 61534, 61566, 61596, 61625, 61654, 61681, 61707, 61731, 61755, 61778, 61799, 61820, 61839, 61857, 61875, 61891, 61905, 61919, 61932, 61943, 61953, 61963, 61971, 61977, 61983, 61988, 61991, 61993, 61994, 61994, 61993, 61991, 61987, 61982, 61976, 61969, 61961, 61951, 61940, 61928, 61915, 61901, 61885, 61868, 61851, 61831, 61811, 61789, 61767, 61742, 61717, 61691, 61663, 61634, 61604, 61573, 61540, 61506, 61471, 61435, 61397, 61358, 61318, 61277, 61235, 61191, 61146, 61100, 61052, 61004, 60954, 60903, 60850, 60796, 60742, 60685, 60628, 60569, 60509, 60448, 60386, 60322, 60257, 60191, 60124, 60055, 59986, 59914, 59842, 59769, 59694, 59618, 59540, 59462, 59382, 59301, 59219, 59135, 59051, 58965, 58878, 58789, 58700, 58609, 58517, 58424, 58329, 58233, 58136, 58038, 57939, 57838, 57737, 57634, 57529, 57424, 57318, 57210, 57101, 56991, 56879, 56767, 56653, 56538, 56422, 56305, 56187, 56067, 55947, 55825, 55702, 55578, 55453, 55326, 55199, 55070, 54940, 54809, 54677, 54544, 54410, 54275, 54138, 54001, 53862, 53722, 53582, 53440, 53297, 53153, 53008, 52862, 52714, 52566, 52417, 52267, 52115, 51963, 51810, 51655, 51500, 51343, 51186, 51028, 50868, 50708, 50547, 50385, 50221, 50057, 49892, 49726, 49559, 49391, 49222, 49053, 48882, 48711, 48538, 48365, 48191, 48016, 47840, 47663, 47486, 47307, 47128, 46948, 46767, 46586, 46403, 46220, 46036, 45851, 45666, 45480, 45292, 45105, 44916, 44727, 44537, 44346, 44155, 43963, 43770, 43577, 43383, 43188, 42993, 42797, 42600, 42403, 42205, 42007, 41808, 41608, 41408, 41207, 41006, 40804, 40602, 40399, 40196, 39992, 39788, 39583, 39377, 39172, 38965, 38759, 38552, 38344, 38136, 37928, 37719, 37510, 37301, 37091, 36881, 36670, 36459, 36248, 36036, 35825, 35613, 35400, 35188, 34975, 34762, 34548, 34335, 34121, 33907, 33693, 33478, 33264, 33049, 32834, 32619, 32404, 32189, 31973, 31758, 31543, 31327, 31111, 30896, 30680, 30464, 30248, 30033, 29817, 29601, 29385, 29170, 28954, 28738, 28523, 28308, 28092, 27877, 27662, 27447, 27232, 27018, 26803, 26589, 26375, 26161, 25947, 25733, 25520, 25307, 25094, 24882, 24670, 24458, 24246, 24035, 23824, 23613, 23402, 23192, 22983, 22774, 22565, 22356, 22148, 21940, 21733, 21526, 21320, 21114, 20909, 20704, 20500, 20296, 20092, 19889, 19687, 19485, 19284, 19084, 18884, 18684, 18485, 18287, 18089, 17892, 17696, 17500, 17305, 17111, 16917, 16724, 16532, 16341, 16150, 15960, 15770, 15582, 15394, 15207, 15021, 14835, 14651, 14467, 14284, 14102, 13920, 13740, 13560, 13381, 13204, 13027, 12850, 12675, 12501, 12328, 12155, 11984, 11813, 11644, 11475, 11308, 11141, 10975, 10811, 10647, 10484, 10323, 10162, 10003, 9844, 9687, 9531, 9376, 9221, 9068, 8916, 8765, 8616, 8467, 8320, 8173, 8028, 7884, 7741, 7599, 7458, 7319, 7181, 7044, 6908, 6773, 6640, 6507, 6376, 6246, 6118, 5990, 5864, 5739, 5616, 5493, 5372, 5252, 5134, 5016, 4900, 4786, 4672, 4560, 4449, 4340, 4231, 4124, 4019, 3914, 3811, 3710, 3609, 3510, 3413, 3316, 3221, 3128, 3036, 2945, 2855, 2767, 2680, 2595, 2510, 2428, 2346, 2266, 2188, 2111, 2035, 1960, 1887, 1815, 1745, 1676, 1609, 1543, 1478, 1414, 1352, 1292, 1233, 1175, 1119, 1064, 1010, 958, 907, 858, 810, 763, 718, 674, 632, 591, 551, 513, 476, 441, 407, 374, 343, 313, 284, 257, 231, 207, 184, 162, 142, 123, 106, 90, 75, 61, 49, 39, 29, 21, 15, 9, 6], [17584, 17849, 18118, 18390, 18667, 18947, 19231, 19520, 19812, 20108, 20409, 20713, 21022, 21335, 21652, 21974, 22300, 22631, 22966, 23306, 23650, 24000, 24353, 24712, 25076, 25444, 25818, 26197, 26581, 26970, 27364, 27763, 28168, 28579, 28995, 29416, 29843, 30276, 30715, 31159, 31610, 32066, 32529, 32997, 33472, 33954, 34441, 34935, 35435, 35942, 36456, 36977, 37504, 38038, 38579, 39128, 39683, 40246, 40815, 41393, 41978, 42570, 43170, 43778, 44393, 45017, 45649, 46288, 46936, 47592, 48257, 48930, 49611, 50302, 51001, 51709, 52425, 53151, 53887, 54631, 55385, 56148, 56921, 57703, 58496, 59298, 59750, 59821, 59891, 59960, 60028, 60096, 60162, 60227, 60292, 60356, 60418, 60480, 60541, 60601, 60660, 60718, 60775, 60831, 60886, 60941, 60994, 61046, 61097, 61147, 61197, 61245, 61292, 61338, 61384, 61428, 61471, 61513, 61554, 61594, 61634, 61672, 61708, 61744, 61779, 61813, 61846, 61877, 61908, 61937, 61966, 61993, 62019, 62045, 62069, 62092, 62113, 62134, 62154, 62172, 62190, 62206, 62221, 62235, 62248, 62260, 62270, 62279, 62288, 62295, 62301, 62306, 62309, 62312, 62313, 62313, 62312, 62310, 62307, 62302, 62296, 62289, 62281, 62272, 62261, 62250, 62237, 62223, 62207, 62191, 62173, 62154, 62134, 62112, 62090, 62066, 62041, 62015, 61987, 61959, 61929, 61897, 61865, 61831, 61796, 61760, 61723, 61684, 61645, 61604, 61561, 61518, 61473, 61427, 61380, 61331, 61281, 61230, 61178, 61125, 61070, 61014, 60957, 60898, 60839, 60778, 60715, 60652, 60587, 60521, 60454, 60385, 60316, 60245, 60173, 60099, 60025, 59949, 59871, 59793, 59713, 59633, 59550, 59467, 59382, 59297, 59210, 59121, 59032, 58941, 58849, 58756, 58661, 58566, 58469, 58371, 58272, 58171, 58069, 57967, 57862, 57757, 57651, 57543, 57434, 57324, 57213, 57100, 56987, 56872, 56756, 56639, 56520, 56401, 56280, 56158, 56035, 55911, 55786, 55660, 55532, 55403, 55274, 55143, 55011, 54878, 54743, 54608, 54471, 54334, 54195, 54055, 53914, 53772, 53629, 53485, 53340, 53194, 53047, 52898, 52749, 52599, 52447, 52295, 52141, 51987, 51831, 51675, 51517, 51359, 51199, 51039, 50877, 50715, 50552, 50387, 50222, 50056, 49889, 49721, 49552, 49382, 49211, 49039, 48867, 48693, 48519, 48343, 48167, 47990, 47813, 47634, 47455, 47274, 47093, 46911, 46728, 46545, 46361, 46176, 45990, 45803, 45616, 45428, 45239, 45049, 44859, 44668, 44476, 44284, 44091, 43897, 43703, 43508, 43312, 43115, 42919, 42721, 42523, 42324, 42124, 41924, 41724, 41523, 41321, 41119, 40916, 40713, 40509, 40304, 40100, 39894, 39688, 39482, 39275, 39068, 38861, 38653, 38444, 38235, 38026, 37816, 37606, 37396, 37185, 36974, 36762, 36551, 36339, 36126, 35913, 35700, 35487, 35274, 35060, 34846, 34632, 34417, 34203, 33988, 33773, 33557, 33342, 33126, 32911, 32695, 32479, 32263, 32047, 31830, 31614, 31398, 31181, 30965, 30748, 30532, 30315, 30099, 29882, 29666, 29449, 29233, 29016, 28800, 28584, 28368, 28151, 27936, 27720, 27504, 27288, 27073, 26858, 26643, 26428, 26213, 25999, 25785, 25571, 25357, 25144, 24930, 24718, 24505, 24293, 24081, 23869, 23658, 23447, 23236, 23026, 22816, 22606, 22397, 22189, 21980, 21773, 21565, 21358, 21152, 20946, 20740, 20535, 20331, 20127, 19924, 19721, 19518, 19317, 19116, 18915, 18715, 18516, 18317, 18119, 17921, 17725, 17528, 17333, 17138, 16944, 16750, 16558, 16366, 16174, 15984, 15794, 15605, 15417, 15229, 15043, 14857, 14672, 14488, 14304, 14122, 13940, 13759, 13579, 13400, 13222, 13044, 12868, 12692, 12518, 12344, 12171, 11999, 11829, 11659, 11490, 11322, 11155, 10989, 10824, 10660, 10497, 10335, 10175, 10015, 9856, 9698, 9542, 9386, 9232, 9079, 8926, 8775, 8625, 8476, 8329, 8182, 8036, 7892, 7749, 7607, 7466, 7326, 7188, 7051, 6915, 6780, 6646, 6514, 6382, 6252, 6123, 5996, 5870, 5744, 5621, 5498, 5377, 5257, 5138, 5021, 4904, 4790, 4676, 4564, 4453, 4343, 4235, 4127, 4022, 3917, 3814, 3712, 3612, 3513, 3415, 3319, 3224, 3130, 3038, 2947, 2857, 2769, 2682, 2596, 2512, 2429, 2348, 2268, 2189, 2112, 2036, 1961, 1888, 1816, 1746, 1677, 1609, 1543, 1478, 1415, 1353, 1292, 1233, 1175, 1119, 1064, 1010, 958, 907, 858, 810, 763, 718, 674, 632, 591, 551, 513, 476, 441, 407, 374, 343, 313, 284, 257, 231, 207, 184, 162, 142, 123, 106, 90, 75, 61, 49, 39, 29, 21, 15, 9, 6], [18040, 18311, 18586, 18865, 19148, 19434, 19724, 20019, 20318, 20620, 20927, 21238, 21554, 21873, 22198, 22526, 22859, 23197, 23539, 23886, 24238, 24594, 24956, 25322, 25693, 26069, 26451, 26837, 27229, 27626, 28028, 28436, 28849, 29268, 29692, 30122, 30558, 31000, 31447, 31901, 32360, 32826, 33297, 33775, 34259, 34750, 35247, 35751, 36261, 36778, 37301, 37832, 38369, 38914, 39465, 40024, 40590, 41163, 41744, 42332, 42928, 43532, 44143, 44762, 45389, 46024, 46668, 47319, 47979, 48647, 49324, 50009, 50703, 51406, 52118, 52838, 53568, 54307, 55055, 55813, 56580, 57357, 58144, 58940, 59746, 60193, 60263, 60331, 60399, 60465, 60531, 60596, 60660, 60723, 60785, 60846, 60906, 60966, 61024, 61081, 61138, 61193, 61248, 61301, 61354, 61405, 61456, 61505, 61554, 61601, 61648, 61693, 61738, 61781, 61824, 61865, 61906, 61945, 61983, 62021, 62057, 62092, 62126, 62159, 62191, 62222, 62251, 62280, 62308, 62334, 62360, 62384, 62407, 62429, 62450, 62470, 62489, 62507, 62523, 62538, 62553, 62566, 62578, 62589, 62598, 62607, 62614, 62620, 62625, 62629, 62632, 62634, 62634, 62633, 62631, 62628, 62624, 62618, 62611, 62604, 62594, 62584, 62573, 62560, 62546, 62531, 62515, 62497, 62478, 62459, 62437, 62415, 62391, 62367, 62340, 62313, 62285, 62255, 62224, 62192, 62158, 62124, 62088, 62051, 62012, 61973, 61932, 61890, 61846, 61802, 61756, 61709, 61660, 61611, 61560, 61508, 61455, 61400, 61344, 61287, 61229, 61169, 61108, 61046, 60983, 60919, 60853, 60786, 60717, 60648, 60577, 60505, 60432, 60357, 60281, 60204, 60126, 60046, 59966, 59884, 59800, 59716, 59630, 59543, 59455, 59366, 59275, 59183, 59090, 58996, 58900, 58803, 58705, 58606, 58506, 58404, 58301, 58197, 58092, 57985, 57878, 57769, 57659, 57548, 57435, 57322, 57207, 57091, 56974, 56855, 56736, 56615, 56494, 56371, 56246, 56121, 55995, 55867, 55738, 55609, 55478, 55346, 55212, 55078, 54943, 54806, 54668, 54530, 54390, 54249, 54107, 53964, 53820, 53674, 53528, 53381, 53232, 53083, 52932, 52781, 52628, 52475, 52320, 52164, 52008, 51850, 51691, 51532, 51371, 51209, 51047, 50883, 50719, 50553, 50387, 50220, 50051, 49882, 49712, 49541, 49369, 49196, 49023, 48848, 48673, 48496, 48319, 48141, 47962, 47782, 47602, 47420, 47238, 47055, 46871, 46687, 46501, 46315, 46128, 45941, 45752, 45563, 45373, 45183, 44991, 44799, 44606, 44413, 44219, 44024, 43829, 43632, 43436, 43238, 43040, 42842, 42642, 42443, 42242, 42041, 41840, 41637, 41435, 41231, 41028, 40823, 40618, 40413, 40207, 40001, 39794, 39587, 39379, 39171, 38962, 38753, 38544, 38334, 38124, 37913, 37702, 37491, 37279, 37067, 36855, 36642, 36429, 36216, 36002, 35788, 35574, 35360, 35145, 34930, 34715, 34500, 34284, 34069, 33853, 33637, 33420, 33204, 32987, 32771, 32554, 32337, 32120, 31903, 31686, 31469, 31251, 31034, 30817, 30599, 30382, 30165, 29947, 29730, 29513, 29296, 29078, 28861, 28644, 28428, 28211, 27994, 27778, 27561, 27345, 27129, 26913, 26697, 26482, 26266, 26051, 25836, 25622, 25407, 25193, 24979, 24766, 24552, 24339, 24127, 23914, 23702, 23491, 23280, 23069, 22858, 22648, 22438, 22229, 22020, 21812, 21604, 21396, 21189, 20983, 20777, 20571, 20366, 20162, 19958, 19754, 19552, 19349, 19148, 18947, 18746, 18546, 18347, 18148, 17950, 17753, 17556, 17360, 17165, 16970, 16777, 16583, 16391, 16199, 16008, 15818, 15629, 15440, 15252, 15065, 14879, 14693, 14509, 14325, 14142, 13960, 13778, 13598, 13418, 13240, 13062, 12885, 12709, 12534, 12360, 12187, 12015, 11844, 11674, 11504, 11336, 11169, 11003, 10837, 10673, 10510, 10348, 10187, 10027, 9868, 9710, 9553, 9397, 9242, 9089, 8936, 8785, 8635, 8486, 8338, 8191, 8045, 7900, 7757, 7615, 7474, 7334, 7195, 7058, 6921, 6786, 6652, 6520, 6388, 6258, 6129, 6001, 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Tables01 9 core · 0 supporting Proposed integer upper bounds for the rounded low-frequency cells, ten parameter rows per table.
Low Prawitz certificate: candidate bound tables 9 through 17
Proposed integer upper bounds for the rounded low-frequency cells, ten parameter rows per table. They are data only; every entry is checked by the block theorems.
def lowBounds09 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 90 through 99.
Definition (Lean source)
given by
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81496, 81403, 81309, 81214, 81117, 81019, 80920, 80819, 80717, 80613, 80509, 80402, 80295, 80186, 80076, 79964, 79851, 79736, 79621, 79504, 79385, 79265, 79144, 79022, 78898, 78773, 78646, 78518, 78389, 78258, 78127, 77993, 77859, 77723, 77586, 77447, 77307, 77166, 77024, 76880, 76735, 76589, 76441, 76292, 76142, 75990, 75837, 75683, 75528, 75371, 75213, 75054, 74893, 74731, 74568, 74404, 74239, 74072, 73904, 73734, 73564, 73392, 73219, 73045, 72870, 72693, 72515, 72336, 72156, 71975, 71792, 71608, 71423, 71237, 71050, 70862, 70672, 70481, 70290, 70097, 69902, 69707, 69511, 69313, 69115, 68915, 68714, 68512, 68309, 68105, 67900, 67694, 67487, 67279, 67069, 66859, 66648, 66435, 66222, 66008, 65792, 65576, 65358, 65140, 64921, 64700, 64479, 64257, 64034, 63810, 63585, 63359, 63132, 62905, 62676, 62447, 62216, 61985, 61753, 61520, 61287, 61052, 60817, 60581, 60344, 60106, 59867, 59628, 59388, 59147, 58905, 58663, 58420, 58176, 57932, 57686, 57440, 57194, 56947, 56699, 56450, 56201, 55951, 55700, 55449, 55198, 54945, 54692, 54439, 54185, 53930, 53675, 53420, 53163, 52907, 52650, 52392, 52134, 51875, 51616, 51356, 51096, 50836, 50575, 50314, 50052, 49790, 49528, 49265, 49002, 48739, 48475, 48211, 47946, 47682, 47417, 47151, 46886, 46620, 46354, 46088, 45822, 45555, 45288, 45021, 44754, 44487, 44219, 43951, 43684, 43416, 43148, 42880, 42612, 42343, 42075, 41807, 41539, 41270, 41002, 40734, 40465, 40197, 39929, 39660, 39392, 39124, 38856, 38588, 38321, 38053, 37786, 37518, 37251, 36984, 36717, 36450, 36184, 35918, 35652, 35386, 35121, 34855, 34590, 34326, 34061, 33797, 33534, 33270, 33007, 32745, 32482, 32220, 31959, 31698, 31437, 31177, 30917, 30658, 30399, 30141, 29883, 29625, 29368, 29112, 28856, 28601, 28346, 28092, 27838, 27585, 27333, 27081, 26830, 26580, 26330, 26081, 25832, 25584, 25337, 25091, 24845, 24600, 24356, 24112, 23870, 23628, 23386, 23146, 22907, 22668, 22430, 22193, 21956, 21721, 21486, 21253, 21020, 20788, 20557, 20327, 20098, 19870, 19642, 19416, 19191, 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def lowBounds10 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 100 through 109.
Definition (Lean source)
given by
#[ [39810, 40315, 40826, 41343, 41866, 42395, 42931, 43472, 44020, 44575, 45136, 45703, 46277, 46858, 47445, 48040, 48641, 49249, 49864, 50487, 51116, 51753, 52397, 53049, 53707, 54374, 55048, 55730, 56420, 57117, 57823, 58536, 59258, 59987, 60725, 61472, 62227, 62990, 63762, 64542, 65332, 66130, 66937, 67753, 68579, 69413, 70257, 71110, 71973, 72845, 73727, 74619, 75521, 76432, 77354, 78285, 79227, 80180, 81142, 82116, 83100, 84094, 85100, 86116, 86170, 86123, 86075, 86026, 85975, 85923, 85870, 85815, 85759, 85702, 85643, 85583, 85521, 85458, 85394, 85329, 85262, 85193, 85123, 85052, 84980, 84906, 84831, 84754, 84676, 84597, 84516, 84434, 84350, 84265, 84179, 84091, 84002, 83912, 83820, 83727, 83632, 83537, 83439, 83341, 83240, 83139, 83036, 82932, 82826, 82720, 82611, 82502, 82391, 82278, 82164, 82049, 81933, 81815, 81695, 81575, 81453, 81330, 81205, 81079, 80951, 80823, 80693, 80561, 80428, 80294, 80159, 80022, 79884, 79744, 79603, 79461, 79318, 79173, 79027, 78879, 78731, 78580, 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def lowBounds11 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 110 through 119.
Definition (Lean source)
given by
#[ [62604, 63311, 64025, 64747, 65477, 66215, 66960, 67713, 68474, 69243, 70020, 70805, 71598, 72400, 73210, 74028, 74855, 75691, 76535, 77388, 78250, 79120, 80000, 80888, 81786, 82693, 83610, 84535, 85471, 86415, 87370, 88334, 89308, 90292, 91286, 92290, 93304, 94329, 95363, 96409, 97464, 98531, 99608, 100696, 101795, 102905, 104026, 105158, 105616, 105444, 105270, 105095, 104919, 104741, 104562, 104382, 104200, 104016, 103832, 103646, 103458, 103269, 103079, 102888, 102695, 102500, 102305, 102108, 101909, 101710, 101509, 101306, 101102, 100897, 100691, 100483, 100274, 100064, 99852, 99639, 99424, 99209, 98992, 98773, 98554, 98333, 98111, 97887, 97662, 97436, 97209, 96980, 96750, 96519, 96287, 96053, 95818, 95582, 95345, 95106, 94866, 94625, 94383, 94139, 93894, 93649, 93401, 93153, 92904, 92653, 92401, 92148, 91894, 91639, 91382, 91124, 90866, 90606, 90345, 90083, 89819, 89555, 89290, 89023, 88755, 88487, 88217, 87946, 87674, 87401, 87127, 86852, 86576, 86299, 86021, 85742, 85462, 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85734, 85389, 85043, 84697, 84350, 84002, 83654, 83305, 82956, 82606, 82255, 81904, 81553, 81200, 80847, 80494, 80140, 79786, 79431, 79075, 78720, 78363, 78006, 77649, 77291, 76933, 76575, 76216, 75856, 75497, 75136, 74776, 74415, 74054, 73692, 73331, 72968, 72606, 72243, 71880, 71517, 71154, 70790, 70426, 70062, 69697, 69333, 68968, 68603, 68238, 67873, 67508, 67142, 66777, 66411, 66045, 65680, 65314, 64948, 64582, 64216, 63850, 63484, 63118, 62752, 62386, 62021, 61655, 61289, 60924, 60558, 60193, 59828, 59463, 59098, 58733, 58368, 58004, 57640, 57276, 56912, 56548, 56185, 55822, 55459, 55097, 54735, 54373, 54012, 53650, 53290, 52929, 52569, 52209, 51850, 51491, 51133, 50775, 50417, 50060, 49704, 49348, 48992, 48637, 48283, 47929, 47575, 47222, 46870, 46518, 46167, 45817, 45467, 45118, 44769, 44421, 44074, 43728, 43382, 43037, 42692, 42349, 42006, 41664, 41322, 40982, 40642, 40303, 39965, 39628, 39291, 38956, 38621, 38287, 37954, 37622, 37291, 36961, 36632, 36303, 35976, 35650, 35324, 35000, 34677, 34354, 34033, 33713, 33394, 33075, 32758, 32442, 32127, 31814, 31501, 31190, 30879, 30570, 30262, 29955, 29649, 29345, 29041, 28739, 28438, 28139, 27840, 27543, 27247, 26953, 26659, 26367, 26077, 25787, 25499, 25212, 24927, 24643, 24360, 24079, 23799, 23520, 23243, 22967, 22693, 22420, 22148, 21878, 21609, 21342, 21076, 20812, 20549, 20288, 20028, 19770, 19513, 19258, 19004, 18752, 18501, 18252, 18004, 17758, 17513, 17270, 17029, 16789, 16551, 16315, 16080, 15846, 15614, 15384, 15156, 14929, 14704, 14480, 14258, 14038, 13819, 13602, 13387, 13173, 12961, 12751, 12542, 12335, 12130, 11927, 11725, 11525, 11326, 11130, 10935, 10741, 10550, 10360, 10172, 9986, 9801, 9618, 9437, 9258, 9080, 8904, 8730, 8558, 8387, 8219, 8052, 7886, 7723, 7561, 7401, 7243, 7086, 6932, 6779, 6627, 6478, 6330, 6185, 6040, 5898, 5758, 5619, 5482, 5347, 5213, 5082, 4952, 4823, 4697, 4573, 4450, 4329, 4209, 4092, 3976, 3862, 3750, 3639, 3530, 3423, 3318, 3214, 3112, 3012, 2914, 2817, 2722, 2629, 2538, 2448, 2360, 2274, 2189, 2106, 2025, 1946, 1868, 1792, 1717, 1644, 1573, 1504, 1436, 1370, 1305, 1243, 1181, 1122, 1064, 1007, 953, 900, 848, 798, 750, 703, 658, 615, 573, 532, 493, 456, 420, 386, 353, 322, 292, 264, 237, 212, 188, 166, 145, 125, 107, 91, 76, 62, 50, 39, 30, 21, 15, 10, 6], [78625, 79459, 80301, 81152, 82012, 82880, 83756, 84641, 85535, 86438, 87350, 88271, 89201, 90140, 91088, 92046, 93013, 93990, 94976, 95972, 96977, 97992, 99018, 100053, 101098, 102154, 103219, 104295, 105382, 106478, 107586, 108704, 109833, 110973, 112124, 113285, 114458, 115642, 116827, 116570, 116312, 116053, 115792, 115530, 115267, 115003, 114737, 114470, 114202, 113933, 113662, 113390, 113117, 112843, 112567, 112290, 112012, 111733, 111452, 111171, 110888, 110604, 110318, 110032, 109744, 109455, 109165, 108874, 108582, 108288, 107994, 107698, 107401, 107103, 106804, 106503, 106202, 105899, 105596, 105291, 104985, 104678, 104370, 104061, 103751, 103440, 103127, 102814, 102500, 102184, 101868, 101550, 101232, 100912, 100592, 100270, 99948, 99625, 99300, 98975, 98649, 98321, 97993, 97664, 97334, 97003, 96671, 96339, 96005, 95670, 95335, 94999, 94662, 94324, 93985, 93645, 93305, 92963, 92621, 92278, 91935, 91590, 91245, 90899, 90552, 90205, 89857, 89508, 89158, 88808, 88457, 88105, 87753, 87400, 87046, 86692, 86337, 85981, 85625, 85268, 84911, 84552, 84194, 83835, 83475, 83115, 82754, 82393, 82031, 81668, 81306, 80942, 80578, 80214, 79849, 79484, 79119, 78753, 78386, 78019, 77652, 77285, 76917, 76549, 76180, 75811, 75442, 75072, 74702, 74332, 73962, 73591, 73220, 72849, 72478, 72106, 71734, 71362, 70990, 70618, 70245, 69873, 69500, 69127, 68754, 68381, 68008, 67635, 67261, 66888, 66515, 66141, 65768, 65395, 65021, 64648, 64275, 63901, 63528, 63155, 62782, 62409, 62036, 61664, 61291, 60919, 60546, 60174, 59803, 59431, 59059, 58688, 58317, 57947, 57576, 57206, 56836, 56466, 56097, 55728, 55360, 54991, 54623, 54256, 53889, 53522, 53156, 52790, 52424, 52059, 51695, 51331, 50967, 50604, 50242, 49880, 49518, 49157, 48797, 48437, 48078, 47720, 47362, 47004, 46648, 46292, 45936, 45582, 45228, 44874, 44522, 44170, 43819, 43468, 43119, 42770, 42422, 42075, 41728, 41383, 41038, 40694, 40351, 40009, 39668, 39327, 38988, 38649, 38312, 37975, 37639, 37304, 36971, 36638, 36306, 35975, 35645, 35317, 34989, 34662, 34337, 34012, 33689, 33367, 33045, 32725, 32406, 32089, 31772, 31457, 31142, 30829, 30517, 30207, 29897, 29589, 29282, 28976, 28671, 28368, 28066, 27766, 27466, 27168, 26871, 26576, 26282, 25989, 25698, 25408, 25119, 24832, 24546, 24261, 23978, 23697, 23416, 23138, 22860, 22584, 22310, 22037, 21765, 21495, 21227, 20960, 20694, 20430, 20168, 19907, 19648, 19390, 19133, 18879, 18625, 18374, 18124, 17875, 17628, 17383, 17140, 16898, 16657, 16418, 16181, 15946, 15712, 15480, 15249, 15020, 14793, 14567, 14343, 14121, 13901, 13682, 13465, 13249, 13036, 12824, 12613, 12405, 12198, 11993, 11789, 11587, 11388, 11189, 10993, 10798, 10605, 10414, 10225, 10037, 9851, 9667, 9484, 9304, 9125, 8948, 8772, 8599, 8427, 8257, 8089, 7923, 7758, 7595, 7434, 7275, 7117, 6962, 6808, 6656, 6505, 6357, 6210, 6065, 5922, 5781, 5641, 5503, 5367, 5233, 5101, 4970, 4841, 4714, 4589, 4466, 4344, 4224, 4106, 3989, 3875, 3762, 3651, 3542, 3434, 3328, 3224, 3122, 3021, 2923, 2826, 2730, 2637, 2545, 2455, 2366, 2280, 2195, 2112, 2030, 1950, 1872, 1796, 1721, 1648, 1577, 1507, 1439, 1373, 1308, 1245, 1184, 1124, 1066, 1009, 954, 901, 850, 800, 751, 704, 659, 615, 573, 533, 494, 456, 421, 386, 353, 322, 292, 264, 237, 212, 188, 166, 145, 125, 107, 91, 76, 62, 50, 39, 30, 21, 15, 10, 6], [80883, 81733, 82591, 83458, 84333, 85217, 86110, 87012, 87922, 88842, 89770, 90707, 91654, 92610, 93575, 94550, 95534, 96528, 97531, 98545, 99568, 100600, 101643, 102696, 103759, 104833, 105916, 107011, 108115, 109230, 110356, 111493, 112640, 113799, 114968, 116149, 117341, 118544, 118395, 118123, 117849, 117574, 117297, 117020, 116741, 116461, 116179, 115897, 115613, 115328, 115042, 114754, 114466, 114176, 113885, 113593, 113299, 113005, 112709, 112412, 112114, 111814, 111514, 111212, 110910, 110606, 110301, 109995, 109688, 109379, 109070, 108759, 108447, 108135, 107821, 107506, 107190, 106873, 106555, 106236, 105915, 105594, 105272, 104949, 104624, 104299, 103973, 103645, 103317, 102987, 102657, 102326, 101994, 101660, 101326, 100991, 100655, 100318, 99980, 99642, 99302, 98961, 98620, 98278, 97934, 97590, 97245, 96900, 96553, 96206, 95857, 95508, 95159, 94808, 94457, 94104, 93751, 93398, 93043, 92688, 92332, 91975, 91618, 91260, 90901, 90542, 90182, 89821, 89460, 89097, 88735, 88371, 88007, 87643, 87278, 86912, 86546, 86179, 85812, 85444, 85075, 84706, 84337, 83966, 83596, 83225, 82854, 82482, 82109, 81736, 81363, 80989, 80615, 80241, 79866, 79491, 79115, 78739, 78363, 77987, 77610, 77232, 76855, 76477, 76099, 75721, 75342, 74963, 74584, 74205, 73826, 73446, 73066, 72686, 72306, 71926, 71546, 71165, 70785, 70404, 70023, 69642, 69261, 68880, 68499, 68118, 67737, 67356, 66975, 66594, 66213, 65832, 65452, 65071, 64690, 64310, 63929, 63549, 63169, 62789, 62409, 62029, 61650, 61270, 60891, 60512, 60134, 59755, 59377, 59000, 58622, 58245, 57868, 57491, 57115, 56739, 56364, 55988, 55614, 55239, 54865, 54492, 54119, 53746, 53374, 53002, 52631, 52260, 51890, 51521, 51152, 50783, 50415, 50048, 49681, 49315, 48949, 48584, 48220, 47856, 47493, 47131, 46769, 46408, 46048, 45689, 45330, 44972, 44615, 44258, 43903, 43548, 43194, 42840, 42488, 42137, 41786, 41436, 41087, 40739, 40392, 40046, 39701, 39356, 39013, 38671, 38329, 37989, 37650, 37311, 36974, 36637, 36302, 35968, 35635, 35303, 34972, 34642, 34313, 33986, 33659, 33334, 33010, 32687, 32365, 32044, 31725, 31406, 31089, 30774, 30459, 30146, 29834, 29523, 29214, 28906, 28599, 28293, 27989, 27686, 27384, 27084, 26785, 26488, 26192, 25897, 25604, 25312, 25021, 24732, 24445, 24159, 23874, 23591, 23309, 23028, 22750, 22472, 22196, 21922, 21649, 21378, 21108, 20840, 20573, 20308, 20045, 19783, 19522, 19263, 19006, 18750, 18496, 18244, 17993, 17744, 17496, 17250, 17006, 16763, 16523, 16283, 16046, 15810, 15575, 15343, 15112, 14882, 14655, 14429, 14205, 13983, 13762, 13543, 13326, 13110, 12896, 12684, 12474, 12266, 12059, 11854, 11651, 11449, 11249, 11051, 10855, 10661, 10468, 10277, 10088, 9901, 9715, 9532, 9350, 9170, 8991, 8815, 8640, 8467, 8296, 8127, 7959, 7793, 7629, 7467, 7307, 7149, 6992, 6837, 6684, 6533, 6383, 6236, 6090, 5946, 5804, 5664, 5525, 5388, 5253, 5120, 4989, 4859, 4732, 4606, 4481, 4359, 4239, 4120, 4003, 3888, 3774, 3663, 3553, 3445, 3339, 3234, 3131, 3030, 2931, 2834, 2738, 2644, 2552, 2461, 2373, 2286, 2201, 2117, 2035, 1955, 1877, 1800, 1725, 1652, 1580, 1510, 1442, 1376, 1311, 1247, 1186, 1126, 1068, 1011, 956, 903, 851, 801, 752, 705, 660, 616, 574, 533, 494, 457, 421, 387, 354, 322, 293, 264, 237, 212, 188, 166, 145, 126, 108, 91, 76, 62, 50, 39, 30, 21, 15, 10, 6], [84061, 84936, 85819, 86710, 87611, 88520, 89438, 90365, 91302, 92247, 93201, 94165, 95138, 96120, 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82905, 82523, 82140, 81757, 81373, 80989, 80605, 80221, 79836, 79451, 79066, 78680, 78294, 77908, 77521, 77135, 76748, 76361, 75974, 75586, 75198, 74811, 74423, 74034, 73646, 73258, 72869, 72481, 72092, 71704, 71315, 70926, 70537, 70148, 69759, 69371, 68982, 68593, 68204, 67815, 67427, 67038, 66650, 66261, 65873, 65485, 65097, 64709, 64321, 63934, 63546, 63159, 62772, 62386, 61999, 61613, 61227, 60842, 60456, 60071, 59686, 59302, 58918, 58534, 58151, 57768, 57385, 57003, 56621, 56240, 55859, 55479, 55099, 54719, 54340, 53962, 53584, 53206, 52829, 52453, 52077, 51702, 51327, 50953, 50580, 50207, 49835, 49464, 49093, 48723, 48353, 47985, 47617, 47249, 46883, 46517, 46152, 45788, 45425, 45062, 44700, 44339, 43979, 43620, 43261, 42904, 42547, 42191, 41836, 41482, 41129, 40777, 40426, 40076, 39727, 39379, 39032, 38686, 38340, 37996, 37653, 37311, 36971, 36631, 36292, 35955, 35618, 35283, 34949, 34616, 34284, 33953, 33623, 33295, 32968, 32642, 32317, 31994, 31672, 31351, 31031, 30713, 30396, 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97863, 97490, 97117, 96744, 96369, 95994, 95619, 95242, 94865, 94488, 94109, 93730, 93351, 92971, 92590, 92209, 91827, 91444, 91061, 90678, 90294, 89909, 89524, 89138, 88752, 88366, 87979, 87591, 87203, 86815, 86426, 86036, 85647, 85257, 84866, 84475, 84084, 83692, 83300, 82908, 82516, 82123, 81730, 81336, 80942, 80548, 80154, 79759, 79365, 78970, 78575, 78179, 77784, 77388, 76992, 76596, 76200, 75803, 75407, 75010, 74614, 74217, 73820, 73424, 73027, 72630, 72233, 71836, 71439, 71042, 70645, 70248, 69852, 69455, 69058, 68662, 68265, 67869, 67473, 67077, 66681, 66285, 65890, 65494, 65099, 64704, 64310, 63915, 63521, 63127, 62733, 62340, 61947, 61554, 61162, 60770, 60378, 59987, 59596, 59205, 58815, 58425, 58036, 57647, 57258, 56871, 56483, 56096, 55710, 55324, 54938, 54553, 54169, 53785, 53402, 53019, 52637, 52256, 51875, 51495, 51116, 50737, 50359, 49982, 49605, 49229, 48854, 48479, 48105, 47733, 47360, 46989, 46618, 46249, 45880, 45512, 45144, 44778, 44413, 44048, 43684, 43321, 42960, 42599, 42239, 41880, 41522, 41165, 40809, 40453, 40099, 39746, 39395, 39044, 38694, 38345, 37997, 37651, 37305, 36961, 36618, 36276, 35935, 35595, 35257, 34919, 34583, 34248, 33915, 33582, 33251, 32921, 32592, 32265, 31938, 31614, 31290, 30968, 30647, 30327, 30009, 29692, 29377, 29062, 28750, 28438, 28128, 27820, 27513, 27207, 26903, 26600, 26298, 25998, 25700, 25403, 25108, 24814, 24521, 24230, 23941, 23653, 23367, 23082, 22799, 22517, 22237, 21958, 21682, 21406, 21133, 20860, 20590, 20321, 20054, 19788, 19524, 19262, 19002, 18743, 18485, 18230, 17976, 17724, 17473, 17224, 16977, 16732, 16488, 16246, 16006, 15767, 15531, 15296, 15063, 14831, 14601, 14373, 14147, 13923, 13700, 13479, 13260, 13043, 12827, 12614, 12402, 12192, 11984, 11777, 11572, 11370, 11169, 10969, 10772, 10577, 10383, 10191, 10001, 9813, 9626, 9442, 9259, 9078, 8899, 8722, 8547, 8374, 8202, 8032, 7864, 7698, 7534, 7372, 7211, 7053, 6896, 6741, 6588, 6437, 6287, 6140, 5994, 5850, 5708, 5568, 5430, 5293, 5159, 5026, 4895, 4766, 4639, 4513, 4390, 4268, 4148, 4030, 3914, 3799, 3687, 3576, 3467, 3359, 3254, 3150, 3048, 2948, 2850, 2754, 2659, 2566, 2475, 2385, 2298, 2212, 2128, 2045, 1965, 1886, 1808, 1733, 1659, 1587, 1517, 1448, 1381, 1316, 1252, 1190, 1130, 1072, 1015, 959, 906, 854, 803, 755, 708, 662, 618, 576, 535, 496, 458, 422, 387, 355, 323, 293, 265, 238, 212, 189, 166, 145, 126, 108, 91, 76, 62, 50, 39, 30, 21, 15, 10, 6] ]
def lowBounds12 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 120 through 129.
Definition (Lean source)
given by
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46380, 45968, 45557, 45148, 44741, 44334, 43929, 43526, 43124, 42724, 42325, 41927, 41531, 41137, 40744, 40352, 39962, 39574, 39187, 38802, 38418, 38036, 37656, 37277, 36899, 36524, 36150, 35777, 35407, 35038, 34670, 34305, 33940, 33578, 33218, 32859, 32501, 32146, 31792, 31440, 31090, 30742, 30395, 30050, 29707, 29366, 29026, 28689, 28353, 28019, 27687, 27356, 27028, 26701, 26376, 26054, 25733, 25413, 25096, 24781, 24467, 24156, 23846, 23539, 23233, 22929, 22627, 22327, 22029, 21733, 21439, 21147, 20857, 20569, 20283, 19999, 19717, 19437, 19159, 18882, 18608, 18336, 18066, 17798, 17532, 17268, 17006, 16746, 16488, 16233, 15979, 15727, 15477, 15230, 14984, 14741, 14499, 14260, 14023, 13788, 13554, 13323, 13094, 12868, 12643, 12420, 12199, 11981, 11764, 11550, 11337, 11127, 10919, 10713, 10509, 10307, 10107, 9910, 9714, 9520, 9329, 9140, 8952, 8767, 8584, 8403, 8224, 8047, 7872, 7699, 7529, 7360, 7193, 7029, 6866, 6706, 6548, 6391, 6237, 6085, 5935, 5787, 5641, 5496, 5354, 5214, 5076, 4941, 4807, 4675, 4545, 4417, 4291, 4167, 4045, 3925, 3807, 3691, 3577, 3464, 3354, 3246, 3140, 3035, 2933, 2832, 2734, 2637, 2542, 2449, 2358, 2269, 2182, 2096, 2013, 1931, 1851, 1773, 1697, 1622, 1550, 1479, 1410, 1343, 1277, 1213, 1152, 1091, 1033, 976, 921, 868, 816, 766, 718, 672, 627, 584, 542, 502, 464, 427, 392, 358, 326, 296, 267, 240, 214, 190, 167, 146, 126, 108, 92, 76, 62, 50, 39, 30, 22, 15, 10, 6] ]
def lowBounds13 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 130 through 139.
Definition (Lean source)
given by
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17621, 17348, 17077, 16808, 16542, 16277, 16015, 15756, 15498, 15243, 14990, 14739, 14491, 14244, 14000, 13758, 13519, 13282, 13047, 12814, 12583, 12355, 12129, 11905, 11684, 11464, 11247, 11032, 10820, 10609, 10401, 10196, 9992, 9791, 9591, 9394, 9200, 9007, 8817, 8629, 8443, 8260, 8078, 7899, 7722, 7547, 7375, 7204, 7036, 6870, 6706, 6545, 6385, 6228, 6073, 5920, 5769, 5620, 5474, 5329, 5187, 5047, 4909, 4773, 4639, 4507, 4378, 4250, 4125, 4001, 3880, 3761, 3643, 3528, 3415, 3304, 3195, 3088, 2983, 2880, 2779, 2680, 2583, 2488, 2395, 2304, 2214, 2127, 2042, 1958, 1877, 1797, 1719, 1644, 1570, 1497, 1427, 1359, 1292, 1227, 1164, 1103, 1044, 986, 930, 876, 824, 773, 725, 677, 632, 588, 546, 506, 467, 430, 394, 361, 328, 298, 269, 241, 215, 191, 168, 147, 127, 109, 92, 77, 63, 50, 39, 30, 22, 15, 10, 6], [137868, 139095, 140332, 141580, 142838, 144108, 145388, 146680, 147982, 149296, 150620, 150910, 150331, 149753, 149175, 148596, 148017, 147438, 146859, 146280, 145700, 145120, 144541, 143961, 143381, 142800, 142220, 141640, 141059, 140479, 139898, 139317, 138737, 138156, 137575, 136994, 136413, 135832, 135251, 134670, 134089, 133508, 132927, 132346, 131765, 131184, 130603, 130022, 129441, 128860, 128280, 127699, 127119, 126539, 125958, 125378, 124798, 124218, 123639, 123059, 122480, 121901, 121322, 120743, 120165, 119586, 119008, 118430, 117853, 117275, 116698, 116121, 115545, 114969, 114393, 113817, 113242, 112667, 112092, 111518, 110944, 110371, 109798, 109225, 108653, 108081, 107509, 106938, 106368, 105798, 105228, 104659, 104090, 103522, 102954, 102387, 101821, 101255, 100689, 100125, 99560, 98997, 98434, 97871, 97309, 96748, 96187, 95628, 95068, 94510, 93952, 93395, 92839, 92283, 91728, 91174, 90620, 90068, 89516, 88965, 88415, 87865, 87317, 86769, 86222, 85676, 85131, 84587, 84043, 83501, 82959, 82419, 81879, 81341, 80803, 80266, 79731, 79196, 78662, 78130, 77598, 77068, 76538, 76010, 75483, 74957, 74431, 73908, 73385, 72863, 72343, 71823, 71305, 70789, 70273, 69758, 69245, 68733, 68222, 67713, 67205, 66698, 66192, 65688, 65185, 64684, 64183, 63685, 63187, 62691, 62196, 61703, 61211, 60720, 60231, 59744, 59258, 58773, 58290, 57808, 57328, 56849, 56372, 55897, 55423, 54950, 54479, 54010, 53542, 53076, 52612, 52149, 51688, 51228, 50770, 50314, 49860, 49407, 48956, 48506, 48058, 47612, 47168, 46725, 46285, 45846, 45408, 44973, 44539, 44108, 43678, 43249, 42823, 42398, 41976, 41555, 41136, 40719, 40304, 39891, 39479, 39070, 38662, 38257, 37853, 37451, 37052, 36654, 36258, 35864, 35473, 35083, 34695, 34309, 33925, 33544, 33164, 32786, 32411, 32037, 31665, 31296, 30929, 30563, 30200, 29839, 29480, 29123, 28768, 28416, 28065, 27717, 27371, 27027, 26685, 26345, 26007, 25672, 25338, 25007, 24678, 24352, 24027, 23705, 23385, 23067, 22751, 22437, 22126, 21817, 21510, 21205, 20903, 20603, 20305, 20009, 19716, 19424, 19136, 18849, 18564, 18282, 18002, 17724, 17449, 17176, 16905, 16636, 16370, 16106, 15844, 15585, 15327, 15072, 14820, 14569, 14321, 14075, 13832, 13590, 13351, 13115, 12880, 12648, 12418, 12190, 11965, 11742, 11521, 11302, 11086, 10872, 10660, 10451, 10244, 10039, 9836, 9635, 9437, 9241, 9048, 8856, 8667, 8480, 8295, 8113, 7933, 7755, 7579, 7405, 7234, 7065, 6898, 6733, 6570, 6410, 6252, 6096, 5942, 5790, 5641, 5493, 5348, 5205, 5064, 4926, 4789, 4655, 4522, 4392, 4264, 4138, 4014, 3892, 3772, 3655, 3539, 3425, 3314, 3204, 3097, 2991, 2888, 2787, 2687, 2590, 2494, 2401, 2309, 2220, 2132, 2047, 1963, 1881, 1801, 1723, 1647, 1573, 1501, 1430, 1361, 1295, 1230, 1167, 1105, 1046, 988, 932, 878, 825, 775, 726, 678, 633, 589, 547, 506, 468, 430, 395, 361, 329, 298, 269, 241, 215, 191, 168, 147, 127, 109, 92, 77, 63, 50, 39, 30, 22, 15, 10, 6], [141297, 142545, 143803, 145072, 146352, 147643, 148944, 150257, 151581, 152812, 152217, 151622, 151026, 150431, 149835, 149239, 148644, 148048, 147452, 146856, 146259, 145663, 145067, 144471, 143874, 143278, 142682, 142085, 141489, 140893, 140296, 139700, 139104, 138507, 137911, 137315, 136719, 136123, 135527, 134931, 134335, 133739, 133144, 132548, 131953, 131357, 130762, 130167, 129572, 128978, 128383, 127789, 127195, 126601, 126007, 125414, 124821, 124228, 123635, 123042, 122450, 121858, 121266, 120675, 120084, 119493, 118903, 118313, 117723, 117133, 116544, 115956, 115367, 114779, 114192, 113605, 113018, 112432, 111846, 111260, 110676, 110091, 109507, 108924, 108341, 107758, 107176, 106595, 106014, 105434, 104854, 104275, 103696, 103118, 102541, 101964, 101388, 100813, 100238, 99664, 99091, 98518, 97946, 97374, 96804, 96234, 95665, 95096, 94529, 93962, 93396, 92831, 92266, 91703, 91140, 90578, 90017, 89457, 88897, 88339, 87781, 87225, 86669, 86114, 85561, 85008, 84456, 83905, 83355, 82806, 82258, 81712, 81166, 80621, 80078, 79535, 78994, 78453, 77914, 77376, 76839, 76303, 75768, 75235, 74702, 74171, 73641, 73113, 72585, 72059, 71534, 71010, 70488, 69967, 69447, 68928, 68411, 67895, 67381, 66867, 66356, 65845, 65336, 64828, 64322, 63817, 63314, 62812, 62312, 61813, 61315, 60819, 60325, 59832, 59340, 58850, 58362, 57875, 57390, 56906, 56424, 55944, 55465, 54987, 54512, 54038, 53566, 53095, 52626, 52159, 51693, 51229, 50767, 50307, 49848, 49391, 48936, 48482, 48031, 47581, 47133, 46686, 46242, 45799, 45359, 44920, 44483, 44047, 43614, 43183, 42753, 42325, 41899, 41476, 41054, 40634, 40216, 39800, 39385, 38973, 38563, 38155, 37749, 37344, 36942, 36542, 36144, 35748, 35354, 34962, 34572, 34184, 33798, 33414, 33032, 32653, 32275, 31900, 31527, 31155, 30786, 30419, 30055, 29692, 29332, 28973, 28617, 28263, 27911, 27562, 27214, 26869, 26526, 26185, 25846, 25510, 25176, 24844, 24514, 24186, 23861, 23538, 23217, 22898, 22582, 22268, 21956, 21646, 21339, 21034, 20731, 20430, 20132, 19836, 19543, 19251, 18962, 18675, 18391, 18108, 17828, 17551, 17275, 17002, 16731, 16463, 16197, 15933, 15671, 15412, 15155, 14901, 14648, 14398, 14150, 13905, 13662, 13421, 13183, 12946, 12713, 12481, 12252, 12025, 11800, 11578, 11358, 11140, 10924, 10711, 10500, 10292, 10085, 9881, 9680, 9480, 9283, 9088, 8895, 8705, 8517, 8331, 8147, 7966, 7787, 7610, 7436, 7263, 7093, 6925, 6760, 6596, 6435, 6276, 6119, 5964, 5812, 5662, 5513, 5368, 5224, 5082, 4943, 4806, 4670, 4537, 4407, 4278, 4151, 4027, 3904, 3784, 3666, 3550, 3436, 3324, 3214, 3106, 3000, 2896, 2794, 2694, 2597, 2501, 2407, 2315, 2225, 2137, 2052, 1968, 1885, 1805, 1727, 1651, 1576, 1504, 1433, 1364, 1297, 1232, 1169, 1107, 1048, 990, 934, 879, 827, 776, 727, 679, 634, 590, 548, 507, 468, 431, 395, 361, 329, 298, 269, 242, 216, 191, 168, 147, 127, 109, 92, 77, 63, 50, 39, 30, 22, 15, 10, 6], [144784, 146053, 147332, 148622, 149924, 151236, 152559, 153894, 154098, 153485, 152873, 152260, 151647, 151035, 150422, 149810, 149197, 148584, 147972, 147359, 146746, 146134, 145521, 144909, 144297, 143684, 143072, 142460, 141848, 141236, 140624, 140012, 139401, 138789, 138178, 137567, 136956, 136345, 135734, 135124, 134513, 133903, 133293, 132683, 132074, 131464, 130855, 130246, 129638, 129030, 128421, 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52160, 51690, 51222, 50756, 50291, 49828, 49368, 48908, 48451, 47996, 47542, 47090, 46640, 46192, 45746, 45302, 44859, 44419, 43980, 43544, 43109, 42676, 42245, 41817, 41390, 40965, 40542, 40121, 39702, 39285, 38871, 38458, 38047, 37638, 37232, 36827, 36425, 36024, 35626, 35229, 34835, 34443, 34053, 33665, 33280, 32896, 32515, 32135, 31758, 31383, 31010, 30640, 30271, 29905, 29541, 29179, 28819, 28462, 28106, 27753, 27402, 27054, 26707, 26363, 26021, 25682, 25344, 25009, 24676, 24346, 24017, 23691, 23368, 23046, 22727, 22410, 22095, 21783, 21473, 21165, 20860, 20556, 20256, 19957, 19661, 19367, 19075, 18786, 18499, 18215, 17932, 17653, 17375, 17100, 16827, 16556, 16288, 16022, 15758, 15497, 15238, 14982, 14727, 14475, 14226, 13979, 13734, 13491, 13251, 13013, 12777, 12544, 12313, 12085, 11859, 11635, 11413, 11194, 10977, 10762, 10550, 10340, 10132, 9927, 9724, 9523, 9325, 9129, 8935, 8743, 8554, 8367, 8182, 8000, 7820, 7642, 7466, 7293, 7122, 6953, 6786, 6622, 6460, 6300, 6142, 5987, 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41727, 41298, 40870, 40444, 40021, 39599, 39180, 38762, 38347, 37933, 37522, 37113, 36706, 36302, 35899, 35498, 35100, 34704, 34309, 33918, 33528, 33140, 32755, 32371, 31990, 31612, 31235, 30861, 30488, 30118, 29751, 29385, 29022, 28661, 28302, 27946, 27591, 27239, 26890, 26542, 26197, 25854, 25514, 25175, 24840, 24506, 24174, 23845, 23519, 23194, 22872, 22552, 22235, 21920, 21607, 21297, 20989, 20683, 20379, 20078, 19780, 19483, 19189, 18898, 18608, 18321, 18037, 17755, 17475, 17197, 16922, 16650, 16379, 16111, 15846, 15582, 15321, 15063, 14807, 14553, 14301, 14052, 13806, 13561, 13319, 13080, 12842, 12608, 12375, 12145, 11917, 11692, 11469, 11248, 11029, 10813, 10600, 10388, 10179, 9973, 9768, 9566, 9367, 9169, 8974, 8781, 8591, 8403, 8217, 8034, 7852, 7673, 7497, 7322, 7150, 6981, 6813, 6648, 6485, 6324, 6165, 6009, 5855, 5703, 5554, 5406, 5261, 5118, 4977, 4839, 4702, 4568, 4436, 4306, 4178, 4052, 3929, 3808, 3688, 3571, 3456, 3343, 3232, 3123, 3017, 2912, 2809, 2709, 2610, 2514, 2419, 2327, 2236, 2148, 2061, 1977, 1894, 1813, 1735, 1658, 1583, 1510, 1439, 1370, 1302, 1237, 1173, 1111, 1051, 993, 937, 882, 829, 778, 729, 681, 636, 591, 549, 508, 469, 432, 396, 362, 330, 299, 270, 242, 216, 191, 169, 147, 127, 109, 92, 77, 63, 50, 39, 30, 22, 15, 10, 6] ]
def lowBounds14 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 140 through 149.
Definition (Lean source)
given by
#[ [151931, 153242, 154565, 155898, 157243, 157194, 156547, 155900, 155253, 154606, 153959, 153313, 152666, 152020, 151374, 150728, 150083, 149437, 148792, 148147, 147502, 146858, 146214, 145570, 144926, 144282, 143639, 142996, 142353, 141711, 141069, 140427, 139786, 139145, 138504, 137863, 137223, 136583, 135944, 135305, 134666, 134028, 133390, 132753, 132116, 131479, 130843, 130207, 129572, 128937, 128302, 127669, 127035, 126402, 125770, 125138, 124506, 123875, 123245, 122615, 121986, 121357, 120729, 120102, 119475, 118848, 118222, 117597, 116973, 116349, 115726, 115103, 114481, 113860, 113240, 112620, 112001, 111383, 110765, 110148, 109532, 108917, 108302, 107688, 107075, 106463, 105852, 105241, 104631, 104022, 103414, 102807, 102201, 101596, 100991, 100388, 99785, 99183, 98582, 97983, 97384, 96786, 96189, 95593, 94998, 94404, 93811, 93220, 92629, 92039, 91450, 90863, 90277, 89691, 89107, 88524, 87942, 87361, 86782, 86203, 85626, 85050, 84475, 83901, 83329, 82758, 82188, 81619, 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46493, 46016, 45542, 45070, 44600, 44133, 43668, 43205, 42745, 42287, 41832, 41379, 40928, 40480, 40035, 39591, 39150, 38712, 38276, 37842, 37411, 36982, 36556, 36132, 35711, 35292, 34876, 34462, 34051, 33642, 33236, 32832, 32431, 32032, 31636, 31242, 30851, 30462, 30076, 29692, 29311, 28933, 28557, 28184, 27813, 27445, 27079, 26716, 26355, 25997, 25642, 25289, 24939, 24591, 24246, 23904, 23564, 23226, 22892, 22560, 22230, 21903, 21579, 21257, 20938, 20621, 20307, 19996, 19687, 19381, 19078, 18777, 18478, 18183, 17889, 17599, 17311, 17026, 16743, 16463, 16185, 15910, 15638, 15368, 15101, 14836, 14574, 14315, 14058, 13803, 13552, 13302, 13056, 12812, 12570, 12331, 12095, 11861, 11630, 11401, 11175, 10951, 10730, 10511, 10295, 10082, 9871, 9662, 9456, 9252, 9051, 8853, 8657, 8463, 8272, 8083, 7897, 7713, 7531, 7352, 7176, 7002, 6830, 6661, 6494, 6329, 6167, 6007, 5850, 5695, 5542, 5392, 5244, 5098, 4955, 4814, 4675, 4539, 4404, 4273, 4143, 4015, 3890, 3767, 3647, 3528, 3412, 3298, 3186, 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def lowBounds15 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 150 through 159.
Definition (Lean source)
given by
#[ [165380, 164565, 163751, 162938, 162126, 161316, 160507, 159698, 158892, 158086, 157281, 156478, 155676, 154876, 154076, 153278, 152481, 151685, 150891, 150098, 149306, 148516, 147726, 146938, 146152, 145367, 144583, 143800, 143019, 142239, 141460, 140683, 139907, 139132, 138359, 137587, 136817, 136048, 135280, 134514, 133749, 132986, 132224, 131464, 130705, 129947, 129191, 128436, 127683, 126931, 126181, 125433, 124685, 123940, 123195, 122453, 121712, 120972, 120234, 119498, 118763, 118030, 117298, 116568, 115839, 115112, 114387, 113664, 112942, 112221, 111502, 110785, 110070, 109356, 108644, 107934, 107225, 106519, 105813, 105110, 104408, 103708, 103010, 102314, 101619, 100926, 100235, 99546, 98859, 98173, 97489, 96807, 96127, 95449, 94773, 94098, 93426, 92755, 92086, 91419, 90754, 90091, 89430, 88771, 88114, 87459, 86805, 86154, 85505, 84858, 84212, 83569, 82928, 82289, 81652, 81017, 80384, 79753, 79124, 78497, 77873, 77250, 76630, 76012, 75396, 74782, 74170, 73560, 72953, 72348, 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107646, 106870, 106096, 105324, 104556, 103789, 103025, 102264, 101505, 100749, 99995, 99244, 98495, 97749, 97005, 96264, 95525, 94789, 94056, 93325, 92597, 91871, 91148, 90428, 89710, 88994, 88282, 87572, 86865, 86160, 85458, 84758, 84062, 83368, 82676, 81988, 81302, 80618, 79938, 79260, 78585, 77912, 77243, 76576, 75912, 75250, 74591, 73935, 73282, 72632, 71984, 71340, 70698, 70058, 69422, 68788, 68158, 67530, 66904, 66282, 65663, 65046, 64432, 63822, 63214, 62608, 62006, 61407, 60810, 60217, 59626, 59038, 58453, 57871, 57292, 56716, 56143, 55573, 55006, 54441, 53880, 53321, 52766, 52213, 51664, 51117, 50574, 50033, 49495, 48961, 48429, 47901, 47375, 46852, 46333, 45816, 45302, 44792, 44284, 43780, 43278, 42780, 42284, 41792, 41303, 40816, 40333, 39853, 39376, 38901, 38430, 37962, 37497, 37036, 36577, 36121, 35668, 35219, 34772, 34329, 33888, 33451, 33017, 32586, 32157, 31732, 31310, 30892, 30476, 30063, 29653, 29247, 28843, 28443, 28046, 27651, 27260, 26872, 26487, 26105, 25726, 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156819, 155896, 154976, 154058, 153142, 152228, 151317, 150408, 149501, 148597, 147694, 146795, 145897, 145002, 144109, 143219, 142331, 141445, 140562, 139681, 138802, 137926, 137052, 136180, 135311, 134444, 133579, 132717, 131858, 131000, 130145, 129293, 128443, 127595, 126750, 125907, 125067, 124229, 123393, 122560, 121730, 120901, 120076, 119252, 118432, 117613, 116798, 115984, 115173, 114365, 113559, 112756, 111955, 111157, 110361, 109568, 108777, 107989, 107204, 106421, 105640, 104863, 104087, 103315, 102544, 101777, 101012, 100250, 99490, 98733, 97979, 97227, 96478, 95731, 94987, 94246, 93508, 92772, 92038, 91308, 90580, 89855, 89133, 88413, 87696, 86982, 86270, 85561, 84855, 84152, 83451, 82754, 82059, 81366, 80677, 79990, 79306, 78625, 77947, 77271, 76599, 75929, 75262, 74598, 73936, 73278, 72622, 71969, 71319, 70672, 70028, 69387, 68748, 68113, 67480, 66850, 66224, 65600, 64979, 64361, 63745, 63133, 62524, 61918, 61314, 60714, 60117, 59522, 58931, 58342, 57756, 57174, 56594, 56018, 55444, 54874, 54306, 53742, 53180, 52622, 52066, 51514, 50964, 50418, 49875, 49334, 48797, 48263, 47732, 47204, 46679, 46157, 45638, 45122, 44610, 44100, 43593, 43090, 42590, 42092, 41598, 41107, 40619, 40134, 39653, 39174, 38698, 38226, 37757, 37290, 36827, 36367, 35910, 35457, 35006, 34558, 34114, 33673, 33235, 32799, 32368, 31939, 31513, 31090, 30671, 30255, 29842, 29431, 29025, 28621, 28220, 27822, 27428, 27037, 26648, 26263, 25881, 25502, 25127, 24754, 24384, 24018, 23654, 23294, 22937, 22583, 22232, 21884, 21539, 21197, 20859, 20523, 20191, 19861, 19535, 19211, 18891, 18574, 18260, 17949, 17640, 17335, 17033, 16734, 16438, 16145, 15855, 15568, 15284, 15003, 14725, 14450, 14178, 13909, 13643, 13380, 13119, 12862, 12608, 12356, 12108, 11862, 11619, 11379, 11142, 10908, 10677, 10448, 10223, 10000, 9780, 9563, 9349, 9138, 8929, 8723, 8520, 8320, 8122, 7927, 7735, 7546, 7359, 7175, 6994, 6815, 6639, 6466, 6296, 6128, 5962, 5800, 5639, 5482, 5327, 5175, 5025, 4877, 4733, 4590, 4451, 4313, 4179, 4046, 3916, 3789, 3664, 3541, 3421, 3303, 3188, 3075, 2964, 2855, 2749, 2645, 2544, 2445, 2348, 2253, 2160, 2070, 1982, 1896, 1812, 1730, 1650, 1573, 1498, 1424, 1353, 1284, 1217, 1152, 1088, 1027, 968, 911, 855, 802, 751, 701, 653, 607, 563, 521, 481, 442, 405, 370, 336, 305, 275, 246, 219, 194, 171, 149, 129, 110, 93, 77, 63, 51, 40, 30, 22, 15, 10, 6] ]
def lowBounds16 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 160 through 169.
Definition (Lean source)
given by
#[ [165431, 164473, 163519, 162566, 161616, 160669, 159723, 158781, 157840, 156902, 155966, 155033, 154103, 153174, 152248, 151325, 150404, 149485, 148569, 147655, 146744, 145835, 144928, 144024, 143123, 142224, 141327, 140433, 139541, 138652, 137765, 136881, 135999, 135120, 134243, 133368, 132497, 131627, 130760, 129896, 129034, 128175, 127318, 126464, 125612, 124763, 123916, 123072, 122230, 121391, 120555, 119721, 118890, 118061, 117235, 116411, 115590, 114772, 113956, 113143, 112332, 111525, 110719, 109917, 109116, 108319, 107524, 106732, 105943, 105156, 104372, 103590, 102812, 102036, 101262, 100491, 99723, 98958, 98196, 97436, 96679, 95924, 95173, 94424, 93678, 92934, 92194, 91456, 90721, 89988, 89259, 88532, 87808, 87087, 86369, 85653, 84941, 84231, 83524, 82820, 82118, 81420, 80724, 80032, 79342, 78655, 77971, 77289, 76611, 75936, 75263, 74594, 73927, 73263, 72602, 71944, 71289, 70637, 69988, 69342, 68699, 68059, 67421, 66787, 66156, 65528, 64902, 64280, 63661, 63044, 62431, 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6149, 5983, 5820, 5659, 5500, 5345, 5192, 5041, 4893, 4748, 4605, 4465, 4327, 4191, 4058, 3928, 3800, 3674, 3551, 3431, 3312, 3196, 3083, 2972, 2863, 2756, 2652, 2550, 2451, 2353, 2258, 2165, 2074, 1986, 1900, 1816, 1734, 1654, 1576, 1500, 1427, 1356, 1286, 1219, 1154, 1090, 1029, 970, 912, 857, 803, 752, 702, 654, 608, 564, 522, 481, 442, 405, 370, 337, 305, 275, 246, 220, 195, 171, 149, 129, 110, 93, 77, 63, 51, 40, 30, 22, 15, 10, 6], [164616, 163648, 162682, 161719, 160758, 159800, 158845, 157891, 156941, 155993, 155047, 154104, 153164, 152226, 151290, 150357, 149427, 148499, 147574, 146651, 145731, 144814, 143899, 142986, 142077, 141169, 140265, 139362, 138463, 137566, 136672, 135780, 134891, 134004, 133120, 132239, 131360, 130484, 129610, 128739, 127871, 127005, 126142, 125282, 124424, 123569, 122716, 121867, 121019, 120175, 119333, 118494, 117658, 116824, 115993, 115164, 114339, 113516, 112696, 111878, 111063, 110251, 109442, 108635, 107831, 107030, 106232, 105436, 104643, 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22132, 21782, 21435, 21091, 20750, 20413, 20078, 19747, 19419, 19094, 18772, 18453, 18138, 17825, 17516, 17210, 16906, 16606, 16309, 16015, 15724, 15436, 15152, 14870, 14591, 14315, 14043, 13773, 13506, 13243, 12982, 12724, 12470, 12218, 11969, 11724, 11481, 11241, 11004, 10770, 10539, 10311, 10085, 9863, 9643, 9427, 9213, 9002, 8794, 8588, 8386, 8186, 7989, 7795, 7604, 7415, 7229, 7046, 6865, 6688, 6513, 6341, 6171, 6004, 5840, 5678, 5519, 5363, 5209, 5058, 4909, 4763, 4619, 4478, 4340, 4204, 4071, 3940, 3811, 3685, 3561, 3440, 3322, 3205, 3091, 2980, 2870, 2763, 2659, 2557, 2457, 2359, 2263, 2170, 2079, 1990, 1904, 1819, 1737, 1657, 1579, 1503, 1430, 1358, 1289, 1221, 1156, 1092, 1031, 971, 914, 858, 804, 753, 703, 655, 609, 565, 522, 482, 443, 406, 371, 337, 305, 275, 247, 220, 195, 171, 149, 129, 110, 93, 77, 63, 51, 40, 30, 22, 15, 10, 6], [164714, 163732, 162753, 161777, 160803, 159832, 158864, 157899, 156936, 155975, 155018, 154063, 153110, 152160, 151213, 150269, 149327, 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def lowBounds17 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 170 through 179.
Definition (Lean source)
given by
#[ [160640, 159574, 158511, 157452, 156396, 155345, 154296, 153252, 152211, 151173, 150139, 149109, 148083, 147060, 146040, 145024, 144012, 143004, 141999, 140997, 139999, 139005, 138015, 137028, 136044, 135065, 134088, 133116, 132147, 131181, 130219, 129261, 128307, 127356, 126408, 125464, 124524, 123587, 122654, 121725, 120799, 119876, 118958, 118043, 117131, 116223, 115319, 114418, 113521, 112628, 111738, 110851, 109969, 109090, 108214, 107342, 106474, 105609, 104748, 103891, 103037, 102187, 101340, 100497, 99658, 98822, 97990, 97161, 96337, 95515, 94698, 93884, 93074, 92267, 91464, 90664, 89869, 89077, 88288, 87503, 86722, 85945, 85171, 84400, 83634, 82871, 82112, 81356, 80604, 79856, 79111, 78370, 77633, 76900, 76170, 75443, 74721, 74002, 73287, 72575, 71867, 71163, 70463, 69766, 69073, 68384, 67698, 67016, 66337, 65663, 64992, 64325, 63661, 63001, 62345, 61693, 61044, 60399, 59757, 59120, 58486, 57856, 57229, 56606, 55987, 55372, 54760, 54152, 53548, 52947, 52350, 51757, 51167, 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Tables02 9 core · 0 supporting Proposed integer upper bounds for the rounded low-frequency cells, ten parameter rows per table.
Low Prawitz certificate: candidate bound tables 18 through 26
Proposed integer upper bounds for the rounded low-frequency cells, ten parameter rows per table. They are data only; every entry is checked by the block theorems.
def lowBounds18 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 180 through 189.
Definition (Lean source)
given by
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52234, 51592, 50955, 50322, 49694, 49070, 48451, 47837, 47227, 46621, 46021, 45425, 44833, 44246, 43663, 43085, 42512, 41943, 41379, 40819, 40263, 39712, 39166, 38623, 38086, 37553, 37024, 36500, 35980, 35464, 34953, 34446, 33944, 33446, 32953, 32463, 31979, 31498, 31022, 30550, 30082, 29619, 29160, 28705, 28254, 27808, 27366, 26928, 26494, 26065, 25640, 25219, 24802, 24389, 23980, 23576, 23176, 22779, 22387, 21999, 21615, 21235, 20859, 20487, 20119, 19756, 19396, 19040, 18688, 18340, 17996, 17656, 17319, 16987, 16659, 16334, 16013, 15696, 15383, 15074, 14768, 14466, 14168, 13874, 13584, 13297, 13014, 12734, 12458, 12186, 11918, 11653, 11391, 11133, 10879, 10629, 10381, 10138, 9898, 9661, 9428, 9198, 8972, 8749, 8529, 8313, 8100, 7890, 7684, 7481, 7281, 7085, 6892, 6702, 6515, 6331, 6151, 5973, 5799, 5628, 5460, 5295, 5132, 4973, 4817, 4664, 4514, 4367, 4223, 4081, 3943, 3807, 3674, 3544, 3417, 3292, 3171, 3052, 2935, 2821, 2710, 2602, 2496, 2393, 2292, 2194, 2098, 2005, 1914, 1826, 1740, 1657, 1576, 1497, 1420, 1346, 1274, 1205, 1138, 1072, 1010, 949, 890, 834, 779, 727, 677, 628, 582, 538, 495, 455, 417, 380, 345, 312, 281, 252, 224, 198, 174, 152, 131, 112, 94, 78, 64, 51, 40, 30, 22, 15, 10, 6], [148094, 146914, 145739, 144570, 143406, 142248, 141096, 139948, 138807, 137670, 136539, 135414, 134294, 133179, 132070, 130966, 129867, 128774, 127686, 126604, 125527, 124455, 123388, 122327, 121271, 120220, 119175, 118134, 117099, 116070, 115045, 114026, 113012, 112003, 110999, 110001, 109008, 108020, 107037, 106059, 105086, 104119, 103156, 102199, 101247, 100300, 99358, 98422, 97490, 96563, 95642, 94725, 93814, 92908, 92007, 91110, 90219, 89333, 88452, 87576, 86705, 85839, 84977, 84121, 83270, 82424, 81583, 80747, 79915, 79089, 78268, 77451, 76640, 75833, 75032, 74235, 73443, 72656, 71874, 71097, 70325, 69557, 68795, 68037, 67284, 66536, 65793, 65055, 64321, 63593, 62869, 62150, 61436, 60726, 60021, 59322, 58626, 57936, 57250, 56570, 55894, 55222, 54556, 53894, 53236, 52584, 51936, 51293, 50655, 50021, 49392, 48767, 48148, 47532, 46922, 46316, 45715, 45118, 44526, 43939, 43356, 42778, 42204, 41635, 41071, 40510, 39955, 39404, 38858, 38316, 37778, 37245, 36717, 36193, 35673, 35158, 34648, 34142, 33640, 33142, 32649, 32161, 31677, 31197, 30721, 30250, 29783, 29321, 28863, 28409, 27960, 27514, 27073, 26637, 26204, 25776, 25352, 24932, 24516, 24105, 23698, 23295, 22896, 22501, 22110, 21724, 21341, 20963, 20588, 20218, 19852, 19490, 19131, 18777, 18427, 18081, 17739, 17400, 17066, 16735, 16409, 16086, 15767, 15452, 15141, 14834, 14530, 14230, 13934, 13642, 13354, 13069, 12788, 12510, 12237, 11967, 11700, 11437, 11178, 10923, 10671, 10422, 10177, 9936, 9698, 9463, 9233, 9005, 8781, 8560, 8343, 8129, 7918, 7711, 7507, 7306, 7109, 6915, 6724, 6536, 6352, 6171, 5992, 5817, 5645, 5477, 5311, 5148, 4988, 4832, 4678, 4527, 4380, 4235, 4093, 3954, 3818, 3684, 3554, 3426, 3301, 3179, 3059, 2942, 2828, 2717, 2608, 2502, 2398, 2297, 2199, 2103, 2009, 1918, 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1922, 1833, 1747, 1663, 1582, 1502, 1426, 1351, 1279, 1209, 1141, 1076, 1013, 952, 893, 836, 781, 729, 678, 630, 584, 539, 497, 456, 417, 381, 346, 313, 282, 252, 224, 199, 174, 152, 131, 112, 94, 78, 64, 51, 40, 30, 22, 15, 10, 6], [150963, 149750, 148544, 147344, 146149, 144960, 143776, 142599, 141427, 140261, 139100, 137945, 136796, 135653, 134515, 133382, 132256, 131135, 130019, 128909, 127805, 126706, 125613, 124525, 123443, 122366, 121295, 120230, 119169, 118115, 117065, 116022, 114983, 113950, 112923, 111900, 110884, 109872, 108866, 107866, 106871, 105881, 104896, 103917, 102943, 101974, 101011, 100053, 99101, 98153, 97211, 96274, 95343, 94416, 93495, 92579, 91669, 90763, 89863, 88968, 88078, 87194, 86314, 85440, 84571, 83707, 82848, 81995, 81146, 80303, 79464, 78631, 77803, 76980, 76162, 75349, 74541, 73739, 72941, 72149, 71361, 70578, 69801, 69028, 68261, 67498, 66741, 65988, 65241, 64498, 63761, 63028, 62300, 61578, 60860, 60147, 59439, 58736, 58038, 57344, 56656, 55972, 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2213, 2116, 2022, 1930, 1841, 1754, 1670, 1588, 1508, 1431, 1356, 1283, 1213, 1145, 1079, 1016, 955, 896, 839, 784, 731, 680, 632, 585, 540, 498, 457, 418, 381, 346, 313, 282, 253, 225, 199, 175, 152, 131, 112, 94, 78, 64, 51, 40, 30, 22, 15, 10, 6] ]
def lowBounds19 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 190 through 199.
Definition (Lean source)
given by
#[ [153867, 152623, 151384, 150151, 148925, 147704, 146490, 145281, 144079, 142882, 141692, 140507, 139328, 138155, 136988, 135827, 134672, 133523, 132379, 131241, 130109, 128983, 127863, 126749, 125640, 124537, 123439, 122348, 121262, 120182, 119107, 118039, 116976, 115918, 114866, 113820, 112779, 111745, 110715, 109691, 108673, 107661, 106653, 105652, 104656, 103666, 102681, 101701, 100727, 99759, 98796, 97838, 96886, 95940, 94998, 94063, 93132, 92207, 91288, 90374, 89465, 88562, 87664, 86771, 85884, 85002, 84125, 83254, 82388, 81527, 80671, 79821, 78976, 78137, 77302, 76473, 75649, 74831, 74017, 73209, 72406, 71608, 70815, 70028, 69246, 68469, 67697, 66930, 66168, 65411, 64660, 63913, 63172, 62436, 61705, 60979, 60258, 59542, 58831, 58125, 57424, 56728, 56038, 55352, 54671, 53995, 53324, 52658, 51997, 51341, 50690, 50044, 49403, 48766, 48135, 47508, 46886, 46270, 45658, 45050, 44448, 43850, 43258, 42670, 42087, 41508, 40935, 40366, 39802, 39243, 38688, 38138, 37593, 37052, 36516, 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15, 10, 6], [155333, 154072, 152817, 151568, 150326, 149089, 147859, 146635, 145417, 144205, 142999, 141799, 140605, 139418, 138236, 137060, 135891, 134727, 133569, 132417, 131271, 130132, 128998, 127869, 126747, 125631, 124520, 123416, 122317, 121224, 120137, 119055, 117980, 116910, 115846, 114787, 113735, 112688, 111647, 110611, 109581, 108557, 107539, 106526, 105519, 104517, 103521, 102531, 101547, 100567, 99594, 98626, 97663, 96707, 95755, 94810, 93869, 92934, 92005, 91081, 90163, 89250, 88343, 87441, 86544, 85653, 84768, 83887, 83012, 82143, 81279, 80420, 79567, 78719, 77876, 77039, 76207, 75380, 74559, 73743, 72932, 72126, 71326, 70531, 69741, 68957, 68177, 67403, 66634, 65871, 65112, 64359, 63611, 62868, 62130, 61397, 60670, 59947, 59230, 58518, 57810, 57108, 56412, 55720, 55033, 54351, 53674, 53003, 52336, 51674, 51018, 50366, 49719, 49077, 48441, 47809, 47182, 46560, 45943, 45331, 44723, 44121, 43523, 42931, 42343, 41760, 41182, 40608, 40040, 39476, 38917, 38363, 37813, 37269, 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64, 51, 40, 30, 22, 15, 10, 6], [159786, 158474, 157169, 155871, 154579, 153294, 152016, 150744, 149478, 148219, 146967, 145721, 144482, 143249, 142022, 140802, 139588, 138381, 137180, 135985, 134797, 133615, 132439, 131270, 130106, 128949, 127799, 126654, 125516, 124384, 123258, 122138, 121024, 119917, 118815, 117720, 116631, 115548, 114470, 113399, 112334, 111275, 110222, 109175, 108134, 107099, 106069, 105046, 104029, 103017, 102012, 101012, 100018, 99030, 98048, 97071, 96101, 95136, 94177, 93224, 92277, 91335, 90399, 89469, 88545, 87626, 86713, 85806, 84904, 84008, 83118, 82233, 81354, 80480, 79612, 78750, 77893, 77042, 76197, 75357, 74522, 73693, 72870, 72052, 71239, 70432, 69631, 68835, 68044, 67259, 66479, 65705, 64936, 64173, 63414, 62662, 61914, 61172, 60436, 59704, 58978, 58257, 57542, 56832, 56127, 55427, 54732, 54043, 53359, 52681, 52007, 51339, 50675, 50017, 49364, 48717, 48074, 47437, 46804, 46177, 45555, 44937, 44325, 43718, 43116, 42519, 41927, 41340, 40758, 40181, 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112, 95, 79, 64, 51, 40, 30, 22, 15, 10, 6], [161289, 159960, 158638, 157323, 156014, 154713, 153418, 152130, 150848, 149574, 148305, 147044, 145789, 144541, 143299, 142064, 140835, 139613, 138397, 137188, 135985, 134789, 133599, 132416, 131238, 130068, 128903, 127745, 126594, 125448, 124309, 123176, 122050, 120930, 119816, 118708, 117606, 116511, 115421, 114338, 113261, 112190, 111125, 110067, 109014, 107967, 106927, 105893, 104864, 103842, 102825, 101815, 100810, 99812, 98819, 97833, 96852, 95877, 94908, 93945, 92988, 92036, 91091, 90151, 89217, 88289, 87367, 86451, 85540, 84635, 83736, 82842, 81954, 81072, 80196, 79325, 78460, 77601, 76747, 75899, 75057, 74220, 73389, 72563, 71743, 70928, 70119, 69316, 68518, 67726, 66939, 66157, 65381, 64611, 63846, 63086, 62332, 61584, 60840, 60103, 59370, 58643, 57921, 57205, 56494, 55788, 55088, 54393, 53703, 53018, 52339, 51665, 50996, 50333, 49674, 49021, 48373, 47731, 47093, 46461, 45834, 45211, 44594, 43983, 43376, 42774, 42177, 41586, 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462, 422, 385, 350, 316, 284, 254, 226, 200, 176, 153, 132, 113, 95, 79, 64, 51, 40, 30, 22, 15, 10, 6], [167392, 165993, 164602, 163218, 161842, 160473, 159111, 157757, 156410, 155070, 153737, 152412, 151094, 149783, 148479, 147182, 145893, 144610, 143335, 142066, 140805, 139550, 138303, 137062, 135829, 134602, 133382, 132169, 130963, 129764, 128571, 127386, 126207, 125034, 123869, 122710, 121558, 120412, 119273, 118141, 117016, 115897, 114784, 113678, 112579, 111486, 110400, 109320, 108247, 107180, 106119, 105065, 104017, 102976, 101941, 100913, 99890, 98875, 97865, 96862, 95865, 94874, 93889, 92911, 91939, 90973, 90013, 89060, 88112, 87171, 86236, 85307, 84384, 83467, 82556, 81651, 80752, 79859, 78973, 78092, 77217, 76348, 75485, 74628, 73777, 72932, 72093, 71259, 70432, 69610, 68794, 67984, 67180, 66381, 65589, 64802, 64021, 63245, 62475, 61711, 60953, 60200, 59453, 58712, 57976, 57246, 56522, 55803, 55089, 54381, 53679, 52983, 52291, 51606, 50925, 50251, 49581, 48918, 48259, 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640, 592, 547, 504, 462, 423, 385, 350, 316, 285, 255, 227, 200, 176, 153, 132, 113, 95, 79, 64, 51, 40, 30, 22, 15, 10, 6] ]
def lowBounds20 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 200 through 209.
Definition (Lean source)
given by
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56763, 56014, 55271, 54534, 53803, 53078, 52359, 51647, 50940, 50239, 49545, 48856, 48174, 47497, 46826, 46161, 45502, 44849, 44202, 43561, 42925, 42295, 41671, 41053, 40440, 39834, 39232, 38637, 38047, 37463, 36884, 36311, 35744, 35182, 34626, 34075, 33529, 32989, 32455, 31926, 31402, 30884, 30371, 29864, 29361, 28864, 28373, 27886, 27405, 26929, 26458, 25993, 25532, 25077, 24627, 24181, 23741, 23306, 22876, 22451, 22031, 21616, 21205, 20800, 20399, 20004, 19613, 19227, 18845, 18469, 18097, 17730, 17368, 17010, 16657, 16308, 15964, 15625, 15290, 14960, 14634, 14313, 13996, 13683, 13375, 13071, 12772, 12477, 12186, 11900, 11617, 11339, 11065, 10795, 10530, 10268, 10011, 9757, 9508, 9263, 9021, 8784, 8550, 8321, 8095, 7873, 7655, 7441, 7230, 7023, 6820, 6620, 6425, 6232, 6044, 5859, 5677, 5499, 5325, 5154, 4986, 4822, 4661, 4503, 4349, 4198, 4050, 3906, 3764, 3626, 3491, 3359, 3230, 3104, 2982, 2862, 2745, 2631, 2520, 2412, 2306, 2204, 2104, 2007, 1913, 1821, 1732, 1646, 1562, 1481, 1403, 1327, 1253, 1182, 1113, 1047, 983, 921, 862, 805, 750, 698, 647, 599, 553, 509, 467, 427, 389, 353, 319, 287, 257, 228, 202, 177, 154, 133, 113, 95, 79, 65, 52, 40, 30, 22, 15, 10, 6], [183310, 181726, 180151, 178586, 177029, 175481, 173943, 172413, 170893, 169381, 167878, 166384, 164898, 163422, 161954, 160495, 159044, 157602, 156169, 154744, 153328, 151920, 150520, 149129, 147746, 146372, 145006, 143648, 142299, 140957, 139624, 138299, 136982, 135673, 134373, 133080, 131795, 130518, 129250, 127989, 126736, 125490, 124253, 123023, 121802, 120587, 119381, 118182, 116991, 115808, 114632, 113464, 112303, 111150, 110005, 108866, 107736, 106613, 105497, 104388, 103287, 102193, 101107, 100028, 98956, 97891, 96834, 95783, 94740, 93704, 92675, 91654, 90639, 89631, 88631, 87637, 86651, 85671, 84698, 83733, 82774, 81822, 80877, 79938, 79007, 78082, 77164, 76253, 75349, 74451, 73560, 72676, 71798, 70927, 70062, 69204, 68353, 67508, 66670, 65838, 65013, 64194, 63382, 62576, 61776, 60983, 60196, 59415, 58641, 57873, 57112, 56357, 55607, 54865, 54128, 53397, 52673, 51955, 51243, 50537, 49837, 49143, 48455, 47773, 47097, 46428, 45764, 45106, 44454, 43808, 43167, 42533, 41904, 41282, 40665, 40053, 39448, 38848, 38254, 37666, 37083, 36506, 35935, 35369, 34809, 34254, 33705, 33162, 32624, 32091, 31564, 31042, 30526, 30015, 29509, 29009, 28514, 28025, 27540, 27061, 26588, 26119, 25656, 25197, 24744, 24296, 23853, 23416, 22983, 22555, 22133, 21715, 21302, 20894, 20491, 20093, 19700, 19312, 18928, 18550, 18176, 17807, 17442, 17082, 16727, 16377, 16031, 15690, 15353, 15021, 14694, 14371, 14052, 13738, 13428, 13123, 12822, 12525, 12233, 11945, 11661, 11382, 11106, 10835, 10568, 10306, 10047, 9792, 9542, 9295, 9053, 8814, 8580, 8349, 8122, 7899, 7680, 7465, 7253, 7046, 6842, 6641, 6445, 6252, 6062, 5876, 5694, 5515, 5340, 5168, 5000, 4835, 4674, 4515, 4361, 4209, 4061, 3916, 3774, 3635, 3500, 3367, 3238, 3112, 2989, 2868, 2751, 2637, 2525, 2417, 2311, 2209, 2108, 2011, 1917, 1825, 1736, 1649, 1565, 1484, 1405, 1329, 1255, 1184, 1115, 1049, 984, 923, 863, 806, 751, 699, 648, 600, 553, 509, 467, 427, 389, 353, 319, 287, 257, 228, 202, 177, 154, 133, 113, 95, 79, 65, 52, 40, 30, 22, 15, 10, 6] ]
def lowBounds21 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 210 through 219.
Definition (Lean source)
given by
#[ [184955, 183352, 181758, 180173, 178597, 177031, 175474, 173926, 172387, 170857, 169337, 167825, 166322, 164828, 163343, 161867, 160400, 158941, 157491, 156050, 154618, 153194, 151778, 150372, 148973, 147584, 146202, 144830, 143465, 142109, 140761, 139422, 138090, 136767, 135453, 134146, 132847, 131557, 130275, 129000, 127734, 126476, 125225, 123983, 122748, 121522, 120303, 119092, 117889, 116693, 115506, 114326, 113153, 111988, 110831, 109682, 108540, 107406, 106279, 105160, 104048, 102943, 101846, 100757, 99674, 98600, 97532, 96472, 95419, 94373, 93334, 92303, 91279, 90262, 89252, 88250, 87254, 86265, 85284, 84309, 83342, 82381, 81428, 80481, 79541, 78608, 77682, 76763, 75851, 74945, 74047, 73155, 72269, 71391, 70519, 69654, 68795, 67943, 67098, 66259, 65427, 64601, 63782, 62970, 62163, 61364, 60571, 59784, 59003, 58229, 57462, 56700, 55945, 55196, 54454, 53718, 52988, 52264, 51546, 50835, 50130, 49431, 48738, 48051, 47370, 46695, 46026, 45363, 44706, 44055, 43410, 42771, 42138, 41511, 40890, 40274, 39664, 39060, 38462, 37870, 37283, 36702, 36127, 35557, 34993, 34434, 33882, 33334, 32793, 32256, 31726, 31201, 30681, 30167, 29658, 29154, 28656, 28163, 27676, 27194, 26717, 26246, 25779, 25318, 24862, 24412, 23966, 23525, 23090, 22660, 22235, 21814, 21399, 20989, 20584, 20183, 19788, 19397, 19012, 18631, 18255, 17883, 17517, 17155, 16798, 16446, 16098, 15755, 15417, 15083, 14753, 14429, 14108, 13792, 13481, 13174, 12872, 12574, 12280, 11990, 11705, 11424, 11148, 10875, 10607, 10343, 10083, 9827, 9576, 9328, 9084, 8845, 8609, 8377, 8149, 7926, 7705, 7489, 7277, 7068, 6863, 6662, 6465, 6271, 6081, 5894, 5711, 5532, 5356, 5183, 5014, 4849, 4687, 4528, 4372, 4220, 4072, 3926, 3784, 3644, 3509, 3376, 3246, 3119, 2996, 2875, 2757, 2643, 2531, 2422, 2316, 2213, 2113, 2015, 1921, 1828, 1739, 1652, 1568, 1487, 1408, 1331, 1257, 1186, 1117, 1050, 986, 924, 865, 807, 752, 699, 649, 600, 554, 510, 468, 428, 390, 354, 320, 287, 257, 229, 202, 177, 154, 133, 113, 95, 79, 65, 52, 40, 30, 22, 15, 10, 6], [186610, 184987, 183373, 181769, 180175, 178590, 177014, 175447, 173890, 172342, 170804, 169274, 167754, 166242, 164740, 163247, 161763, 160287, 158821, 157363, 155915, 154475, 153043, 151621, 150207, 148802, 147405, 146017, 144638, 143267, 141904, 140550, 139204, 137867, 136538, 135217, 133905, 132601, 131305, 130017, 128737, 127466, 126203, 124947, 123700, 122461, 121229, 120006, 118790, 117583, 116383, 115191, 114007, 112831, 111662, 110501, 109348, 108202, 107065, 105934, 104812, 103696, 102589, 101489, 100396, 99311, 98233, 97163, 96100, 95045, 93996, 92955, 91922, 90895, 89876, 88864, 87860, 86862, 85872, 84888, 83912, 82943, 81981, 81026, 80078, 79137, 78202, 77275, 76355, 75442, 74535, 73635, 72742, 71856, 70977, 70105, 69239, 68380, 67527, 66682, 65842, 65010, 64184, 63365, 62552, 61746, 60946, 60153, 59367, 58586, 57813, 57045, 56284, 55530, 54781, 54039, 53304, 52574, 51851, 51134, 50424, 49719, 49021, 48329, 47643, 46963, 46289, 45621, 44960, 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154, 133, 113, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [188274, 186631, 184998, 183375, 181761, 180157, 178563, 176978, 175402, 173836, 172279, 170732, 169193, 167665, 166145, 164635, 163133, 161641, 160158, 158684, 157218, 155762, 154315, 152876, 151447, 150026, 148614, 147211, 145816, 144430, 143053, 141684, 140324, 138972, 137629, 136294, 134968, 133650, 132340, 131039, 129746, 128461, 127184, 125916, 124656, 123404, 122160, 120924, 119696, 118476, 117264, 116061, 114865, 113677, 112496, 111324, 110159, 109003, 107854, 106712, 105579, 104453, 103335, 102224, 101121, 100026, 98938, 97857, 96784, 95719, 94661, 93610, 92567, 91531, 90503, 89482, 88468, 87461, 86462, 85470, 84485, 83507, 82536, 81573, 80616, 79667, 78724, 77789, 76861, 75940, 75025, 74118, 73217, 72324, 71437, 70557, 69684, 68818, 67958, 67106, 66260, 65420, 64588, 63762, 62942, 62130, 61324, 60524, 59731, 58945, 58165, 57391, 56624, 55864, 55110, 54362, 53621, 52886, 52157, 51435, 50718, 50009, 49305, 48608, 47917, 47232, 46553, 45880, 45214, 44553, 43899, 43250, 42608, 41972, 41342, 40717, 40099, 39486, 38879, 38279, 37684, 37095, 36511, 35934, 35362, 34796, 34236, 33681, 33132, 32589, 32051, 31519, 30992, 30471, 29956, 29446, 28941, 28442, 27948, 27460, 26977, 26500, 26028, 25561, 25099, 24643, 24192, 23746, 23305, 22870, 22439, 22014, 21594, 21179, 20769, 20364, 19964, 19569, 19179, 18793, 18413, 18038, 17667, 17301, 16940, 16584, 16232, 15886, 15543, 15206, 14873, 14545, 14221, 13902, 13588, 13277, 12972, 12671, 12374, 12082, 11794, 11510, 11231, 10956, 10685, 10418, 10156, 9897, 9643, 9393, 9147, 8906, 8668, 8434, 8204, 7978, 7756, 7538, 7324, 7113, 6907, 6704, 6505, 6309, 6118, 5930, 5745, 5564, 5387, 5213, 5043, 4876, 4713, 4553, 4396, 4243, 4093, 3946, 3803, 3663, 3526, 3392, 3262, 3134, 3010, 2888, 2770, 2655, 2542, 2433, 2326, 2222, 2122, 2023, 1928, 1836, 1746, 1658, 1574, 1492, 1413, 1336, 1262, 1190, 1120, 1054, 989, 927, 867, 810, 754, 701, 651, 602, 555, 511, 469, 429, 391, 354, 320, 288, 257, 229, 202, 177, 154, 133, 113, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [189949, 188286, 186633, 184990, 183357, 181734, 180120, 178516, 176922, 175338, 173763, 172197, 170641, 169095, 167557, 166030, 164511, 163002, 161502, 160011, 158529, 157057, 155593, 154139, 152693, 151257, 149829, 148411, 147001, 145600, 144207, 142824, 141449, 140083, 138725, 137376, 136036, 134704, 133380, 132065, 130759, 129461, 128171, 126890, 125616, 124352, 123095, 121846, 120606, 119374, 118150, 116934, 115726, 114526, 113335, 112151, 110975, 109807, 108646, 107494, 106349, 105213, 104084, 102963, 101849, 100743, 99645, 98554, 97471, 96396, 95328, 94268, 93215, 92170, 91132, 90101, 89078, 88063, 87054, 86053, 85059, 84073, 83094, 82122, 81157, 80199, 79249, 78305, 77369, 76440, 75517, 74602, 73694, 72793, 71899, 71011, 70131, 69258, 68391, 67531, 66678, 65832, 64992, 64160, 63334, 62515, 61702, 60896, 60097, 59304, 58518, 57738, 56965, 56199, 55439, 54685, 53938, 53198, 52464, 51736, 51014, 50299, 49590, 48888, 48191, 47501, 46818, 46140, 45469, 44803, 44144, 43491, 42844, 42203, 41568, 40940, 40317, 39700, 39089, 38484, 37885, 37292, 36705, 36123, 35547, 34977, 34413, 33855, 33302, 32755, 32214, 31678, 31148, 30624, 30105, 29592, 29084, 28582, 28085, 27594, 27108, 26627, 26152, 25682, 25218, 24759, 24305, 23856, 23413, 22975, 22542, 22114, 21692, 21274, 20862, 20454, 20052, 19655, 19262, 18875, 18492, 18115, 17742, 17374, 17011, 16653, 16300, 15951, 15607, 15268, 14933, 14603, 14278, 13957, 13641, 13329, 13022, 12719, 12421, 12127, 11838, 11553, 11272, 10996, 10724, 10456, 10192, 9933, 9677, 9426, 9179, 8936, 8697, 8462, 8232, 8005, 7782, 7563, 7347, 7136, 6929, 6725, 6525, 6329, 6136, 5947, 5762, 5581, 5403, 5228, 5057, 4890, 4726, 4565, 4408, 4254, 4104, 3957, 3813, 3672, 3535, 3401, 3270, 3142, 3017, 2895, 2776, 2661, 2548, 2438, 2331, 2227, 2126, 2028, 1932, 1839, 1749, 1662, 1577, 1495, 1415, 1338, 1264, 1192, 1122, 1055, 990, 928, 868, 811, 755, 702, 651, 603, 556, 512, 469, 429, 391, 355, 320, 288, 258, 229, 202, 178, 155, 133, 114, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [191633, 189950, 188277, 186615, 184962, 183320, 181687, 180064, 178451, 176848, 175255, 173671, 172097, 170533, 168978, 167432, 165897, 164370, 162853, 161346, 159847, 158358, 156878, 155408, 153946, 152494, 151051, 149617, 148191, 146775, 145368, 143969, 142580, 141199, 139827, 138464, 137109, 135763, 134426, 133097, 131777, 130465, 129162, 127868, 126582, 125304, 124034, 122773, 121520, 120276, 119040, 117812, 116592, 115380, 114176, 112981, 111793, 110614, 109443, 108279, 107124, 105976, 104836, 103704, 102580, 101464, 100355, 99255, 98162, 97076, 95998, 94928, 93866, 92811, 91764, 90724, 89691, 88667, 87649, 86639, 85636, 84641, 83653, 82673, 81699, 80733, 79775, 78823, 77879, 76941, 76011, 75088, 74173, 73264, 72362, 71467, 70580, 69699, 68825, 67958, 67098, 66245, 65399, 64559, 63727, 62901, 62082, 61269, 60464, 59665, 58872, 58087, 57308, 56535, 55769, 55010, 54257, 53511, 52771, 52038, 51311, 50590, 49876, 49168, 48467, 47772, 47083, 46400, 45724, 45054, 44390, 43732, 43081, 42435, 41796, 41163, 40536, 39914, 39299, 38690, 38087, 37490, 36898, 36313, 35733, 35160, 34592, 34029, 33473, 32923, 32378, 31839, 31305, 30777, 30255, 29738, 29227, 28722, 28222, 27728, 27239, 26755, 26277, 25804, 25337, 24875, 24419, 23967, 23521, 23081, 22645, 22215, 21790, 21370, 20955, 20545, 20140, 19741, 19346, 18957, 18572, 18192, 17818, 17448, 17083, 16723, 16367, 16017, 15671, 15330, 14993, 14662, 14335, 14012, 13694, 13381, 13072, 12768, 12468, 12173, 11882, 11596, 11314, 11036, 10763, 10493, 10228, 9968, 9711, 9459, 9211, 8967, 8727, 8491, 8259, 8031, 7807, 7587, 7371, 7159, 6950, 6746, 6545, 6348, 6155, 5965, 5779, 5597, 5418, 5243, 5071, 4903, 4739, 4578, 4420, 4266, 4115, 3967, 3823, 3682, 3544, 3409, 3278, 3149, 3024, 2902, 2783, 2667, 2554, 2443, 2336, 2232, 2130, 2032, 1936, 1843, 1752, 1665, 1580, 1497, 1418, 1340, 1266, 1194, 1124, 1057, 992, 930, 870, 812, 756, 703, 652, 603, 557, 512, 470, 430, 391, 355, 321, 288, 258, 229, 203, 178, 155, 133, 114, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [193327, 191624, 189931, 188249, 186576, 184914, 183262, 181621, 179989, 178367, 176755, 175153, 173561, 171979, 170406, 168843, 167290, 165746, 164212, 162687, 161172, 159667, 158170, 156684, 155206, 153738, 152279, 150829, 149388, 147957, 146534, 145121, 143716, 142321, 140934, 139556, 138188, 136827, 135476, 134134, 132800, 131475, 130158, 128850, 127551, 126260, 124978, 123704, 122439, 121182, 119933, 118693, 117461, 116238, 115022, 113815, 112616, 111425, 110242, 109068, 107901, 106742, 105592, 104449, 103314, 102188, 101069, 99958, 98854, 97759, 96671, 95591, 94519, 93455, 92398, 91349, 90307, 89273, 88246, 87227, 86216, 85212, 84215, 83226, 82244, 81270, 80303, 79343, 78390, 77445, 76507, 75576, 74653, 73736, 72827, 71925, 71030, 70142, 69261, 68387, 67520, 66660, 65806, 64960, 64121, 63288, 62463, 61644, 60832, 60027, 59228, 58436, 57651, 56873, 56101, 55336, 54577, 53825, 53080, 52341, 51609, 50883, 50163, 49450, 48744, 48043, 47349, 46662, 45981, 45306, 44637, 43974, 43318, 42668, 42024, 41387, 40755, 40130, 39510, 38897, 38289, 37688, 37093, 36503, 35920, 35342, 34770, 34204, 33644, 33090, 32542, 31999, 31462, 30931, 30405, 29885, 29371, 28862, 28359, 27862, 27370, 26883, 26402, 25927, 25457, 24992, 24532, 24078, 23630, 23186, 22748, 22315, 21888, 21465, 21048, 20636, 20229, 19827, 19430, 19039, 18652, 18270, 17893, 17521, 17154, 16792, 16435, 16082, 15735, 15392, 15054, 14720, 14392, 14067, 13748, 13433, 13123, 12817, 12516, 12219, 11927, 11639, 11355, 11076, 10802, 10531, 10265, 10003, 9745, 9492, 9243, 8997, 8756, 8519, 8287, 8058, 7833, 7612, 7395, 7182, 6972, 6767, 6565, 6367, 6173, 5983, 5796, 5613, 5434, 5258, 5086, 4917, 4752, 4590, 4432, 4277, 4125, 3977, 3832, 3691, 3553, 3417, 3285, 3157, 3031, 2909, 2789, 2673, 2559, 2449, 2341, 2237, 2135, 2036, 1940, 1846, 1756, 1668, 1583, 1500, 1420, 1343, 1268, 1196, 1126, 1058, 994, 931, 871, 813, 757, 704, 653, 604, 557, 513, 470, 430, 392, 355, 321, 289, 258, 230, 203, 178, 155, 133, 114, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [195031, 193307, 191594, 189892, 188200, 186518, 184847, 183186, 181535, 179894, 178264, 176643, 175033, 173432, 171842, 170261, 168690, 167129, 165578, 164036, 162504, 160982, 159469, 157966, 156472, 154988, 153513, 152047, 150591, 149144, 147706, 146278, 144858, 143448, 142047, 140655, 139271, 137897, 136532, 135175, 133828, 132489, 131159, 129838, 128525, 127222, 125926, 124640, 123362, 122092, 120831, 119579, 118335, 117099, 115872, 114653, 113442, 112240, 111045, 109859, 108682, 107512, 106351, 105197, 104052, 102914, 101785, 100664, 99550, 98445, 97347, 96257, 95175, 94101, 93035, 91976, 90925, 89882, 88846, 87818, 86797, 85785, 84779, 83781, 82791, 81808, 80833, 79865, 78904, 77951, 77005, 76066, 75135, 74211, 73294, 72384, 71482, 70586, 69698, 68817, 67943, 67076, 66216, 65363, 64516, 63677, 62845, 62020, 61201, 60390, 59585, 58787, 57996, 57211, 56434, 55663, 54898, 54141, 53390, 52645, 51907, 51176, 50451, 49733, 49021, 48315, 47616, 46924, 46238, 45558, 44884, 44217, 43556, 42902, 42253, 41611, 40975, 40345, 39721, 39104, 38492, 37887, 37287, 36694, 36107, 35525, 34950, 34380, 33816, 33258, 32706, 32160, 31620, 31085, 30556, 30033, 29515, 29003, 28497, 27996, 27501, 27012, 26528, 26049, 25576, 25109, 24647, 24190, 23738, 23292, 22852, 22416, 21986, 21561, 21142, 20727, 20318, 19914, 19515, 19121, 18732, 18348, 17969, 17595, 17226, 16862, 16503, 16148, 15799, 15454, 15114, 14779, 14449, 14123, 13802, 13485, 13173, 12866, 12563, 12265, 11971, 11682, 11397, 11117, 10841, 10569, 10302, 10038, 9780, 9525, 9274, 9028, 8786, 8548, 8314, 8084, 7858, 7636, 7418, 7204, 6994, 6788, 6585, 6387, 6192, 6001, 5813, 5630, 5450, 5273, 5100, 4931, 4765, 4603, 4444, 4288, 4136, 3988, 3842, 3700, 3561, 3426, 3293, 3164, 3038, 2915, 2795, 2679, 2565, 2454, 2346, 2241, 2139, 2040, 1944, 1850, 1759, 1671, 1586, 1503, 1423, 1345, 1270, 1198, 1128, 1060, 995, 932, 872, 814, 758, 705, 654, 605, 558, 513, 471, 431, 392, 356, 321, 289, 258, 230, 203, 178, 155, 133, 114, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [196745, 195001, 193267, 191545, 189833, 188131, 186441, 184760, 183090, 181430, 179781, 178142, 176513, 174894, 173286, 171687, 170099, 168520, 166951, 165392, 163844, 162304, 160775, 159255, 157745, 156244, 154754, 153272, 151800, 150338, 148884, 147441, 146006, 144581, 143165, 141758, 140361, 138972, 137593, 136222, 134861, 133508, 132165, 130830, 129504, 128187, 126879, 125580, 124289, 123007, 121733, 120468, 119212, 117964, 116725, 115494, 114272, 113058, 111852, 110655, 109466, 108285, 107113, 105948, 104792, 103644, 102504, 101373, 100249, 99133, 98026, 96926, 95834, 94750, 93674, 92606, 91545, 90493, 89448, 88411, 87381, 86360, 85346, 84339, 83340, 82349, 81365, 80389, 79420, 78458, 77504, 76558, 75619, 74687, 73762, 72845, 71935, 71032, 70137, 69248, 68367, 67493, 66626, 65766, 64913, 64068, 63229, 62397, 61572, 60754, 59943, 59139, 58342, 57551, 56767, 55991, 55220, 54457, 53700, 52950, 52207, 51470, 50740, 50016, 49299, 48588, 47884, 47187, 46496, 45811, 45133, 44461, 43795, 43136, 42483, 41836, 41196, 40562, 39933, 39312, 38696, 38086, 37483, 36885, 36294, 35709, 35129, 34556, 33988, 33427, 32871, 32321, 31777, 31239, 30707, 30180, 29660, 29144, 28635, 28131, 27633, 27141, 26654, 26172, 25696, 25226, 24761, 24302, 23847, 23399, 22956, 22518, 22085, 21658, 21236, 20819, 20407, 20001, 19599, 19203, 18812, 18426, 18045, 17669, 17298, 16932, 16571, 16214, 15863, 15516, 15175, 14838, 14506, 14178, 13855, 13537, 13224, 12915, 12611, 12311, 12016, 11725, 11439, 11157, 10880, 10607, 10338, 10074, 9814, 9558, 9306, 9059, 8816, 8577, 8342, 8111, 7884, 7661, 7442, 7227, 7016, 6809, 6606, 6406, 6211, 6019, 5831, 5646, 5465, 5288, 5115, 4945, 4778, 4615, 4456, 4300, 4147, 3998, 3852, 3709, 3570, 3434, 3301, 3172, 3045, 2922, 2802, 2685, 2570, 2459, 2351, 2246, 2144, 2044, 1947, 1854, 1762, 1674, 1588, 1505, 1425, 1347, 1272, 1200, 1129, 1062, 997, 934, 873, 815, 759, 706, 655, 606, 559, 514, 471, 431, 393, 356, 322, 289, 259, 230, 203, 178, 155, 133, 114, 96, 79, 65, 52, 40, 30, 22, 15, 10, 6], [198469, 196704, 194950, 193207, 191475, 189754, 188043, 186343, 184654, 182975, 181307, 179649, 178001, 176364, 174737, 173121, 171514, 169918, 168332, 166756, 165190, 163634, 162087, 160551, 159024, 157508, 156000, 154503, 153015, 151537, 150069, 148609, 147160, 145720, 144289, 142867, 141455, 140052, 138659, 137274, 135899, 134532, 133175, 131827, 130488, 129158, 127836, 126524, 125220, 123925, 122639, 121362, 120093, 118833, 117582, 116339, 115105, 113880, 112662, 111454, 110254, 109062, 107878, 106703, 105536, 104377, 103227, 102085, 100951, 99825, 98707, 97597, 96495, 95402, 94316, 93238, 92168, 91106, 90052, 89006, 87968, 86937, 85914, 84899, 83891, 82891, 81899, 80914, 79937, 78968, 78006, 77051, 76104, 75165, 74232, 73308, 72390, 71480, 70577, 69682, 68793, 67912, 67038, 66171, 65312, 64459, 63614, 62775, 61944, 61120, 60302, 59492, 58689, 57892, 57102, 56320, 55544, 54774, 54012, 53256, 52507, 51765, 51029, 50300, 49578, 48862, 48153, 47451, 46754, 46065, 45382, 44705, 44035, 43371, 42713, 42062, 41417, 40778, 40146, 39520, 38900, 38286, 37679, 37077, 36482, 35893, 35309, 34732, 34161, 33596, 33037, 32483, 31936, 31394, 30858, 30329, 29804, 29286, 28773, 28266, 27765, 27270, 26780, 26295, 25817, 25343, 24876, 24413, 23957, 23505, 23059, 22619, 22184, 21754, 21329, 20910, 20496, 20087, 19684, 19285, 18892, 18504, 18121, 17743, 17370, 17002, 16639, 16281, 15927, 15579, 15235, 14897, 14563, 14234, 13909, 13590, 13275, 12964, 12658, 12357, 12061, 11769, 11481, 11198, 10919, 10645, 10375, 10109, 9848, 9591, 9338, 9090, 8845, 8605, 8369, 8137, 7909, 7686, 7466, 7250, 7038, 6830, 6626, 6426, 6229, 6037, 5848, 5662, 5481, 5303, 5129, 4958, 4791, 4628, 4468, 4311, 4158, 4008, 3862, 3719, 3579, 3443, 3309, 3179, 3052, 2929, 2808, 2691, 2576, 2465, 2356, 2251, 2148, 2048, 1951, 1857, 1766, 1677, 1591, 1508, 1428, 1350, 1274, 1201, 1131, 1063, 998, 935, 875, 816, 760, 707, 656, 606, 559, 515, 472, 431, 393, 356, 322, 289, 259, 230, 203, 178, 155, 134, 114, 96, 80, 65, 52, 40, 30, 22, 15, 10, 6], [200203, 198417, 196643, 194879, 193127, 191385, 189655, 187935, 186226, 184528, 182841, 181164, 179498, 177842, 176197, 174562, 172938, 171324, 169720, 168126, 166543, 164970, 163407, 161854, 160310, 158777, 157254, 155740, 154237, 152743, 151259, 149784, 148319, 146864, 145418, 143982, 142555, 141138, 139730, 138331, 136941, 135561, 134190, 132829, 131476, 130132, 128798, 127472, 126156, 124848, 123550, 122260, 120979, 119707, 118443, 117188, 115942, 114705, 113476, 112256, 111045, 109841, 108647, 107461, 106283, 105113, 103952, 102800, 101655, 100519, 99391, 98271, 97160, 96056, 94961, 93873, 92794, 91723, 90659, 89604, 88556, 87516, 86485, 85461, 84444, 83436, 82435, 81442, 80457, 79479, 78509, 77547, 76592, 75644, 74704, 73772, 72847, 71929, 71019, 70116, 69221, 68332, 67452, 66578, 65711, 64852, 64000, 63155, 62317, 61487, 60663, 59846, 59037, 58234, 57438, 56650, 55868, 55093, 54325, 53563, 52809, 52061, 51320, 50586, 49858, 49137, 48423, 47715, 47014, 46319, 45631, 44950, 44275, 43606, 42944, 42288, 41639, 40996, 40359, 39729, 39105, 38487, 37875, 37270, 36670, 36077, 35490, 34909, 34334, 33765, 33202, 32646, 32095, 31549, 31010, 30477, 29950, 29428, 28912, 28402, 27898, 27399, 26906, 26419, 25937, 25461, 24991, 24526, 24066, 23612, 23164, 22721, 22283, 21851, 21424, 21002, 20586, 20175, 19769, 19368, 18973, 18582, 18197, 17817, 17442, 17072, 16707, 16347, 15992, 15642, 15296, 14956, 14620, 14289, 13963, 13642, 13325, 13013, 12706, 12404, 12105, 11812, 11523, 11238, 10958, 10683, 10412, 10145, 9882, 9624, 9370, 9121, 8875, 8634, 8397, 8164, 7935, 7710, 7490, 7273, 7060, 6851, 6646, 6445, 6248, 6055, 5865, 5679, 5497, 5318, 5143, 4972, 4804, 4640, 4480, 4322, 4169, 4019, 3872, 3728, 3588, 3451, 3317, 3187, 3060, 2936, 2815, 2697, 2582, 2470, 2361, 2255, 2152, 2052, 1955, 1861, 1769, 1680, 1594, 1511, 1430, 1352, 1276, 1203, 1133, 1065, 1000, 936, 876, 817, 761, 708, 656, 607, 560, 515, 473, 432, 393, 357, 322, 290, 259, 230, 203, 178, 155, 134, 114, 96, 80, 65, 52, 40, 30, 22, 15, 10, 6] ]
def lowBounds22 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 220 through 229.
Definition (Lean source)
given by
#[ [201947, 200140, 198345, 196561, 194788, 193026, 191276, 189536, 187808, 186090, 184383, 182688, 181003, 179328, 177665, 176011, 174369, 172737, 171115, 169504, 167904, 166313, 164733, 163163, 161603, 160053, 158514, 156984, 155464, 153955, 152455, 150965, 149484, 148014, 146553, 145102, 143660, 142228, 140806, 139393, 137989, 136595, 135210, 133835, 132469, 131112, 129764, 128425, 127096, 125775, 124464, 123162, 121868, 120584, 119308, 118041, 116783, 115534, 114294, 113062, 111839, 110625, 109419, 108222, 107033, 105853, 104681, 103518, 102363, 101216, 100078, 98948, 97826, 96713, 95608, 94511, 93422, 92341, 91268, 90204, 89147, 88098, 87058, 86025, 85000, 83983, 82973, 81972, 80978, 79992, 79014, 78044, 77081, 76126, 75178, 74238, 73305, 72380, 71463, 70552, 69650, 68754, 67866, 66986, 66112, 65246, 64388, 63536, 62692, 61855, 61025, 60202, 59386, 58577, 57775, 56981, 56193, 55412, 54638, 53871, 53111, 52358, 51611, 50872, 50139, 49413, 48693, 47980, 47274, 46575, 45882, 45196, 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80, 65, 52, 40, 30, 22, 15, 10, 6], [203701, 201873, 200057, 198252, 196458, 194676, 192906, 191146, 189398, 187661, 185935, 184220, 182515, 180822, 179140, 177469, 175808, 174158, 172518, 170890, 169271, 167663, 166066, 164479, 162902, 161336, 159780, 158234, 156698, 155172, 153657, 152151, 150655, 149170, 147694, 146227, 144771, 143324, 141887, 140460, 139042, 137634, 136235, 134846, 133466, 132096, 130734, 129383, 128040, 126707, 125382, 124067, 122761, 121465, 120177, 118898, 117628, 116367, 115115, 113871, 112637, 111411, 110194, 108986, 107786, 106595, 105412, 104239, 103073, 101916, 100768, 99628, 98496, 97373, 96258, 95151, 94052, 92962, 91880, 90806, 89740, 88682, 87633, 86591, 85557, 84531, 83514, 82504, 81502, 80508, 79521, 78543, 77572, 76609, 75653, 74705, 73765, 72833, 71908, 70990, 70080, 69178, 68283, 67395, 66515, 65642, 64777, 63918, 63068, 62224, 61387, 60558, 59736, 58921, 58113, 57313, 56519, 55732, 54953, 54180, 53414, 52656, 51904, 51159, 50420, 49689, 48964, 48246, 47535, 46831, 46133, 45442, 44757, 44079, 43408, 42743, 42085, 41433, 40788, 40149, 39516, 38890, 38270, 37656, 37049, 36448, 35853, 35264, 34682, 34106, 33535, 32971, 32413, 31861, 31315, 30775, 30241, 29713, 29191, 28674, 28164, 27659, 27160, 26667, 26179, 25697, 25221, 24751, 24286, 23827, 23373, 22925, 22482, 22045, 21613, 21186, 20765, 20349, 19939, 19534, 19134, 18739, 18350, 17966, 17587, 17213, 16844, 16480, 16121, 15767, 15418, 15074, 14735, 14401, 14072, 13747, 13427, 13112, 12802, 12496, 12195, 11899, 11607, 11320, 11037, 10759, 10485, 10216, 9951, 9691, 9434, 9183, 8935, 8692, 8452, 8218, 7987, 7760, 7537, 7319, 7104, 6894, 6687, 6484, 6285, 6090, 5899, 5712, 5528, 5348, 5172, 5000, 4831, 4665, 4504, 4345, 4191, 4039, 3891, 3747, 3606, 3468, 3333, 3202, 3074, 2949, 2827, 2709, 2593, 2481, 2371, 2265, 2161, 2061, 1963, 1868, 1776, 1687, 1600, 1516, 1435, 1357, 1281, 1207, 1137, 1068, 1003, 939, 878, 820, 764, 710, 658, 609, 561, 516, 474, 433, 394, 357, 323, 290, 259, 231, 204, 179, 155, 134, 114, 96, 80, 65, 52, 40, 30, 22, 15, 10, 6], [205465, 203616, 201779, 199953, 198138, 196336, 194545, 192765, 190997, 189240, 187494, 185760, 184037, 182325, 180624, 178933, 177254, 175586, 173929, 172282, 170646, 169021, 167406, 165802, 164209, 162625, 161053, 159490, 157938, 156396, 154865, 153343, 151832, 150331, 148840, 147358, 145887, 144426, 142974, 141532, 140100, 138677, 137265, 135862, 134468, 133084, 131709, 130344, 128988, 127642, 126305, 124977, 123659, 122349, 121049, 119758, 118476, 117203, 115939, 114684, 113438, 112201, 110973, 109753, 108542, 107340, 106147, 104962, 103786, 102619, 101460, 100310, 99168, 98035, 96910, 95793, 94685, 93585, 92494, 91411, 90335, 89269, 88210, 87159, 86117, 85082, 84056, 83038, 82027, 81025, 80030, 79043, 78064, 77093, 76130, 75175, 74227, 73287, 72354, 71429, 70512, 69603, 68700, 67806, 66919, 66039, 65167, 64302, 63444, 62594, 61752, 60916, 60088, 59267, 58453, 57646, 56846, 56054, 55268, 54490, 53719, 52954, 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474, 433, 395, 358, 323, 290, 260, 231, 204, 179, 155, 134, 114, 96, 80, 65, 52, 40, 30, 22, 15, 10, 6], [207240, 205369, 203510, 201663, 199828, 198005, 196193, 194393, 192605, 190828, 189063, 187309, 185566, 183835, 182115, 180406, 178709, 177022, 175346, 173682, 172028, 170385, 168753, 167132, 165521, 163921, 162332, 160753, 159185, 157627, 156079, 154542, 153015, 151498, 149991, 148495, 147008, 145532, 144066, 142609, 141163, 139726, 138299, 136882, 135475, 134077, 132689, 131310, 129941, 128582, 127232, 125891, 124560, 123238, 121926, 120622, 119328, 118043, 116767, 115501, 114243, 112994, 111754, 110524, 109302, 108089, 106885, 105689, 104503, 103325, 102156, 100995, 99843, 98700, 97565, 96439, 95321, 94211, 93110, 92017, 90933, 89857, 88789, 87730, 86678, 85635, 84600, 83573, 82554, 81544, 80541, 79546, 78559, 77580, 76609, 75646, 74690, 73742, 72802, 71870, 70946, 70029, 69120, 68218, 67324, 66437, 65558, 64687, 63823, 62966, 62117, 61275, 60440, 59613, 58793, 57980, 57175, 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881, 822, 766, 711, 660, 610, 563, 518, 475, 434, 395, 358, 323, 291, 260, 231, 204, 179, 156, 134, 114, 96, 80, 65, 52, 40, 30, 22, 15, 10, 6], [209025, 207132, 205252, 203383, 201527, 199683, 197851, 196030, 194222, 192425, 190640, 188866, 187104, 185354, 183615, 181887, 180171, 178466, 176772, 175089, 173417, 171757, 170107, 168469, 166841, 165224, 163618, 162022, 160437, 158863, 157299, 155746, 154203, 152671, 151149, 149637, 148135, 146644, 145163, 143692, 142231, 140780, 139339, 137907, 136486, 135075, 133673, 132281, 130899, 129526, 128163, 126809, 125465, 124131, 122806, 121490, 120184, 118887, 117599, 116320, 115051, 113791, 112540, 111298, 110065, 108841, 107625, 106419, 105222, 104034, 102854, 101683, 100521, 99367, 98222, 97086, 95959, 94840, 93729, 92627, 91533, 90448, 89371, 88302, 87242, 86190, 85147, 84111, 83084, 82064, 81053, 80050, 79055, 78068, 77089, 76118, 75155, 74200, 73252, 72313, 71381, 70457, 69540, 68632, 67730, 66837, 65951, 65073, 64202, 63339, 62483, 61635, 60794, 59961, 59134, 58316, 57504, 56700, 55903, 55113, 54330, 53555, 52786, 52025, 51270, 50523, 49783, 49050, 48323, 47604, 46891, 46185, 45487, 44794, 44109, 43430, 42758, 42093, 41434, 40782, 40137, 39498, 38866, 38240, 37620, 37007, 36401, 35801, 35207, 34619, 34038, 33463, 32894, 32332, 31775, 31225, 30681, 30143, 29611, 29085, 28565, 28051, 27543, 27041, 26545, 26054, 25569, 25091, 24617, 24150, 23688, 23232, 22782, 22337, 21898, 21464, 21036, 20613, 20196, 19784, 19378, 18976, 18581, 18190, 17805, 17425, 17050, 16680, 16316, 15957, 15602, 15253, 14909, 14569, 14235, 13905, 13581, 13261, 12946, 12636, 12331, 12030, 11734, 11443, 11156, 10874, 10596, 10323, 10055, 9791, 9531, 9276, 9025, 8778, 8536, 8298, 8064, 7835, 7609, 7388, 7171, 6957, 6748, 6543, 6342, 6145, 5951, 5762, 5576, 5394, 5216, 5041, 4870, 4703, 4540, 4380, 4223, 4070, 3921, 3775, 3632, 3493, 3357, 3225, 3095, 2969, 2846, 2727, 2610, 2497, 2386, 2279, 2174, 2073, 1974, 1879, 1786, 1696, 1609, 1524, 1443, 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67238, 66345, 65460, 64583, 63713, 62851, 61996, 61149, 60309, 59477, 58652, 57834, 57024, 56221, 55426, 54637, 53856, 53082, 52315, 51556, 50803, 50057, 49319, 48587, 47863, 47145, 46435, 45731, 45034, 44344, 43661, 42984, 42314, 41651, 40995, 40345, 39702, 39065, 38435, 37812, 37195, 36585, 35980, 35383, 34791, 34207, 33628, 33056, 32490, 31930, 31376, 30829, 30287, 29752, 29223, 28700, 28182, 27671, 27166, 26667, 26174, 25686, 25204, 24728, 24258, 23794, 23335, 22882, 22435, 21993, 21557, 21127, 20701, 20282, 19868, 19459, 19056, 18658, 18265, 17878, 17496, 17119, 16748, 16381, 16020, 15664, 15313, 14967, 14626, 14290, 13958, 13632, 13311, 12994, 12683, 12376, 12074, 11777, 11484, 11196, 10912, 10634, 10359, 10090, 9824, 9563, 9307, 9055, 8807, 8564, 8325, 8090, 7860, 7633, 7411, 7193, 6979, 6769, 6563, 6361, 6163, 5968, 5778, 5592, 5409, 5230, 5055, 4884, 4716, 4552, 4391, 4234, 4081, 3931, 3784, 3641, 3502, 3365, 3232, 3103, 2976, 2853, 2733, 2616, 2502, 2391, 2284, 2179, 2077, 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73202, 72255, 71317, 70386, 69463, 68548, 67640, 66741, 65849, 64965, 64089, 63220, 62359, 61505, 60659, 59820, 58989, 58166, 57350, 56541, 55739, 54945, 54159, 53379, 52607, 51842, 51084, 50333, 49589, 48852, 48123, 47400, 46685, 45976, 45274, 44580, 43892, 43211, 42536, 41869, 41208, 40554, 39906, 39266, 38632, 38004, 37383, 36769, 36161, 35559, 34964, 34375, 33793, 33217, 32648, 32084, 31527, 30976, 30432, 29893, 29361, 28834, 28314, 27800, 27292, 26790, 26293, 25803, 25318, 24840, 24367, 23900, 23439, 22983, 22533, 22089, 21650, 21217, 20790, 20368, 19952, 19541, 19135, 18735, 18341, 17951, 17567, 17188, 16815, 16447, 16083, 15725, 15373, 15025, 14682, 14344, 14012, 13684, 13361, 13043, 12730, 12421, 12118, 11819, 11525, 11236, 10951, 10671, 10395, 10124, 9858, 9596, 9338, 9085, 8836, 8592, 8352, 8116, 7885, 7657, 7434, 7215, 7000, 6789, 6582, 6380, 6181, 5986, 5795, 5608, 5424, 5245, 5069, 4897, 4729, 4564, 4403, 4245, 4091, 3941, 3794, 3650, 3510, 3373, 3240, 3110, 2983, 2859, 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93436, 92313, 91199, 90093, 88997, 87909, 86830, 85759, 84698, 83644, 82600, 81564, 80536, 79517, 78507, 77504, 76510, 75525, 74548, 73578, 72618, 71665, 70720, 69784, 68856, 67935, 67023, 66119, 65222, 64334, 63453, 62580, 61715, 60858, 60008, 59166, 58332, 57506, 56687, 55875, 55071, 54275, 53486, 52705, 51930, 51164, 50404, 49652, 48907, 48170, 47439, 46716, 46000, 45291, 44589, 43894, 43206, 42525, 41851, 41184, 40523, 39870, 39223, 38583, 37950, 37324, 36704, 36091, 35485, 34885, 34291, 33705, 33124, 32550, 31983, 31422, 30867, 30319, 29777, 29241, 28711, 28188, 27670, 27159, 26654, 26155, 25662, 25175, 24694, 24219, 23750, 23286, 22829, 22377, 21931, 21491, 21057, 20628, 20204, 19787, 19375, 18968, 18567, 18172, 17782, 17397, 17017, 16643, 16275, 15911, 15553, 15200, 14852, 14509, 14171, 13839, 13511, 13188, 12871, 12558, 12250, 11947, 11649, 11355, 11067, 10783, 10503, 10229, 9959, 9693, 9432, 9176, 8924, 8676, 8433, 8194, 7960, 7730, 7504, 7282, 7064, 6851, 6642, 6436, 6235, 6038, 5845, 5655, 5470, 5289, 5111, 4937, 4767, 4600, 4437, 4278, 4123, 3971, 3822, 3677, 3536, 3398, 3263, 3131, 3003, 2879, 2757, 2639, 2524, 2412, 2303, 2197, 2094, 1994, 1897, 1803, 1712, 1623, 1538, 1455, 1375, 1298, 1223, 1151, 1082, 1015, 950, 888, 829, 772, 717, 665, 615, 567, 521, 478, 436, 397, 360, 325, 292, 261, 232, 205, 180, 156, 134, 115, 96, 80, 65, 52, 40, 30, 22, 15, 10, 6] ]
def lowBounds23 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 230 through 239.
Definition (Lean source)
given by
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6400, 6196, 5996, 5800, 5608, 5421, 5237, 5058, 4882, 4710, 4542, 4378, 4217, 4061, 3908, 3758, 3613, 3470, 3332, 3197, 3065, 2937, 2812, 2690, 2572, 2457, 2345, 2237, 2131, 2029, 1930, 1834, 1740, 1650, 1563, 1478, 1396, 1317, 1241, 1168, 1097, 1028, 963, 900, 839, 781, 725, 672, 621, 573, 526, 482, 441, 401, 363, 328, 295, 263, 234, 206, 181, 157, 135, 115, 97, 80, 65, 52, 41, 30, 22, 15, 10, 6], [237053, 234813, 232588, 230379, 228186, 226008, 223845, 221698, 219567, 217450, 215348, 213262, 211190, 209133, 207091, 205063, 203050, 201051, 199067, 197097, 195140, 193198, 191270, 189356, 187456, 185569, 183696, 181837, 179991, 178158, 176339, 174533, 172740, 170960, 169194, 167440, 165699, 163971, 162255, 160552, 158862, 157184, 155519, 153866, 152225, 150597, 148981, 147377, 145784, 144204, 142636, 141079, 139534, 138001, 136480, 134970, 133472, 131985, 130509, 129045, 127592, 126151, 124720, 123301, 121892, 120495, 119108, 117733, 116368, 115014, 113670, 112338, 111015, 109704, 108403, 107112, 105832, 104562, 103302, 102053, 100813, 99584, 98365, 97156, 95957, 94768, 93588, 92419, 91259, 90109, 88969, 87838, 86717, 85606, 84504, 83411, 82328, 81254, 80189, 79134, 78088, 77051, 76024, 75005, 73995, 72995, 72003, 71021, 70047, 69082, 68126, 67178, 66239, 65309, 64388, 63475, 62571, 61675, 60787, 59908, 59038, 58175, 57321, 56476, 55638, 54809, 53987, 53174, 52369, 51572, 50783, 50001, 49228, 48462, 47705, 46955, 46213, 45478, 44751, 44032, 43320, 42616, 41919, 41230, 40548, 39874, 39207, 38547, 37894, 37249, 36611, 35980, 35356, 34739, 34130, 33527, 32931, 32342, 31760, 31185, 30617, 30055, 29500, 28952, 28410, 27875, 27347, 26825, 26310, 25801, 25299, 24802, 24313, 23829, 23352, 22881, 22416, 21958, 21505, 21059, 20619, 20184, 19756, 19333, 18917, 18506, 18101, 17702, 17308, 16920, 16538, 16162, 15791, 15425, 15065, 14711, 14362, 14018, 13680, 13347, 13019, 12696, 12379, 12067, 11759, 11457, 11160, 10868, 10581, 10299, 10022, 9749, 9481, 9218, 8960, 8706, 8457, 8213, 7973, 7738, 7507, 7281, 7059, 6841, 6628, 6418, 6214, 6013, 5816, 5624, 5436, 5251, 5071, 4895, 4722, 4554, 4389, 4228, 4071, 3917, 3767, 3621, 3479, 3340, 3204, 3072, 2943, 2818, 2696, 2578, 2462, 2350, 2241, 2136, 2033, 1934, 1837, 1744, 1653, 1565, 1481, 1399, 1319, 1243, 1169, 1098, 1030, 964, 901, 840, 782, 726, 673, 622, 573, 527, 483, 441, 401, 364, 328, 295, 263, 234, 206, 181, 157, 135, 115, 97, 80, 65, 52, 41, 31, 22, 15, 10, 6] ]
def lowBounds24 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 240 through 249.
Definition (Lean source)
given by
#[ [239007, 236742, 234493, 232260, 230042, 227841, 225655, 223485, 221330, 219191, 217067, 214959, 212865, 210786, 208723, 206674, 204640, 202620, 200615, 198625, 196649, 194687, 192739, 190806, 188886, 186980, 185089, 183211, 181346, 179496, 177658, 175835, 174024, 172227, 170443, 168672, 166915, 165170, 163438, 161719, 160012, 158319, 156638, 154969, 153313, 151670, 150038, 148419, 146812, 145218, 143635, 142064, 140505, 138958, 137423, 135900, 134388, 132888, 131399, 129922, 128457, 127002, 125559, 124127, 122707, 121297, 119899, 118511, 117135, 115769, 114415, 113071, 111737, 110415, 109103, 107801, 106510, 105230, 103960, 102700, 101451, 100212, 98983, 97764, 96555, 95356, 94168, 92989, 91820, 90661, 89512, 88372, 87242, 86122, 85012, 83911, 82819, 81737, 80665, 79601, 78548, 77503, 76468, 75441, 74424, 73416, 72417, 71428, 70447, 69475, 68512, 67557, 66612, 65675, 64747, 63828, 62917, 62015, 61121, 60236, 59359, 58491, 57631, 56779, 55936, 55101, 54274, 53455, 52645, 51842, 51048, 50262, 49483, 48713, 47950, 47195, 46448, 45709, 44977, 44253, 43537, 42828, 42127, 41434, 40748, 40069, 39398, 38734, 38077, 37428, 36786, 36151, 35524, 34903, 34290, 33683, 33084, 32492, 31906, 31328, 30756, 30191, 29633, 29082, 28537, 27999, 27468, 26943, 26425, 25913, 25408, 24909, 24417, 23931, 23451, 22977, 22510, 22049, 21594, 21145, 20703, 20266, 19835, 19411, 18992, 18579, 18172, 17771, 17375, 16986, 16602, 16223, 15850, 15483, 15121, 14765, 14415, 14069, 13729, 13395, 13065, 12741, 12422, 12109, 11800, 11497, 11198, 10905, 10617, 10333, 10055, 9781, 9512, 9248, 8989, 8734, 8484, 8239, 7998, 7762, 7530, 7302, 7080, 6861, 6647, 6437, 6231, 6030, 5833, 5639, 5450, 5265, 5085, 4908, 4735, 4565, 4400, 4239, 4081, 3927, 3777, 3630, 3487, 3347, 3211, 3079, 2950, 2824, 2702, 2583, 2467, 2355, 2246, 2140, 2037, 1937, 1840, 1747, 1656, 1568, 1483, 1401, 1322, 1245, 1171, 1100, 1032, 966, 902, 842, 783, 727, 674, 623, 574, 528, 483, 441, 402, 364, 328, 295, 264, 234, 207, 181, 157, 135, 115, 97, 80, 65, 52, 41, 31, 22, 15, 10, 6], [240972, 238682, 236408, 234151, 231909, 229684, 227475, 225281, 223104, 220942, 218795, 216664, 214549, 212448, 210363, 208293, 206238, 204197, 202172, 200161, 198164, 196183, 194215, 192262, 190323, 188398, 186488, 184591, 182708, 180839, 178984, 177142, 175314, 173500, 171698, 169910, 168136, 166374, 164626, 162890, 161168, 159458, 157762, 156077, 154406, 152747, 151101, 149467, 147845, 146236, 144638, 143053, 141481, 139920, 138371, 136834, 135308, 133795, 132293, 130803, 129325, 127857, 126402, 124958, 123525, 122103, 120693, 119293, 117905, 116528, 115162, 113806, 112462, 111128, 109805, 108493, 107192, 105901, 104620, 103350, 102091, 100841, 99603, 98374, 97155, 95947, 94749, 93561, 92383, 91215, 90057, 88908, 87770, 86641, 85522, 84412, 83313, 82222, 81142, 80070, 79009, 77956, 76913, 75879, 74855, 73839, 72833, 71836, 70848, 69869, 68899, 67938, 66985, 66042, 65107, 64181, 63264, 62356, 61456, 60564, 59682, 58807, 57942, 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484, 442, 402, 364, 329, 295, 264, 234, 207, 181, 157, 135, 115, 97, 80, 65, 52, 41, 31, 22, 15, 10, 6], [242948, 240633, 238334, 236052, 233787, 231537, 229304, 227087, 224887, 222702, 220532, 218379, 216241, 214119, 212012, 209920, 207844, 205782, 203736, 201704, 199688, 197686, 195699, 193726, 191767, 189823, 187894, 185978, 184077, 182189, 180316, 178456, 176610, 174778, 172960, 171154, 169363, 167584, 165819, 164068, 162329, 160603, 158890, 157190, 155503, 153829, 152167, 150518, 148882, 147258, 145646, 144047, 142460, 140885, 139322, 137771, 136233, 134706, 133191, 131687, 130196, 128716, 127248, 125791, 124346, 122912, 121490, 120078, 118678, 117289, 115912, 114545, 113189, 111845, 110511, 109188, 107875, 106574, 105283, 104003, 102733, 101474, 100225, 98986, 97758, 96540, 95333, 94135, 92948, 91771, 90603, 89446, 88299, 87161, 86034, 84916, 83807, 82709, 81620, 80541, 79471, 78411, 77360, 76318, 75286, 74263, 73250, 72245, 71250, 70264, 69287, 68319, 67360, 66410, 65469, 64536, 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968, 905, 844, 785, 729, 676, 624, 575, 529, 485, 442, 403, 365, 329, 296, 264, 234, 207, 181, 157, 136, 115, 97, 80, 65, 52, 41, 31, 22, 15, 10, 6], [244935, 242594, 240271, 237964, 235674, 233401, 231144, 228903, 226679, 224471, 222279, 220103, 217943, 215798, 213669, 211556, 209458, 207375, 205308, 203256, 201219, 199197, 197189, 195197, 193219, 191255, 189307, 187372, 185452, 183546, 181654, 179777, 177913, 176063, 174227, 172404, 170595, 168800, 167018, 165250, 163495, 161753, 160024, 158309, 156606, 154916, 153239, 151575, 149924, 148285, 146658, 145045, 143443, 141854, 140278, 138713, 137161, 135620, 134092, 132576, 131071, 129578, 128097, 126628, 125170, 123724, 122290, 120866, 119455, 118054, 116665, 115287, 113920, 112564, 111219, 109885, 108562, 107250, 105948, 104658, 103378, 102108, 100849, 99601, 98363, 97135, 95918, 94711, 93515, 92328, 91152, 89986, 88830, 87683, 86547, 85421, 84304, 83197, 82100, 81013, 79935, 78867, 77808, 76759, 75719, 74689, 73668, 72656, 71654, 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1665, 1576, 1491, 1408, 1328, 1251, 1177, 1105, 1036, 970, 906, 845, 786, 730, 676, 625, 576, 529, 485, 443, 403, 365, 329, 296, 264, 235, 207, 181, 158, 136, 115, 97, 80, 66, 52, 41, 31, 22, 15, 10, 6], [246933, 244567, 242218, 239886, 237572, 235274, 232993, 230729, 228481, 226250, 224034, 221836, 219653, 217486, 215335, 213200, 211081, 208977, 206888, 204815, 202758, 200715, 198687, 196675, 194677, 192695, 190726, 188773, 186834, 184909, 182999, 181103, 179221, 177353, 175500, 173660, 171834, 170022, 168223, 166438, 164666, 162908, 161163, 159432, 157713, 156008, 154316, 152636, 150970, 149316, 147675, 146047, 144431, 142828, 141237, 139659, 138093, 136539, 134997, 133467, 131950, 130444, 128950, 127468, 125998, 124540, 123093, 121658, 120234, 118822, 117421, 116031, 114653, 113286, 111930, 110585, 109251, 107928, 106616, 105315, 104025, 102745, 101476, 100218, 98970, 97733, 96506, 95290, 94084, 92888, 91703, 90527, 89362, 88207, 87062, 85927, 84802, 83687, 82582, 81486, 80401, 79325, 78258, 77201, 76154, 75116, 74088, 73069, 72059, 71059, 70067, 69086, 68113, 67149, 66195, 65249, 64312, 63385, 62466, 61556, 60655, 59763, 58879, 58004, 57137, 56280, 55430, 54589, 53757, 52933, 52117, 51310, 50511, 49720, 48937, 48163, 47396, 46638, 45887, 45145, 44410, 43683, 42965, 42254, 41550, 40855, 40167, 39486, 38814, 38148, 37491, 36841, 36198, 35562, 34934, 34313, 33700, 33093, 32494, 31902, 31317, 30739, 30168, 29604, 29047, 28497, 27953, 27417, 26887, 26364, 25847, 25338, 24834, 24338, 23848, 23364, 22887, 22416, 21951, 21493, 21041, 20595, 20156, 19722, 19295, 18873, 18458, 18049, 17645, 17248, 16856, 16470, 16090, 15716, 15347, 14984, 14627, 14275, 13929, 13588, 13252, 12922, 12598, 12278, 11964, 11655, 11352, 11053, 10760, 10471, 10188, 9909, 9636, 9367, 9104, 8845, 8591, 8341, 8096, 7856, 7621, 7390, 7164, 6942, 6724, 6511, 6302, 6098, 5898, 5702, 5510, 5322, 5139, 4959, 4784, 4612, 4445, 4281, 4121, 3965, 3813, 3664, 3520, 3378, 3241, 3107, 2976, 2849, 2725, 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3673, 3528, 3386, 3248, 3114, 2983, 2855, 2731, 2610, 2493, 2379, 2268, 2161, 2057, 1956, 1858, 1763, 1671, 1582, 1496, 1413, 1332, 1255, 1180, 1108, 1039, 973, 909, 847, 788, 732, 678, 627, 577, 531, 486, 444, 404, 366, 330, 296, 265, 235, 207, 182, 158, 136, 116, 97, 81, 66, 52, 41, 31, 22, 15, 10, 6], [250961, 248544, 246144, 243762, 241398, 239051, 236721, 234409, 232114, 229835, 227573, 225328, 223100, 220888, 218693, 216514, 214351, 212204, 210073, 207958, 205858, 203774, 201706, 199653, 197616, 195594, 193587, 191595, 189618, 187655, 185708, 183775, 181857, 179953, 178064, 176189, 174328, 172481, 170648, 168830, 167025, 165234, 163456, 161693, 159943, 158206, 156483, 154773, 153076, 151392, 149721, 148064, 146419, 144787, 143168, 141562, 139968, 138387, 136818, 135262, 133718, 132186, 130667, 129159, 127664, 126180, 124709, 123250, 121802, 120366, 118941, 117529, 116127, 114738, 113359, 111992, 110637, 109292, 107959, 106637, 105326, 104026, 102736, 101458, 100191, 98934, 97688, 96453, 95228, 94013, 92810, 91616, 90433, 89261, 88098, 86946, 85804, 84672, 83550, 82438, 81336, 80244, 79162, 78090, 77027, 75974, 74931, 73897, 72873, 71858, 70853, 69857, 68870, 67893, 66925, 65966, 65017, 64076, 63145, 62222, 61309, 60404, 59508, 58621, 57743, 56874, 56013, 55161, 54318, 53483, 52656, 51839, 51029, 50228, 49435, 48650, 47874, 47106, 46346, 45594, 44850, 44114, 43387, 42667, 41955, 41251, 40554, 39866, 39185, 38511, 37846, 37188, 36537, 35894, 35259, 34630, 34010, 33396, 32790, 32191, 31599, 31015, 30437, 29867, 29304, 28747, 28198, 27655, 27120, 26591, 26069, 25553, 25045, 24543, 24047, 23558, 23076, 22600, 22131, 21668, 21211, 20761, 20317, 19879, 19447, 19021, 18602, 18189, 17781, 17380, 16984, 16595, 16211, 15833, 15461, 15094, 14734, 14378, 14029, 13685, 13346, 13013, 12686, 12363, 12046, 11735, 11428, 11127, 10831, 10540, 10255, 9974, 9698, 9427, 9161, 8900, 8644, 8393, 8146, 7904, 7667, 7434, 7206, 6982, 6763, 6548, 6338, 6132, 5930, 5733, 5540, 5351, 5166, 4985, 4809, 4636, 4467, 4302, 4142, 3985, 3831, 3682, 3536, 3394, 3255, 3120, 2989, 2861, 2737, 2616, 2498, 2384, 2273, 2165, 2061, 1959, 1861, 1766, 1674, 1585, 1498, 1415, 1335, 1257, 1182, 1110, 1041, 974, 910, 848, 789, 733, 679, 627, 578, 531, 487, 444, 404, 366, 330, 297, 265, 235, 207, 182, 158, 136, 116, 97, 81, 66, 52, 41, 31, 22, 15, 10, 6], [252993, 250549, 248124, 245716, 243327, 240955, 238601, 236264, 233944, 231642, 229357, 227089, 224837, 222603, 220385, 218183, 215998, 213830, 211677, 209541, 207420, 205316, 203227, 201154, 199096, 197054, 195027, 193016, 191019, 189038, 187072, 185120, 183184, 181262, 179355, 177462, 175583, 173719, 171870, 170034, 168212, 166405, 164611, 162831, 161065, 159312, 157573, 155848, 154136, 152437, 150751, 149079, 147420, 145773, 144140, 142519, 140912, 139317, 137734, 136165, 134607, 133062, 131530, 130010, 128502, 127006, 125522, 124050, 122590, 121142, 119706, 118282, 116869, 115468, 114078, 112700, 111334, 109978, 108634, 107302, 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6782, 6567, 6356, 6149, 5947, 5749, 5555, 5365, 5180, 4998, 4821, 4648, 4478, 4313, 4152, 3994, 3840, 3690, 3544, 3402, 3263, 3127, 2996, 2867, 2743, 2621, 2503, 2389, 2278, 2169, 2065, 1963, 1865, 1769, 1677, 1587, 1501, 1417, 1337, 1259, 1184, 1112, 1042, 975, 911, 850, 791, 734, 680, 628, 579, 532, 487, 445, 405, 366, 331, 297, 265, 235, 208, 182, 158, 136, 116, 97, 81, 66, 52, 41, 31, 22, 15, 10, 6], [255035, 252565, 250114, 247681, 245266, 242869, 240490, 238128, 235785, 233458, 231150, 228858, 226583, 224326, 222085, 219861, 217654, 215464, 213289, 211132, 208990, 206864, 204755, 202661, 200583, 198521, 196475, 194444, 192428, 190428, 188442, 186472, 184517, 182577, 180652, 178741, 176845, 174963, 173096, 171243, 169405, 167581, 165770, 163974, 162192, 160423, 158669, 156927, 155200, 153486, 151785, 150098, 148424, 146763, 145116, 143481, 141859, 140250, 138654, 137071, 135500, 133942, 132397, 130864, 129343, 127834, 126338, 124854, 123382, 121922, 120474, 119038, 117613, 116201, 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11239, 10939, 10645, 10355, 10071, 9792, 9518, 9248, 8984, 8725, 8470, 8221, 7976, 7736, 7500, 7269, 7043, 6821, 6604, 6392, 6183, 5980, 5780, 5585, 5394, 5207, 5024, 4846, 4671, 4501, 4335, 4172, 4013, 3859, 3708, 3561, 3417, 3277, 3141, 3009, 2880, 2754, 2632, 2514, 2398, 2287, 2178, 2073, 1970, 1871, 1775, 1683, 1593, 1506, 1422, 1341, 1263, 1188, 1115, 1045, 978, 914, 852, 793, 736, 682, 630, 580, 533, 488, 446, 405, 367, 331, 297, 266, 236, 208, 182, 158, 136, 116, 97, 81, 66, 52, 41, 31, 22, 15, 10, 6] ]
def lowBounds25 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 250 through 259.
Definition (Lean source)
given by
#[ [259153, 256630, 254127, 251642, 249175, 246728, 244299, 241888, 239495, 237120, 234763, 232424, 230103, 227799, 225513, 223243, 220991, 218756, 216538, 214337, 212153, 209985, 207834, 205699, 203580, 201477, 199391, 197320, 195265, 193226, 191203, 189195, 187203, 185225, 183264, 181317, 179385, 177468, 175566, 173679, 171806, 169948, 168105, 166276, 164461, 162660, 160874, 159101, 157343, 155598, 153867, 152150, 150446, 148756, 147079, 145416, 143766, 142129, 140506, 138895, 137297, 135713, 134141, 132582, 131035, 129501, 127980, 126471, 124974, 123490, 122018, 120558, 119111, 117675, 116251, 114840, 113440, 112052, 110675, 109310, 107957, 106615, 105285, 103966, 102658, 101362, 100077, 98803, 97540, 96288, 95047, 93817, 92598, 91389, 90191, 89004, 87828, 86662, 85506, 84361, 83227, 82102, 80988, 79884, 78791, 77707, 76633, 75570, 74516, 73472, 72438, 71414, 70400, 69395, 68400, 67414, 66438, 65471, 64514, 63566, 62628, 61699, 60778, 59868, 58966, 58073, 57189, 56315, 55449, 54592, 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158, 136, 116, 97, 81, 66, 52, 41, 31, 22, 15, 10, 6], [261229, 258680, 256149, 253638, 251146, 248673, 246218, 243782, 241365, 238965, 236584, 234221, 231876, 229549, 227239, 224947, 222673, 220415, 218175, 215952, 213746, 211557, 209384, 207228, 205089, 202966, 200859, 198769, 196694, 194636, 192593, 190566, 188555, 186559, 184579, 182614, 180664, 178729, 176810, 174905, 173015, 171140, 169280, 167434, 165603, 163786, 161983, 160195, 158421, 156661, 154915, 153182, 151464, 149759, 148067, 146390, 144726, 143075, 141437, 139813, 138201, 136603, 135018, 133446, 131886, 130340, 128806, 127284, 125775, 124279, 122795, 121323, 119864, 118416, 116981, 115558, 114147, 112748, 111360, 109985, 108621, 107269, 105928, 104599, 103281, 101975, 100679, 99396, 98123, 96862, 95611, 94372, 93143, 91926, 90719, 89523, 88338, 87163, 85999, 84846, 83703, 82571, 81448, 80337, 79235, 78144, 77062, 75991, 74930, 73879, 72838, 71806, 70785, 69773, 68771, 67779, 66796, 65823, 64859, 63905, 62960, 62025, 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534, 489, 447, 406, 368, 332, 298, 266, 236, 208, 182, 158, 136, 116, 97, 81, 66, 52, 41, 31, 22, 15, 10, 6], [263316, 260740, 258183, 255645, 253127, 250628, 248148, 245687, 243244, 240820, 238415, 236028, 233659, 231308, 228975, 226660, 224362, 222083, 219820, 217575, 215347, 213136, 210943, 208766, 206605, 204462, 202335, 200224, 198130, 196052, 193989, 191943, 189913, 187898, 185900, 183916, 181948, 179996, 178059, 176137, 174230, 172337, 170460, 168598, 166750, 164917, 163098, 161294, 159504, 157728, 155966, 154219, 152485, 150766, 149060, 147367, 145689, 144024, 142372, 140734, 139109, 137497, 135899, 134313, 132741, 131181, 129635, 128101, 126579, 125071, 123575, 122091, 120620, 119161, 117714, 116279, 114857, 113447, 112048, 110662, 109287, 107924, 106573, 105234, 103906, 102589, 101284, 99991, 98708, 97437, 96177, 94929, 93691, 92464, 91249, 90044, 88850, 87667, 86494, 85332, 84181, 83040, 81910, 80790, 79681, 78582, 77493, 76414, 75345, 74287, 73238, 72200, 71171, 70153, 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1193, 1120, 1050, 983, 918, 855, 796, 739, 684, 632, 582, 535, 490, 447, 407, 368, 332, 298, 266, 236, 208, 182, 158, 136, 116, 98, 81, 66, 52, 41, 31, 22, 15, 10, 6], [265415, 262811, 260227, 257663, 255119, 252594, 250088, 247601, 245133, 242685, 240255, 237843, 235450, 233076, 230719, 228381, 226061, 223758, 221473, 219206, 216956, 214724, 212509, 210310, 208129, 205965, 203817, 201687, 199572, 197474, 195393, 193327, 191278, 189244, 187227, 185225, 183239, 181268, 179313, 177374, 175449, 173540, 171646, 169766, 167902, 166052, 164218, 162397, 160591, 158800, 157023, 155260, 153511, 151777, 150056, 148349, 146656, 144977, 143311, 141659, 140020, 138395, 136783, 135184, 133599, 132026, 130467, 128920, 127386, 125865, 124357, 122861, 121378, 119908, 118449, 117003, 115570, 114148, 112739, 111341, 109956, 108582, 107221, 105871, 104533, 103206, 101891, 100588, 99295, 98015, 96745, 95487, 94240, 93005, 91780, 90566, 89364, 88172, 86991, 85820, 84661, 83512, 82373, 81245, 80128, 79021, 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87489, 86310, 85142, 83985, 82838, 81702, 80577, 79462, 78358, 77264, 76180, 75107, 74044, 72991, 71948, 70915, 69892, 68879, 67876, 66883, 65900, 64926, 63963, 63008, 62063, 61128, 60202, 59286, 58379, 57481, 56593, 55714, 54844, 53983, 53131, 52288, 51453, 50628, 49812, 49004, 48206, 47416, 46634, 45861, 45097, 44341, 43594, 42854, 42124, 41401, 40687, 39981, 39283, 38594, 37912, 37238, 36573, 35915, 35265, 34623, 33988, 33362, 32743, 32131, 31527, 30931, 30342, 29761, 29187, 28620, 28061, 27508, 26963, 26426, 25895, 25371, 24854, 24345, 23842, 23346, 22857, 22374, 21899, 21430, 20967, 20512, 20062, 19620, 19183, 18753, 18330, 17913, 17502, 17097, 16698, 16306, 15919, 15539, 15164, 14796, 14433, 14077, 13726, 13380, 13041, 12707, 12379, 12056, 11739, 11427, 11121, 10820, 10524, 10234, 9949, 9669, 9394, 9125, 8860, 8600, 8346, 8096, 7851, 7611, 7376, 7145, 6919, 6698, 6482, 6269, 6062, 5859, 5660, 5466, 5276, 5090, 4908, 4731, 4558, 4388, 4223, 4062, 3905, 3752, 3602, 3456, 3315, 3176, 3042, 2911, 2784, 2660, 2540, 2423, 2309, 2199, 2092, 1989, 1889, 1792, 1698, 1607, 1519, 1434, 1352, 1273, 1197, 1124, 1053, 985, 920, 858, 798, 741, 686, 633, 584, 536, 491, 448, 407, 369, 333, 299, 267, 237, 209, 183, 159, 136, 116, 98, 81, 66, 52, 41, 31, 22, 15, 10, 6], [269647, 266988, 264350, 261732, 259134, 256556, 253998, 251460, 248942, 246443, 243963, 241503, 239061, 236638, 234235, 231849, 229483, 227134, 224804, 222492, 220198, 217922, 215663, 213422, 211199, 208993, 206804, 204632, 202478, 200340, 198219, 196114, 194026, 191955, 189899, 187860, 185838, 183831, 181840, 179864, 177905, 175961, 174032, 172119, 170221, 168339, 166471, 164618, 162780, 160957, 159149, 157355, 155576, 153811, 152061, 150325, 148603, 146895, 145201, 143520, 141854, 140201, 138562, 136937, 135325, 133726, 132141, 130569, 129010, 127464, 125931, 124411, 122904, 121410, 119928, 118459, 117003, 115559, 114127, 112708, 111300, 109906, 108523, 107152, 105793, 104446, 103111, 101788, 100476, 99176, 97888, 96611, 95345, 94091, 92848, 91616, 90396, 89187, 87988, 86801, 85625, 84459, 83304, 82160, 81027, 79904, 78792, 77690, 76599, 75518, 74448, 73388, 72338, 71298, 70268, 69248, 68239, 67239, 66249, 65269, 64299, 63338, 62387, 61446, 60514, 59592, 58679, 57775, 56881, 55996, 55120, 54254, 53396, 52548, 51709, 50879, 50057, 49245, 48441, 47646, 46860, 46082, 45313, 44553, 43801, 43057, 42322, 41596, 40877, 40167, 39465, 38771, 38086, 37408, 36739, 36077, 35423, 34778, 34140, 33509, 32887, 32272, 31665, 31065, 30473, 29889, 29312, 28742, 28179, 27624, 27076, 26536, 26002, 25476, 24956, 24444, 23939, 23440, 22948, 22464, 21986, 21514, 21050, 20591, 20140, 19695, 19257, 18825, 18399, 17980, 17567, 17160, 16760, 16365, 15977, 15595, 15219, 14849, 14484, 14126, 13773, 13427, 13086, 12750, 12421, 12096, 11778, 11465, 11157, 10855, 10558, 10267, 9980, 9699, 9423, 9153, 8887, 8626, 8371, 8120, 7874, 7633, 7397, 7166, 6939, 6717, 6500, 6287, 6078, 5875, 5675, 5480, 5289, 5103, 4921, 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6736, 6518, 6304, 6095, 5890, 5690, 5495, 5303, 5116, 4933, 4755, 4580, 4410, 4244, 4082, 3923, 3769, 3619, 3472, 3329, 3190, 3055, 2923, 2795, 2671, 2550, 2433, 2318, 2208, 2100, 1996, 1896, 1798, 1704, 1612, 1524, 1439, 1357, 1277, 1201, 1127, 1056, 988, 923, 860, 800, 742, 687, 635, 585, 537, 492, 449, 408, 370, 333, 299, 267, 237, 209, 183, 159, 137, 116, 98, 81, 66, 52, 41, 31, 22, 15, 10, 6], [273925, 271210, 268516, 265844, 263192, 260561, 257950, 255360, 252790, 250240, 247710, 245200, 242709, 240238, 237786, 235353, 232939, 230544, 228168, 225811, 223472, 221151, 218849, 216565, 214298, 212050, 209819, 207606, 205410, 203232, 201071, 198927, 196800, 194690, 192597, 190520, 188460, 186416, 184389, 182377, 180382, 178403, 176440, 174492, 172561, 170644, 168744, 166858, 164988, 163133, 161293, 159468, 157658, 155863, 154083, 152317, 150565, 148828, 147105, 145397, 143702, 142022, 140356, 138703, 137065, 135440, 133828, 132230, 130646, 129075, 127518, 125973, 124442, 122924, 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147288, 145566, 143857, 142163, 140484, 138818, 137166, 135529, 133905, 132295, 130699, 129116, 127547, 125991, 124448, 122919, 121403, 119901, 118411, 116934, 115470, 114019, 112581, 111155, 109742, 108341, 106953, 105577, 104213, 102862, 101522, 100195, 98880, 97577, 96285, 95006, 93738, 92481, 91237, 90003, 88781, 87571, 86372, 85184, 84007, 82842, 81687, 80544, 79411, 78289, 77178, 76078, 74989, 73910, 72841, 71783, 70736, 69699, 68672, 67656, 66649, 65653, 64667, 63691, 62724, 61768, 60822, 59885, 58958, 58041, 57133, 56235, 55347, 54468, 53598, 52737, 51886, 51044, 50212, 49388, 48574, 47768, 46971, 46184, 45405, 44635, 43874, 43121, 42377, 41642, 40915, 40197, 39487, 38785, 38092, 37407, 36730, 36062, 35401, 34749, 34104, 33468, 32839, 32219, 31606, 31001, 30404, 29814, 29232, 28657, 28090, 27531, 26978, 26434, 25896, 25366, 24843, 24327, 23818, 23317, 22822, 22334, 21853, 21379, 20912, 20452, 19998, 19551, 19111, 18677, 18250, 17829, 17415, 17006, 16605, 16209, 15820, 15437, 15060, 14689, 14324, 13965, 13612, 13265, 12924, 12589, 12259, 11935, 11616, 11304, 10996, 10694, 10398, 10107, 9821, 9541, 9266, 8996, 8731, 8472, 8217, 7967, 7723, 7483, 7248, 7018, 6793, 6572, 6356, 6145, 5938, 5736, 5538, 5345, 5156, 4971, 4791, 4614, 4442, 4275, 4111, 3951, 3795, 3644, 3496, 3352, 3211, 3075, 2942, 2813, 2688, 2566, 2447, 2332, 2221, 2112, 2008, 1906, 1808, 1713, 1621, 1532, 1446, 1363, 1283, 1206, 1132, 1061, 992, 927, 864, 803, 745, 690, 637, 587, 539, 493, 450, 409, 371, 334, 300, 268, 238, 209, 183, 159, 137, 116, 98, 81, 66, 53, 41, 31, 22, 15, 10, 6] ]
def lowBounds26 reviewed
⚑ flagged
Causalean.Stat.CLT.BerryEsseen
Integer upper-bound candidates for parameter rows 260 through 269.
Definition (Lean source)
given by
#[ [280428, 277628, 274850, 272094, 269360, 266647, 263956, 261286, 258637, 256010, 253403, 250816, 248250, 245705, 243179, 240674, 238189, 235723, 233277, 230850, 228443, 226054, 223685, 221335, 219003, 216690, 214396, 212119, 209861, 207621, 205399, 203195, 201009, 198840, 196689, 194554, 192438, 190338, 188255, 186189, 184140, 182107, 180091, 178091, 176108, 174141, 172190, 170254, 168335, 166431, 164544, 162671, 160814, 158973, 157146, 155335, 153539, 151758, 149991, 148240, 146503, 144780, 143072, 141379, 139700, 138035, 136384, 134747, 133124, 131515, 129919, 128338, 126770, 125215, 123674, 122146, 120632, 119130, 117642, 116167, 114705, 113255, 111819, 110395, 108984, 107585, 106199, 104825, 103463, 102114, 100777, 99452, 98139, 96838, 95549, 94272, 93007, 91753, 90511, 89281, 88062, 86854, 85658, 84473, 83299, 82137, 80985, 79845, 78715, 77597, 76489, 75392, 74306, 73230, 72165, 71111, 70067, 69033, 68010, 66997, 65994, 65001, 64019, 63046, 62084, 61132, 60189, 59256, 58333, 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