run2_check.py: J = 120, seed = 4242
[R1] Lemma 2.1(b) as a symbolic identity in c_0..c_d, a_0..a_22: 161 pairs (d <= 6, n <= 22), 0 differences; (zf)^(n) = z f^(n) + n f^(n-1) for 1 <= n < 22: 0 differences
[R2] E1 size: J = 120, degrees of g_1..g_24: [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], max degree 1
[R2] E1 size, A-least: (A1), (A2), disjoint blocks: True; n_1..n_8 = [2, 5, 12, 21, 34, 50, 69, 92]; n_J = 23770
[R3] E1 size, A-least: Theorem A, p = z: all 192 non-zero values n a_(n-1) have modulus >= 2: True; monomials c z^d (|c| from 1e-6 to 1.4e5, d = 1..15): |values| >= 2|c|: True; Remark 3.3 (|m a_m| >= 2 at every non-zero a_m, m >= 1): True
[R10] E1 size, A-least: a_(n_j - 1) = 0 for all j <= 120: True; s_(n_j) = g_j(0): True; n <= n_J + d_J = 23771 with ((1+z) f_A)^(n)(0) not in {0} u {|w| >= 2}: 96, all block starts: True; in the disc |w - 1| < 1: 15
[R7] E1 size, A-least: for all 7140 pairs 1 <= j < i <= 120, sum over block/zone i of (|Re a_m| + |Im a_m|) j^(m-n_j)/(m-n_j)! <= 2^-i: True (largest ratio to 2^-i: 0.9636; 0 pairs decided in exact arithmetic)
[R2] E1 size, A-explicit: (A1), (A2), disjoint blocks: True; n_1..n_8 = [2, 8, 19, 36, 58, 86, 119, 158]; n_J = 38878
[R3] E1 size, A-explicit: Theorem A, p = z: all 192 non-zero values n a_(n-1) have modulus >= 2: True; monomials c z^d (|c| from 1e-6 to 1.4e5, d = 1..15): |values| >= 2|c|: True; Remark 3.3 (|m a_m| >= 2 at every non-zero a_m, m >= 1): True
[R2] E1 size, B-least: conditions of the layout and (L1), (L2): True; n_1..n_8 = [3, 11, 25, 45, 72, 106, 146, 193]; n_J = 54162
[R4] E1 size, B-least: p = z: d = 1, S = 1, c_min = 1, j_0 = 6, n_* = 100; 7432 non-zero s_n for n_* <= n <= 54164 (Case R 7245, Case K 187, of these i* = d: 187; windows n_j <= n < n_j + d: 115, in Case R: 115); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 49
[R4] E1 size, B-least: p = 1 - z: d = 1, S = 2, c_min = 1, j_0 = 8, n_* = 185; 7530 non-zero s_n for n_* <= n <= 54164 (Case R 7345, Case K 185, of these i* = d: 185; windows n_j <= n < n_j + d: 113, in Case R: 113); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 68.6
[R4] E1 size, B-least: p = 1/2 + (3+4i)/5 z^2: d = 2, S = 3/2, c_min = 1/2, j_0 = 14, n_* = 610; 7557 non-zero s_n for n_* <= n <= 54165 (Case R 7383, Case K 174, of these i* = d: 174; windows n_j <= n < n_j + d: 214, in Case R: 214); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1.5e+05
[R4] E1 size, B-least: p = 2 - 3z + z^2 - (5+12i)/13 z^3: d = 3, S = 7, c_min = 1, j_0 = 18, n_* = 1036; 7582 non-zero s_n for n_* <= n <= 54166 (Case R 7416, Case K 166, of these i* = d: 166; windows n_j <= n < n_j + d: 309, in Case R: 309); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1.31e+08
[R4] E1 size, B-least: p = 1/4 + z^4/4: d = 4, S = 1/2, c_min = 1/4, j_0 = 20, n_* = 1293; 7636 non-zero s_n for n_* <= n <= 54167 (Case R 7474, Case K 162, of these i* = d: 162; windows n_j <= n < n_j + d: 404, in Case R: 404); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 2.99e+11
[R4] E1 size, B-least: p = 1/10 + z: d = 1, S = 11/10, c_min = 1/10, j_0 = 62, n_* = 13729; 5506 non-zero s_n for n_* <= n <= 54164 (Case R 5428, Case K 78, of these i* = d: 78; windows n_j <= n < n_j + d: 59, in Case R: 59); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 4.45e+03
[R4] E1 size, B-least: p = -z + z^2 - z^3 + z^4 - z^5: d = 5, S = 5, c_min = 1, j_0 = 14, n_* = 610; 7771 non-zero s_n for n_* <= n <= 54168 (Case R 7597, Case K 174, of these i* = d: 174; windows n_j <= n < n_j + d: 535, in Case R: 535); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1.96e+13
[R4] E1 size, B-least: p = 2 + (8+15i)/17 z^7: d = 7, S = 3, c_min = 1, j_0 = 10, n_* = 298; 8174 non-zero s_n for n_* <= n <= 54170 (Case R 7992, Case K 182, of these i* = d: 182; windows n_j <= n < n_j + d: 777, in Case R: 777); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1.28e+05
[R4] E1 size, B-least: p = 1000 z: d = 1, S = 1000, c_min = 1000, j_0 = 3, n_* = 22; 7447 non-zero s_n for n_* <= n <= 54164 (Case R 7257, Case K 190, of these i* = d: 190; windows n_j <= n < n_j + d: 118, in Case R: 118); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 36.7
[R4] E1 size, B-least: p = 7/3 + 7/3 z^2: d = 2, S = 14/3, c_min = 7/3, j_0 = 6, n_* = 100; 7662 non-zero s_n for n_* <= n <= 54165 (Case R 7475, Case K 187, of these i* = d: 187; windows n_j <= n < n_j + d: 230, in Case R: 230); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 5.72e+03
[R4] E1 size, B-least: p = (3-4i)/5 + z^12: d = 12, S = 2, c_min = 1, j_0 = 12, n_* = 439; 8680 non-zero s_n for n_* <= n <= 54175 (Case R 8502, Case K 178, of these i* = d: 178; windows n_j <= n < n_j + d: 1308, in Case R: 1308); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 12
[R4] E1 size, B-least: p = 1/3 - z/3 + z^2/3: d = 2, S = 1, c_min = 1/3, j_0 = 18, n_* = 1036; 7479 non-zero s_n for n_* <= n <= 54165 (Case R 7313, Case K 166, of these i* = d: 166; windows n_j <= n < n_j + d: 206, in Case R: 206); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1.24e+05
[R4] E1 size, B-least: p = i z^3: d = 3, S = 1, c_min = 1, j_0 = 6, n_* = 100; 7432 non-zero s_n for n_* <= n <= 54166 (Case R 7245, Case K 187, of these i* = d: 187; windows n_j <= n < n_j + d: 345, in Case R: 345); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 5.94e+05
[R4] E1 size, B-least: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 97888 non-zero s_n at n >= n_* (Case R 95672, Case K 2216; i* = d in 2216 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 12
[R7] E1 size, B-least: for all 7140 pairs 1 <= j < i <= 120, sum over block/zone i of (|Re a_m| + |Im a_m|) j^(m-n_j)/(m-n_j)! <= 2^-i: True (largest ratio to 2^-i: 0.1824; 0 pairs decided in exact arithmetic)
[R8] E1 size, B-least: p = (1+i) + z: S = 2.4142135623730950488016887242096980785696718753769, c_min = 1.0, j_0 = 9, n_* = 238: 7520 non-zero s_n, |s_n| >= S+2 proved by interval arithmetic for 7520, violated 0, undecided 0
[R8] E1 size, B-least: p = 1 + (1+2i) z^2: S = 3.2360679774997896964091736687312762354406183596115, c_min = 1.0, j_0 = 11, n_* = 365: 7605 non-zero s_n, |s_n| >= S+2 proved by interval arithmetic for 7605, violated 0, undecided 0
[R8] E1 size, B-least: p = (2+i)/3 + (1-i) z + z^3: S = 3.1595695548730249476047466137867901570498779952475, c_min = 0.74535599249992989880305788957709207848020611987051, j_0 = 14, n_* = 610: 7664 non-zero s_n, |s_n| >= S+2 proved by interval arithmetic for 7664, violated 0, undecided 0
[R8] E1 size, B-least: p = i/7 + (1+i)/7 z: S = 0.34488765176758500697166981774424258265281026791099, c_min = 0.14285714285714285714285714285714285714285714285714, j_0 = 33, n_* = 3691: 6956 non-zero s_n, |s_n| >= S+2 proved by interval arithmetic for 6956, violated 0, undecided 0
[R2] E1 size, B-explicit: conditions of the layout and (L1), (L2): True; n_1..n_8 = [5, 15, 32, 55, 85, 123, 167, 220]; n_J = 67560
[R4] E1 size, B-explicit: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 97888 non-zero s_n at n >= n_* (Case R 95672, Case K 2216; i* = d in 2216 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 12
[R2] E1 size, B-min: conditions of the layout and (L1), (L2): True; n_1..n_8 = [3, 8, 15, 24, 35, 48, 63, 80]; n_J = 14711
[R4] E1 size, B-min: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 97888 non-zero s_n at n >= n_* (Case R 95672, Case K 2216; i* = d in 2216 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 12
[R2] E1 size, B-weak: conditions of the layout and (L1), (L2): True; n_1..n_8 = [3, 8, 15, 24, 35, 48, 63, 80]; n_J = 14711
[R4] E1 size, B-weak: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 97888 non-zero s_n at n >= n_* (Case R 95672, Case K 2216; i* = d in 2216 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 12
[R6] E1 size, mutation B-noramp: 13 polynomials, 4214 non-zero s_n at n >= n_*: |s_n| < S+2 in 1247 windows (with m* in a ramp: 0; with m* in a block: 1247, of which i* = 0: 1247); 0 < |s_n| < 2 in 759
[R6] E1 size, mutation B-tinyramp: 13 polynomials, 97888 non-zero s_n at n >= n_*: |s_n| < S+2 in 33672 windows (with m* in a ramp: 33672; with m* in a block: 0, of which i* = 0: 0); 0 < |s_n| < 2 in 26422
[R6] E1 size, mutation B-noB1: 13 polynomials, 97888 non-zero s_n at n >= n_*: |s_n| < S+2 in 0 windows (with m* in a ramp: 0; with m* in a block: 0, of which i* = 0: 0); 0 < |s_n| < 2 in 0
[R2] E2 adversarial: J = 100, degrees of g_1..g_24: [4, 0, 7, 0, 14, 2, 7, 0, 0, 2, 12, 14, 0, 14, 3, 4, 12, 5, 5, 0, 1, 9, 1, 0], max degree 14
[R2] E2 adversarial, A-least: (A1), (A2), disjoint blocks: True; n_1..n_8 = [5417, 5422, 10794, 226667, 226700, 226725, 226757, 226788]; n_J = 12005318
[R3] E2 adversarial, A-least: Theorem A, p = z: all 589 non-zero values n a_(n-1) have modulus >= 2: True; monomials c z^d (|c| from 1e-6 to 1.4e5, d = 1..15): |values| >= 2|c|: True; Remark 3.3 (|m a_m| >= 2 at every non-zero a_m, m >= 1): True
[R2] E2 adversarial, A-explicit: (A1), (A2), disjoint blocks: True; n_1..n_8 = [5417, 5423, 10794, 226667, 226723, 226751, 226784, 226823]; n_J = 12008419
[R3] E2 adversarial, A-explicit: Theorem A, p = z: all 589 non-zero values n a_(n-1) have modulus >= 2: True; monomials c z^d (|c| from 1e-6 to 1.4e5, d = 1..15): |values| >= 2|c|: True; Remark 3.3 (|m a_m| >= 2 at every non-zero a_m, m >= 1): True
[R2] E2 adversarial, B-least: conditions of the layout and (L1), (L2): True; n_1..n_8 = [1547619049, 1547619058, 10793650797, 10793650817, 134719200000000005, 134719200000000045, 134719200000000094, 134719200000000148]; n_J = 2196892938240000000037204
[R4] E2 adversarial, B-least: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 72732 non-zero s_n at n >= n_* (Case R 66182, Case K 6550; i* = d in 6550 Case-K windows; windows n_j <= n < n_j + d: 3853, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1669
[R2] E2 adversarial, B-explicit: conditions of the layout and (L1), (L2): True; n_1..n_8 = [1547619049, 1547619059, 10793650797, 10793650820, 134719200000000005, 134719200000000058, 134719200000000126, 134719200000000195]; n_J = 2196892938240000000046613
[R4] E2 adversarial, B-explicit: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 72732 non-zero s_n at n >= n_* (Case R 66182, Case K 6550; i* = d in 6550 Case-K windows; windows n_j <= n < n_j + d: 3853, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1669
[R2] E2 adversarial, B-min: conditions of the layout and (L1), (L2): True; n_1..n_8 = [1547619049, 1547619058, 10793650797, 10793650813, 134719200000000005, 134719200000000032, 134719200000000049, 134719200000000073]; n_J = 2196892938240000000010476
[R4] E2 adversarial, B-min: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 72732 non-zero s_n at n >= n_* (Case R 66182, Case K 6550; i* = d in 6550 Case-K windows; windows n_j <= n < n_j + d: 3853, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1669
[R2] E2 adversarial, B-weak: conditions of the layout and (L1), (L2): True; n_1..n_8 = [1547619048, 1547619057, 10793650794, 10793650810, 134719200000000000, 134719200000000027, 134719200000000044, 134719200000000068]; n_J = 2196892938240000000010464
[R4] E2 adversarial, B-weak: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 72732 non-zero s_n at n >= n_* (Case R 66182, Case K 6550; i* = d in 6550 Case-K windows; windows n_j <= n < n_j + d: 3853, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 1669
[R6] E2 adversarial, mutation B-noramp: 13 polynomials, 8946 non-zero s_n at n >= n_*: |s_n| < S+2 in 1067 windows (with m* in a ramp: 0; with m* in a block: 1067, of which i* = 0: 1067); 0 < |s_n| < 2 in 899
[R6] E2 adversarial, mutation B-tinyramp: 13 polynomials, 72732 non-zero s_n at n >= n_*: |s_n| < S+2 in 2691 windows (with m* in a ramp: 2691; with m* in a block: 0, of which i* = 0: 0); 0 < |s_n| < 2 in 2691
[R6] E2 adversarial, mutation B-noB1: 13 polynomials, 72732 non-zero s_n at n >= n_*: |s_n| < S+2 in 196 windows (with m* in a ramp: 0; with m* in a block: 196, of which i* = 0: 0); 0 < |s_n| < 2 in 125
[R2] E3 v2: J = 120, degrees of g_1..g_24: [7, 7, 7, 12, 7, 7, 7, 10, 7, 7, 7, 12, 7, 7, 7, 0, 7, 7, 7, 12, 7, 7, 7, 10], max degree 12
[R2] E3 v2, A-least: (A1), (A2), disjoint blocks: True; n_1..n_8 = [2666667, 2666680, 2666689, 2666714, 2666730, 2666759, 2666782, 6000000]; n_J = 6024635
[R3] E3 v2, A-least: Theorem A, p = z: all 1013 non-zero values n a_(n-1) have modulus >= 2: True; monomials c z^d (|c| from 1e-6 to 1.4e5, d = 1..15): |values| >= 2|c|: True; Remark 3.3 (|m a_m| >= 2 at every non-zero a_m, m >= 1): True
[R2] E3 v2, A-explicit: (A1), (A2), disjoint blocks: True; n_1..n_8 = [2666667, 2666697, 2666708, 2666751, 2666773, 2666807, 2666840, 6000000]; n_J = 6038720
[R3] E3 v2, A-explicit: Theorem A, p = z: all 1013 non-zero values n a_(n-1) have modulus >= 2: True; monomials c z^d (|c| from 1e-6 to 1.4e5, d = 1..15): |values| >= 2|c|: True; Remark 3.3 (|m a_m| >= 2 at every non-zero a_m, m >= 1): True
[R2] E3 v2, B-least: conditions of the layout and (L1), (L2): True; n_1..n_8 = [12728472, 30000002, 38185415, 282854901960789, 282854901960818, 282854901960861, 282854901960903, 551577600000008]; n_J = 8273664000000120
[R4] E3 v2, B-least: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 107258 non-zero s_n at n >= n_* (Case R 95672, Case K 11586; i* = d in 11586 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 28.58
[R2] E3 v2, B-explicit: conditions of the layout and (L1), (L2): True; n_1..n_8 = [12728472, 30000002, 38185415, 282854901960789, 282854901960823, 282854901960885, 282854901960933, 551577600000008]; n_J = 8273664000000120
[R4] E3 v2, B-explicit: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 107258 non-zero s_n at n >= n_* (Case R 95672, Case K 11586; i* = d in 11586 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 28.58
[R2] E3 v2, B-min: conditions of the layout and (L1), (L2): True; n_1..n_8 = [12728472, 30000002, 38185415, 282854901960789, 282854901960812, 282854901960832, 282854901960854, 551577600000008]; n_J = 8273664000000120
[R4] E3 v2, B-min: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 107258 non-zero s_n at n >= n_* (Case R 95672, Case K 11586; i* = d in 11586 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 28.58
[R2] E3 v2, B-weak: conditions of the layout and (L1), (L2): True; n_1..n_8 = [12728471, 30000000, 38185412, 282854901960785, 282854901960808, 282854901960828, 282854901960850, 551577600000000]; n_J = 8273664000000000
[R4] E3 v2, B-weak: Proposition 4.2 for 13 polynomials (j_0 from 3 to 62): 107258 non-zero s_n at n >= n_* (Case R 95672, Case K 11586; i* = d in 11586 Case-K windows; windows n_j <= n < n_j + d: 4733, all in Case R: True); |s_n| < S+2: 0; proof chain broken: 0; min |s_n|/(S+2) = 28.58
[R6] E3 v2, mutation B-noramp: 13 polynomials, 15163 non-zero s_n at n >= n_*: |s_n| < S+2 in 1855 windows (with m* in a ramp: 0; with m* in a block: 1855, of which i* = 0: 1855); 0 < |s_n| < 2 in 1506
[R6] E3 v2, mutation B-tinyramp: 13 polynomials, 107258 non-zero s_n at n >= n_*: |s_n| < S+2 in 3311 windows (with m* in a ramp: 3311; with m* in a block: 0, of which i* = 0: 0); 0 < |s_n| < 2 in 3311
[R6] E3 v2, mutation B-noB1: 13 polynomials, 107258 non-zero s_n at n >= n_*: |s_n| < S+2 in 513 windows (with m* in a ramp: 0; with m* in a block: 513, of which i* = 0: 0); 0 < |s_n| < 2 in 338
[R9] p = 3 - 3z + z^2/10: j_0 = 162; zones j = j_0, j_0+1, 2j_0 (4 random blocks each, degrees 0..7, moduli 1e-4..1e4, n_j = ceil(j M_j/delta_j) + offset): 2675 windows, 0 with |s_n| < S+2; min |s_n|/(S+2) = 2.006e+04
[R9] p = (1 + z + z^2 + z^3)/100: j_0 = 408; zones j = j_0, j_0+1, 2j_0 (4 random blocks each, degrees 0..9, moduli 1e-4..1e4, n_j = ceil(j M_j/delta_j) + offset): 3616 windows, 0 with |s_n| < S+2; min |s_n|/(S+2) = 6.501e+13
[R9] p = i/2 + 50 z^6: j_0 = 210; zones j = j_0, j_0+1, 2j_0 (4 random blocks each, degrees 0..15, moduli 1e-4..1e4, n_j = ceil(j M_j/delta_j) + offset): 3551 windows, 0 with |s_n| < S+2; min |s_n|/(S+2) = 2.854e+36
[R9] p = 1 + (3+4i)/500 z^5: j_0 = 602; zones j = j_0, j_0+1, 2j_0 (4 random blocks each, degrees 0..13, moduli 1e-4..1e4, n_j = ceil(j M_j/delta_j) + offset): 5242 windows, 0 with |s_n| < S+2; min |s_n|/(S+2) = 9.836e+29
[R9] p = 5 - 7z + 9z^2 - 11z^3 + z^4/20: j_0 = 1362; zones j = j_0, j_0+1, 2j_0 (4 random blocks each, degrees 0..11, moduli 1e-4..1e4, n_j = ceil(j M_j/delta_j) + offset): 848 windows, 0 with |s_n| < S+2; min |s_n|/(S+2) = 3.479e+19 (for j > 700: all windows within 4d+8 of the block and 40 random deeper ones)
[R9] p = 1 + z/1000: j_0 = 6002; zones j = j_0, j_0+1, 2j_0 (2 random blocks each, degrees 0..5, moduli 1e-4..1e4, n_j = ceil(j M_j/delta_j) + offset): 336 windows, 0 with |s_n| < S+2; min |s_n|/(S+2) = 2.5 (for j > 700: all windows within 4d+8 of the block and 40 random deeper ones)
[R9] total: 16268 windows, 0 with |s_n| < S+2
checks: 202, failed: 0; elapsed 102.1 s
ALL CHECKS PASSED
