{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FTAFGPOAFGVYM3XQSI2JFFKFK3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"613b401d1c043d339ecc91baf93841c2e59d74edf2c3c2c653e4157701d829ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-06T06:56:14Z","title_canon_sha256":"0ede7462f44f08c80062d56db5c40afdc2a6b23eca67c3b513797e31202601ca"},"schema_version":"1.0","source":{"id":"2605.04551","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.04551","created_at":"2026-05-27T01:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.04551v2","created_at":"2026-05-27T01:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.04551","created_at":"2026-05-27T01:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"FTAFGPOAFGVY","created_at":"2026-05-27T01:04:58Z"},{"alias_kind":"pith_short_16","alias_value":"FTAFGPOAFGVYM3XQ","created_at":"2026-05-27T01:04:58Z"},{"alias_kind":"pith_short_8","alias_value":"FTAFGPOA","created_at":"2026-05-27T01:04:58Z"}],"graph_snapshots":[{"event_id":"sha256:ed15e5c213699c35a1eaddaa40ea656540fab3c7f891406dc372af189a9c58bc","target":"graph","created_at":"2026-05-27T01:04:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We derive a super-polynomial upper bound on the failure probability; its convergence, together with the Borel-Cantelli lemma, provides heuristic evidence that counterexamples, if any exist, form a finite set."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the super-polynomial upper bound on failure probability derived from the FCT framework is tight enough and that the failure events across primes satisfy the conditions needed for the Borel-Cantelli lemma to conclude finiteness."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A new ceiling continued fraction method finds no counterexamples in searches over 10^9 primes near 10^17 and 10^52 plus 10^7 near 10^131, and derives a super-polynomial failure probability bound whose convergence with the Borel-Cantelli lemma heuristically implies only finitely many counterexamples,"},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A ceiling continued fraction approach provides heuristic evidence that the Erdős-Straus conjecture has only finitely many counterexamples."}],"snapshot_sha256":"7ff0940faec8ceb13ee2ffdcf0a6d1edee8c977a8cf6e624a806ac1b3534fdce"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T11:40:16.025766Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:20.135323Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T14:20:24.898780Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.04551/integrity.json","findings":[],"snapshot_sha256":"8f673fe68a97fcb5314e0c7f4e710ba85f6d2a3b784f692b9980b69a501da77c","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the Ceiling Continued Fractions (FCT) framework for constructing three-term Egyptian fraction representations in the Erd\\H{o}s-Straus conjecture. The approach exploits divisor structures of shifted integers p+i rather than congruence-based techniques. We derive a super-polynomial upper bound on the failure probability; its convergence, together with the Borel-Cantelli lemma, provides heuristic evidence that counterexamples, if any exist, form a finite set. Computational tests on 10^9 primes in ranges around 10^17, 10^52, and 10^131, show no counterexamples with very small search d","authors_text":"Andres Ventas","cross_cats":[],"headline":"A ceiling continued fraction approach provides heuristic evidence that the Erdős-Straus conjecture has only finitely many counterexamples.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-06T06:56:14Z","title":"A Ceiling Continued Fraction Approach to the Erd\\H{o}s-Straus Conjecture: Heuristic finiteness of counterexamples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.04551","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-08T15:56:37.095426Z","id":"310e7fc7-91f3-4d0a-b923-cb1f8a0f9717","model_set":{"reader":"grok-4.3"},"one_line_summary":"A new ceiling continued fraction method finds no counterexamples in searches over 10^9 primes near 10^17 and 10^52 plus 10^7 near 10^131, and derives a super-polynomial failure probability bound whose convergence with the Borel-Cantelli lemma heuristically implies only finitely many counterexamples,","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A ceiling continued fraction approach provides heuristic evidence that the Erdős-Straus conjecture has only finitely many counterexamples.","strongest_claim":"We derive a super-polynomial upper bound on the failure probability; its convergence, together with the Borel-Cantelli lemma, provides heuristic evidence that counterexamples, if any exist, form a finite set.","weakest_assumption":"That the super-polynomial upper bound on failure probability derived from the FCT framework is tight enough and that the failure events across primes satisfy the conditions needed for the Borel-Cantelli lemma to conclude finiteness."}},"verdict_id":"310e7fc7-91f3-4d0a-b923-cb1f8a0f9717"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c8eed752ab0bf37bdb07198c79507b631d68db9c750fe490aeff23b72a70f0c9","target":"record","created_at":"2026-05-27T01:04:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"613b401d1c043d339ecc91baf93841c2e59d74edf2c3c2c653e4157701d829ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-06T06:56:14Z","title_canon_sha256":"0ede7462f44f08c80062d56db5c40afdc2a6b23eca67c3b513797e31202601ca"},"schema_version":"1.0","source":{"id":"2605.04551","kind":"arxiv","version":2}},"canonical_sha256":"2cc0533dc029ab866ef0923492954556ff12b3e4648488b42bf299f3f66bb2d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cc0533dc029ab866ef0923492954556ff12b3e4648488b42bf299f3f66bb2d9","first_computed_at":"2026-05-27T01:04:58.697326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:04:58.697326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uUpngwxAkd48gEtd8WGfIR0p5Xhq4e0/UAhNJ4ScrFrRfjgqya3T1944OsJC6DtvZ/nShoJHqPS8PReBnsq6DQ==","signature_status":"signed_v1","signed_at":"2026-05-27T01:04:58.698137Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.04551","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8eed752ab0bf37bdb07198c79507b631d68db9c750fe490aeff23b72a70f0c9","sha256:ed15e5c213699c35a1eaddaa40ea656540fab3c7f891406dc372af189a9c58bc"],"state_sha256":"3697b01ef85717178e991ae6c31caf218dac4b7ba339064aeea2f8c457070e35"}