{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YUTUJG6C373CQJ42FOPXFLFY7F","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":"de9ceeeaa8b6d8eb90b0bfca93da656e86ce1b10a090c7058021edb0f2f8e024","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-19T06:17:20Z","title_canon_sha256":"53d045305609f92b7ba2a2fa5d088c1b782a61ddbf163a8850928ac1c0273a11"},"schema_version":"1.0","source":{"id":"2507.02885","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.02885","created_at":"2026-07-05T11:31:48Z"},{"alias_kind":"arxiv_version","alias_value":"2507.02885v1","created_at":"2026-07-05T11:31:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02885","created_at":"2026-07-05T11:31:48Z"},{"alias_kind":"pith_short_12","alias_value":"YUTUJG6C373C","created_at":"2026-07-05T11:31:48Z"},{"alias_kind":"pith_short_16","alias_value":"YUTUJG6C373CQJ42","created_at":"2026-07-05T11:31:48Z"},{"alias_kind":"pith_short_8","alias_value":"YUTUJG6C","created_at":"2026-07-05T11:31:48Z"}],"graph_snapshots":[{"event_id":"sha256:77ca14716cfd6ad585959c35d962835311b6355e1dcf3323919d2427a7e86f70","target":"graph","created_at":"2026-07-05T11:31:48Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.02885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $abc$ conjecture states that there are only finitely many triples of coprime positive integers $(a,b,c)$ such that $a+b=c$ and $\\operatorname{rad}(abc) < c^{1-\\epsilon}$ for any $\\epsilon > 0$. Using the optimized methods in a recent work of Browning, Lichtman and Ter\\\"av\\\"ainen, we showed that the number of those triples with $c \\leqslant X$ is $O\\left(X^{56/85+\\varepsilon}\\right)$ for any $\\varepsilon > 0$, where $\\frac{56}{85} \\approx 0.658824$. This constitutes an improvement of the previous bound $O\\left(X^{33/50}\\right)$.","authors_text":"Runbo Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-19T06:17:20Z","title":"On the exceptional set in the $abc$ conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02885","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ce70410a125115d1ebd8acb2d4ee2670cbb5502daf0951b4896c91ea21b0b1a1","target":"record","created_at":"2026-07-05T11:31:48Z","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":"de9ceeeaa8b6d8eb90b0bfca93da656e86ce1b10a090c7058021edb0f2f8e024","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-19T06:17:20Z","title_canon_sha256":"53d045305609f92b7ba2a2fa5d088c1b782a61ddbf163a8850928ac1c0273a11"},"schema_version":"1.0","source":{"id":"2507.02885","kind":"arxiv","version":1}},"canonical_sha256":"c527449bc2dff628279a2b9f72acb8f972aa2266fcb25606d15a958127dbd32f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c527449bc2dff628279a2b9f72acb8f972aa2266fcb25606d15a958127dbd32f","first_computed_at":"2026-07-05T11:31:48.177567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:48.177567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rAqCGCYRpPW40234TC3T8kmBG89Ta9vFrw7P9G/0i4ApMUwT/p8h4oUNVivvjyeOWRXF8HosEG/GmkdPcTE1Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:48.177979Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.02885","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce70410a125115d1ebd8acb2d4ee2670cbb5502daf0951b4896c91ea21b0b1a1","sha256:77ca14716cfd6ad585959c35d962835311b6355e1dcf3323919d2427a7e86f70"],"state_sha256":"fde92987fbc19a150391d50288b26e015913d3dfaf1e8f0f15b1165d5a5f5744"}