{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3NZBXWTIKGTSES3AETTI5KBQ6X","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":"3c765817b893839bdb59b5b095587633b8321a9b850f741fa5dbdf993e7b33ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-05-11T06:51:42Z","title_canon_sha256":"0c115d245ef413491f1da85a4ff51df748eb304d6afb2037da73d5345405bd6b"},"schema_version":"1.0","source":{"id":"2105.04811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.04811","created_at":"2026-07-05T02:39:24Z"},{"alias_kind":"arxiv_version","alias_value":"2105.04811v1","created_at":"2026-07-05T02:39:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.04811","created_at":"2026-07-05T02:39:24Z"},{"alias_kind":"pith_short_12","alias_value":"3NZBXWTIKGTS","created_at":"2026-07-05T02:39:24Z"},{"alias_kind":"pith_short_16","alias_value":"3NZBXWTIKGTSES3A","created_at":"2026-07-05T02:39:24Z"},{"alias_kind":"pith_short_8","alias_value":"3NZBXWTI","created_at":"2026-07-05T02:39:24Z"}],"graph_snapshots":[{"event_id":"sha256:54158834a3313dd9f8cb2c194c95f3170a5a674577c15720badc5fc899004a0f","target":"graph","created_at":"2026-07-05T02:39:24Z","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/2105.04811/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus four, five, and six. We find that the only such curves with exceptional rational points are of levels $137$ and $311$. In particular there are no exceptional rational points on those curves of genus five and six. More precisely, we determine the rational points on the curves $X_0^+(N)$ for $N=137,173,199,251,311,157,181,227,263,163,197,211,223,269,271,359$.","authors_text":"Boya Wen, Lea Beneish, Mingjie Chen, Nikola Ad\\v{z}aga, Shiva Chidambaram, Timo Keller, Vishal Arul","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-05-11T06:51:42Z","title":"Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.04811","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":"sha256:532246cbc33370b20d89c4ab61c9ece92d293691e2ec95b41cfcfbd6426dd08f","target":"record","created_at":"2026-07-05T02:39:24Z","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":"3c765817b893839bdb59b5b095587633b8321a9b850f741fa5dbdf993e7b33ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-05-11T06:51:42Z","title_canon_sha256":"0c115d245ef413491f1da85a4ff51df748eb304d6afb2037da73d5345405bd6b"},"schema_version":"1.0","source":{"id":"2105.04811","kind":"arxiv","version":1}},"canonical_sha256":"db721bda6851a7224b6024e68ea830f5f794202a8ac75f2c8c5d82fb48ea7c4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db721bda6851a7224b6024e68ea830f5f794202a8ac75f2c8c5d82fb48ea7c4c","first_computed_at":"2026-07-05T02:39:24.525557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:39:24.525557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZJsr2X52V0ed2JnAAMuwV85ByEuKuDBUtVvwCq0Y1oMb9BXkQC5QRCz5+CjHqtAT60+dinYJBJuGLNUa0iFDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:39:24.526012Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.04811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:532246cbc33370b20d89c4ab61c9ece92d293691e2ec95b41cfcfbd6426dd08f","sha256:54158834a3313dd9f8cb2c194c95f3170a5a674577c15720badc5fc899004a0f"],"state_sha256":"dd9623f65dae9f52651b3b8987a953c6aaba5e24919819039a2a8093d43ba9d1"}