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These appear to be the first proved and reasonable irrationality measures for gamma quotients."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2510.00215","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-09-30T19:45:28Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"e8f605825096bab955e9186c6d0b617ab09cbb8c79710afa1b9e299fcacc6827","abstract_canon_sha256":"801849dd02bf25f5ae5cc0cc71d8464f533d7cecdf9872423ada59810acda7b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:20:46.413366Z","signature_b64":"y2kT31unyPujNM4hMyb6QhlAlD0jNPxpanhRKPuCBVXMqltdJeoiIjmV7N5bu3c77i1upZdev54tyOCVemvOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5837feb24b84a38b756c2cdb3196f27a212a77ad206453f5bcef686c19ec61c2","last_reissued_at":"2026-07-14T01:20:46.412466Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:20:46.412466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Henri Cohen, Wadim Zudilin","submitted_at":"2025-09-30T19:45:28Z","abstract_excerpt":"We give 39 rapidly convergent continued fractions for Chowla--Selberg gamma quotients, and deduce good irrationality measures for 20 of them, including for $\\operatorname{CS}(-3)=(\\Gamma(1/3)/\\Gamma(2/3))^3$, for $a^{1/4}\\operatorname{CS}(-4)=a^{1/4}(\\Gamma(1/4)/\\Gamma(3/4))^2$ with $a=12$ and $a=1/5$, and for $\\operatorname{CS}(-7)=\\Gamma(1/7)\\Gamma(2/7)\\Gamma(4/7)/(\\Gamma(3/7)\\Gamma(5/7)\\Gamma(6/7))$. These appear to be the first proved and reasonable irrationality measures for gamma quotients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00215","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.00215/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2510.00215","created_at":"2026-07-14T01:20:46.412889+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.00215v4","created_at":"2026-07-14T01:20:46.412889+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.00215","created_at":"2026-07-14T01:20:46.412889+00:00"},{"alias_kind":"pith_short_12","alias_value":"LA375MSLQSRY","created_at":"2026-07-14T01:20:46.412889+00:00"},{"alias_kind":"pith_short_16","alias_value":"LA375MSLQSRYW5LM","created_at":"2026-07-14T01:20:46.412889+00:00"},{"alias_kind":"pith_short_8","alias_value":"LA375MSL","created_at":"2026-07-14T01:20:46.412889+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI","json":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI.json","graph_json":"https://pith.science/api/pith-number/LA375MSLQSRYW5LMFTNTDFXSPI/graph.json","events_json":"https://pith.science/api/pith-number/LA375MSLQSRYW5LMFTNTDFXSPI/events.json","paper":"https://pith.science/paper/LA375MSL"},"agent_actions":{"view_html":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI","download_json":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI.json","view_paper":"https://pith.science/paper/LA375MSL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.00215&json=true","fetch_graph":"https://pith.science/api/pith-number/LA375MSLQSRYW5LMFTNTDFXSPI/graph.json","fetch_events":"https://pith.science/api/pith-number/LA375MSLQSRYW5LMFTNTDFXSPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI/action/storage_attestation","attest_author":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI/action/author_attestation","sign_citation":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI/action/citation_signature","submit_replication":"https://pith.science/pith/LA375MSLQSRYW5LMFTNTDFXSPI/action/replication_record"}},"created_at":"2026-07-14T01:20:46.412889+00:00","updated_at":"2026-07-14T01:20:46.412889+00:00"}