{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:G3RXHKBECOLDOVY2HGGQMZ55TK","short_pith_number":"pith:G3RXHKBE","schema_version":"1.0","canonical_sha256":"36e373a824139637571a398d0667bd9a8ee32174ceaee498d9af90b09c8a7ad6","source":{"kind":"arxiv","id":"2501.05321","version":2},"attestation_state":"computed","paper":{"title":"A note on the number of irrational odd zeta values, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Li Lai","submitted_at":"2025-01-09T15:44:37Z","abstract_excerpt":"We prove that there are at least $1.284 \\cdot \\sqrt{s/\\log s}$ irrational numbers among $\\zeta(3)$, $\\zeta(5)$, $\\zeta(7)$, $\\ldots$, $\\zeta(s-1)$ for any sufficiently large even integer $s$. This result improves upon the previous finding by a constant factor. The proof combines the elimination technique of Fischler-Sprang-Zudilin (2019) with the $\\Phi_n$ factor method of Zudilin (2001)."},"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":"2501.05321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-01-09T15:44:37Z","cross_cats_sorted":[],"title_canon_sha256":"f3d09a8669c50c96a2a1fa6afa7f37bba66cd9393a18bea151a5569cef305c15","abstract_canon_sha256":"f34e61208a95a8c0bc81eac545ae24f446c41a4c1ff7f13e667d276796d87e9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:59.598138Z","signature_b64":"cNZXhWwPUqBj5C5bXiSiRU0pMqavDA/NTY6NH9WdRKmdemlOAve/aimeLol28CPGxrWh3bOPF+vxIhFS5WXbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36e373a824139637571a398d0667bd9a8ee32174ceaee498d9af90b09c8a7ad6","last_reissued_at":"2026-07-05T09:59:59.597733Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:59.597733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the number of irrational odd zeta values, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Li Lai","submitted_at":"2025-01-09T15:44:37Z","abstract_excerpt":"We prove that there are at least $1.284 \\cdot \\sqrt{s/\\log s}$ irrational numbers among $\\zeta(3)$, $\\zeta(5)$, $\\zeta(7)$, $\\ldots$, $\\zeta(s-1)$ for any sufficiently large even integer $s$. This result improves upon the previous finding by a constant factor. The proof combines the elimination technique of Fischler-Sprang-Zudilin (2019) with the $\\Phi_n$ factor method of Zudilin (2001)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.05321","kind":"arxiv","version":2},"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/2501.05321/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":"2501.05321","created_at":"2026-07-05T09:59:59.597786+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.05321v2","created_at":"2026-07-05T09:59:59.597786+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.05321","created_at":"2026-07-05T09:59:59.597786+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3RXHKBECOLD","created_at":"2026-07-05T09:59:59.597786+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3RXHKBECOLDOVY2","created_at":"2026-07-05T09:59:59.597786+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3RXHKBE","created_at":"2026-07-05T09:59:59.597786+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.23088","citing_title":"On the irrationality of certain $p$-adic zeta values","ref_index":14,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK","json":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK.json","graph_json":"https://pith.science/api/pith-number/G3RXHKBECOLDOVY2HGGQMZ55TK/graph.json","events_json":"https://pith.science/api/pith-number/G3RXHKBECOLDOVY2HGGQMZ55TK/events.json","paper":"https://pith.science/paper/G3RXHKBE"},"agent_actions":{"view_html":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK","download_json":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK.json","view_paper":"https://pith.science/paper/G3RXHKBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.05321&json=true","fetch_graph":"https://pith.science/api/pith-number/G3RXHKBECOLDOVY2HGGQMZ55TK/graph.json","fetch_events":"https://pith.science/api/pith-number/G3RXHKBECOLDOVY2HGGQMZ55TK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK/action/storage_attestation","attest_author":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK/action/author_attestation","sign_citation":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK/action/citation_signature","submit_replication":"https://pith.science/pith/G3RXHKBECOLDOVY2HGGQMZ55TK/action/replication_record"}},"created_at":"2026-07-05T09:59:59.597786+00:00","updated_at":"2026-07-05T09:59:59.597786+00:00"}