{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QBDEM54C33T47CNXRYRC3HHPYC","short_pith_number":"pith:QBDEM54C","schema_version":"1.0","canonical_sha256":"8046467782dee7cf89b78e222d9cefc0ba4edb2fed6a1af938bfab828fc8d5f4","source":{"kind":"arxiv","id":"1601.00950","version":3},"attestation_state":"computed","paper":{"title":"Odd zeta motive and linear forms in odd zeta values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Cl\\'ement Dupont","submitted_at":"2016-01-05T20:09:06Z","abstract_excerpt":"We study a family of mixed Tate motives over $\\mathbb{Z}$ whose periods are linear forms in the zeta values $\\zeta(n)$. They naturally include the Beukers-Rhin-Viola integrals for $\\zeta(2)$ and the Ball-Rivoal linear forms in odd zeta values. We give a general integral formula for the coefficients of the linear forms and a geometric interpretation of the vanishing of the coefficients of a given parity. The main underlying result is a geometric construction of a minimal ind-object in the category of mixed Tate motives over $\\mathbb{Z}$ which contains all the non-trivial extensions between simp"},"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":"1601.00950","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-05T20:09:06Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"d0dfd46546b9517bef4c111b9afb52d109973abbfd007e47ffe44445fc2cdf80","abstract_canon_sha256":"f71a81599d59d928535653063c72aa8fead07b281b139e91d33d96195e14fc34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:13.446208Z","signature_b64":"5vxBGiZhGxFrFt1Xf7cjU7VMtNzWd00HqCkR+ZTqLxYmvofVYKBqq8KZdVmJqA6t9bOyvnnSwNxgmoI1O/ixDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8046467782dee7cf89b78e222d9cefc0ba4edb2fed6a1af938bfab828fc8d5f4","last_reissued_at":"2026-05-17T23:53:13.445619Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:13.445619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Odd zeta motive and linear forms in odd zeta values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Cl\\'ement Dupont","submitted_at":"2016-01-05T20:09:06Z","abstract_excerpt":"We study a family of mixed Tate motives over $\\mathbb{Z}$ whose periods are linear forms in the zeta values $\\zeta(n)$. They naturally include the Beukers-Rhin-Viola integrals for $\\zeta(2)$ and the Ball-Rivoal linear forms in odd zeta values. We give a general integral formula for the coefficients of the linear forms and a geometric interpretation of the vanishing of the coefficients of a given parity. The main underlying result is a geometric construction of a minimal ind-object in the category of mixed Tate motives over $\\mathbb{Z}$ which contains all the non-trivial extensions between simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00950","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1601.00950","created_at":"2026-05-17T23:53:13.445706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1601.00950v3","created_at":"2026-05-17T23:53:13.445706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00950","created_at":"2026-05-17T23:53:13.445706+00:00"},{"alias_kind":"pith_short_12","alias_value":"QBDEM54C33T4","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QBDEM54C33T47CNX","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QBDEM54C","created_at":"2026-05-18T12:30:39.010887+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/QBDEM54C33T47CNXRYRC3HHPYC","json":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC.json","graph_json":"https://pith.science/api/pith-number/QBDEM54C33T47CNXRYRC3HHPYC/graph.json","events_json":"https://pith.science/api/pith-number/QBDEM54C33T47CNXRYRC3HHPYC/events.json","paper":"https://pith.science/paper/QBDEM54C"},"agent_actions":{"view_html":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC","download_json":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC.json","view_paper":"https://pith.science/paper/QBDEM54C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1601.00950&json=true","fetch_graph":"https://pith.science/api/pith-number/QBDEM54C33T47CNXRYRC3HHPYC/graph.json","fetch_events":"https://pith.science/api/pith-number/QBDEM54C33T47CNXRYRC3HHPYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC/action/storage_attestation","attest_author":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC/action/author_attestation","sign_citation":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC/action/citation_signature","submit_replication":"https://pith.science/pith/QBDEM54C33T47CNXRYRC3HHPYC/action/replication_record"}},"created_at":"2026-05-17T23:53:13.445706+00:00","updated_at":"2026-05-17T23:53:13.445706+00:00"}