{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:B72AZGK5VCG3SFH5P5IAX4HFA6","short_pith_number":"pith:B72AZGK5","schema_version":"1.0","canonical_sha256":"0ff40c995da88db914fd7f500bf0e50783f7f3c2f8cabae11291183c71fd2949","source":{"kind":"arxiv","id":"1404.5026","version":1},"attestation_state":"computed","paper":{"title":"The second Hilbert coefficients and the sectional genera of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kazuho Ozeki","submitted_at":"2014-04-20T07:44:26Z","abstract_excerpt":"This paper gives an upper bound of the second Hilbert coefficients ${\\mathrm{e}}_2(I)$ of $\\mathfrak{m}$-primary ideals $I$ in a Cohen-Macaulay local ring $(A,{\\mathfrak{m}})$ in terms of the sectional genera of $I$."},"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":"1404.5026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-04-20T07:44:26Z","cross_cats_sorted":[],"title_canon_sha256":"4a352c314120884dfeb189dc0fb0089bec46d126ccd47b51bcc8c49e885f83eb","abstract_canon_sha256":"38fcfa8a906e592b741374982377b63e47ffe03733cf558a9ca3b7aaf4718a63"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:52.161976Z","signature_b64":"erpsJLsHFuV7ws9Dvxhahg/jHlb7z4wnEkxa8seE4DPcXUStOwuDE8Snqbo2gy3NmWpN8lWU41aPBaGmrlI6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ff40c995da88db914fd7f500bf0e50783f7f3c2f8cabae11291183c71fd2949","last_reissued_at":"2026-05-18T02:53:52.160984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:52.160984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The second Hilbert coefficients and the sectional genera of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Kazuho Ozeki","submitted_at":"2014-04-20T07:44:26Z","abstract_excerpt":"This paper gives an upper bound of the second Hilbert coefficients ${\\mathrm{e}}_2(I)$ of $\\mathfrak{m}$-primary ideals $I$ in a Cohen-Macaulay local ring $(A,{\\mathfrak{m}})$ in terms of the sectional genera of $I$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5026","kind":"arxiv","version":1},"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":"1404.5026","created_at":"2026-05-18T02:53:52.161149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5026v1","created_at":"2026-05-18T02:53:52.161149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5026","created_at":"2026-05-18T02:53:52.161149+00:00"},{"alias_kind":"pith_short_12","alias_value":"B72AZGK5VCG3","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"B72AZGK5VCG3SFH5","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"B72AZGK5","created_at":"2026-05-18T12:28:22.404517+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/B72AZGK5VCG3SFH5P5IAX4HFA6","json":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6.json","graph_json":"https://pith.science/api/pith-number/B72AZGK5VCG3SFH5P5IAX4HFA6/graph.json","events_json":"https://pith.science/api/pith-number/B72AZGK5VCG3SFH5P5IAX4HFA6/events.json","paper":"https://pith.science/paper/B72AZGK5"},"agent_actions":{"view_html":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6","download_json":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6.json","view_paper":"https://pith.science/paper/B72AZGK5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5026&json=true","fetch_graph":"https://pith.science/api/pith-number/B72AZGK5VCG3SFH5P5IAX4HFA6/graph.json","fetch_events":"https://pith.science/api/pith-number/B72AZGK5VCG3SFH5P5IAX4HFA6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6/action/storage_attestation","attest_author":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6/action/author_attestation","sign_citation":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6/action/citation_signature","submit_replication":"https://pith.science/pith/B72AZGK5VCG3SFH5P5IAX4HFA6/action/replication_record"}},"created_at":"2026-05-18T02:53:52.161149+00:00","updated_at":"2026-05-18T02:53:52.161149+00:00"}