{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:3774ODV73SFCRS45HON3LPMCUX","short_pith_number":"pith:3774ODV7","schema_version":"1.0","canonical_sha256":"dfffc70ebfdc8a28cb9d3b9bb5bd82a5c2fdea66ab054698363e171fb39d3438","source":{"kind":"arxiv","id":"2407.01276","version":3},"attestation_state":"computed","paper":{"title":"The Noether inequality for threefolds and three moduli spaces with minimal volumes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chen Jiang, Meng Chen, Yong Hu","submitted_at":"2024-07-01T13:31:49Z","abstract_excerpt":"We establish the Noether inequality\n  \\[\\textrm{Vol}(X)\\geq \\frac{4}{3}p_g(X)-\\frac{10}{3}\\] for all projective $3$-folds $X$ of general type with geometric genus $5\\leq p_g(X)\\leq 10$ where $\\textrm{Vol}(X)$ is the canonical volume. This result resolves all remaining cases of the Noether inequality for $3$-folds.\n  We further investigate the moduli spaces of canonical $3$-folds with small genera and minimal volumes. For a $3$-fold of general type with geometric genus $2$ and with minimal canonical volume $\\frac{1}{3}$, we prove that its canonical model is a hypersurface of degree $16$ in $\\ma"},"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":"2407.01276","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-07-01T13:31:49Z","cross_cats_sorted":[],"title_canon_sha256":"4e85d100462a86d9485ded716673ad6d94ee2a765a44f98e0e4e75839880740c","abstract_canon_sha256":"064a61780fa16c970c26c0366a68a3cbac3c70898f8b37642aafb31fd547658a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:19.346906Z","signature_b64":"We13y4NjSwmsVcOAM+WNhEaS9TixScsZBsX+XtADVOj0x4/cHVB59v6HHFpjhP/kvsYa89WPT3TjXcoQQuh9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfffc70ebfdc8a28cb9d3b9bb5bd82a5c2fdea66ab054698363e171fb39d3438","last_reissued_at":"2026-07-05T11:58:19.346453Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:19.346453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Noether inequality for threefolds and three moduli spaces with minimal volumes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chen Jiang, Meng Chen, Yong Hu","submitted_at":"2024-07-01T13:31:49Z","abstract_excerpt":"We establish the Noether inequality\n  \\[\\textrm{Vol}(X)\\geq \\frac{4}{3}p_g(X)-\\frac{10}{3}\\] for all projective $3$-folds $X$ of general type with geometric genus $5\\leq p_g(X)\\leq 10$ where $\\textrm{Vol}(X)$ is the canonical volume. This result resolves all remaining cases of the Noether inequality for $3$-folds.\n  We further investigate the moduli spaces of canonical $3$-folds with small genera and minimal volumes. For a $3$-fold of general type with geometric genus $2$ and with minimal canonical volume $\\frac{1}{3}$, we prove that its canonical model is a hypersurface of degree $16$ in $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01276","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.01276/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":"2407.01276","created_at":"2026-07-05T11:58:19.346510+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.01276v3","created_at":"2026-07-05T11:58:19.346510+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01276","created_at":"2026-07-05T11:58:19.346510+00:00"},{"alias_kind":"pith_short_12","alias_value":"3774ODV73SFC","created_at":"2026-07-05T11:58:19.346510+00:00"},{"alias_kind":"pith_short_16","alias_value":"3774ODV73SFCRS45","created_at":"2026-07-05T11:58:19.346510+00:00"},{"alias_kind":"pith_short_8","alias_value":"3774ODV7","created_at":"2026-07-05T11:58:19.346510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.17633","citing_title":"Normal stable degenerations of Noether-Horikawa surfaces","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX","json":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX.json","graph_json":"https://pith.science/api/pith-number/3774ODV73SFCRS45HON3LPMCUX/graph.json","events_json":"https://pith.science/api/pith-number/3774ODV73SFCRS45HON3LPMCUX/events.json","paper":"https://pith.science/paper/3774ODV7"},"agent_actions":{"view_html":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX","download_json":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX.json","view_paper":"https://pith.science/paper/3774ODV7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.01276&json=true","fetch_graph":"https://pith.science/api/pith-number/3774ODV73SFCRS45HON3LPMCUX/graph.json","fetch_events":"https://pith.science/api/pith-number/3774ODV73SFCRS45HON3LPMCUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX/action/storage_attestation","attest_author":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX/action/author_attestation","sign_citation":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX/action/citation_signature","submit_replication":"https://pith.science/pith/3774ODV73SFCRS45HON3LPMCUX/action/replication_record"}},"created_at":"2026-07-05T11:58:19.346510+00:00","updated_at":"2026-07-05T11:58:19.346510+00:00"}