{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:VN34RYDRGTPC2NCFQ7EKDF3DQP","short_pith_number":"pith:VN34RYDR","schema_version":"1.0","canonical_sha256":"ab77c8e07134de2d344587c8a1976383c0f307d861586933b7d22173f5675b9e","source":{"kind":"arxiv","id":"2502.19419","version":1},"attestation_state":"computed","paper":{"title":"A Supplement to the anticanonical Volumes of weak $\\mathbb{Q}$-Fano threefolds of Picard rank two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ching-Jui Lai, Tsung-Ju Lee","submitted_at":"2025-01-23T09:18:56Z","abstract_excerpt":"We show that for a weak $\\mathbb{Q}$-Fano threefold $X$ ($\\mathbb{Q}$-factorial with terminal singularities and $-K_X$ is nef and big) of Picard rank $\\rho(X)\\leq 2$, either $-K_X^3\\leq 64$ or $-K_X^3=72$ and $X=\\mathbb{P}_{\\mathbb{P}^2}(\\mathcal{O}_{\\mathbb{P}^2}\\oplus\\mathcal{O}_{\\mathbb{P}^2}(3))$. This is supplementary to the previous work in arXiv:2501.12555."},"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":"2502.19419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-01-23T09:18:56Z","cross_cats_sorted":[],"title_canon_sha256":"248a61a40fec0370b7efe874600e1bb1aa42a422845231d44d41b8ebb7b7d67c","abstract_canon_sha256":"919ea6581e928bf29ed5332fdc0f7b53b68f11780d5db0bfb0d4fe81ab6f272d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:45.906889Z","signature_b64":"2YC9hJFya+QV9BewK+wj1VNbw9dXKI5LpLLcklKLAG01sKaZW8ODMyKZgXLjF33y02XZVRijjqR8UodTLU4HDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab77c8e07134de2d344587c8a1976383c0f307d861586933b7d22173f5675b9e","last_reissued_at":"2026-07-05T10:20:45.906390Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:45.906390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Supplement to the anticanonical Volumes of weak $\\mathbb{Q}$-Fano threefolds of Picard rank two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ching-Jui Lai, Tsung-Ju Lee","submitted_at":"2025-01-23T09:18:56Z","abstract_excerpt":"We show that for a weak $\\mathbb{Q}$-Fano threefold $X$ ($\\mathbb{Q}$-factorial with terminal singularities and $-K_X$ is nef and big) of Picard rank $\\rho(X)\\leq 2$, either $-K_X^3\\leq 64$ or $-K_X^3=72$ and $X=\\mathbb{P}_{\\mathbb{P}^2}(\\mathcal{O}_{\\mathbb{P}^2}\\oplus\\mathcal{O}_{\\mathbb{P}^2}(3))$. This is supplementary to the previous work in arXiv:2501.12555."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.19419","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.19419/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":"2502.19419","created_at":"2026-07-05T10:20:45.906444+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.19419v1","created_at":"2026-07-05T10:20:45.906444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.19419","created_at":"2026-07-05T10:20:45.906444+00:00"},{"alias_kind":"pith_short_12","alias_value":"VN34RYDRGTPC","created_at":"2026-07-05T10:20:45.906444+00:00"},{"alias_kind":"pith_short_16","alias_value":"VN34RYDRGTPC2NCF","created_at":"2026-07-05T10:20:45.906444+00:00"},{"alias_kind":"pith_short_8","alias_value":"VN34RYDR","created_at":"2026-07-05T10:20:45.906444+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.08508","citing_title":"Re:Verse -- Can Your VLM Read a Manga?","ref_index":30,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP","json":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP.json","graph_json":"https://pith.science/api/pith-number/VN34RYDRGTPC2NCFQ7EKDF3DQP/graph.json","events_json":"https://pith.science/api/pith-number/VN34RYDRGTPC2NCFQ7EKDF3DQP/events.json","paper":"https://pith.science/paper/VN34RYDR"},"agent_actions":{"view_html":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP","download_json":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP.json","view_paper":"https://pith.science/paper/VN34RYDR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.19419&json=true","fetch_graph":"https://pith.science/api/pith-number/VN34RYDRGTPC2NCFQ7EKDF3DQP/graph.json","fetch_events":"https://pith.science/api/pith-number/VN34RYDRGTPC2NCFQ7EKDF3DQP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP/action/storage_attestation","attest_author":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP/action/author_attestation","sign_citation":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP/action/citation_signature","submit_replication":"https://pith.science/pith/VN34RYDRGTPC2NCFQ7EKDF3DQP/action/replication_record"}},"created_at":"2026-07-05T10:20:45.906444+00:00","updated_at":"2026-07-05T10:20:45.906444+00:00"}