{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KAJIF64NACJABUNAMZ5J7BSANB","short_pith_number":"pith:KAJIF64N","schema_version":"1.0","canonical_sha256":"501282fb8d009200d1a0667a9f8640685f887d54d6511f2a95e6541f0f50ff37","source":{"kind":"arxiv","id":"2411.03506","version":1},"attestation_state":"computed","paper":{"title":"Algebraic tori in the complement of quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eduardo Alves da Silva, Fernando Figueroa, Joaqu\\'in Moraga","submitted_at":"2024-11-05T20:46:10Z","abstract_excerpt":"Let $B\\subset \\mathbb{P}^3$ be an slc quartic surface. The existence of an embedding $\\mathbb{G}_m^3\\hookrightarrow \\mathbb{P}^3\\setminus B$ implies that $B$ has coregularity zero. In this article, we initiate the classification of coregularity zero slc quartic surfaces $B\\subset \\mathbb{P}^3$ for which $\\mathbb{P}^3\\setminus B$ contains an algebraic torus $\\mathbb{G}_m^3$. Equivalently, the classification of cluster type pairs $(\\mathbb{P}^3,B)$. Along the way, we give criteria for a log Calabi--Yau pair $(X,B)$ over a toric variety $T$ to be of cluster type."},"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":"2411.03506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-05T20:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"2473453a15b444f79653f49e7e9c2bacb402dbf490f401ed4db993c0d46ac12a","abstract_canon_sha256":"14fec317ac758f242ca9cd95b05cf1c3e94193435bdbcf586c172e5affa6620a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:31:33.581365Z","signature_b64":"HeZZwB7Nz7iaRe63HYwn04rXH5Ga66CLlhyJWcx/L+GHgiyn6G4tPUWXRURYnOQVEgRBU6whcqBSaRUNg6OzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"501282fb8d009200d1a0667a9f8640685f887d54d6511f2a95e6541f0f50ff37","last_reissued_at":"2026-07-05T09:31:33.580217Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:31:33.580217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic tori in the complement of quartic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eduardo Alves da Silva, Fernando Figueroa, Joaqu\\'in Moraga","submitted_at":"2024-11-05T20:46:10Z","abstract_excerpt":"Let $B\\subset \\mathbb{P}^3$ be an slc quartic surface. The existence of an embedding $\\mathbb{G}_m^3\\hookrightarrow \\mathbb{P}^3\\setminus B$ implies that $B$ has coregularity zero. In this article, we initiate the classification of coregularity zero slc quartic surfaces $B\\subset \\mathbb{P}^3$ for which $\\mathbb{P}^3\\setminus B$ contains an algebraic torus $\\mathbb{G}_m^3$. Equivalently, the classification of cluster type pairs $(\\mathbb{P}^3,B)$. Along the way, we give criteria for a log Calabi--Yau pair $(X,B)$ over a toric variety $T$ to be of cluster type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03506","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/2411.03506/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":"2411.03506","created_at":"2026-07-05T09:31:33.580274+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.03506v1","created_at":"2026-07-05T09:31:33.580274+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03506","created_at":"2026-07-05T09:31:33.580274+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAJIF64NACJA","created_at":"2026-07-05T09:31:33.580274+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAJIF64NACJABUNA","created_at":"2026-07-05T09:31:33.580274+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAJIF64N","created_at":"2026-07-05T09:31:33.580274+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.18830","citing_title":"Calabi-Yau pairs of complexity two","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB","json":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB.json","graph_json":"https://pith.science/api/pith-number/KAJIF64NACJABUNAMZ5J7BSANB/graph.json","events_json":"https://pith.science/api/pith-number/KAJIF64NACJABUNAMZ5J7BSANB/events.json","paper":"https://pith.science/paper/KAJIF64N"},"agent_actions":{"view_html":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB","download_json":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB.json","view_paper":"https://pith.science/paper/KAJIF64N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.03506&json=true","fetch_graph":"https://pith.science/api/pith-number/KAJIF64NACJABUNAMZ5J7BSANB/graph.json","fetch_events":"https://pith.science/api/pith-number/KAJIF64NACJABUNAMZ5J7BSANB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB/action/storage_attestation","attest_author":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB/action/author_attestation","sign_citation":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB/action/citation_signature","submit_replication":"https://pith.science/pith/KAJIF64NACJABUNAMZ5J7BSANB/action/replication_record"}},"created_at":"2026-07-05T09:31:33.580274+00:00","updated_at":"2026-07-05T09:31:33.580274+00:00"}