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Existence of an upper bound for anticanonical volumes is related the Borisov-Alexeev-Borisov Conjecture which asserts boundedness of the set of $\\epsilon$-klt log $\\QQ$-Fano varieties of a given dimension $n$."},"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":"1204.2593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-04-12T00:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"2b162dce4e7a5b67ab0159791ab78ea2ce759b4328aebe301b7a7a4c422342c1","abstract_canon_sha256":"2fa210e383930dbcc26a86bcf92d598f38e6bae80d1399eb2cabce14df0dfba3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:03.950559Z","signature_b64":"fCIXtVOCbQ275+ydxiex2RYSc3vVdjYzpYfa0agE2Mh4RFpesgnUaCKCDideBOrWUWc0qNbzB9Kf/FCRzltTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93aa100195bac0102ec390cfcc7d9c0d883020f84526c017a82816772ab77e07","last_reissued_at":"2026-05-18T03:58:03.950002Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:03.950002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounding the volumes of singular Fano threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ching-Jui Lai","submitted_at":"2012-04-12T00:03:34Z","abstract_excerpt":"Let $(X,\\Delta)$ be an $n$-dimensional $\\epsilon$-klt log $\\QQ$-Fano pair. 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Existence of an upper bound for anticanonical volumes is related the Borisov-Alexeev-Borisov Conjecture which asserts boundedness of the set of $\\epsilon$-klt log $\\QQ$-Fano varieties of a given dimension $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2593","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":"1204.2593","created_at":"2026-05-18T03:58:03.950082+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2593v1","created_at":"2026-05-18T03:58:03.950082+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2593","created_at":"2026-05-18T03:58:03.950082+00:00"},{"alias_kind":"pith_short_12","alias_value":"SOVBAAMVXLAB","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"SOVBAAMVXLABALWD","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"SOVBAAMV","created_at":"2026-05-18T12:27:20.899486+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/SOVBAAMVXLABALWDSDH4Y7M4BW","json":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW.json","graph_json":"https://pith.science/api/pith-number/SOVBAAMVXLABALWDSDH4Y7M4BW/graph.json","events_json":"https://pith.science/api/pith-number/SOVBAAMVXLABALWDSDH4Y7M4BW/events.json","paper":"https://pith.science/paper/SOVBAAMV"},"agent_actions":{"view_html":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW","download_json":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW.json","view_paper":"https://pith.science/paper/SOVBAAMV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2593&json=true","fetch_graph":"https://pith.science/api/pith-number/SOVBAAMVXLABALWDSDH4Y7M4BW/graph.json","fetch_events":"https://pith.science/api/pith-number/SOVBAAMVXLABALWDSDH4Y7M4BW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW/action/storage_attestation","attest_author":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW/action/author_attestation","sign_citation":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW/action/citation_signature","submit_replication":"https://pith.science/pith/SOVBAAMVXLABALWDSDH4Y7M4BW/action/replication_record"}},"created_at":"2026-05-18T03:58:03.950082+00:00","updated_at":"2026-05-18T03:58:03.950082+00:00"}