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As a consequence, if $X$ is a nonsingular Fano threefold which is very general in its deformation family, then $\\varepsilon(X,-K_X;x)\\leq 1$ for all points $x\\in X$ if and only if $\\vert-K_X\\vert$ is not base point free."},"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":"1806.05087","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-13T14:34:42Z","cross_cats_sorted":[],"title_canon_sha256":"2da24e0edf7a848fc23f0d806a584e246eacacb1ff475b7c3da22384f73fd6bd","abstract_canon_sha256":"8d08572c124c52e350a5ffb694e1deff0fd84c88292d2179c4f88557f9063823"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:42.698586Z","signature_b64":"HxsJZ6P1OJXFo9vDUfL8M2/M7S2eDFy83sDs67rGY9UicJ3Lk9M9dA0ZM9QLAzTHPdXON5F2EX94h1N/YfM+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fff4ea87b11e0852566192c6102e4a090170b48f050598882d60f4b435977c63","last_reissued_at":"2026-05-17T23:50:42.698135Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:42.698135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Seshadri constants of the anticanonical divisors of Fano manifolds with large index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jie Liu","submitted_at":"2018-06-13T14:34:42Z","abstract_excerpt":"Seshadri constants, introduced by Demailly, measure the local positivity of a nef divisor at a point. In this paper, we compute the Seshadri constants of the anticanonical divisors of Fano manifolds with coindex at most $3$ at a very general point. As a consequence, if $X$ is a nonsingular Fano threefold which is very general in its deformation family, then $\\varepsilon(X,-K_X;x)\\leq 1$ for all points $x\\in X$ if and only if $\\vert-K_X\\vert$ is not base point free."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05087","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":""},"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":"1806.05087","created_at":"2026-05-17T23:50:42.698204+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.05087v3","created_at":"2026-05-17T23:50:42.698204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05087","created_at":"2026-05-17T23:50:42.698204+00:00"},{"alias_kind":"pith_short_12","alias_value":"772OVB5RDYEF","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"772OVB5RDYEFEVTB","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"772OVB5R","created_at":"2026-05-18T12:32:11.075285+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/772OVB5RDYEFEVTBSLDBALSKBE","json":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE.json","graph_json":"https://pith.science/api/pith-number/772OVB5RDYEFEVTBSLDBALSKBE/graph.json","events_json":"https://pith.science/api/pith-number/772OVB5RDYEFEVTBSLDBALSKBE/events.json","paper":"https://pith.science/paper/772OVB5R"},"agent_actions":{"view_html":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE","download_json":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE.json","view_paper":"https://pith.science/paper/772OVB5R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.05087&json=true","fetch_graph":"https://pith.science/api/pith-number/772OVB5RDYEFEVTBSLDBALSKBE/graph.json","fetch_events":"https://pith.science/api/pith-number/772OVB5RDYEFEVTBSLDBALSKBE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE/action/storage_attestation","attest_author":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE/action/author_attestation","sign_citation":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE/action/citation_signature","submit_replication":"https://pith.science/pith/772OVB5RDYEFEVTBSLDBALSKBE/action/replication_record"}},"created_at":"2026-05-17T23:50:42.698204+00:00","updated_at":"2026-05-17T23:50:42.698204+00:00"}