{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:I227XAU5VCQ5T5HPZYJITUPOZI","short_pith_number":"pith:I227XAU5","schema_version":"1.0","canonical_sha256":"46b5fb829da8a1d9f4efce1289d1eeca36b635139d219c5ed5e8f35f92ee343d","source":{"kind":"arxiv","id":"1409.7303","version":2},"attestation_state":"computed","paper":{"title":"A bound for the splitting of smooth Fano polytopes with many vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Benjamin Assarf, Benjamin Nill","submitted_at":"2014-09-25T15:39:51Z","abstract_excerpt":"The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex set of each facet forms a lattice basis. Casagrande showed that any smooth $d$-dimensional Fano polytope has at most $3d$ vertices. Smooth Fano polytopes in dimension $d$ with at least $3d-2$ vertices are completely known. The main result of this paper deals with the case of $3d-k$ vertices for $k$ fixed and $d$ large. It implies that there "},"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":"1409.7303","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-25T15:39:51Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cac96daea2ea46f00ece22e2f2c432a11003cfd3c0768eadc02c84c8b9dc9750","abstract_canon_sha256":"622156fed523dd42f4dae8423f56565130af4e55f42d1f50033d26be8fa77cf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:35.286229Z","signature_b64":"Rsnc6M3MCZxjIfRowedyFLasP/ubLIP3/78bopv8YSQZdFnSeDTy02U9yadBN0fuVGNCV6SgUIjiFwRR4LTfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b5fb829da8a1d9f4efce1289d1eeca36b635139d219c5ed5e8f35f92ee343d","last_reissued_at":"2026-05-18T01:35:35.285586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:35.285586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A bound for the splitting of smooth Fano polytopes with many vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Benjamin Assarf, Benjamin Nill","submitted_at":"2014-09-25T15:39:51Z","abstract_excerpt":"The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex set of each facet forms a lattice basis. Casagrande showed that any smooth $d$-dimensional Fano polytope has at most $3d$ vertices. Smooth Fano polytopes in dimension $d$ with at least $3d-2$ vertices are completely known. The main result of this paper deals with the case of $3d-k$ vertices for $k$ fixed and $d$ large. It implies that there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7303","kind":"arxiv","version":2},"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":"1409.7303","created_at":"2026-05-18T01:35:35.285708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.7303v2","created_at":"2026-05-18T01:35:35.285708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7303","created_at":"2026-05-18T01:35:35.285708+00:00"},{"alias_kind":"pith_short_12","alias_value":"I227XAU5VCQ5","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"I227XAU5VCQ5T5HP","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"I227XAU5","created_at":"2026-05-18T12:28:33.132498+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/I227XAU5VCQ5T5HPZYJITUPOZI","json":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI.json","graph_json":"https://pith.science/api/pith-number/I227XAU5VCQ5T5HPZYJITUPOZI/graph.json","events_json":"https://pith.science/api/pith-number/I227XAU5VCQ5T5HPZYJITUPOZI/events.json","paper":"https://pith.science/paper/I227XAU5"},"agent_actions":{"view_html":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI","download_json":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI.json","view_paper":"https://pith.science/paper/I227XAU5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.7303&json=true","fetch_graph":"https://pith.science/api/pith-number/I227XAU5VCQ5T5HPZYJITUPOZI/graph.json","fetch_events":"https://pith.science/api/pith-number/I227XAU5VCQ5T5HPZYJITUPOZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI/action/storage_attestation","attest_author":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI/action/author_attestation","sign_citation":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI/action/citation_signature","submit_replication":"https://pith.science/pith/I227XAU5VCQ5T5HPZYJITUPOZI/action/replication_record"}},"created_at":"2026-05-18T01:35:35.285708+00:00","updated_at":"2026-05-18T01:35:35.285708+00:00"}