{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GHVIQJ2WHYOWIET5KFYX6WMEU5","short_pith_number":"pith:GHVIQJ2W","schema_version":"1.0","canonical_sha256":"31ea8827563e1d64127d51717f5984a767ae6f8c47fe87545128f74217dcd5ab","source":{"kind":"arxiv","id":"1705.07530","version":1},"attestation_state":"computed","paper":{"title":"Classification of toric manifolds over an $n$-cube with one vertex cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AT","authors_text":"Hideya Kuwata, Mikiya Masuda, Seonjeong Park, Sho Hasui","submitted_at":"2017-05-22T01:26:00Z","abstract_excerpt":"We say that a complete nonsingular toric variety (called a toric manifold in this paper) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with corners. Bott manifolds (or Bott towers) are toric manifolds over an $n$-cube $I^n$ and blowing them up at a fixed point produces toric manifolds over $\\mathrm{vc}(I^n)$ an $n$-cube with one vertex cut. They are all projective. On the other hand, Oda's $3$-fold, the simplest non-projective toric manifold, is over $\\mathrm{vc}(I^n)$. In this paper, we classify toric manifolds over $\\mathrm{vc}(I^n)$ $(n\\ge 3)$ as vari"},"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":"1705.07530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-22T01:26:00Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"c41e969df10e6a0d61fb9d7afc56be2d886cc1aaac6ca0e6f6a2b103dbaacfb5","abstract_canon_sha256":"5553e8e7c6b0eb1b3be1bf2cd5ade2aa4aeb2446574440584e6a266e48b12a1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:05.290679Z","signature_b64":"2k/9L75c+DvDtzyy/e7voegU+YAX0bw4zIzNtBQsVjX3ZKY4PdDwOhsDtw5R9lEgUW+ELgjUTmaefh2KImQsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ea8827563e1d64127d51717f5984a767ae6f8c47fe87545128f74217dcd5ab","last_reissued_at":"2026-05-18T00:44:05.290065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:05.290065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of toric manifolds over an $n$-cube with one vertex cut","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AT","authors_text":"Hideya Kuwata, Mikiya Masuda, Seonjeong Park, Sho Hasui","submitted_at":"2017-05-22T01:26:00Z","abstract_excerpt":"We say that a complete nonsingular toric variety (called a toric manifold in this paper) is over $P$ if its quotient by the compact torus is homeomorphic to $P$ as a manifold with corners. Bott manifolds (or Bott towers) are toric manifolds over an $n$-cube $I^n$ and blowing them up at a fixed point produces toric manifolds over $\\mathrm{vc}(I^n)$ an $n$-cube with one vertex cut. They are all projective. On the other hand, Oda's $3$-fold, the simplest non-projective toric manifold, is over $\\mathrm{vc}(I^n)$. In this paper, we classify toric manifolds over $\\mathrm{vc}(I^n)$ $(n\\ge 3)$ as vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07530","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":"1705.07530","created_at":"2026-05-18T00:44:05.290149+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07530v1","created_at":"2026-05-18T00:44:05.290149+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07530","created_at":"2026-05-18T00:44:05.290149+00:00"},{"alias_kind":"pith_short_12","alias_value":"GHVIQJ2WHYOW","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GHVIQJ2WHYOWIET5","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GHVIQJ2W","created_at":"2026-05-18T12:31:18.294218+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/GHVIQJ2WHYOWIET5KFYX6WMEU5","json":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5.json","graph_json":"https://pith.science/api/pith-number/GHVIQJ2WHYOWIET5KFYX6WMEU5/graph.json","events_json":"https://pith.science/api/pith-number/GHVIQJ2WHYOWIET5KFYX6WMEU5/events.json","paper":"https://pith.science/paper/GHVIQJ2W"},"agent_actions":{"view_html":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5","download_json":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5.json","view_paper":"https://pith.science/paper/GHVIQJ2W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07530&json=true","fetch_graph":"https://pith.science/api/pith-number/GHVIQJ2WHYOWIET5KFYX6WMEU5/graph.json","fetch_events":"https://pith.science/api/pith-number/GHVIQJ2WHYOWIET5KFYX6WMEU5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5/action/storage_attestation","attest_author":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5/action/author_attestation","sign_citation":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5/action/citation_signature","submit_replication":"https://pith.science/pith/GHVIQJ2WHYOWIET5KFYX6WMEU5/action/replication_record"}},"created_at":"2026-05-18T00:44:05.290149+00:00","updated_at":"2026-05-18T00:44:05.290149+00:00"}