{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GHVIQJ2WHYOWIET5KFYX6WMEU5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5553e8e7c6b0eb1b3be1bf2cd5ade2aa4aeb2446574440584e6a266e48b12a1b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-22T01:26:00Z","title_canon_sha256":"c41e969df10e6a0d61fb9d7afc56be2d886cc1aaac6ca0e6f6a2b103dbaacfb5"},"schema_version":"1.0","source":{"id":"1705.07530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07530","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07530v1","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07530","created_at":"2026-05-18T00:44:05Z"},{"alias_kind":"pith_short_12","alias_value":"GHVIQJ2WHYOW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHVIQJ2WHYOWIET5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHVIQJ2W","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:8a3e8d7e39477521c6388c3baf51ee9b727c4d9115dba43f9ec0a8ab5fb15ffe","target":"graph","created_at":"2026-05-18T00:44:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Hideya Kuwata, Mikiya Masuda, Seonjeong Park, Sho Hasui","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-22T01:26:00Z","title":"Classification of toric manifolds over an $n$-cube with one vertex cut"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07530","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:540c75c7dbe47c8c0480d9153eabaccc641af1fae3f7667ca3679287951c9968","target":"record","created_at":"2026-05-18T00:44:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5553e8e7c6b0eb1b3be1bf2cd5ade2aa4aeb2446574440584e6a266e48b12a1b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-22T01:26:00Z","title_canon_sha256":"c41e969df10e6a0d61fb9d7afc56be2d886cc1aaac6ca0e6f6a2b103dbaacfb5"},"schema_version":"1.0","source":{"id":"1705.07530","kind":"arxiv","version":1}},"canonical_sha256":"31ea8827563e1d64127d51717f5984a767ae6f8c47fe87545128f74217dcd5ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31ea8827563e1d64127d51717f5984a767ae6f8c47fe87545128f74217dcd5ab","first_computed_at":"2026-05-18T00:44:05.290065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:05.290065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2k/9L75c+DvDtzyy/e7voegU+YAX0bw4zIzNtBQsVjX3ZKY4PdDwOhsDtw5R9lEgUW+ELgjUTmaefh2KImQsBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:05.290679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:540c75c7dbe47c8c0480d9153eabaccc641af1fae3f7667ca3679287951c9968","sha256:8a3e8d7e39477521c6388c3baf51ee9b727c4d9115dba43f9ec0a8ab5fb15ffe"],"state_sha256":"1c17692bd64aa3ee5ccea12d8825ec922595d7dfe8cd27807aee0873addf83ee"}