{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:YPADJ34BWYV5ODEGUNIN3PVZ5V","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":"1ea5fe6beef80e5d84cda28f5272560a3099572bc00df877580c835081768658","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.CO","submitted_at":"2000-12-18T23:15:29Z","title_canon_sha256":"8ff24275f658c1429774f9dadd64a486037d7b455f45a133c0005d9928ac7c56"},"schema_version":"1.0","source":{"id":"math/0012169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0012169","created_at":"2026-05-18T03:26:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0012169v1","created_at":"2026-05-18T03:26:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0012169","created_at":"2026-05-18T03:26:53Z"},{"alias_kind":"pith_short_12","alias_value":"YPADJ34BWYV5","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"YPADJ34BWYV5ODEG","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"YPADJ34B","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:44b85ea6eecd99423afcfe3bbb916e9307375efae68e2f9d873398b80ab8b09c","target":"graph","created_at":"2026-05-18T03:26:53Z","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":"A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex. The size of a dissection is the number of d-simplices it contains. This paper compares triangulations of maximal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal size triangulations for specific non-simplicial polytopes: prisms, antiprisms,","authors_text":"Davis), Francisco Santos (Univ. de Cantabria), Fumihiko Takeuchi (Univ. of Tokyo), Jes\\'us A. De Loera (Univ. of California","cross_cats":["math.MG"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2000-12-18T23:15:29Z","title":"Extremal properties for dissections of convex 3-polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012169","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":"sha256:2cc9bc9f067f358e1acef0fa1e0ad0f391271df2d7e26b15fab5159267046794","target":"record","created_at":"2026-05-18T03:26:53Z","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":"1ea5fe6beef80e5d84cda28f5272560a3099572bc00df877580c835081768658","cross_cats_sorted":["math.MG"],"license":"","primary_cat":"math.CO","submitted_at":"2000-12-18T23:15:29Z","title_canon_sha256":"8ff24275f658c1429774f9dadd64a486037d7b455f45a133c0005d9928ac7c56"},"schema_version":"1.0","source":{"id":"math/0012169","kind":"arxiv","version":1}},"canonical_sha256":"c3c034ef81b62bd70c86a350ddbeb9ed7d2108b41ead6997c4e53256f810b46d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3c034ef81b62bd70c86a350ddbeb9ed7d2108b41ead6997c4e53256f810b46d","first_computed_at":"2026-05-18T03:26:53.168452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:53.168452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9zaXw+XrHZYdTed7AWyNlCfZO7iyf3J8pTwUUUZm8e7HAwgEuqXoai272cmYz/TcpjGuEls81/wftseGq3oaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:53.169377Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0012169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cc9bc9f067f358e1acef0fa1e0ad0f391271df2d7e26b15fab5159267046794","sha256:44b85ea6eecd99423afcfe3bbb916e9307375efae68e2f9d873398b80ab8b09c"],"state_sha256":"d58ef4e338c2a28d06391f1c2a58ff475e337f0bb3a29e1d50866873e45f9b20"}