{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:5RXJVQCRMYDWYTMMZR6J7QGU72","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":"5a0a0a565a2ba0a44c7559900fdd213ebee495ccdaec158d88a5d459f29a4e74","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.MG","submitted_at":"2001-06-07T12:18:18Z","title_canon_sha256":"04eb6e0bb56ae22b9fe459dba96ea89bedaee15438deaa7e00eabf6fb919cd66"},"schema_version":"1.0","source":{"id":"math/0106043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0106043","created_at":"2026-07-04T14:35:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0106043v2","created_at":"2026-07-04T14:35:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0106043","created_at":"2026-07-04T14:35:21Z"},{"alias_kind":"pith_short_12","alias_value":"5RXJVQCRMYDW","created_at":"2026-07-04T14:35:21Z"},{"alias_kind":"pith_short_16","alias_value":"5RXJVQCRMYDWYTMM","created_at":"2026-07-04T14:35:21Z"},{"alias_kind":"pith_short_8","alias_value":"5RXJVQCR","created_at":"2026-07-04T14:35:21Z"}],"graph_snapshots":[{"event_id":"sha256:f0a8880e8df6e90cfccb9bc40ffb97b9f5167393090740e2f8b55a2c57111496","target":"graph","created_at":"2026-07-04T14:35:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0106043/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an algorithm that constructs the Hasse diagram of the face lattice of a convex polytope P from its vertex-facet incidences in time O(min{n,m}*a*f), where n is the number of vertices, m is the number of facets, a is the number of vertex-facet incidences, and f is the total number of faces of P. This improves results of Fukuda and Rosta (1994), who described an algorithm for enumerating all faces of a d-polytope in O(min{n,m}*d*f^2) steps. For simple or simplicial d-polytopes our algorithm can be specialized to run in time O(d*a*f). Furthermore, applications of the algorithm to other ato","authors_text":"Marc E. Pfetsch, Volker Kaibel","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.MG","submitted_at":"2001-06-07T12:18:18Z","title":"Computing the Face Lattice of a Polytope from its Vertex-Facet Incidences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106043","kind":"arxiv","version":2},"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":"sha256:91cdddf7a81f2d3a402dca91dfce56c1ab852f261d9cfd66994fe2783cac4b35","target":"record","created_at":"2026-07-04T14:35:21Z","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":"5a0a0a565a2ba0a44c7559900fdd213ebee495ccdaec158d88a5d459f29a4e74","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.MG","submitted_at":"2001-06-07T12:18:18Z","title_canon_sha256":"04eb6e0bb56ae22b9fe459dba96ea89bedaee15438deaa7e00eabf6fb919cd66"},"schema_version":"1.0","source":{"id":"math/0106043","kind":"arxiv","version":2}},"canonical_sha256":"ec6e9ac05166076c4d8ccc7c9fc0d4feafd6916c8b7ed4994d2435a725c07cb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec6e9ac05166076c4d8ccc7c9fc0d4feafd6916c8b7ed4994d2435a725c07cb3","first_computed_at":"2026-07-04T14:35:21.966687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:21.966687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dWJVNYucUCf1sOxbctt0awvLPV+turym6MP7UEJiY5gt9z16ofanH7ZQc/vP5v3+pCljyHUo/kQN3fFiDFF3CA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:21.967068Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0106043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91cdddf7a81f2d3a402dca91dfce56c1ab852f261d9cfd66994fe2783cac4b35","sha256:f0a8880e8df6e90cfccb9bc40ffb97b9f5167393090740e2f8b55a2c57111496"],"state_sha256":"3f2f23d512145f8a1dafeff6ea8bc7bba0eda5a946b980a04bfe3e073206683d"}