{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SSHYB3JRF7KIJ3WO2QCZDUTA7Q","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":"7a883403febb0b74241dd546644160a6741a8c36065af35af541ae7e4fdd97f5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-15T11:17:48Z","title_canon_sha256":"493b3587b554f8187e48138bd1c0b6b457d9e8259a8b1c7862ae9ec89335da40"},"schema_version":"1.0","source":{"id":"1004.2605","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.2605","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1004.2605v2","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.2605","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"SSHYB3JRF7KI","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SSHYB3JRF7KIJ3WO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SSHYB3JR","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:2d0f792e4c65cce303b978632f97a9fbbc90246234f350d3280f282dae0ed4c4","target":"graph","created_at":"2026-05-18T04:31:13Z","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":"The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system.\n  To achieve these results we examine the layout of admissible poi","authors_text":"Benjamin A. Burton","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-15T11:17:48Z","title":"Maximal admissible faces and asymptotic bounds for the normal surface solution space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.2605","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:a1449df23d2b4207c9f5bdb075e6dd0e94cfece91ed540b0ebc5f6613df5d4f0","target":"record","created_at":"2026-05-18T04:31:13Z","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":"7a883403febb0b74241dd546644160a6741a8c36065af35af541ae7e4fdd97f5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2010-04-15T11:17:48Z","title_canon_sha256":"493b3587b554f8187e48138bd1c0b6b457d9e8259a8b1c7862ae9ec89335da40"},"schema_version":"1.0","source":{"id":"1004.2605","kind":"arxiv","version":2}},"canonical_sha256":"948f80ed312fd484eeced40591d260fc2b3892ea27c1562e3b76df68e9ec3d02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"948f80ed312fd484eeced40591d260fc2b3892ea27c1562e3b76df68e9ec3d02","first_computed_at":"2026-05-18T04:31:13.099393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:13.099393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bye3x9Y3BwU31dzo21ewcoTsGPUQVOvo6Wi8Lg9r1pLEv7hweRf7kurkKe2cWGTcTjKRBOLL+iDuXYnk8v7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:13.100096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.2605","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1449df23d2b4207c9f5bdb075e6dd0e94cfece91ed540b0ebc5f6613df5d4f0","sha256:2d0f792e4c65cce303b978632f97a9fbbc90246234f350d3280f282dae0ed4c4"],"state_sha256":"d11bb8c2379f13db88c15e9f14324097018eb4463fab3a3151a70e7766d540b4"}