{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F5HOXYO3WWRK7ZBJ57Z6Y7KLWG","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":"c796a355b8ac8f98f555f994b381eae53747f5f681f89737a63861e08935ffe0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-07-25T00:54:33Z","title_canon_sha256":"bb0af79ed8ce9787db0ad13c3edd398bbdd20c92579a7c2bfdd7d7012d9e2bca"},"schema_version":"1.0","source":{"id":"1407.6767","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6767","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6767v3","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6767","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"F5HOXYO3WWRK","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F5HOXYO3WWRK7ZBJ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F5HOXYO3","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:63bcf2c3028fca6fc2aa1e89d46a6356d366efa737e290fff450b6e7a1050014","target":"graph","created_at":"2026-05-18T01:12:25Z","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 prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension $d \\geq 4$, if $\\Delta$ is a tight connected closed homology $d$-manifold whose $i$th homology vanishes for $1 < i < d-1$, then $\\Delta$ is a stacked triangulation of a manifold.These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.","authors_text":"Basudeb Datta, Satoshi Murai","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-07-25T00:54:33Z","title":"On stacked triangulated manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6767","kind":"arxiv","version":3},"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":"sha256:78d4799d4cc3a8aa0a463c9ed6814692dbbf6827a79524099aa393ea8dc00e8f","target":"record","created_at":"2026-05-18T01:12:25Z","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":"c796a355b8ac8f98f555f994b381eae53747f5f681f89737a63861e08935ffe0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-07-25T00:54:33Z","title_canon_sha256":"bb0af79ed8ce9787db0ad13c3edd398bbdd20c92579a7c2bfdd7d7012d9e2bca"},"schema_version":"1.0","source":{"id":"1407.6767","kind":"arxiv","version":3}},"canonical_sha256":"2f4eebe1dbb5a2afe429eff3ec7d4bb1ba3477bb24b3975742957614e082adb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f4eebe1dbb5a2afe429eff3ec7d4bb1ba3477bb24b3975742957614e082adb1","first_computed_at":"2026-05-18T01:12:25.366412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:25.366412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+DMgHtSiEK5W0gBLOc4JDGxaF7ttnsju+EbPjkSD2BcmoeJRq4zUaQjzXb1bG4pssyvuSBa5Mv2MHaFGSi4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:25.366741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6767","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78d4799d4cc3a8aa0a463c9ed6814692dbbf6827a79524099aa393ea8dc00e8f","sha256:63bcf2c3028fca6fc2aa1e89d46a6356d366efa737e290fff450b6e7a1050014"],"state_sha256":"b49e47a003271e12fa07a91ba81823b278873b4932d230991a4f2caf2204ea55"}