{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AOLRC7S55FXOASAVYQVCREW5CQ","short_pith_number":"pith:AOLRC7S5","canonical_record":{"source":{"id":"1003.2037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-10T07:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"32ee9030125ef761de25f2c7c252ae271cd00b90170b9c7e2b96a33ffa1732ef","abstract_canon_sha256":"df67d070d1dedc940d7256e5fdd548ea7f5567727693911318a49525a2b61dd2"},"schema_version":"1.0"},"canonical_sha256":"0397117e5de96ee04815c42a2892dd1425d50eafd5da32eba55eb3848fb19457","source":{"kind":"arxiv","id":"1003.2037","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2037","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2037v2","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2037","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"AOLRC7S55FXO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AOLRC7S55FXOASAV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AOLRC7S5","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AOLRC7S55FXOASAVYQVCREW5CQ","target":"record","payload":{"canonical_record":{"source":{"id":"1003.2037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-10T07:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"32ee9030125ef761de25f2c7c252ae271cd00b90170b9c7e2b96a33ffa1732ef","abstract_canon_sha256":"df67d070d1dedc940d7256e5fdd548ea7f5567727693911318a49525a2b61dd2"},"schema_version":"1.0"},"canonical_sha256":"0397117e5de96ee04815c42a2892dd1425d50eafd5da32eba55eb3848fb19457","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:14.490790Z","signature_b64":"T8Hk/g9wYveUYW27LuV0NkstOKO3VGCiJv6Z/QvXkjXS/KjNPAOoypz7dgpbXDSfpc5kNW1VJiep7hu6zHArDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0397117e5de96ee04815c42a2892dd1425d50eafd5da32eba55eb3848fb19457","last_reissued_at":"2026-05-18T04:30:14.490275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:14.490275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.2037","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UfFpgTxvjKjs/EM8L2roftBDE9C1eFXANiNBubzkQ1xIzbKrn5f5UNSUcF55FUE3UnqVSXYSzElB8yQ1Z5GuCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:20:23.583948Z"},"content_sha256":"e9c64d244448408ebb28e871742fa81aa628c3ba92ba78d0e3bf04a452d37301","schema_version":"1.0","event_id":"sha256:e9c64d244448408ebb28e871742fa81aa628c3ba92ba78d0e3bf04a452d37301"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AOLRC7S55FXOASAVYQVCREW5CQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kenji Kashiwabara, Masahiro Hachimori","submitted_at":"2010-03-10T07:55:46Z","abstract_excerpt":"For a property $\\cal P$ of simplicial complexes, a simplicial complex $\\Gamma$ is an obstruction to $\\cal P$ if $\\Gamma$ itself does not satisfy $\\cal P$ but all of its proper restrictions satisfy $\\cal P$. In this paper, we determine all obstructions to shellability of dimension $\\le 2$, refining the previous work by Wachs. As a consequence we obtain that the set of obstructions to shellability, that to partitionability and that to sequential Cohen-Macaulayness all coincide for dimensions $\\le 2$. We also show that these three sets of obstructions coincide in the class of flag complexes. Thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2037","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btD6V7pHeVcUm5NX/obeVLXXwjdtyY3DweMRajFykKgaKJhs/zmPCAT6mFmg4bYVRUqZ4dTsVZMSsu+iVT2QAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:20:23.584298Z"},"content_sha256":"2c9923407805376e4de84e5728b6e74af7f80fb3c2208c8799669492219769e6","schema_version":"1.0","event_id":"sha256:2c9923407805376e4de84e5728b6e74af7f80fb3c2208c8799669492219769e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOLRC7S55FXOASAVYQVCREW5CQ/bundle.json","state_url":"https://pith.science/pith/AOLRC7S55FXOASAVYQVCREW5CQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOLRC7S55FXOASAVYQVCREW5CQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T17:20:23Z","links":{"resolver":"https://pith.science/pith/AOLRC7S55FXOASAVYQVCREW5CQ","bundle":"https://pith.science/pith/AOLRC7S55FXOASAVYQVCREW5CQ/bundle.json","state":"https://pith.science/pith/AOLRC7S55FXOASAVYQVCREW5CQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOLRC7S55FXOASAVYQVCREW5CQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AOLRC7S55FXOASAVYQVCREW5CQ","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":"df67d070d1dedc940d7256e5fdd548ea7f5567727693911318a49525a2b61dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-10T07:55:46Z","title_canon_sha256":"32ee9030125ef761de25f2c7c252ae271cd00b90170b9c7e2b96a33ffa1732ef"},"schema_version":"1.0","source":{"id":"1003.2037","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2037","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2037v2","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2037","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"AOLRC7S55FXO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AOLRC7S55FXOASAV","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AOLRC7S5","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:2c9923407805376e4de84e5728b6e74af7f80fb3c2208c8799669492219769e6","target":"graph","created_at":"2026-05-18T04:30:14Z","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":"For a property $\\cal P$ of simplicial complexes, a simplicial complex $\\Gamma$ is an obstruction to $\\cal P$ if $\\Gamma$ itself does not satisfy $\\cal P$ but all of its proper restrictions satisfy $\\cal P$. In this paper, we determine all obstructions to shellability of dimension $\\le 2$, refining the previous work by Wachs. As a consequence we obtain that the set of obstructions to shellability, that to partitionability and that to sequential Cohen-Macaulayness all coincide for dimensions $\\le 2$. We also show that these three sets of obstructions coincide in the class of flag complexes. Thes","authors_text":"Kenji Kashiwabara, Masahiro Hachimori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-10T07:55:46Z","title":"Obstructions to shellability, partitionability, and sequential Cohen-Macaulayness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2037","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:e9c64d244448408ebb28e871742fa81aa628c3ba92ba78d0e3bf04a452d37301","target":"record","created_at":"2026-05-18T04:30:14Z","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":"df67d070d1dedc940d7256e5fdd548ea7f5567727693911318a49525a2b61dd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-03-10T07:55:46Z","title_canon_sha256":"32ee9030125ef761de25f2c7c252ae271cd00b90170b9c7e2b96a33ffa1732ef"},"schema_version":"1.0","source":{"id":"1003.2037","kind":"arxiv","version":2}},"canonical_sha256":"0397117e5de96ee04815c42a2892dd1425d50eafd5da32eba55eb3848fb19457","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0397117e5de96ee04815c42a2892dd1425d50eafd5da32eba55eb3848fb19457","first_computed_at":"2026-05-18T04:30:14.490275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:14.490275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T8Hk/g9wYveUYW27LuV0NkstOKO3VGCiJv6Z/QvXkjXS/KjNPAOoypz7dgpbXDSfpc5kNW1VJiep7hu6zHArDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:14.490790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2037","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9c64d244448408ebb28e871742fa81aa628c3ba92ba78d0e3bf04a452d37301","sha256:2c9923407805376e4de84e5728b6e74af7f80fb3c2208c8799669492219769e6"],"state_sha256":"d86f0f64f8a8db01ac33f01c4b85f9215290ca60ca4f8a885f8768d6b8107f37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZsX0ocqRMwG1X0DHENBmfpYND1KXzOgGtZz2xVb01zdPvZmfQ6nS/MMJ5Ho5J0SkMgqMOBLsjXY6ZkFGlqcAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:20:23.586449Z","bundle_sha256":"407148cf7fdfc533d09f752b92597e39977013078fa7a50c317128e45b5b61f8"}}