{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GAKBVLQG36NFK4HJ44A3CVOWMY","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":"fdca508059e3a9d4faaae31f9928f2052992bb4cf8d7ad330a6b9f844cf261ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-12T00:01:21Z","title_canon_sha256":"a586bc10ff4287640183bef36e0204f35a580f2e633e05ce2fe3f6576cb38ca8"},"schema_version":"1.0","source":{"id":"1505.02838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02838","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02838v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02838","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"GAKBVLQG36NF","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAKBVLQG36NFK4HJ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAKBVLQG","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f927466fc5553c38741245e514f999c39dbcd7ff29260c13bbe9317cbbe26618","target":"graph","created_at":"2026-05-18T02:14:15Z","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 investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that every graph in this family has the property that the independence complex of each graph is shellable, but not vertex decomposable.","authors_text":"Adam Van Tuyl, Kevin N. Vander Meulen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-12T00:01:21Z","title":"Shellability, vertex decomposability, and lexicographical products of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02838","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":"sha256:170f9c06a5b685b90522e6a69b35ec51f91840841bbc88f0197d9181858cb050","target":"record","created_at":"2026-05-18T02:14:15Z","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":"fdca508059e3a9d4faaae31f9928f2052992bb4cf8d7ad330a6b9f844cf261ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-12T00:01:21Z","title_canon_sha256":"a586bc10ff4287640183bef36e0204f35a580f2e633e05ce2fe3f6576cb38ca8"},"schema_version":"1.0","source":{"id":"1505.02838","kind":"arxiv","version":1}},"canonical_sha256":"30141aae06df9a5570e9e701b155d66618377a79a6c7b2313b850707ec8e345e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30141aae06df9a5570e9e701b155d66618377a79a6c7b2313b850707ec8e345e","first_computed_at":"2026-05-18T02:14:15.894090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:15.894090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VdeAg2k8X9iVfBFVHrIeZIa4ud0YlrX6TrRmSnPCW2R9ycOGKIkdzhA/axrV2ofKWklXiP0ULO3DFazoATH1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:15.894853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:170f9c06a5b685b90522e6a69b35ec51f91840841bbc88f0197d9181858cb050","sha256:f927466fc5553c38741245e514f999c39dbcd7ff29260c13bbe9317cbbe26618"],"state_sha256":"1bf37afeac42e05a944b2c48684ddcf2500741bea4d6832a22a0e81de20486e3"}