{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HSWSFHZUAGK2MMIZHKTATWQ3EU","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":"866054cc086fdd1113e47191f23b733308961113a5db33c55e58bdba13ea745e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-23T18:42:46Z","title_canon_sha256":"c39979d5296d5bc994272f7bbc20d20b7054a368ba5ab1a05923ebd50890518f"},"schema_version":"1.0","source":{"id":"1802.08672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.08672","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1802.08672v1","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.08672","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"HSWSFHZUAGK2","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HSWSFHZUAGK2MMIZ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HSWSFHZU","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:edbecc56614846f6ae6923a095538d8d58f0acca1dd74b8aa2bdfa6a5a0b2935","target":"graph","created_at":"2026-05-18T00:22:40Z","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 introduce the poset of mesh patterns, which generalises the permutation pattern poset. We fully classify the mesh patterns for which the interval [1^\\emptyset,m] is non-pure, where 1^\\emptyset is the unshaded singleton mesh pattern. We present some results on the M\\\"obius function of the poset, and show that {\\mu}(1^\\emptyset,m) is almost always zero. Finally, we introduce a class of disconnected and non-shellable intervals by generalising the direct product operation from permutations to mesh patterns.","authors_text":"Henning Ulfarsson, Jason P. Smith","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-23T18:42:46Z","title":"The Poset of Mesh Patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08672","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:e4b2ad3d62c77cc868c82e2f40e462a237b8d1cfe52c24acca1452dd1a479191","target":"record","created_at":"2026-05-18T00:22:40Z","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":"866054cc086fdd1113e47191f23b733308961113a5db33c55e58bdba13ea745e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-23T18:42:46Z","title_canon_sha256":"c39979d5296d5bc994272f7bbc20d20b7054a368ba5ab1a05923ebd50890518f"},"schema_version":"1.0","source":{"id":"1802.08672","kind":"arxiv","version":1}},"canonical_sha256":"3cad229f340195a631193aa609da1b251ce4d13b59da6c51fc751a5ef5305e55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cad229f340195a631193aa609da1b251ce4d13b59da6c51fc751a5ef5305e55","first_computed_at":"2026-05-18T00:22:40.829190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:40.829190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VNq65rKNsoDbbKquW2xO/y6RY2r73A9a4AdH3g0kT4+bbvk5KiCnVk/7uGKKuVkCaLOkltnfL2F7fbMKjOcrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:40.829683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.08672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4b2ad3d62c77cc868c82e2f40e462a237b8d1cfe52c24acca1452dd1a479191","sha256:edbecc56614846f6ae6923a095538d8d58f0acca1dd74b8aa2bdfa6a5a0b2935"],"state_sha256":"493b8dcae23d65380d067751072fcdaf9915a880c44243b43b0080f0c47d2534"}