{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:XLTZKRNHLRCUQBINV3BOWHY6XJ","short_pith_number":"pith:XLTZKRNH","schema_version":"1.0","canonical_sha256":"bae79545a75c4548050daec2eb1f1eba416f138c3bcbe3d18d428d2ca333b715","source":{"kind":"arxiv","id":"0910.4376","version":2},"attestation_state":"computed","paper":{"title":"Posets from Admissible Coxeter Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henning S. Mortveit, Matthew Macauley","submitted_at":"2009-10-22T18:52:01Z","abstract_excerpt":"We study the equivalence relation on the set of acyclic orientations of an undirected graph G generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in turn, the admissible sequences. This allows us to construct an explicit bijection from the equivalence classes over G to those over G' and G\", the graphs obtained from G by edge deletion and edge contractio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0910.4376","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-22T18:52:01Z","cross_cats_sorted":[],"title_canon_sha256":"0ca269b2054793751d6b8dc4f16b1721cd9203006b26a1b4f75a822580601ef5","abstract_canon_sha256":"f233b6c98cafe46bd1de5319692ba07d37988323db9a51bd0cf81b09f606a29c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:33.675896Z","signature_b64":"jw7X9ejHuBfebzlfIQ7jasLeC2g7PBUglHBQAphMJwkgWvNq8G8t/JM6YmuSmx5UYAdOE050TR90yJoSRn5DDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bae79545a75c4548050daec2eb1f1eba416f138c3bcbe3d18d428d2ca333b715","last_reissued_at":"2026-05-18T04:08:33.675334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:33.675334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Posets from Admissible Coxeter Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henning S. Mortveit, Matthew Macauley","submitted_at":"2009-10-22T18:52:01Z","abstract_excerpt":"We study the equivalence relation on the set of acyclic orientations of an undirected graph G generated by source-to-sink conversions. These conversions arise in the contexts of admissible sequences in Coxeter theory, quiver representations, and asynchronous graph dynamical systems. To each equivalence class we associate a poset, characterize combinatorial properties of these posets, and in turn, the admissible sequences. This allows us to construct an explicit bijection from the equivalence classes over G to those over G' and G\", the graphs obtained from G by edge deletion and edge contractio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.4376","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0910.4376","created_at":"2026-05-18T04:08:33.675429+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.4376v2","created_at":"2026-05-18T04:08:33.675429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.4376","created_at":"2026-05-18T04:08:33.675429+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLTZKRNHLRCU","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLTZKRNHLRCUQBIN","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLTZKRNH","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ","json":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ.json","graph_json":"https://pith.science/api/pith-number/XLTZKRNHLRCUQBINV3BOWHY6XJ/graph.json","events_json":"https://pith.science/api/pith-number/XLTZKRNHLRCUQBINV3BOWHY6XJ/events.json","paper":"https://pith.science/paper/XLTZKRNH"},"agent_actions":{"view_html":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ","download_json":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ.json","view_paper":"https://pith.science/paper/XLTZKRNH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.4376&json=true","fetch_graph":"https://pith.science/api/pith-number/XLTZKRNHLRCUQBINV3BOWHY6XJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XLTZKRNHLRCUQBINV3BOWHY6XJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ/action/storage_attestation","attest_author":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ/action/author_attestation","sign_citation":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ/action/citation_signature","submit_replication":"https://pith.science/pith/XLTZKRNHLRCUQBINV3BOWHY6XJ/action/replication_record"}},"created_at":"2026-05-18T04:08:33.675429+00:00","updated_at":"2026-05-18T04:08:33.675429+00:00"}