{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:F5KAIIHKZNH2NYAZTESMWVVGFP","short_pith_number":"pith:F5KAIIHK","schema_version":"1.0","canonical_sha256":"2f540420eacb4fa6e0199924cb56a62be15d1189de3ddaa52805b98b5440b0f7","source":{"kind":"arxiv","id":"1405.3522","version":3},"attestation_state":"computed","paper":{"title":"On Reflection Orders Compatible with a Coxeter Element","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henri M\\\"uhle","submitted_at":"2014-05-14T14:58:11Z","abstract_excerpt":"In this article we give a simple, almost uniform proof that the lattice of noncrossing partitions associated with a well-generated complex reflection group is lexicographically shellable. So far a uniform proof is available only for Coxeter groups. In particular we show that, for any complex reflection group $W$ and any element $x\\in W$, every $x$-compatible reflection order is a recursive atom order of the corresponding interval in absolute order. Since any Coxeter element $\\gamma$ in any well-generated complex reflection group admits a $\\gamma$-compatible reflection order, the lexicographic "},"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":"1405.3522","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T14:58:11Z","cross_cats_sorted":[],"title_canon_sha256":"293d4b7ad04a7f753afb97ae7700df25c850c7d74143b24de8ddba4737f86393","abstract_canon_sha256":"639e48bd324fa3e97c2fc830e3032accb178fb33f26bc036532ed8339b375ddd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:28.783466Z","signature_b64":"xTIhY288A46TJcpmZ69CW/YMQJWYJNdhCQHIlRdVZydf6Ww+vqLNjQYIYvfDOD1wmRe3LP/1gnZkjcLyuLJMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f540420eacb4fa6e0199924cb56a62be15d1189de3ddaa52805b98b5440b0f7","last_reissued_at":"2026-05-18T01:37:28.782865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:28.782865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Reflection Orders Compatible with a Coxeter Element","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henri M\\\"uhle","submitted_at":"2014-05-14T14:58:11Z","abstract_excerpt":"In this article we give a simple, almost uniform proof that the lattice of noncrossing partitions associated with a well-generated complex reflection group is lexicographically shellable. So far a uniform proof is available only for Coxeter groups. In particular we show that, for any complex reflection group $W$ and any element $x\\in W$, every $x$-compatible reflection order is a recursive atom order of the corresponding interval in absolute order. Since any Coxeter element $\\gamma$ in any well-generated complex reflection group admits a $\\gamma$-compatible reflection order, the lexicographic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3522","kind":"arxiv","version":3},"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":"1405.3522","created_at":"2026-05-18T01:37:28.782941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.3522v3","created_at":"2026-05-18T01:37:28.782941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3522","created_at":"2026-05-18T01:37:28.782941+00:00"},{"alias_kind":"pith_short_12","alias_value":"F5KAIIHKZNH2","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"F5KAIIHKZNH2NYAZ","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"F5KAIIHK","created_at":"2026-05-18T12:28:28.263976+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/F5KAIIHKZNH2NYAZTESMWVVGFP","json":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP.json","graph_json":"https://pith.science/api/pith-number/F5KAIIHKZNH2NYAZTESMWVVGFP/graph.json","events_json":"https://pith.science/api/pith-number/F5KAIIHKZNH2NYAZTESMWVVGFP/events.json","paper":"https://pith.science/paper/F5KAIIHK"},"agent_actions":{"view_html":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP","download_json":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP.json","view_paper":"https://pith.science/paper/F5KAIIHK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.3522&json=true","fetch_graph":"https://pith.science/api/pith-number/F5KAIIHKZNH2NYAZTESMWVVGFP/graph.json","fetch_events":"https://pith.science/api/pith-number/F5KAIIHKZNH2NYAZTESMWVVGFP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP/action/storage_attestation","attest_author":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP/action/author_attestation","sign_citation":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP/action/citation_signature","submit_replication":"https://pith.science/pith/F5KAIIHKZNH2NYAZTESMWVVGFP/action/replication_record"}},"created_at":"2026-05-18T01:37:28.782941+00:00","updated_at":"2026-05-18T01:37:28.782941+00:00"}