{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CVGCEAXZ6J3ILWRTZTVJSPG6MS","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":"de45ec0ef68623a01b11f3541eedd5f9b9d1aec29d0106ca1d07c52abb99f5eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-22T09:54:11Z","title_canon_sha256":"5f4289fec38020da1097aed438512ccfe5eaaf0fdc0b35487d9e7ff155c27f9e"},"schema_version":"1.0","source":{"id":"1308.4813","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4813","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4813v3","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4813","created_at":"2026-05-18T02:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"CVGCEAXZ6J3I","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CVGCEAXZ6J3ILWRT","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CVGCEAXZ","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:3f82f740f1d644375338a400a55f88a18aab50831decdc2284cdd92073aacce9","target":"graph","created_at":"2026-05-18T02:45:23Z","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 positive integers $m$ and $k$, we introduce a family of lattices $\\mathcal{C}_{k}^{(m)}$ associated to the Cambrian lattice $\\mathcal{C}_{k}$ of the dihedral group $I_{2}(k)$. We show that $\\mathcal{C}_{k}^{(m)}$ satisfies some basic properties of a Fuss-Catalan generalization of $\\mathcal{C}_{k}$, namely that $\\mathcal{C}_{k}^{(1)}=\\mathcal{C}_{k}$ and $\\bigl\\lvert\\mathcal{C}_{k}^{(m)}\\bigr\\rvert=\\mbox{Cat}^{(m)}\\bigl(I_{2}(k)\\bigr)$. Subsequently, we prove some structural and topological properties of these lattices---namely that they are trim and EL-shellable---which were known for $\\ma","authors_text":"Henri M\\\"uhle, Myrto Kallipoliti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-22T09:54:11Z","title":"Towards m-Cambrian Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4813","kind":"arxiv","version":3},"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":"sha256:666cc12361b62ff12f8d522b31e6432c25dac672c0d6577c57c5ca14815f388f","target":"record","created_at":"2026-05-18T02:45:23Z","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":"de45ec0ef68623a01b11f3541eedd5f9b9d1aec29d0106ca1d07c52abb99f5eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-22T09:54:11Z","title_canon_sha256":"5f4289fec38020da1097aed438512ccfe5eaaf0fdc0b35487d9e7ff155c27f9e"},"schema_version":"1.0","source":{"id":"1308.4813","kind":"arxiv","version":3}},"canonical_sha256":"154c2202f9f27685da33ccea993cde648772b14ceef30be074b5b22966d90eff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"154c2202f9f27685da33ccea993cde648772b14ceef30be074b5b22966d90eff","first_computed_at":"2026-05-18T02:45:23.343612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:23.343612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0ytlpwg8QP2fqhKto5XUHnLTyS6XWTwoGtApcyxuc5mAiTSigi/2VSIYFOFNXEoEMrOArZfeO2BKQ2jHnow4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:23.344063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4813","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:666cc12361b62ff12f8d522b31e6432c25dac672c0d6577c57c5ca14815f388f","sha256:3f82f740f1d644375338a400a55f88a18aab50831decdc2284cdd92073aacce9"],"state_sha256":"ae91909e5ba34cccab04d1816f27068f9896370fbbb86ea84c899763ff28886f"}