{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FX53P2ADGPJKUOWTZ4TNKH7P22","short_pith_number":"pith:FX53P2AD","schema_version":"1.0","canonical_sha256":"2dfbb7e80333d2aa3ad3cf26d51fefd6aba21bd4e1bfef8c0f9b58129994aa76","source":{"kind":"arxiv","id":"2502.07198","version":1},"attestation_state":"computed","paper":{"title":"The Affine Tamari Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CO","authors_text":"Colin Defant, Grant Barkley","submitted_at":"2025-02-11T02:43:13Z","abstract_excerpt":"Given a fixed integer $n\\geq 2$, we construct two new finite lattices that we call the cyclic Tamari lattice and the affine Tamari lattice. The cyclic Tamari lattice is a sublattice and a quotient lattice of the cyclic Dyer lattice, which is the infinite lattice of translation-invariant total orders under containment of inversion sets. The affine Tamari lattice is a quotient of the Dyer lattice, which in turn is a quotient of the cyclic Dyer lattice and is isomorphic to the collection of biclosed sets of the root system of type $\\widetilde{A}_{n-1}$ under inclusion. We provide numerous combina"},"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":"2502.07198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-11T02:43:13Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"bd98fb686e405b2a039f4c6b55867fd50e46b25ff86d382794d5bad0c99bd4b3","abstract_canon_sha256":"d43e5590cbe25fdba81e8b61d1d6aed5895f156e9765edc97e2dfd5e3245aff8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:34.168989Z","signature_b64":"0oXX097vNbrX4UakFzxSmIuzic7B67EaDgDbiAg64l8Nc1nCBx/ssZxB9hw0jORuz8QdLRlnaf3fTkCafIF0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dfbb7e80333d2aa3ad3cf26d51fefd6aba21bd4e1bfef8c0f9b58129994aa76","last_reissued_at":"2026-07-05T10:12:34.168531Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:34.168531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Affine Tamari Lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CO","authors_text":"Colin Defant, Grant Barkley","submitted_at":"2025-02-11T02:43:13Z","abstract_excerpt":"Given a fixed integer $n\\geq 2$, we construct two new finite lattices that we call the cyclic Tamari lattice and the affine Tamari lattice. The cyclic Tamari lattice is a sublattice and a quotient lattice of the cyclic Dyer lattice, which is the infinite lattice of translation-invariant total orders under containment of inversion sets. The affine Tamari lattice is a quotient of the Dyer lattice, which in turn is a quotient of the cyclic Dyer lattice and is isomorphic to the collection of biclosed sets of the root system of type $\\widetilde{A}_{n-1}$ under inclusion. We provide numerous combina"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07198","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07198/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.07198","created_at":"2026-07-05T10:12:34.168580+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.07198v1","created_at":"2026-07-05T10:12:34.168580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07198","created_at":"2026-07-05T10:12:34.168580+00:00"},{"alias_kind":"pith_short_12","alias_value":"FX53P2ADGPJK","created_at":"2026-07-05T10:12:34.168580+00:00"},{"alias_kind":"pith_short_16","alias_value":"FX53P2ADGPJKUOWT","created_at":"2026-07-05T10:12:34.168580+00:00"},{"alias_kind":"pith_short_8","alias_value":"FX53P2AD","created_at":"2026-07-05T10:12:34.168580+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.09601","citing_title":"Flip of lattices","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02668","citing_title":"A generalization in affine type A of Coxeter sortable elements and Reading's bijection with noncrossing partitions","ref_index":36,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22","json":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22.json","graph_json":"https://pith.science/api/pith-number/FX53P2ADGPJKUOWTZ4TNKH7P22/graph.json","events_json":"https://pith.science/api/pith-number/FX53P2ADGPJKUOWTZ4TNKH7P22/events.json","paper":"https://pith.science/paper/FX53P2AD"},"agent_actions":{"view_html":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22","download_json":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22.json","view_paper":"https://pith.science/paper/FX53P2AD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.07198&json=true","fetch_graph":"https://pith.science/api/pith-number/FX53P2ADGPJKUOWTZ4TNKH7P22/graph.json","fetch_events":"https://pith.science/api/pith-number/FX53P2ADGPJKUOWTZ4TNKH7P22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22/action/storage_attestation","attest_author":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22/action/author_attestation","sign_citation":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22/action/citation_signature","submit_replication":"https://pith.science/pith/FX53P2ADGPJKUOWTZ4TNKH7P22/action/replication_record"}},"created_at":"2026-07-05T10:12:34.168580+00:00","updated_at":"2026-07-05T10:12:34.168580+00:00"}