{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:G4WLDCQRRB7TG5XVKLCGCIZOTQ","short_pith_number":"pith:G4WLDCQR","schema_version":"1.0","canonical_sha256":"372cb18a11887f3376f552c461232e9c373120da0a747ab2b6aa230b85078567","source":{"kind":"arxiv","id":"1911.12459","version":1},"attestation_state":"computed","paper":{"title":"Some Algebraic Properties of Lecture Hall Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Liam Solus, Petter Br\\\"and\\'en","submitted_at":"2019-11-27T23:09:11Z","abstract_excerpt":"In this note, we investigate some of the fundamental algebraic and geometric properties of $s$-lecture hall simplices and their generalizations. We show that all $s$-lecture hall order polytopes, which simultaneously generalize $s$-lecture hall simplices and order polytopes, satisfy a property which implies the integer decomposition property. This answers one conjecture of Hibi, Olsen and Tsuchiya. By relating $s$-lecture hall polytopes to alcoved polytopes, we then use this property to show that families of $s$-lecture hall simplices admit a quadratic Gr\\\"obner basis with a square-free initia"},"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":"1911.12459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-11-27T23:09:11Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bfa32d285f32f5d28c395146af5bb97554fa3211d9b6e1fc20920e1cf5369fb7","abstract_canon_sha256":"714777fe109b878552215fc5d37ef92a6aa6461e99a0aebc2c2fe24989fd9c85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:45.393370Z","signature_b64":"GX3QXbV1UOAHC7JhMlLhgTTN12kGwjQFtesS1IolNx5AcYH4UOn1vGmCDjFEqiHaCEiCaQs7AsFV803fBnocDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"372cb18a11887f3376f552c461232e9c373120da0a747ab2b6aa230b85078567","last_reissued_at":"2026-07-05T00:22:45.392984Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:45.392984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Algebraic Properties of Lecture Hall Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Liam Solus, Petter Br\\\"and\\'en","submitted_at":"2019-11-27T23:09:11Z","abstract_excerpt":"In this note, we investigate some of the fundamental algebraic and geometric properties of $s$-lecture hall simplices and their generalizations. We show that all $s$-lecture hall order polytopes, which simultaneously generalize $s$-lecture hall simplices and order polytopes, satisfy a property which implies the integer decomposition property. This answers one conjecture of Hibi, Olsen and Tsuchiya. By relating $s$-lecture hall polytopes to alcoved polytopes, we then use this property to show that families of $s$-lecture hall simplices admit a quadratic Gr\\\"obner basis with a square-free initia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.12459","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/1911.12459/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":"1911.12459","created_at":"2026-07-05T00:22:45.393053+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.12459v1","created_at":"2026-07-05T00:22:45.393053+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.12459","created_at":"2026-07-05T00:22:45.393053+00:00"},{"alias_kind":"pith_short_12","alias_value":"G4WLDCQRRB7T","created_at":"2026-07-05T00:22:45.393053+00:00"},{"alias_kind":"pith_short_16","alias_value":"G4WLDCQRRB7TG5XV","created_at":"2026-07-05T00:22:45.393053+00:00"},{"alias_kind":"pith_short_8","alias_value":"G4WLDCQR","created_at":"2026-07-05T00:22:45.393053+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/G4WLDCQRRB7TG5XVKLCGCIZOTQ","json":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ.json","graph_json":"https://pith.science/api/pith-number/G4WLDCQRRB7TG5XVKLCGCIZOTQ/graph.json","events_json":"https://pith.science/api/pith-number/G4WLDCQRRB7TG5XVKLCGCIZOTQ/events.json","paper":"https://pith.science/paper/G4WLDCQR"},"agent_actions":{"view_html":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ","download_json":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ.json","view_paper":"https://pith.science/paper/G4WLDCQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.12459&json=true","fetch_graph":"https://pith.science/api/pith-number/G4WLDCQRRB7TG5XVKLCGCIZOTQ/graph.json","fetch_events":"https://pith.science/api/pith-number/G4WLDCQRRB7TG5XVKLCGCIZOTQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ/action/storage_attestation","attest_author":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ/action/author_attestation","sign_citation":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ/action/citation_signature","submit_replication":"https://pith.science/pith/G4WLDCQRRB7TG5XVKLCGCIZOTQ/action/replication_record"}},"created_at":"2026-07-05T00:22:45.393053+00:00","updated_at":"2026-07-05T00:22:45.393053+00:00"}