{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NHVCOBP7EMDIXAQQBHOU6R35HG","short_pith_number":"pith:NHVCOBP7","schema_version":"1.0","canonical_sha256":"69ea2705ff23068b821009dd4f477d39b694df0549b7156ca6e79215e80dd087","source":{"kind":"arxiv","id":"1809.01377","version":1},"attestation_state":"computed","paper":{"title":"The Lecture Hall Cone as a toric deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lukas Katth\\\"an","submitted_at":"2018-09-05T08:22:10Z","abstract_excerpt":"The Lecture Hall cone is a simplicial cone whose lattice points naturally correspond to Lecture Hall partitions. The celebrated Lecture Hall Theorem of Bousquet-M\\'elou and Eriksson states that a particular specialization of its multivariate Ehrhart series factors in a very nice and unexpected way. Over the years, several proofs of this result have been found, but it is still not considered to be well-understood from a geometric perspective. In this note we propose two conjectures which aim at clarifying this result. Our main conjecture is that the Ehrhart ring of the Lecture Hall cone is actu"},"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":"1809.01377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-05T08:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"4a78a3b10785af3afacae11a3a8f15afa43af6e286e5629eac2ed4b2e3f4900c","abstract_canon_sha256":"35dc89d2de6245df2a612778e4db9ba25138abcd1385d23e72fd0b35884b0461"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:27.785101Z","signature_b64":"YdtmIJPUN45iaOKEY+/IjceGR8+pEoKJHVmxNHFlkxIZYNsHay0VM99BG9VQrsOjhWipiuF2msKP4ieu+QYmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69ea2705ff23068b821009dd4f477d39b694df0549b7156ca6e79215e80dd087","last_reissued_at":"2026-05-18T00:06:27.784519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:27.784519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Lecture Hall Cone as a toric deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lukas Katth\\\"an","submitted_at":"2018-09-05T08:22:10Z","abstract_excerpt":"The Lecture Hall cone is a simplicial cone whose lattice points naturally correspond to Lecture Hall partitions. The celebrated Lecture Hall Theorem of Bousquet-M\\'elou and Eriksson states that a particular specialization of its multivariate Ehrhart series factors in a very nice and unexpected way. Over the years, several proofs of this result have been found, but it is still not considered to be well-understood from a geometric perspective. In this note we propose two conjectures which aim at clarifying this result. Our main conjecture is that the Ehrhart ring of the Lecture Hall cone is actu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01377","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":""},"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":"1809.01377","created_at":"2026-05-18T00:06:27.784611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.01377v1","created_at":"2026-05-18T00:06:27.784611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01377","created_at":"2026-05-18T00:06:27.784611+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHVCOBP7EMDI","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHVCOBP7EMDIXAQQ","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHVCOBP7","created_at":"2026-05-18T12:32:40.477152+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/NHVCOBP7EMDIXAQQBHOU6R35HG","json":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG.json","graph_json":"https://pith.science/api/pith-number/NHVCOBP7EMDIXAQQBHOU6R35HG/graph.json","events_json":"https://pith.science/api/pith-number/NHVCOBP7EMDIXAQQBHOU6R35HG/events.json","paper":"https://pith.science/paper/NHVCOBP7"},"agent_actions":{"view_html":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG","download_json":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG.json","view_paper":"https://pith.science/paper/NHVCOBP7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.01377&json=true","fetch_graph":"https://pith.science/api/pith-number/NHVCOBP7EMDIXAQQBHOU6R35HG/graph.json","fetch_events":"https://pith.science/api/pith-number/NHVCOBP7EMDIXAQQBHOU6R35HG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG/action/storage_attestation","attest_author":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG/action/author_attestation","sign_citation":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG/action/citation_signature","submit_replication":"https://pith.science/pith/NHVCOBP7EMDIXAQQBHOU6R35HG/action/replication_record"}},"created_at":"2026-05-18T00:06:27.784611+00:00","updated_at":"2026-05-18T00:06:27.784611+00:00"}