{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CMBL7T33ZIWVRVX5DMKGHNJPYL","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":"821cae7eb8354963f1a7ed784111ce4bd2843280af1f3ea0eca10b6fcd72a93e","cross_cats_sorted":["math.AC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-01T19:24:58Z","title_canon_sha256":"98cfb4be1d15f03ce197ef68e00b654e72541c72df9ec3bc5b5380b841c20116"},"schema_version":"1.0","source":{"id":"1211.0258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0258","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0258v2","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0258","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"CMBL7T33ZIWV","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CMBL7T33ZIWVRVX5","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CMBL7T33","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:06139ccdc02dd8c7f68b81e9716593745ea3355dc2893f97ea9b97575216335a","target":"graph","created_at":"2026-05-18T00:53:40Z","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":"In 1997, Bousquet-Melou and Eriksson initiated the study of lecture hall partitions, a fascinating family of partitions that yield a finite version of Euler's celebrated odd/distinct partition theorem. In subsequent work on s-lecture hall partitions, they considered the self-reciprocal property for various associated generating functions, with the goal of characterizing those sequences s that give rise to generating functions of the form $((1-q^{e_1})(1-q^{e_2})...(1-q^{e_n}))^{-1}$.\n  We continue this line of investigation, connecting their work to the more general context of Gorenstein cones","authors_text":"Benjamin Braun, Carla Savage, Matthias Beck, Matthias K\\\"oppe, Zafeirakis Zafeirakopoulos","cross_cats":["math.AC","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-01T19:24:58Z","title":"s-Lecture Hall Partitions, Self-Reciprocal Polynomials, and Gorenstein Cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0258","kind":"arxiv","version":2},"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:dccfcdd4546173844834db60476e4636bf82759f718dfd48bcc41f95f1fad56f","target":"record","created_at":"2026-05-18T00:53:40Z","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":"821cae7eb8354963f1a7ed784111ce4bd2843280af1f3ea0eca10b6fcd72a93e","cross_cats_sorted":["math.AC","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-01T19:24:58Z","title_canon_sha256":"98cfb4be1d15f03ce197ef68e00b654e72541c72df9ec3bc5b5380b841c20116"},"schema_version":"1.0","source":{"id":"1211.0258","kind":"arxiv","version":2}},"canonical_sha256":"1302bfcf7bca2d58d6fd1b1463b52fc2eeaaa432112bf722bce520761295c70b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1302bfcf7bca2d58d6fd1b1463b52fc2eeaaa432112bf722bce520761295c70b","first_computed_at":"2026-05-18T00:53:40.955789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:40.955789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KMYdkYZV+Rz3A17KodvAgAk1VD2NynCg26rQl1AWr5Npi05sHy0OQZYyO+06ylSvSllXdCyVHoWiBgJHz0ZbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:40.956307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dccfcdd4546173844834db60476e4636bf82759f718dfd48bcc41f95f1fad56f","sha256:06139ccdc02dd8c7f68b81e9716593745ea3355dc2893f97ea9b97575216335a"],"state_sha256":"0578fd90d2bdc92a8a6b26b84d96e16e9fee904c23ebb9ac50befc123b44c37a"}