{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:E7OKCLJ4IBIVGLLMAMLJ57XNWB","short_pith_number":"pith:E7OKCLJ4","schema_version":"1.0","canonical_sha256":"27dca12d3c4051532d6c03169efeedb07862112dbce31c70c3e429c3c13e136e","source":{"kind":"arxiv","id":"1510.02213","version":1},"attestation_state":"computed","paper":{"title":"Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"O. Foda, T.A. Welsh","submitted_at":"2015-10-08T07:34:29Z","abstract_excerpt":"We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin's product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of affine sl_r algebras, the M^{r, r+d}_r minimal model characters of W_r algebras, and the r-string abaci generating "},"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":"1510.02213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-10-08T07:34:29Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"b734a39a7bee2135c0a215525af85b8e8e5a87901b76609f4b72572061eb081a","abstract_canon_sha256":"28246b311a8dcda6eef2747a447d8329ac1ef9536d704704a8badeb4d01d8f07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:13.532056Z","signature_b64":"TBeO/VsLVGaP9YqdGPZAZOPZTbu2x+/otA/0NCcHJGQrO5G97Ly8nefUQT7gx9vm5jBqFXqH4qnJsdhMh/eTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27dca12d3c4051532d6c03169efeedb07862112dbce31c70c3e429c3c13e136e","last_reissued_at":"2026-05-18T00:43:13.531477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:13.531477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cylindric partitions, W_r characters and the Andrews-Gordon-Bressoud identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"O. Foda, T.A. Welsh","submitted_at":"2015-10-08T07:34:29Z","abstract_excerpt":"We study the Andrews-Gordon-Bressoud (AGB) generalisations of the Rogers-Ramanujan q-series identities in the context of cylindric partitions. We recall the definition of r-cylindric partitions, and provide a simple proof of Borodin's product expression for their generating functions, that can be regarded as a limiting case of an unpublished proof by Krattenthaler. We also recall the relationships between the r-cylindric partition generating functions, the principal characters of affine sl_r algebras, the M^{r, r+d}_r minimal model characters of W_r algebras, and the r-string abaci generating "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02213","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":"1510.02213","created_at":"2026-05-18T00:43:13.531553+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02213v1","created_at":"2026-05-18T00:43:13.531553+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02213","created_at":"2026-05-18T00:43:13.531553+00:00"},{"alias_kind":"pith_short_12","alias_value":"E7OKCLJ4IBIV","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"E7OKCLJ4IBIVGLLM","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"E7OKCLJ4","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.20793","citing_title":"On W-algebras and ODE/IM correspondence","ref_index":84,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB","json":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB.json","graph_json":"https://pith.science/api/pith-number/E7OKCLJ4IBIVGLLMAMLJ57XNWB/graph.json","events_json":"https://pith.science/api/pith-number/E7OKCLJ4IBIVGLLMAMLJ57XNWB/events.json","paper":"https://pith.science/paper/E7OKCLJ4"},"agent_actions":{"view_html":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB","download_json":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB.json","view_paper":"https://pith.science/paper/E7OKCLJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02213&json=true","fetch_graph":"https://pith.science/api/pith-number/E7OKCLJ4IBIVGLLMAMLJ57XNWB/graph.json","fetch_events":"https://pith.science/api/pith-number/E7OKCLJ4IBIVGLLMAMLJ57XNWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB/action/storage_attestation","attest_author":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB/action/author_attestation","sign_citation":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB/action/citation_signature","submit_replication":"https://pith.science/pith/E7OKCLJ4IBIVGLLMAMLJ57XNWB/action/replication_record"}},"created_at":"2026-05-18T00:43:13.531553+00:00","updated_at":"2026-05-18T00:43:13.531553+00:00"}