{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1999:SUJVIUK6B335TSA3YVGQY6YYO7","short_pith_number":"pith:SUJVIUK6","schema_version":"1.0","canonical_sha256":"951354515e0ef7d9c81bc54d0c7b1877d6851d7f9c2889521cfbe3a181f7b2e1","source":{"kind":"arxiv","id":"math-ph/9908003","version":4},"attestation_state":"computed","paper":{"title":"Combinatorics of the $\\hat{sl}_2$ Spaces of Coinvariants","license":"","headline":"","cross_cats":["math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"B. Feigin, E. Mukhin, R. Kedem, S. Loktev, T. Miwa","submitted_at":"1999-08-02T17:18:00Z","abstract_excerpt":"We consider two types of quotients of the integrable modules of $\\hat{sl}_2$. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-$k$. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For $k=1$, we give the explicit formulas for the characters. We also present recursion relations satisfied by the characters and the monomial bases."},"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":"math-ph/9908003","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"1999-08-02T17:18:00Z","cross_cats_sorted":["math.MP","math.QA","math.RT"],"title_canon_sha256":"0da201e0b513e5b4bd9b7a44291aeb515607587d2a7de90c8b1e95430c557d39","abstract_canon_sha256":"3ee49a1809432a3fc7759035ef840ef7d8238631304cfdf194b41eaf92f8ced9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:10.942895Z","signature_b64":"cX4mWzMHR/enLrOj01p23xPChyig6E+BAd+yZr8dBlqYdDDZ3koLt4ohBDvnzWoVA2MjMcmXGvac592j3XqNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"951354515e0ef7d9c81bc54d0c7b1877d6851d7f9c2889521cfbe3a181f7b2e1","last_reissued_at":"2026-07-04T14:34:10.942527Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:10.942527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorics of the $\\hat{sl}_2$ Spaces of Coinvariants","license":"","headline":"","cross_cats":["math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"B. Feigin, E. Mukhin, R. Kedem, S. Loktev, T. Miwa","submitted_at":"1999-08-02T17:18:00Z","abstract_excerpt":"We consider two types of quotients of the integrable modules of $\\hat{sl}_2$. These spaces of coinvariants have dimensions described in terms of the Verlinde algebra of level-$k$. We describe monomial bases for the spaces of coinvariants, which leads to a fermionic description of these spaces. For $k=1$, we give the explicit formulas for the characters. We also present recursion relations satisfied by the characters and the monomial bases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9908003","kind":"arxiv","version":4},"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/math-ph/9908003/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":"math-ph/9908003","created_at":"2026-07-04T14:34:10.942580+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9908003v4","created_at":"2026-07-04T14:34:10.942580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9908003","created_at":"2026-07-04T14:34:10.942580+00:00"},{"alias_kind":"pith_short_12","alias_value":"SUJVIUK6B335","created_at":"2026-07-04T14:34:10.942580+00:00"},{"alias_kind":"pith_short_16","alias_value":"SUJVIUK6B335TSA3","created_at":"2026-07-04T14:34:10.942580+00:00"},{"alias_kind":"pith_short_8","alias_value":"SUJVIUK6","created_at":"2026-07-04T14:34:10.942580+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.15597","citing_title":"Linear Independence for $A_1^{(1)}$ by Using $C_{2}^{(1)}$","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7","json":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7.json","graph_json":"https://pith.science/api/pith-number/SUJVIUK6B335TSA3YVGQY6YYO7/graph.json","events_json":"https://pith.science/api/pith-number/SUJVIUK6B335TSA3YVGQY6YYO7/events.json","paper":"https://pith.science/paper/SUJVIUK6"},"agent_actions":{"view_html":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7","download_json":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7.json","view_paper":"https://pith.science/paper/SUJVIUK6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/9908003&json=true","fetch_graph":"https://pith.science/api/pith-number/SUJVIUK6B335TSA3YVGQY6YYO7/graph.json","fetch_events":"https://pith.science/api/pith-number/SUJVIUK6B335TSA3YVGQY6YYO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7/action/storage_attestation","attest_author":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7/action/author_attestation","sign_citation":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7/action/citation_signature","submit_replication":"https://pith.science/pith/SUJVIUK6B335TSA3YVGQY6YYO7/action/replication_record"}},"created_at":"2026-07-04T14:34:10.942580+00:00","updated_at":"2026-07-04T14:34:10.942580+00:00"}