{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:QCTEJA7NBJDI3FTESYAAEVLQKV","short_pith_number":"pith:QCTEJA7N","schema_version":"1.0","canonical_sha256":"80a64483ed0a468d966496000255705566855c43992221cb215a0360feaeceea","source":{"kind":"arxiv","id":"1605.05806","version":3},"attestation_state":"computed","paper":{"title":"Kostka-Shoji polynomials and Lusztig's convolution diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Andrei Ionov, Michael Finkelberg","submitted_at":"2016-05-19T04:17:57Z","abstract_excerpt":"We propose an $r$-variable version of Kostka-Shoji polynomials $K^-_{\\lambda\\mu}$ for $r$-multipartitions $\\lambda,\\mu$. Our version has positive integral coefficients and encodes the graded multiplicities in the space of global sections of a line bundle over Lusztig's iterated convolution diagram for the cyclic quiver $\\tilde{A}_{r-1}$."},"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":"1605.05806","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-05-19T04:17:57Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"e38281b4274415554e9e52cccea27ff2762778ec689dbd66aa578cc988b5a4b5","abstract_canon_sha256":"8b3d205c696f1ee5fa05d54d23be331f68e6a83e4ecdb583995fed61dcb9a104"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:05.479221Z","signature_b64":"/xJ4Ao+rGZUYaSf1iO9cvEGxuVIlUfU9spdnnGDr0zEDaS/4tOSgOvGbH8K2pqDWpW2TKK2gEjA9msZkRGRiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80a64483ed0a468d966496000255705566855c43992221cb215a0360feaeceea","last_reissued_at":"2026-05-18T00:31:05.478722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:05.478722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kostka-Shoji polynomials and Lusztig's convolution diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Andrei Ionov, Michael Finkelberg","submitted_at":"2016-05-19T04:17:57Z","abstract_excerpt":"We propose an $r$-variable version of Kostka-Shoji polynomials $K^-_{\\lambda\\mu}$ for $r$-multipartitions $\\lambda,\\mu$. Our version has positive integral coefficients and encodes the graded multiplicities in the space of global sections of a line bundle over Lusztig's iterated convolution diagram for the cyclic quiver $\\tilde{A}_{r-1}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05806","kind":"arxiv","version":3},"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":"1605.05806","created_at":"2026-05-18T00:31:05.478803+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05806v3","created_at":"2026-05-18T00:31:05.478803+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05806","created_at":"2026-05-18T00:31:05.478803+00:00"},{"alias_kind":"pith_short_12","alias_value":"QCTEJA7NBJDI","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"QCTEJA7NBJDI3FTE","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"QCTEJA7N","created_at":"2026-05-18T12:30:39.010887+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/QCTEJA7NBJDI3FTESYAAEVLQKV","json":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV.json","graph_json":"https://pith.science/api/pith-number/QCTEJA7NBJDI3FTESYAAEVLQKV/graph.json","events_json":"https://pith.science/api/pith-number/QCTEJA7NBJDI3FTESYAAEVLQKV/events.json","paper":"https://pith.science/paper/QCTEJA7N"},"agent_actions":{"view_html":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV","download_json":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV.json","view_paper":"https://pith.science/paper/QCTEJA7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05806&json=true","fetch_graph":"https://pith.science/api/pith-number/QCTEJA7NBJDI3FTESYAAEVLQKV/graph.json","fetch_events":"https://pith.science/api/pith-number/QCTEJA7NBJDI3FTESYAAEVLQKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV/action/storage_attestation","attest_author":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV/action/author_attestation","sign_citation":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV/action/citation_signature","submit_replication":"https://pith.science/pith/QCTEJA7NBJDI3FTESYAAEVLQKV/action/replication_record"}},"created_at":"2026-05-18T00:31:05.478803+00:00","updated_at":"2026-05-18T00:31:05.478803+00:00"}