{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:B5U2HZHFF7GD752UMO42OTAHWF","short_pith_number":"pith:B5U2HZHF","schema_version":"1.0","canonical_sha256":"0f69a3e4e52fcc3ff75463b9a74c07b14928e989a50890e4e69a6e74962b3cf0","source":{"kind":"arxiv","id":"1105.1151","version":2},"attestation_state":"computed","paper":{"title":"Compactified Jacobians and q,t-Catalan Numbers, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"E. Gorsky, Mikhail Mazin","submitted_at":"2011-05-05T19:23:44Z","abstract_excerpt":"J. Piontkowski described the homology of the Jacobi factor of a plane curve singularity with one Puiseux pair. We discuss the combinatorial structure of his answer, in particular, relate it to the bigraded deformation of Catalan numbers introduced by A. Garsia and M. Haiman."},"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":"1105.1151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-05T19:23:44Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"40ca3b0dccc5f8a3a38fc9a8f972b611d8f55e899dd11b4b7fbbb7917b080ad5","abstract_canon_sha256":"e08c7a784e9e1111e04b26933b3f1d502a68dd68773c2233c59547d92546438a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:11.032257Z","signature_b64":"3zB2GHNDf/ccIm4R2ntGmaffkJYT005iR3MNej2HqkR3vtUwx6jbAiEOAErJdDDt+TBwgPHeyCzIJZy1ShijDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f69a3e4e52fcc3ff75463b9a74c07b14928e989a50890e4e69a6e74962b3cf0","last_reissued_at":"2026-05-18T03:50:11.031612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:11.031612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compactified Jacobians and q,t-Catalan Numbers, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"E. Gorsky, Mikhail Mazin","submitted_at":"2011-05-05T19:23:44Z","abstract_excerpt":"J. Piontkowski described the homology of the Jacobi factor of a plane curve singularity with one Puiseux pair. We discuss the combinatorial structure of his answer, in particular, relate it to the bigraded deformation of Catalan numbers introduced by A. Garsia and M. Haiman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1151","kind":"arxiv","version":2},"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":"1105.1151","created_at":"2026-05-18T03:50:11.031729+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1151v2","created_at":"2026-05-18T03:50:11.031729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1151","created_at":"2026-05-18T03:50:11.031729+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5U2HZHFF7GD","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5U2HZHFF7GD752U","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5U2HZHF","created_at":"2026-05-18T12:26:24.575870+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/B5U2HZHFF7GD752UMO42OTAHWF","json":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF.json","graph_json":"https://pith.science/api/pith-number/B5U2HZHFF7GD752UMO42OTAHWF/graph.json","events_json":"https://pith.science/api/pith-number/B5U2HZHFF7GD752UMO42OTAHWF/events.json","paper":"https://pith.science/paper/B5U2HZHF"},"agent_actions":{"view_html":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF","download_json":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF.json","view_paper":"https://pith.science/paper/B5U2HZHF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1151&json=true","fetch_graph":"https://pith.science/api/pith-number/B5U2HZHFF7GD752UMO42OTAHWF/graph.json","fetch_events":"https://pith.science/api/pith-number/B5U2HZHFF7GD752UMO42OTAHWF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF/action/storage_attestation","attest_author":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF/action/author_attestation","sign_citation":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF/action/citation_signature","submit_replication":"https://pith.science/pith/B5U2HZHFF7GD752UMO42OTAHWF/action/replication_record"}},"created_at":"2026-05-18T03:50:11.031729+00:00","updated_at":"2026-05-18T03:50:11.031729+00:00"}