{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UDUMYIDG6KGC45O4MT6QQRMRV2","short_pith_number":"pith:UDUMYIDG","schema_version":"1.0","canonical_sha256":"a0e8cc2066f28c2e75dc64fd084591ae9ef381c5de0d958d6e5ce1a37e6b90ca","source":{"kind":"arxiv","id":"1905.00570","version":1},"attestation_state":"computed","paper":{"title":"On self-conjugate $(s, s+1,\\ldots, s+k)$-core partitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Zhou, Sherry H.F. Yan, Yao Yu","submitted_at":"2019-05-02T04:36:30Z","abstract_excerpt":"Simultaneous core partitions have been widely studied since Anderson's work on the enumeration of $(s,t)$-core partitions. Amdeberhan and Leven showed that the number of $(s,s+1, \\ldots, s+k)$-core partitions is equal to the number of $(s, k)$-Dyck paths. In this paper, we prove that self-conjugate $(s,s+1, \\ldots, s+k)$-core partitions are equinumerous with symmetric $(s, k)$-Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn."},"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":"1905.00570","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-02T04:36:30Z","cross_cats_sorted":[],"title_canon_sha256":"99456bfd64c2c218f90cb567d848c088ab124ea91b47f46470fcd28d1c08a5e1","abstract_canon_sha256":"4d668c17687283d1352afbb970a56d8432b70c01b755daae0f83824fcc44cb6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:11.533786Z","signature_b64":"7H+RrwIz6w5EMabQ5001s04asQzzwIO23t+L72yziVKEZzGRPA9z0bwpDQMSvnVisFwnbR4qbhSCKG9KQX+KCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0e8cc2066f28c2e75dc64fd084591ae9ef381c5de0d958d6e5ce1a37e6b90ca","last_reissued_at":"2026-05-17T23:47:11.533402Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:11.533402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On self-conjugate $(s, s+1,\\ldots, s+k)$-core partitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hao Zhou, Sherry H.F. Yan, Yao Yu","submitted_at":"2019-05-02T04:36:30Z","abstract_excerpt":"Simultaneous core partitions have been widely studied since Anderson's work on the enumeration of $(s,t)$-core partitions. Amdeberhan and Leven showed that the number of $(s,s+1, \\ldots, s+k)$-core partitions is equal to the number of $(s, k)$-Dyck paths. In this paper, we prove that self-conjugate $(s,s+1, \\ldots, s+k)$-core partitions are equinumerous with symmetric $(s, k)$-Dyck paths, confirming a conjecture posed by Cho, Huh and Sohn."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00570","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":"1905.00570","created_at":"2026-05-17T23:47:11.533464+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.00570v1","created_at":"2026-05-17T23:47:11.533464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00570","created_at":"2026-05-17T23:47:11.533464+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDUMYIDG6KGC","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDUMYIDG6KGC45O4","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDUMYIDG","created_at":"2026-05-18T12:33:30.264802+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/UDUMYIDG6KGC45O4MT6QQRMRV2","json":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2.json","graph_json":"https://pith.science/api/pith-number/UDUMYIDG6KGC45O4MT6QQRMRV2/graph.json","events_json":"https://pith.science/api/pith-number/UDUMYIDG6KGC45O4MT6QQRMRV2/events.json","paper":"https://pith.science/paper/UDUMYIDG"},"agent_actions":{"view_html":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2","download_json":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2.json","view_paper":"https://pith.science/paper/UDUMYIDG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.00570&json=true","fetch_graph":"https://pith.science/api/pith-number/UDUMYIDG6KGC45O4MT6QQRMRV2/graph.json","fetch_events":"https://pith.science/api/pith-number/UDUMYIDG6KGC45O4MT6QQRMRV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2/action/storage_attestation","attest_author":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2/action/author_attestation","sign_citation":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2/action/citation_signature","submit_replication":"https://pith.science/pith/UDUMYIDG6KGC45O4MT6QQRMRV2/action/replication_record"}},"created_at":"2026-05-17T23:47:11.533464+00:00","updated_at":"2026-05-17T23:47:11.533464+00:00"}