{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NX5BXLM3DCUHEHLYIDRFSA7YTG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"050712aee36c88c7cb9faba2909a3b81a89983aa4a82a5222b8fa4e217dff69c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-09T17:29:05Z","title_canon_sha256":"614fae2be1896ed3340a3c7f968b0500a31dac2be1d526283e50dbdb27ae1beb"},"schema_version":"1.0","source":{"id":"1406.2250","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2250","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2250v3","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2250","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"pith_short_12","alias_value":"NX5BXLM3DCUH","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NX5BXLM3DCUHEHLY","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NX5BXLM3","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:40fb74e6c8a729de07eacd2c57abfbfe23f5504e5da31e539e77bf9ff195fce4","target":"graph","created_at":"2026-05-18T01:37:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Hooks are prominent in representation theory (of symmetric groups) and they play a role in number theory (via cranks associated to Ramanujan's congruences). A partition of a positive integer $n$ has a Young diagram representation. To each cell in the diagram there is an associated statistic called hook length, and if a number $t$ is absent from the diagram then the partition is called a $t$-core. A partition is an $(s,t)$-core if it is both an $s$- and a $t$-core. Since the work of Anderson on $(s,t)$-cores, the topic has received a growing attention. This paper expands the discussion to multi","authors_text":"Emily Leven, Tewodros Amdeberhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-09T17:29:05Z","title":"Multi-cores, posets, and lattice paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2250","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0b22f1d4c3c6f94c7adcd1b5769663d9d113b860f47f6e44f40d472ad20e9e46","target":"record","created_at":"2026-05-18T01:37:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"050712aee36c88c7cb9faba2909a3b81a89983aa4a82a5222b8fa4e217dff69c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-09T17:29:05Z","title_canon_sha256":"614fae2be1896ed3340a3c7f968b0500a31dac2be1d526283e50dbdb27ae1beb"},"schema_version":"1.0","source":{"id":"1406.2250","kind":"arxiv","version":3}},"canonical_sha256":"6dfa1bad9b18a8721d7840e25903f899a6ba9ae26a7b1da758127609c8f75442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dfa1bad9b18a8721d7840e25903f899a6ba9ae26a7b1da758127609c8f75442","first_computed_at":"2026-05-18T01:37:02.294747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:02.294747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CpzSte+lhai9DOkb009weFsUKdu/flqlJxp1SeAamXadvhwwbM882H0bDZ+5sAhMAu5gIw4FbsXW2YU0Uh6iDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:02.295374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2250","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b22f1d4c3c6f94c7adcd1b5769663d9d113b860f47f6e44f40d472ad20e9e46","sha256:40fb74e6c8a729de07eacd2c57abfbfe23f5504e5da31e539e77bf9ff195fce4"],"state_sha256":"ad726f3b2b52e080ab485b59053af9cbdefe7ebcff8727742d3a5a65b933ad09"}