{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HLK2GSRHB3C23QTEAXWEPVRZ6H","short_pith_number":"pith:HLK2GSRH","schema_version":"1.0","canonical_sha256":"3ad5a34a270ec5adc26405ec47d639f1d3b0cea13594f6f63416df2e5d286520","source":{"kind":"arxiv","id":"1512.04320","version":2},"attestation_state":"computed","paper":{"title":"Rational Shi tableaux and the skew length statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robin Sulzgruber","submitted_at":"2015-12-14T14:02:52Z","abstract_excerpt":"We define two refinements of the skew length statistic on simultaneous core partitions. The first one relies on hook lengths and is used to prove a refined version of the theorem stating that the skew length is invariant under conjugation of the core. The second one is equivalent to a generalisation of Shi tableaux to the rational level of Catalan combinatorics. These rational Shi tableaux encode dominant $p$-stable elements in the affine symmetric group. We prove that the rational Shi tableau is injective, that is, each dominant $p$-stable affine permutation is determined uniquely by its Shi "},"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":"1512.04320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-14T14:02:52Z","cross_cats_sorted":[],"title_canon_sha256":"426df83b343cdc596ac297cc1d823d06d20855a3e476f5b295138986fff59f76","abstract_canon_sha256":"cd6ba7d0a0f52ec568ab1347be596abac6ec0a38048318dda50ddc17778e7ae6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:37.704171Z","signature_b64":"Q+x8rJnEh63WEjbVXcz1b1cY3xJMxhv1mkvgqetiw4C3jgADfj3b73lyFDm4J4AKk+8Rf0zBCCOJ3oTsjPGLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ad5a34a270ec5adc26405ec47d639f1d3b0cea13594f6f63416df2e5d286520","last_reissued_at":"2026-05-18T01:04:37.703534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:37.703534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational Shi tableaux and the skew length statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Robin Sulzgruber","submitted_at":"2015-12-14T14:02:52Z","abstract_excerpt":"We define two refinements of the skew length statistic on simultaneous core partitions. The first one relies on hook lengths and is used to prove a refined version of the theorem stating that the skew length is invariant under conjugation of the core. The second one is equivalent to a generalisation of Shi tableaux to the rational level of Catalan combinatorics. These rational Shi tableaux encode dominant $p$-stable elements in the affine symmetric group. We prove that the rational Shi tableau is injective, that is, each dominant $p$-stable affine permutation is determined uniquely by its Shi "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04320","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":"1512.04320","created_at":"2026-05-18T01:04:37.703626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04320v2","created_at":"2026-05-18T01:04:37.703626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04320","created_at":"2026-05-18T01:04:37.703626+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLK2GSRHB3C2","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLK2GSRHB3C23QTE","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLK2GSRH","created_at":"2026-05-18T12:29:25.134429+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/HLK2GSRHB3C23QTEAXWEPVRZ6H","json":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H.json","graph_json":"https://pith.science/api/pith-number/HLK2GSRHB3C23QTEAXWEPVRZ6H/graph.json","events_json":"https://pith.science/api/pith-number/HLK2GSRHB3C23QTEAXWEPVRZ6H/events.json","paper":"https://pith.science/paper/HLK2GSRH"},"agent_actions":{"view_html":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H","download_json":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H.json","view_paper":"https://pith.science/paper/HLK2GSRH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04320&json=true","fetch_graph":"https://pith.science/api/pith-number/HLK2GSRHB3C23QTEAXWEPVRZ6H/graph.json","fetch_events":"https://pith.science/api/pith-number/HLK2GSRHB3C23QTEAXWEPVRZ6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H/action/storage_attestation","attest_author":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H/action/author_attestation","sign_citation":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H/action/citation_signature","submit_replication":"https://pith.science/pith/HLK2GSRHB3C23QTEAXWEPVRZ6H/action/replication_record"}},"created_at":"2026-05-18T01:04:37.703626+00:00","updated_at":"2026-05-18T01:04:37.703626+00:00"}