{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C3X4JI4AGGGIZAPH2QCDW6JUOL","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":"679409294b6cc219a0ca1b82bab5f1688359f73991518a523b893c4906d8f009","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-13T00:09:04Z","title_canon_sha256":"76452f5f1b15f2722628b3f2089f5a4ccb2fd973fe0b3606e60528c518bfd7a0"},"schema_version":"1.0","source":{"id":"1406.3391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3391","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3391v1","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3391","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"C3X4JI4AGGGI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C3X4JI4AGGGIZAPH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C3X4JI4A","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:2915a5c0bb408b9cdda1f87aba939e66a9b63c0432eeb7d9713c5085777cf16b","target":"graph","created_at":"2026-05-18T02:49:46Z","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":"Jack polynomials generalize several classical families of symmetric polynomials, including Schur polynomials, and are further generalized by Macdonald polynomials. In 1989, Richard Stanley conjectured that if the Littlewood-Richardson coefficient for a triple of Schur polynomials is 1, then the corresponding coefficient for Jack polynomials can be expressed as a product of weighted hooks of the Young diagrams associated to the partitions indexing the coefficient. We prove a special case of this conjecture in which the partitions indexing the Littlewood-Richardson coefficient have at most 3 par","authors_text":"Yusra Naqvi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-13T00:09:04Z","title":"A product formula for certain Littlewood-Richardson coefficients for Jack and Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3391","kind":"arxiv","version":1},"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":"sha256:506fa2c342d2056aae83a31278d70648e409f923a3b526d3787a5352f0a1c4a0","target":"record","created_at":"2026-05-18T02:49:46Z","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":"679409294b6cc219a0ca1b82bab5f1688359f73991518a523b893c4906d8f009","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-13T00:09:04Z","title_canon_sha256":"76452f5f1b15f2722628b3f2089f5a4ccb2fd973fe0b3606e60528c518bfd7a0"},"schema_version":"1.0","source":{"id":"1406.3391","kind":"arxiv","version":1}},"canonical_sha256":"16efc4a380318c8c81e7d4043b793472f708dcadba6dc6dc165b995fe6648597","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16efc4a380318c8c81e7d4043b793472f708dcadba6dc6dc165b995fe6648597","first_computed_at":"2026-05-18T02:49:46.792101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:46.792101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dUjrpux1Ef5upIMWFhfNSYTkjNSWj+6bg1G3WPPKu3poTsHttce7B5GVCYw1L6+EW5aigZ3oE2g4FkwR7gceBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:46.792550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:506fa2c342d2056aae83a31278d70648e409f923a3b526d3787a5352f0a1c4a0","sha256:2915a5c0bb408b9cdda1f87aba939e66a9b63c0432eeb7d9713c5085777cf16b"],"state_sha256":"3fea1aa29994206db01645809daf7bfb78afccdb71aebdee204756b8da3a889a"}