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In a previous work of the author's, it was conjectured that the Littlewood-Richardson coefficients for two triples, in which one of the partitions differ by a single box move, are congruent modulo the $\\alpha$-hook length of the pivot box for that move. In this note we prove that conj"},"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":"2606.17822","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T11:49:54Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a11042f260b4ec271f70a816a40d352f21726fef5a7d188f464da1894b699af7","abstract_canon_sha256":"c737d57387cd013d64e1fa10adc0b55d2fa1a1ef227b3b9fd626df9b5d89a187"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:40.576283Z","signature_b64":"n158tcpS/VYwl49mfZ7EtC9CrwdtlYrrekO8qwAi+7BU6wRr+YyLBEzNkHEwrAV0y8W0otW4mKpyNQYDS+80Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90118945ea85c67b21bf65eb636064bc1f69317ad90ae7bc2dcaa7dc831b9bfb","last_reissued_at":"2026-06-19T16:10:40.575917Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:40.575917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Congruences of shifted Jack Littlewood-Richardson coefficients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Ryan Mickler","submitted_at":"2026-06-16T11:49:54Z","abstract_excerpt":"The shifted Jack Littlewood-Richardson coefficients $g^\\lambda_{\\mu\\nu}(\\alpha)$, first studied by Alexandersson-F\\'eray, are Laurent polynomials in the Jack parameter $\\alpha$ attached to triples of partitions, which generalize the classical Jack Littlewood-Richardson coefficients investigated by Stanley, et al. In a previous work of the author's, it was conjectured that the Littlewood-Richardson coefficients for two triples, in which one of the partitions differ by a single box move, are congruent modulo the $\\alpha$-hook length of the pivot box for that move. 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