{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DFKZGSLKPWGXRCBNRG6T6P4KRR","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":"bb449f8d1f8ec48ff55958a97d5fbace372a6256839db3c1bf7bb883fdce8244","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-04-28T09:49:11Z","title_canon_sha256":"1567b7c1c3857099ccf0676b6da2fdf049367326dca0bc83563798e98561e475"},"schema_version":"1.0","source":{"id":"2604.25440","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.25440","created_at":"2026-05-22T01:04:03Z"},{"alias_kind":"arxiv_version","alias_value":"2604.25440v2","created_at":"2026-05-22T01:04:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.25440","created_at":"2026-05-22T01:04:03Z"},{"alias_kind":"pith_short_12","alias_value":"DFKZGSLKPWGX","created_at":"2026-05-22T01:04:03Z"},{"alias_kind":"pith_short_16","alias_value":"DFKZGSLKPWGXRCBN","created_at":"2026-05-22T01:04:03Z"},{"alias_kind":"pith_short_8","alias_value":"DFKZGSLK","created_at":"2026-05-22T01:04:03Z"}],"graph_snapshots":[{"event_id":"sha256:cd07ffe448ba677f5c2ca7294eebc536244d97f2118af5be4a494bbc7b872710","target":"graph","created_at":"2026-05-22T01:04:03Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We prove that the image of this map is always Schur-positive, meaning it expands in the Schur basis with nonnegative integer coefficients. These coefficients are enumerated by a new family of combinatorial objects, called k-Yamanouchi tableaux."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The linear map is well-defined on the Schur basis and the combinatorial interpretation via k-Yamanouchi tableaux correctly enumerates the coefficients without hidden cancellations or sign issues."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A new partition-division map on symmetric functions produces Schur-positive outputs enumerated by k-Yamanouchi tableaux."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A linear map dividing a partition by k sends Schur functions to Schur-positive symmetric functions."}],"snapshot_sha256":"c08c3f9e3a8e3619bbdbef55abcf4c12d9e873087c436999efadede7aa409e3b"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-21T04:40:08.417300Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T21:08:34.337187Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2604.25440/integrity.json","findings":[],"snapshot_sha256":"86eabeaaf5ce90d288721a5b15f78552ec77e107e51a3f0cc57f9364f82c4591","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a linear map on symmetric functions that ``divides'' a partition by a positive integer $k$, sending a Schur function indexed by a partition of $kn$ to a symmetric function indexed by partitions of $n$. We determine its Schur expansion explicitly for Schur and skew Schur functions, showing that the coefficients are enumerated by a new family of combinatorial objects, called $k$-Yamanouchi tableaux, which generalize the classical ballot (Yamanouchi) tableaux appearing in the Littlewood--Richardson rule.\n  We also study the images of elementary symmetric functions under this map, derive ","authors_text":"Lilan Dai, Per Alexandersson","cross_cats":["math.RT"],"headline":"A linear map dividing a partition by k sends Schur functions to Schur-positive symmetric functions.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-04-28T09:49:11Z","title":"Partition division maps, symmetric functions and positivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.25440","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-07T15:45:55.568172Z","id":"7fe08852-876b-4d97-8b12-15be69c580f2","model_set":{"reader":"grok-4.3"},"one_line_summary":"A new partition-division map on symmetric functions produces Schur-positive outputs enumerated by k-Yamanouchi tableaux.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A linear map dividing a partition by k sends Schur functions to Schur-positive symmetric functions.","strongest_claim":"We prove that the image of this map is always Schur-positive, meaning it expands in the Schur basis with nonnegative integer coefficients. These coefficients are enumerated by a new family of combinatorial objects, called k-Yamanouchi tableaux.","weakest_assumption":"The linear map is well-defined on the Schur basis and the combinatorial interpretation via k-Yamanouchi tableaux correctly enumerates the coefficients without hidden cancellations or sign issues."}},"verdict_id":"7fe08852-876b-4d97-8b12-15be69c580f2"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:eb31a4620906edb0891c1b458e9015f3063c5cef64ef0e46177da4100cff1c35","target":"record","created_at":"2026-05-22T01:04:03Z","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":"bb449f8d1f8ec48ff55958a97d5fbace372a6256839db3c1bf7bb883fdce8244","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-04-28T09:49:11Z","title_canon_sha256":"1567b7c1c3857099ccf0676b6da2fdf049367326dca0bc83563798e98561e475"},"schema_version":"1.0","source":{"id":"2604.25440","kind":"arxiv","version":2}},"canonical_sha256":"195593496a7d8d78882d89bd3f3f8a8c60b0e34f4396e6a2f3c8eb9af3acc160","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"195593496a7d8d78882d89bd3f3f8a8c60b0e34f4396e6a2f3c8eb9af3acc160","first_computed_at":"2026-05-22T01:04:03.389855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:03.389855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g2757QIlFu+xbJ3gZHrIMfCLijEKmazq/jUHmD+Qn0JBf/NplVDy51WiV4FMHMxb8cbW03GoGmwI9AYnWIJIAQ==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:03.390732Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.25440","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb31a4620906edb0891c1b458e9015f3063c5cef64ef0e46177da4100cff1c35","sha256:cd07ffe448ba677f5c2ca7294eebc536244d97f2118af5be4a494bbc7b872710"],"state_sha256":"be478db04c99af581d1008c208e3c45ae9034786f772e10cd90e203c08c0bcdf"}