{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AZSAAJMOA4GSEROV5JU7MCF2TZ","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":"34bbf17f283bc9e0347607e42484568d355ca566e96ec3826a81a8c3341c200f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-22T10:13:39Z","title_canon_sha256":"11692f6781e451015d2f975de3107f8b97585d04eb85c0b39502392b9b6d6372"},"schema_version":"1.0","source":{"id":"1307.5645","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5645","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5645v3","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5645","created_at":"2026-05-18T01:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"AZSAAJMOA4GS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AZSAAJMOA4GSEROV","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AZSAAJMO","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:40a85a4cfeeed567fd472494c50d7c09d2f8d21a6fecd86e0b41ddbe34467b49","target":"graph","created_at":"2026-05-18T01:06:29Z","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":"We investigate Robinson-Schensted-Knuth algorithm (RSK) and Sch\\\"utzenberger's jeu de taquin in the infinite setup. We show that the recording tableau in RSK defines an isomorphism of the following two dynamical systems: (i) a sequence of i.i.d. random letters equipped with Bernoulli shift, and (ii) a random infinite Young tableau (with the distribution given by Vershik-Kerov measure, corresponding to some Thoma character of the infinite symmetric group) equipped with jeu de taquin transformation. As a special case we recover the results on non-colliding random walks and multidimensional Pitma","authors_text":"Piotr \\'Sniady","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-22T10:13:39Z","title":"Robinson-Schensted-Knuth algorithm, jeu de taquin and Kerov-Vershik measures on infinite tableaux"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5645","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":"sha256:5c0e1ba1aa604266f150ca97808664fe71840e5c07221d9b11162f9a2757f4e6","target":"record","created_at":"2026-05-18T01:06:29Z","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":"34bbf17f283bc9e0347607e42484568d355ca566e96ec3826a81a8c3341c200f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-22T10:13:39Z","title_canon_sha256":"11692f6781e451015d2f975de3107f8b97585d04eb85c0b39502392b9b6d6372"},"schema_version":"1.0","source":{"id":"1307.5645","kind":"arxiv","version":3}},"canonical_sha256":"066400258e070d2245d5ea69f608ba9e77768689a51da397a98e4021d2c7ce1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"066400258e070d2245d5ea69f608ba9e77768689a51da397a98e4021d2c7ce1a","first_computed_at":"2026-05-18T01:06:29.440511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:29.440511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zjy2Q8zOgjfNbjL/DSTfCSghgY9ArMW+JSJyFuv9lHCHGnv+JGS8b+vV8wB9Ct5l9NW4oAA8RajYbIksPiobDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:29.441016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5645","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c0e1ba1aa604266f150ca97808664fe71840e5c07221d9b11162f9a2757f4e6","sha256:40a85a4cfeeed567fd472494c50d7c09d2f8d21a6fecd86e0b41ddbe34467b49"],"state_sha256":"bef416ae55c922d87edbf04259c2e7fddda5e82bfb87f36da744eaab61bcb5e9"}