{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3YRH36KPDLZ4XAKCWDKVOARX3Q","short_pith_number":"pith:3YRH36KP","canonical_record":{"source":{"id":"1111.0575","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T17:35:14Z","cross_cats_sorted":["math-ph","math.CO","math.DS","math.MP","math.RT"],"title_canon_sha256":"b0694bcfd0357dabfdd0ce967a62f5e20424224a8ed9e1a6811e8990c2a5a164","abstract_canon_sha256":"5e155255c484d38190ff9d278130b973c4cb0bcd3bc15901508653b10e2f60c5"},"schema_version":"1.0"},"canonical_sha256":"de227df94f1af3cb8142b0d5570237dc3dad5cac37612ceaa8ae5843cce22fc3","source":{"kind":"arxiv","id":"1111.0575","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0575","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0575v4","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0575","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"3YRH36KPDLZ4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3YRH36KPDLZ4XAKC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3YRH36KP","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3YRH36KPDLZ4XAKCWDKVOARX3Q","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0575","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T17:35:14Z","cross_cats_sorted":["math-ph","math.CO","math.DS","math.MP","math.RT"],"title_canon_sha256":"b0694bcfd0357dabfdd0ce967a62f5e20424224a8ed9e1a6811e8990c2a5a164","abstract_canon_sha256":"5e155255c484d38190ff9d278130b973c4cb0bcd3bc15901508653b10e2f60c5"},"schema_version":"1.0"},"canonical_sha256":"de227df94f1af3cb8142b0d5570237dc3dad5cac37612ceaa8ae5843cce22fc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:30.367930Z","signature_b64":"ifW7GKS4egql8dYYqJBZGV6+L8pEvshs76BzCu2FbKBK9X6mUZqnUPnkrP+jjg2IattUJ5a0HA2lVg6Q+CV7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de227df94f1af3cb8142b0d5570237dc3dad5cac37612ceaa8ae5843cce22fc3","last_reissued_at":"2026-05-18T02:22:30.367231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:30.367231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0575","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DgSJYtdRxDUpDjvOC2ULLx31ily/Ukfe/8meWRaU6n3iVcmnTvYxYFIAuJ/CxY6CFmUdZEfyIqVOrX5Zw10GDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:43:15.824460Z"},"content_sha256":"9f1cbd84b70493dc0596fd568bae73feb1e8f15fdd377d445731b3f81b907f90","schema_version":"1.0","event_id":"sha256:9f1cbd84b70493dc0596fd568bae73feb1e8f15fdd377d445731b3f81b907f90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3YRH36KPDLZ4XAKCWDKVOARX3Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jeu de taquin dynamics on infinite Young tableaux and second class particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.DS","math.MP","math.RT"],"primary_cat":"math.PR","authors_text":"Dan Romik, Piotr \\'Sniady","submitted_at":"2011-11-02T17:35:14Z","abstract_excerpt":"We study an infinite version of the \"jeu de taquin\" sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson-Schensted-Knuth ($\\operatorname {RSK}$) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variables distributed uniformly on the unit interval. We also show that the jeu de taquin "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0575","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g5T7n99hpCGWc7jfQbLT0IeItO9G1WLLzZGu8W0Ss8hJd9jp4TMoqO1rlOL9H/oQ+dd7ALxDGQHTL0mSvCukAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:43:15.824815Z"},"content_sha256":"1fa3e4654c6290ac8c1134c93a5922c42ffef232306f8997f7038a93bbf21077","schema_version":"1.0","event_id":"sha256:1fa3e4654c6290ac8c1134c93a5922c42ffef232306f8997f7038a93bbf21077"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q/bundle.json","state_url":"https://pith.science/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T21:43:15Z","links":{"resolver":"https://pith.science/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q","bundle":"https://pith.science/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q/bundle.json","state":"https://pith.science/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3YRH36KPDLZ4XAKCWDKVOARX3Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3YRH36KPDLZ4XAKCWDKVOARX3Q","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":"5e155255c484d38190ff9d278130b973c4cb0bcd3bc15901508653b10e2f60c5","cross_cats_sorted":["math-ph","math.CO","math.DS","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T17:35:14Z","title_canon_sha256":"b0694bcfd0357dabfdd0ce967a62f5e20424224a8ed9e1a6811e8990c2a5a164"},"schema_version":"1.0","source":{"id":"1111.0575","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0575","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0575v4","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0575","created_at":"2026-05-18T02:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"3YRH36KPDLZ4","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3YRH36KPDLZ4XAKC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3YRH36KP","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:1fa3e4654c6290ac8c1134c93a5922c42ffef232306f8997f7038a93bbf21077","target":"graph","created_at":"2026-05-18T02:22:30Z","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 study an infinite version of the \"jeu de taquin\" sliding game, which can be thought of as a natural measure-preserving transformation on the set of infinite Young tableaux equipped with the Plancherel probability measure. We use methods from representation theory to show that the Robinson-Schensted-Knuth ($\\operatorname {RSK}$) algorithm gives an isomorphism between this measure-preserving dynamical system and the one-sided shift dynamics on a sequence of independent and identically distributed random variables distributed uniformly on the unit interval. We also show that the jeu de taquin ","authors_text":"Dan Romik, Piotr \\'Sniady","cross_cats":["math-ph","math.CO","math.DS","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T17:35:14Z","title":"Jeu de taquin dynamics on infinite Young tableaux and second class particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0575","kind":"arxiv","version":4},"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":"sha256:9f1cbd84b70493dc0596fd568bae73feb1e8f15fdd377d445731b3f81b907f90","target":"record","created_at":"2026-05-18T02:22:30Z","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":"5e155255c484d38190ff9d278130b973c4cb0bcd3bc15901508653b10e2f60c5","cross_cats_sorted":["math-ph","math.CO","math.DS","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-02T17:35:14Z","title_canon_sha256":"b0694bcfd0357dabfdd0ce967a62f5e20424224a8ed9e1a6811e8990c2a5a164"},"schema_version":"1.0","source":{"id":"1111.0575","kind":"arxiv","version":4}},"canonical_sha256":"de227df94f1af3cb8142b0d5570237dc3dad5cac37612ceaa8ae5843cce22fc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de227df94f1af3cb8142b0d5570237dc3dad5cac37612ceaa8ae5843cce22fc3","first_computed_at":"2026-05-18T02:22:30.367231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:30.367231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ifW7GKS4egql8dYYqJBZGV6+L8pEvshs76BzCu2FbKBK9X6mUZqnUPnkrP+jjg2IattUJ5a0HA2lVg6Q+CV7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:30.367930Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0575","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f1cbd84b70493dc0596fd568bae73feb1e8f15fdd377d445731b3f81b907f90","sha256:1fa3e4654c6290ac8c1134c93a5922c42ffef232306f8997f7038a93bbf21077"],"state_sha256":"f58e885453aaffc4e4f7e49f65082a263c981f7f9aea11bdad14a280d8297ab5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FNjTcSTFdY3YWFgeNLTuttWMolTOIp8JAIJ6/RpBYA7I1DOh6z8DH/DBl048seJDU4L2lp+nhutifAwylJA8CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:43:15.826722Z","bundle_sha256":"79fa22a95bc700d9ac95bf50b3f4624efb205c8d24512a6e1de72538e9a31d9b"}}