{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J4BK2PMFT2EJW4YIAXAMEFXWUT","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":"0bf4b58f434879e50bb6ae941b4cbbb39dd79efc057597452761dac6f85530b8","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T15:05:20Z","title_canon_sha256":"3b421798ed832c146d6cf69696917a93e6e197886c7f74b5cba1df4243c3b4da"},"schema_version":"1.0","source":{"id":"1009.2029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2029","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2029v1","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2029","created_at":"2026-05-18T03:32:08Z"},{"alias_kind":"pith_short_12","alias_value":"J4BK2PMFT2EJ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J4BK2PMFT2EJW4YI","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J4BK2PMF","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:4d6e9eef2e23c9ebdb2c5e7af4e7896f8edcf387ccb7ca3ecd4bf2d97d1f2d40","target":"graph","created_at":"2026-05-18T03:32:08Z","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 construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently, the space of extreme characters of the infinite-dimensional unitary group U(infinity). The process has a unique invariant distribution which arises as the decomposing measure in a natural problem of harmonic analysis on U(infinity) posed in arXiv:math/0109193. As was shown in arXiv:math/0109194, this measure ca","authors_text":"Alexei Borodin, Grigori Olshanski","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T15:05:20Z","title":"Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2029","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:f920e2d6470217a98746e69e37d05f2dcf8f78a28a02bbbeb2b43c258ef7792e","target":"record","created_at":"2026-05-18T03:32:08Z","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":"0bf4b58f434879e50bb6ae941b4cbbb39dd79efc057597452761dac6f85530b8","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-10T15:05:20Z","title_canon_sha256":"3b421798ed832c146d6cf69696917a93e6e197886c7f74b5cba1df4243c3b4da"},"schema_version":"1.0","source":{"id":"1009.2029","kind":"arxiv","version":1}},"canonical_sha256":"4f02ad3d859e889b730805c0c216f6a4c6199ba8fe9814102b764cd5c0cdb3b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f02ad3d859e889b730805c0c216f6a4c6199ba8fe9814102b764cd5c0cdb3b2","first_computed_at":"2026-05-18T03:32:08.256009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:08.256009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tKuXsgEKj27RnU3eeuvgu1Kpx2H1aahvSoWH0dqUwQcSbGv7C82fSn/gA5oQ8sJtlyf/MTMrvLcPIr7phnOUDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:08.257424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f920e2d6470217a98746e69e37d05f2dcf8f78a28a02bbbeb2b43c258ef7792e","sha256:4d6e9eef2e23c9ebdb2c5e7af4e7896f8edcf387ccb7ca3ecd4bf2d97d1f2d40"],"state_sha256":"f0c44a0102ce557eb8929dd97bd21b08fb0e62ae3d05fada76a003f76de6af50"}