{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:FA2K2SNXPEQRM6UTWL2H65D34H","short_pith_number":"pith:FA2K2SNX","schema_version":"1.0","canonical_sha256":"2834ad49b77921167a93b2f47f747be1e0967589f011217cf075d25ac0e58e3c","source":{"kind":"arxiv","id":"1408.3291","version":1},"attestation_state":"computed","paper":{"title":"The problem of describing central measures on path space of graded graphs","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anatoly Vershik","submitted_at":"2014-08-14T14:17:51Z","abstract_excerpt":"We suggest a new method of describing invariant measures on Markov compacta and path spaces of graphs, and thus of describing characters of some groups and traces of AF-algebras. The method relies on properties of filtrations associated with the graph and, in particular, on the notion of a standard filtration. The main tool is the so-called internal metric that we introduce on simplices of measures; it is an iterated Kantorovich metric, and the key result is that the relative compactness in this metric guarantees a constructive enumeration of the ergodic invariant measures. Applications includ"},"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":"1408.3291","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.RT","submitted_at":"2014-08-14T14:17:51Z","cross_cats_sorted":[],"title_canon_sha256":"97293b7fd58e0c7faa8781374e6999f747492a1c79e778958005f8d7c6bdd007","abstract_canon_sha256":"3868420efa1cb7f60b32142c2c6b861a1656a2626ab4411ebed1f88404910bfb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:13.324910Z","signature_b64":"1ZqhoCFwPrzd0xAhU7BTBjfpVmMPut/CDgDxgAJOIBrxZzW2e0p/fJsFChQvWwTofJMHAz9i965QyvdKfbMZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2834ad49b77921167a93b2f47f747be1e0967589f011217cf075d25ac0e58e3c","last_reissued_at":"2026-05-18T02:45:13.324276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:13.324276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The problem of describing central measures on path space of graded graphs","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Anatoly Vershik","submitted_at":"2014-08-14T14:17:51Z","abstract_excerpt":"We suggest a new method of describing invariant measures on Markov compacta and path spaces of graphs, and thus of describing characters of some groups and traces of AF-algebras. The method relies on properties of filtrations associated with the graph and, in particular, on the notion of a standard filtration. The main tool is the so-called internal metric that we introduce on simplices of measures; it is an iterated Kantorovich metric, and the key result is that the relative compactness in this metric guarantees a constructive enumeration of the ergodic invariant measures. Applications includ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3291","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.3291","created_at":"2026-05-18T02:45:13.324361+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.3291v1","created_at":"2026-05-18T02:45:13.324361+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3291","created_at":"2026-05-18T02:45:13.324361+00:00"},{"alias_kind":"pith_short_12","alias_value":"FA2K2SNXPEQR","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"FA2K2SNXPEQRM6UT","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"FA2K2SNX","created_at":"2026-05-18T12:28:28.263976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H","json":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H.json","graph_json":"https://pith.science/api/pith-number/FA2K2SNXPEQRM6UTWL2H65D34H/graph.json","events_json":"https://pith.science/api/pith-number/FA2K2SNXPEQRM6UTWL2H65D34H/events.json","paper":"https://pith.science/paper/FA2K2SNX"},"agent_actions":{"view_html":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H","download_json":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H.json","view_paper":"https://pith.science/paper/FA2K2SNX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.3291&json=true","fetch_graph":"https://pith.science/api/pith-number/FA2K2SNXPEQRM6UTWL2H65D34H/graph.json","fetch_events":"https://pith.science/api/pith-number/FA2K2SNXPEQRM6UTWL2H65D34H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H/action/storage_attestation","attest_author":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H/action/author_attestation","sign_citation":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H/action/citation_signature","submit_replication":"https://pith.science/pith/FA2K2SNXPEQRM6UTWL2H65D34H/action/replication_record"}},"created_at":"2026-05-18T02:45:13.324361+00:00","updated_at":"2026-05-18T02:45:13.324361+00:00"}