{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VSD5YSHIIDBQOIPDRBCKOX43H2","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":"697c75c91d8a7ffb8a529325eaab6c8a26773c3cab35cae8c8457eb9f52fd3dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-07T11:46:57Z","title_canon_sha256":"53307a2713e92dbf76f1b576b333a4c7a43f2f8ee3dbd255d35c6028148c9c03"},"schema_version":"1.0","source":{"id":"1204.1621","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1621","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1621v3","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1621","created_at":"2026-05-18T03:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"VSD5YSHIIDBQ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VSD5YSHIIDBQOIPD","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VSD5YSHI","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:c0cfd93a80d1cb8fd4ffa140dd7617aff95dd6755d55f3469253192aeb976892","target":"graph","created_at":"2026-05-18T03:16:17Z","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":"Given a Bratteli diagram B, we study the set O(B) of all possible orderings w on a Bratteli diagram B and its subset P(B) consisting of `perfect' orderings that produce Bratteli-Vershik dynamical systems (Vershik maps). We give necessary and sufficient conditions for w to be perfect. On the other hand, a wide class of non-simple Bratteli diagrams that do not admit Vershik maps is explicitly described. In the case of finite rank Bratteli diagrams, we show that the existence of perfect orderings with a prescribed number of extreme paths affects significantly the values of the entries of the inci","authors_text":"Jan Kwiatkowski, Reem Yassawi, Sergey Bezuglyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-07T11:46:57Z","title":"Perfect orderings on Bratteli diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1621","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":"sha256:05c2cf1cec5c50481a1c59a7d5baf8a9aa29fe12096b1b4cb835c04837303690","target":"record","created_at":"2026-05-18T03:16:17Z","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":"697c75c91d8a7ffb8a529325eaab6c8a26773c3cab35cae8c8457eb9f52fd3dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-07T11:46:57Z","title_canon_sha256":"53307a2713e92dbf76f1b576b333a4c7a43f2f8ee3dbd255d35c6028148c9c03"},"schema_version":"1.0","source":{"id":"1204.1621","kind":"arxiv","version":3}},"canonical_sha256":"ac87dc48e840c30721e38844a75f9b3eab45d6720e50bb322f6ce4b4ab520ebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac87dc48e840c30721e38844a75f9b3eab45d6720e50bb322f6ce4b4ab520ebf","first_computed_at":"2026-05-18T03:16:17.550013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:17.550013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pn6EA+MokxOCVLhwLWRbP5wl61Wq7sSFmTAqmLp5LBIbY+qZOUkbrCFi+5YhF6+F4HJ4abIZJgbo2Ntvp4zxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:17.550833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1621","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c2cf1cec5c50481a1c59a7d5baf8a9aa29fe12096b1b4cb835c04837303690","sha256:c0cfd93a80d1cb8fd4ffa140dd7617aff95dd6755d55f3469253192aeb976892"],"state_sha256":"85059b059938f0e33c78baee912228610f4ea430c5228f5605d4bc2adfbef58b"}