{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DTMMWYJGSLNQ3VMW4IEI6STVYP","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":"46c753ff389af057134591a45e2d7b49bd8121eaab347bcc5e07eb87fc5b8f0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-07T17:36:55Z","title_canon_sha256":"99b0b9ea6c820baba8230f40f0025f82999e259a2eafbe04c11b6a65036d6310"},"schema_version":"1.0","source":{"id":"1306.1788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1788","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1788v2","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1788","created_at":"2026-05-18T01:12:38Z"},{"alias_kind":"pith_short_12","alias_value":"DTMMWYJGSLNQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DTMMWYJGSLNQ3VMW","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DTMMWYJG","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:f5eceff73040f13fcbee969b411e89439a56814ab0896fb09087747500030c57","target":"graph","created_at":"2026-05-18T01:12:38Z","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 continue our study of orderings on Bratteli diagrams started in previous work, joint with Jan Kwiatkowski, where Bratteli diagrams of finite rank were considered. We extend the notions of languages, permutations (called correspondences in this paper), skeletons and associated graphs to the case of general Bratteli diagrams, and show their relevance to the study of perfect orderings: those that support Vershik maps; in particular, perfect orderings with several extremal paths. A perfect ordering comes equipped with a skeleton and a correspondence, and conversely, given a skeleton and corresp","authors_text":"Reem Yassawi, Sergey Bezuglyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-07T17:36:55Z","title":"Perfect orderings on Bratteli diagrams II: general Bratteli diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1788","kind":"arxiv","version":2},"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:f392702933be886371ff08389f3615655366e100456a3bf7ad477cb8c0b5f933","target":"record","created_at":"2026-05-18T01:12:38Z","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":"46c753ff389af057134591a45e2d7b49bd8121eaab347bcc5e07eb87fc5b8f0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-07T17:36:55Z","title_canon_sha256":"99b0b9ea6c820baba8230f40f0025f82999e259a2eafbe04c11b6a65036d6310"},"schema_version":"1.0","source":{"id":"1306.1788","kind":"arxiv","version":2}},"canonical_sha256":"1cd8cb612692db0dd596e2088f4a75c3da16b4c8c3196f8c391b39eeb8c8dbb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cd8cb612692db0dd596e2088f4a75c3da16b4c8c3196f8c391b39eeb8c8dbb8","first_computed_at":"2026-05-18T01:12:38.286396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:38.286396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OzhaKPP2HBlij1C7hPLQj6bFjbVCPnogYqjx9SW+kmWFc8kG1PLOoxEAgwyazCRulE6LJjNlX2tdaavlIGTUBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:38.286770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f392702933be886371ff08389f3615655366e100456a3bf7ad477cb8c0b5f933","sha256:f5eceff73040f13fcbee969b411e89439a56814ab0896fb09087747500030c57"],"state_sha256":"bc71dced84754cddada9bd3097bebf1d81e13dd2410f941b89b6910dc1349209"}