{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JEDBZRX7RT7RTD2NZX3E4VO5V3","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":"cbd03b2e4a86a40fdbc7308ffde2fd8038c53010256a5c3f1faa874c15caeb90","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-01T10:30:00Z","title_canon_sha256":"17f774613817c279a6040a72ef9ddaa07f518f25d9c67e5c81c14e3965ecb60d"},"schema_version":"1.0","source":{"id":"1107.0185","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0185","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0185v3","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0185","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"JEDBZRX7RT7R","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JEDBZRX7RT7RTD2N","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JEDBZRX7","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:c1f1785d1f942de65fd1eaee502cad937ed530cd48f269645fd132022aac8a06","target":"graph","created_at":"2026-05-18T03:50:59Z","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":"In the paper the notion of {\\em Rauzy scheme} is introduced. From Rauzy graph Rauzy Scheme can be obtaining by uniting sequence of vertices of ingoing and outgoing degree 1 by arches. This notion is a tool to describe Rauzy graph behavior. For morphic superword we prove periodicity of Rauzy schemes. This is generalization of fact that quadratic irrationals have periodic chain fractions.","authors_text":"Alexei Kanel-Belov, Ivan Mitrofanov","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-01T10:30:00Z","title":"Periodicity of Rauzy scheme and substitutional systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0185","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":"sha256:16a6218183663ba8b7595dac4b6dfa9d8f4a9fe352c35fa3199e9099b4162423","target":"record","created_at":"2026-05-18T03:50:59Z","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":"cbd03b2e4a86a40fdbc7308ffde2fd8038c53010256a5c3f1faa874c15caeb90","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-01T10:30:00Z","title_canon_sha256":"17f774613817c279a6040a72ef9ddaa07f518f25d9c67e5c81c14e3965ecb60d"},"schema_version":"1.0","source":{"id":"1107.0185","kind":"arxiv","version":3}},"canonical_sha256":"49061cc6ff8cff198f4dcdf64e55ddaed0ef33e91238a52eb143f93e79202eba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49061cc6ff8cff198f4dcdf64e55ddaed0ef33e91238a52eb143f93e79202eba","first_computed_at":"2026-05-18T03:50:59.175537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:59.175537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hdFBf8DaOm60hvx2gFMPjtts/XToqOgwuCjhIYIK+eU3SlLBctrWOsCn0CdyMq3Va2hNq3vZe471iRKE7TKYAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:59.176225Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0185","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a6218183663ba8b7595dac4b6dfa9d8f4a9fe352c35fa3199e9099b4162423","sha256:c1f1785d1f942de65fd1eaee502cad937ed530cd48f269645fd132022aac8a06"],"state_sha256":"72c935e536c02322f7e0566a10e39c883a5e21d32cd4ccc0b2124b9dd30e6fc6"}