{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7J6QY2DOSPJZ7AMH5MJKPCOU2S","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":"6b223c96426328ab36c5bf7c47a07d47782f30b506501084add5157742588dba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-19T19:45:27Z","title_canon_sha256":"10d6bc7023d458947dd29a739fda88eefe211d4068ad7e5206056ad2d6a3a12f"},"schema_version":"1.0","source":{"id":"2505.13689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13689","created_at":"2026-07-05T11:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13689v1","created_at":"2026-07-05T11:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13689","created_at":"2026-07-05T11:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"7J6QY2DOSPJZ","created_at":"2026-07-05T11:05:49Z"},{"alias_kind":"pith_short_16","alias_value":"7J6QY2DOSPJZ7AMH","created_at":"2026-07-05T11:05:49Z"},{"alias_kind":"pith_short_8","alias_value":"7J6QY2DO","created_at":"2026-07-05T11:05:49Z"}],"graph_snapshots":[{"event_id":"sha256:e4f5dc91292954330fe9f53a9e3267ecc2b3f4a26f1d0275ae4faf3b0b5b8c7e","target":"graph","created_at":"2026-07-05T11:05:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.13689/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, $x\\to x+\\omega~({\\rm mod}~1)$, with rational rotation number $\\omega$ are given. The consequences of the existence of such maps in families of maps is considered and the results are illustrated using two examples: Herman's classic family of piecewise linear maps with two linear components, and a map derived from geometric optics which has four components. These results show how results for piecewise smooth circle homeomorphisms with irrational rotation numbers have natural correspondences with the case of ","authors_text":"James Montaldi, Paul Glendinning, Siyuan Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-19T19:45:27Z","title":"Piecewise linear circle maps and conjugation to rigid rational rotations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13689","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":"sha256:8e97c99930c851b0e9da9ebaddf1c669e7f0008403b7b35aa9fc507f04806913","target":"record","created_at":"2026-07-05T11:05:49Z","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":"6b223c96426328ab36c5bf7c47a07d47782f30b506501084add5157742588dba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-19T19:45:27Z","title_canon_sha256":"10d6bc7023d458947dd29a739fda88eefe211d4068ad7e5206056ad2d6a3a12f"},"schema_version":"1.0","source":{"id":"2505.13689","kind":"arxiv","version":1}},"canonical_sha256":"fa7d0c686e93d39f8187eb12a789d4d493a9f8a0975db415211ed6e891dcfbd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa7d0c686e93d39f8187eb12a789d4d493a9f8a0975db415211ed6e891dcfbd4","first_computed_at":"2026-07-05T11:05:49.645560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:49.645560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5t+S3N2DtuGKpG8pyG3TJhX535tP1JmDHu+FJsnqZYvt9LZ54/h6DRg+GOjxVfxhRHo8y8ZOliJSN55lBIKjCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:49.646016Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e97c99930c851b0e9da9ebaddf1c669e7f0008403b7b35aa9fc507f04806913","sha256:e4f5dc91292954330fe9f53a9e3267ecc2b3f4a26f1d0275ae4faf3b0b5b8c7e"],"state_sha256":"f0bcf08138fb480577ab2f68d2575dfcc41e1590982905daeb2dce98e3b12bf2"}