{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JO6WXZHAWSYHUVLORSMHAJTQ7Z","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":"4567db454dad5e4a1e5aeba75fd3130fe0fd1cf14d9205f49be4b6d307daddb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T21:41:54Z","title_canon_sha256":"173ec499b06326a394739ee6f0df21c7affde402c5a693735ed632027962dad3"},"schema_version":"1.0","source":{"id":"1407.1895","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1895","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1895v3","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1895","created_at":"2026-05-18T01:24:38Z"},{"alias_kind":"pith_short_12","alias_value":"JO6WXZHAWSYH","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JO6WXZHAWSYHUVLO","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JO6WXZHA","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:c4d9cda2396085a03b62da72dd853e7946bdc393325a8c8ae79dff3d4e11998b","target":"graph","created_at":"2026-05-18T01:24:38Z","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":"This survey article is concerned with the study of bifurcations of piecewise-smooth maps. We review the literature in circle maps and quasi-contractions and provide paths through this literature to prove sufficient conditions for the occurrence of two types of bifurcation scenarios involving rich dynamics. The first scenario consists of the appearance of periodic orbits whose symbolic sequences and \"rotation\" numbers follow a Farey tree structure; the periods of the periodic orbits are given by consecutive addition. This is called the {\\em period adding} bifurcation, and its proof relies on re","authors_text":"Albert Granados, Llu\\'is Alsed\\`a, Martin Krupa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T21:41:54Z","title":"The Period adding and incrementing bifurcations: from rotation theory to applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1895","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:e9d8ed7282e9ca16bf3421f899e2797665e88009dbf7b0993537640bd5abb948","target":"record","created_at":"2026-05-18T01:24:38Z","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":"4567db454dad5e4a1e5aeba75fd3130fe0fd1cf14d9205f49be4b6d307daddb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-07T21:41:54Z","title_canon_sha256":"173ec499b06326a394739ee6f0df21c7affde402c5a693735ed632027962dad3"},"schema_version":"1.0","source":{"id":"1407.1895","kind":"arxiv","version":3}},"canonical_sha256":"4bbd6be4e0b4b07a556e8c98702670fe7fdcaa9dec368cd292a1012c4488036a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bbd6be4e0b4b07a556e8c98702670fe7fdcaa9dec368cd292a1012c4488036a","first_computed_at":"2026-05-18T01:24:38.645599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:38.645599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OJinvNBPYUqCh4+Q2lLnRJqc7ASumqTa1JHcrs0fPPL7vMSQ6YDbjTYukQBAZB2WvI3aVIE7VKU3e7bQbFFRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:38.646061Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1895","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9d8ed7282e9ca16bf3421f899e2797665e88009dbf7b0993537640bd5abb948","sha256:c4d9cda2396085a03b62da72dd853e7946bdc393325a8c8ae79dff3d4e11998b"],"state_sha256":"b0d8356b9db3faa559d6ce0f5fa890dfdc45f5614fdfa845bc0eef18e2cc265d"}