{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:367PZU6DG2GD3PSGQDQA532KV2","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":"c7174f85a2b0c06606a1919044dabe1c09b1e8f4ff2d0ee8aba4a0bff9460c04","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-12-06T20:25:23Z","title_canon_sha256":"98117c3375d4b251fce447c8c7d3ed09d5f2874258545ac4a0b0cc2fd5f2be80"},"schema_version":"1.0","source":{"id":"2312.03887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.03887","created_at":"2026-07-05T07:21:16Z"},{"alias_kind":"arxiv_version","alias_value":"2312.03887v1","created_at":"2026-07-05T07:21:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.03887","created_at":"2026-07-05T07:21:16Z"},{"alias_kind":"pith_short_12","alias_value":"367PZU6DG2GD","created_at":"2026-07-05T07:21:16Z"},{"alias_kind":"pith_short_16","alias_value":"367PZU6DG2GD3PSG","created_at":"2026-07-05T07:21:16Z"},{"alias_kind":"pith_short_8","alias_value":"367PZU6D","created_at":"2026-07-05T07:21:16Z"}],"graph_snapshots":[{"event_id":"sha256:e0901d9921b69276dde45e7f7756cd21575c2bd58f4f81cf606bea62365317d7","target":"graph","created_at":"2026-07-05T07:21:16Z","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/2312.03887/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Piecewise-smooth maps are used as discrete-time models of dynamical systems whose evolution is governed by different equations under different conditions (e.g.~switched control systems). By assigning a symbol to each region of phase space where the map is smooth, any period-$p$ solution of the map can be associated to an itinerary of $p$ symbols. As parameters of the map are varied, changes to this itinerary occur at border-collision bifurcations (BCBs) where one point of the periodic solution collides with a region boundary. It is well known that BCBs conform broadly to two cases: {\\em persis","authors_text":"David J.W. Simpson","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-12-06T20:25:23Z","title":"The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.03887","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:f596d563b2c207895c805992f5bed907027d96e3e8412c7611bc00af5e8f431c","target":"record","created_at":"2026-07-05T07:21:16Z","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":"c7174f85a2b0c06606a1919044dabe1c09b1e8f4ff2d0ee8aba4a0bff9460c04","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-12-06T20:25:23Z","title_canon_sha256":"98117c3375d4b251fce447c8c7d3ed09d5f2874258545ac4a0b0cc2fd5f2be80"},"schema_version":"1.0","source":{"id":"2312.03887","kind":"arxiv","version":1}},"canonical_sha256":"dfbefcd3c3368c3dbe4680e00eef4aaeab2683cdf72dd353195485c1a6bc0d22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfbefcd3c3368c3dbe4680e00eef4aaeab2683cdf72dd353195485c1a6bc0d22","first_computed_at":"2026-07-05T07:21:16.127775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:21:16.127775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJXx4q4OQbTtecVT2RTGPfSlzpe2vuGA5FNs7rKZommUX2e/mEG8GguqMM4TAzSFFdLTgBxYGazc4hhgA8OzAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:21:16.128149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.03887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f596d563b2c207895c805992f5bed907027d96e3e8412c7611bc00af5e8f431c","sha256:e0901d9921b69276dde45e7f7756cd21575c2bd58f4f81cf606bea62365317d7"],"state_sha256":"96d0032c7b23dd224b9034033f4ad95450175332f234055065535d41f5269075"}