{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6PPDECWFDYSDVYUYGXGOQAZRP4","short_pith_number":"pith:6PPDECWF","schema_version":"1.0","canonical_sha256":"f3de320ac51e243ae29835cce803317f267c16c91f567cafdfaf62907e8f9028","source":{"kind":"arxiv","id":"1510.01416","version":1},"attestation_state":"computed","paper":{"title":"The structure of mode-locking regions of piecewise-linear continuous maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David J.W. Simpson","submitted_at":"2015-10-06T03:08:15Z","abstract_excerpt":"The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain structure with points of zero width called shrinking points. In this paper we perform a local analysis about an arbitrary shrinking point. This is achieved by studying the symbolic itineraries of periodic solutions in nearby mode-locking regions and performing an asymptotic analysis on one-dimensional slow manifolds in order to build a comprehensive theoretical fram"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.01416","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-10-06T03:08:15Z","cross_cats_sorted":[],"title_canon_sha256":"869a27fe88d5272de0affe083dd8ef96bafc57aa04bdc685e14100edbb5cd899","abstract_canon_sha256":"c6737bc66c0b401acf4305b442ff0b7a54601694ae57640c4127aa36bcf5679d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:56.941395Z","signature_b64":"RCRD4N3GAjZ7rdND7KXL5hUvzgNlH12qduCdBLBEoiWyRsJsi1jgzAxAjt/5Mfjfq6mZ/+vW+q58NIgwiGeuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3de320ac51e243ae29835cce803317f267c16c91f567cafdfaf62907e8f9028","last_reissued_at":"2026-05-18T01:30:56.940946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:56.940946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The structure of mode-locking regions of piecewise-linear continuous maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David J.W. Simpson","submitted_at":"2015-10-06T03:08:15Z","abstract_excerpt":"The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain structure with points of zero width called shrinking points. In this paper we perform a local analysis about an arbitrary shrinking point. This is achieved by studying the symbolic itineraries of periodic solutions in nearby mode-locking regions and performing an asymptotic analysis on one-dimensional slow manifolds in order to build a comprehensive theoretical fram"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01416","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.01416","created_at":"2026-05-18T01:30:56.941016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01416v1","created_at":"2026-05-18T01:30:56.941016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01416","created_at":"2026-05-18T01:30:56.941016+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PPDECWFDYSD","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PPDECWFDYSDVYUY","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PPDECWF","created_at":"2026-05-18T12:29:07.941421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4","json":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4.json","graph_json":"https://pith.science/api/pith-number/6PPDECWFDYSDVYUYGXGOQAZRP4/graph.json","events_json":"https://pith.science/api/pith-number/6PPDECWFDYSDVYUYGXGOQAZRP4/events.json","paper":"https://pith.science/paper/6PPDECWF"},"agent_actions":{"view_html":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4","download_json":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4.json","view_paper":"https://pith.science/paper/6PPDECWF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01416&json=true","fetch_graph":"https://pith.science/api/pith-number/6PPDECWFDYSDVYUYGXGOQAZRP4/graph.json","fetch_events":"https://pith.science/api/pith-number/6PPDECWFDYSDVYUYGXGOQAZRP4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4/action/storage_attestation","attest_author":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4/action/author_attestation","sign_citation":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4/action/citation_signature","submit_replication":"https://pith.science/pith/6PPDECWFDYSDVYUYGXGOQAZRP4/action/replication_record"}},"created_at":"2026-05-18T01:30:56.941016+00:00","updated_at":"2026-05-18T01:30:56.941016+00:00"}