{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JDTZEHBFE2UU4L6LE764MPGIVT","short_pith_number":"pith:JDTZEHBF","schema_version":"1.0","canonical_sha256":"48e7921c2526a94e2fcb27fdc63cc8acf8d0b7a4808a6a2e57a8d0d0ce502714","source":{"kind":"arxiv","id":"1906.11969","version":1},"attestation_state":"computed","paper":{"title":"Constructing robust chaos: invariant manifolds and expanding cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David J.W. Simpson, Paul A. Glendinning","submitted_at":"2019-06-27T21:21:55Z","abstract_excerpt":"Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we provide formal results for robust chaos in the original parameter regime of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049--3052, 1998]. We first construct a trapping region in phase space to prove the existence of a topological attractor. We then construct an invariant expanding cone in tangent space to prove that tangent vect"},"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":"1906.11969","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-06-27T21:21:55Z","cross_cats_sorted":[],"title_canon_sha256":"0424f82a710f116af4829ce5f9c606f2850322f6153034e683cb39c41c655417","abstract_canon_sha256":"42196c78b75f7e7f4593b7895aafb798778df00cf7bf68711296040afc41e805"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:59.644765Z","signature_b64":"zcX/ETBztxeQFYyPIjeSrmaXFlUHZUOLQBGZP7KCjzN5rvxopAFfcBEsDFwJIje0WzQK0xpQvcBZ9IHMivpCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48e7921c2526a94e2fcb27fdc63cc8acf8d0b7a4808a6a2e57a8d0d0ce502714","last_reissued_at":"2026-05-17T23:41:59.644147Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:59.644147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constructing robust chaos: invariant manifolds and expanding cones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David J.W. Simpson, Paul A. Glendinning","submitted_at":"2019-06-27T21:21:55Z","abstract_excerpt":"Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we provide formal results for robust chaos in the original parameter regime of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049--3052, 1998]. We first construct a trapping region in phase space to prove the existence of a topological attractor. We then construct an invariant expanding cone in tangent space to prove that tangent vect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11969","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":"1906.11969","created_at":"2026-05-17T23:41:59.644245+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.11969v1","created_at":"2026-05-17T23:41:59.644245+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11969","created_at":"2026-05-17T23:41:59.644245+00:00"},{"alias_kind":"pith_short_12","alias_value":"JDTZEHBFE2UU","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"JDTZEHBFE2UU4L6L","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"JDTZEHBF","created_at":"2026-05-18T12:33:18.533446+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/JDTZEHBFE2UU4L6LE764MPGIVT","json":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT.json","graph_json":"https://pith.science/api/pith-number/JDTZEHBFE2UU4L6LE764MPGIVT/graph.json","events_json":"https://pith.science/api/pith-number/JDTZEHBFE2UU4L6LE764MPGIVT/events.json","paper":"https://pith.science/paper/JDTZEHBF"},"agent_actions":{"view_html":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT","download_json":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT.json","view_paper":"https://pith.science/paper/JDTZEHBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.11969&json=true","fetch_graph":"https://pith.science/api/pith-number/JDTZEHBFE2UU4L6LE764MPGIVT/graph.json","fetch_events":"https://pith.science/api/pith-number/JDTZEHBFE2UU4L6LE764MPGIVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT/action/storage_attestation","attest_author":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT/action/author_attestation","sign_citation":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT/action/citation_signature","submit_replication":"https://pith.science/pith/JDTZEHBFE2UU4L6LE764MPGIVT/action/replication_record"}},"created_at":"2026-05-17T23:41:59.644245+00:00","updated_at":"2026-05-17T23:41:59.644245+00:00"}