{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7DXSOJ53YBNPVHOKFYQ6RB4NPT","short_pith_number":"pith:7DXSOJ53","schema_version":"1.0","canonical_sha256":"f8ef2727bbc05afa9dca2e21e8878d7ce6a8420cec5cfecbff0303f723ddcb15","source":{"kind":"arxiv","id":"1408.0675","version":2},"attestation_state":"computed","paper":{"title":"On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K. Uldall Kristiansen, S. J. Hogan","submitted_at":"2014-08-04T13:19:16Z","abstract_excerpt":"In this paper we use the blow up method of Dumortier and Roussarie \\cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \\cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \\cite{filippov1988differential} in $\\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \\cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \\cite{reves_regularization_2014} in a simple manner. The"},"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":"1408.0675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-04T13:19:16Z","cross_cats_sorted":[],"title_canon_sha256":"bf71394d192327d3f8f47a0cc0736fca283510e7cab75fb0c977eb9eb30efc87","abstract_canon_sha256":"25d48eb33f02b00a000106f1e553f18b31740cc5358dd38de47548f8495e8d19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:11.262265Z","signature_b64":"RERJQrKdM6t5JWUu03knfUxfItTivN1W5M9b7x5CGfh8MjHSwravAuNEEyiJ6FEcvCg3xUdaZfVz2d9uSDH0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8ef2727bbc05afa9dca2e21e8878d7ce6a8420cec5cfecbff0303f723ddcb15","last_reissued_at":"2026-05-18T02:31:11.261640Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:11.261640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K. Uldall Kristiansen, S. J. Hogan","submitted_at":"2014-08-04T13:19:16Z","abstract_excerpt":"In this paper we use the blow up method of Dumortier and Roussarie \\cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \\cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \\cite{filippov1988differential} in $\\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \\cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \\cite{reves_regularization_2014} in a simple manner. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0675","kind":"arxiv","version":2},"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":"1408.0675","created_at":"2026-05-18T02:31:11.261735+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.0675v2","created_at":"2026-05-18T02:31:11.261735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0675","created_at":"2026-05-18T02:31:11.261735+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DXSOJ53YBNP","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DXSOJ53YBNPVHOK","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DXSOJ53","created_at":"2026-05-18T12:28:16.859392+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/7DXSOJ53YBNPVHOKFYQ6RB4NPT","json":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT.json","graph_json":"https://pith.science/api/pith-number/7DXSOJ53YBNPVHOKFYQ6RB4NPT/graph.json","events_json":"https://pith.science/api/pith-number/7DXSOJ53YBNPVHOKFYQ6RB4NPT/events.json","paper":"https://pith.science/paper/7DXSOJ53"},"agent_actions":{"view_html":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT","download_json":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT.json","view_paper":"https://pith.science/paper/7DXSOJ53","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.0675&json=true","fetch_graph":"https://pith.science/api/pith-number/7DXSOJ53YBNPVHOKFYQ6RB4NPT/graph.json","fetch_events":"https://pith.science/api/pith-number/7DXSOJ53YBNPVHOKFYQ6RB4NPT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT/action/storage_attestation","attest_author":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT/action/author_attestation","sign_citation":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT/action/citation_signature","submit_replication":"https://pith.science/pith/7DXSOJ53YBNPVHOKFYQ6RB4NPT/action/replication_record"}},"created_at":"2026-05-18T02:31:11.261735+00:00","updated_at":"2026-05-18T02:31:11.261735+00:00"}