{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:T47WWFUEYCWU3VCMGCKB4G3TYZ","short_pith_number":"pith:T47WWFUE","schema_version":"1.0","canonical_sha256":"9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b","source":{"kind":"arxiv","id":"1207.0397","version":1},"attestation_state":"computed","paper":{"title":"On non-smooth vector fields having a torus or a sphere as the sliding manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ricardo Miranda Martins","submitted_at":"2012-07-02T14:19:22Z","abstract_excerpt":"In this paper we consider a non-smooth vector field $Z=(X,Y)$, where $X,Y$ are linear vector fields in dimension 3 and the discontinuity manifold $\\Sigma$ of $Z$ is or the usual embedded torus or the unitary sphere at origin. We suppose that $\\Sigma$ is a sliding (stable/unstable) manifold with tangencies, by considering $X,Y$ inelastic over $\\Sigma$. In each case, we study the tangencies of the vector field $Z$ with $\\Sigma$ and describe the behavior of the trajectories of the sliding vector field over $\\Sigma$: they are basically closed."},"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":"1207.0397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-02T14:19:22Z","cross_cats_sorted":[],"title_canon_sha256":"60b28be6e1bdad975b9d5994fde2fb3f3827a8d265bbc42ec46c3d32c2a2e601","abstract_canon_sha256":"1c6bf4425f421c6da27a442cdb8cf8f6285db1d1575e46fc5db92e79564cb3c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:59.429036Z","signature_b64":"L3jA1IoKRiw/V3YOeUSRxNawT+WnktTXQN1Sn0dBh8OyvdZjnO4QAH2qWBOYOHhKPkvnk6jdlwk4DLFPrT0zCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b","last_reissued_at":"2026-05-18T03:51:59.428519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:59.428519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On non-smooth vector fields having a torus or a sphere as the sliding manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ricardo Miranda Martins","submitted_at":"2012-07-02T14:19:22Z","abstract_excerpt":"In this paper we consider a non-smooth vector field $Z=(X,Y)$, where $X,Y$ are linear vector fields in dimension 3 and the discontinuity manifold $\\Sigma$ of $Z$ is or the usual embedded torus or the unitary sphere at origin. We suppose that $\\Sigma$ is a sliding (stable/unstable) manifold with tangencies, by considering $X,Y$ inelastic over $\\Sigma$. In each case, we study the tangencies of the vector field $Z$ with $\\Sigma$ and describe the behavior of the trajectories of the sliding vector field over $\\Sigma$: they are basically closed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0397","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":"1207.0397","created_at":"2026-05-18T03:51:59.428609+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.0397v1","created_at":"2026-05-18T03:51:59.428609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0397","created_at":"2026-05-18T03:51:59.428609+00:00"},{"alias_kind":"pith_short_12","alias_value":"T47WWFUEYCWU","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"T47WWFUEYCWU3VCM","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"T47WWFUE","created_at":"2026-05-18T12:27:23.164592+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/T47WWFUEYCWU3VCMGCKB4G3TYZ","json":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ.json","graph_json":"https://pith.science/api/pith-number/T47WWFUEYCWU3VCMGCKB4G3TYZ/graph.json","events_json":"https://pith.science/api/pith-number/T47WWFUEYCWU3VCMGCKB4G3TYZ/events.json","paper":"https://pith.science/paper/T47WWFUE"},"agent_actions":{"view_html":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ","download_json":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ.json","view_paper":"https://pith.science/paper/T47WWFUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.0397&json=true","fetch_graph":"https://pith.science/api/pith-number/T47WWFUEYCWU3VCMGCKB4G3TYZ/graph.json","fetch_events":"https://pith.science/api/pith-number/T47WWFUEYCWU3VCMGCKB4G3TYZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/action/storage_attestation","attest_author":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/action/author_attestation","sign_citation":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/action/citation_signature","submit_replication":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/action/replication_record"}},"created_at":"2026-05-18T03:51:59.428609+00:00","updated_at":"2026-05-18T03:51:59.428609+00:00"}