{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:T47WWFUEYCWU3VCMGCKB4G3TYZ","short_pith_number":"pith:T47WWFUE","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"},"canonical_sha256":"9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b","source":{"kind":"arxiv","id":"1207.0397","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0397","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0397v1","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0397","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"T47WWFUEYCWU","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T47WWFUEYCWU3VCM","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T47WWFUE","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:T47WWFUEYCWU3VCMGCKB4G3TYZ","target":"record","payload":{"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"},"canonical_sha256":"9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b","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"},"source_kind":"arxiv","source_id":"1207.0397","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ic4grPoxwOr3jszaS/DGNnBZt8NQdT+xqWYStcSh5IJCU0LKo1uYwDVX1rUL5EEPt9UTsHxLqBVdiISyNhifBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T12:38:39.347707Z"},"content_sha256":"cb97aa12104fec2ca656ea475e213dff966ee257ac69031d3c8be29b7ea918af","schema_version":"1.0","event_id":"sha256:cb97aa12104fec2ca656ea475e213dff966ee257ac69031d3c8be29b7ea918af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:T47WWFUEYCWU3VCMGCKB4G3TYZ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fk9UttaGQ3ARl6kA7lk7bcC30RGNPMTTAN1Dr7+adD/4BSLJnIwh9U5XCUcK5sw3Ot5wEpvyD0/RW+N1EBq9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T12:38:39.348054Z"},"content_sha256":"760fd4f366ca6a32ccd0f7b226313f1a5fcd80ec78daec471fd827b5e0486bb8","schema_version":"1.0","event_id":"sha256:760fd4f366ca6a32ccd0f7b226313f1a5fcd80ec78daec471fd827b5e0486bb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/bundle.json","state_url":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T12:38:39Z","links":{"resolver":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ","bundle":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/bundle.json","state":"https://pith.science/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T47WWFUEYCWU3VCMGCKB4G3TYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:T47WWFUEYCWU3VCMGCKB4G3TYZ","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":"1c6bf4425f421c6da27a442cdb8cf8f6285db1d1575e46fc5db92e79564cb3c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-02T14:19:22Z","title_canon_sha256":"60b28be6e1bdad975b9d5994fde2fb3f3827a8d265bbc42ec46c3d32c2a2e601"},"schema_version":"1.0","source":{"id":"1207.0397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0397","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0397v1","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0397","created_at":"2026-05-18T03:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"T47WWFUEYCWU","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"T47WWFUEYCWU3VCM","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"T47WWFUE","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:760fd4f366ca6a32ccd0f7b226313f1a5fcd80ec78daec471fd827b5e0486bb8","target":"graph","created_at":"2026-05-18T03:51:59Z","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"},"paper":{"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.","authors_text":"Ricardo Miranda Martins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-02T14:19:22Z","title":"On non-smooth vector fields having a torus or a sphere as the sliding manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0397","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:cb97aa12104fec2ca656ea475e213dff966ee257ac69031d3c8be29b7ea918af","target":"record","created_at":"2026-05-18T03:51:59Z","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":"1c6bf4425f421c6da27a442cdb8cf8f6285db1d1575e46fc5db92e79564cb3c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-02T14:19:22Z","title_canon_sha256":"60b28be6e1bdad975b9d5994fde2fb3f3827a8d265bbc42ec46c3d32c2a2e601"},"schema_version":"1.0","source":{"id":"1207.0397","kind":"arxiv","version":1}},"canonical_sha256":"9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b","first_computed_at":"2026-05-18T03:51:59.428519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:59.428519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L3jA1IoKRiw/V3YOeUSRxNawT+WnktTXQN1Sn0dBh8OyvdZjnO4QAH2qWBOYOHhKPkvnk6jdlwk4DLFPrT0zCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:59.429036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb97aa12104fec2ca656ea475e213dff966ee257ac69031d3c8be29b7ea918af","sha256:760fd4f366ca6a32ccd0f7b226313f1a5fcd80ec78daec471fd827b5e0486bb8"],"state_sha256":"3ad6b48c7418fff0842f65b3b3b6bcb5bf59253b978157f60dea91fc0dd7799d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywqC69YyT24EY56jowl4ilONg86qshdxBu6NFvd2n6Xn/lfS+vjV0AMsTRmRER8n19L6rUAEfK2KRCTwQkkUBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T12:38:39.350027Z","bundle_sha256":"97cfaff22ea48c71aea27eee86f529fbee1890acf5d7794c5f958a92aeb69226"}}