{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OO5ZET3PDUK2T56O5EWBYFHK5O","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":"c8ccbfef5a0eafe292e5676d233342fba3bc03e610c4fa85674c023a81271254","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-08T10:38:31Z","title_canon_sha256":"c6a71bfedc5dd27ba0f26d393936d7cd74de93b4a7e5a57af3ba436df61e0361"},"schema_version":"1.0","source":{"id":"1203.1741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1741","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1741v1","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1741","created_at":"2026-05-18T04:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"OO5ZET3PDUK2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OO5ZET3PDUK2T56O","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OO5ZET3P","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:6f35994b39e19dccbfafab29761e37c57b9d3ce1a4828cba494920ee5172ffa2","target":"graph","created_at":"2026-05-18T04:00:37Z","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":"We analyze gradient flows with jumps generated by a finite set of complete vector fields in involution using some Radon measures $u\\in \\mathcal{U}_a$ as admissible perturbations. Both the evolution of a bounded gradient flow $\\{x^u(t,\\l)\\in B(x^*,3\\g)\\subseteq \\mbn: \\,t\\in[0,T],\\,\\l\\in B(x^*,2\\g)\\}$ and the unique solution $\\l=\\psi^u(t,x)\\in B(x^*,2\\g)\\subseteq \\mbn$ of integral equation $x^u(t,\\l)=x\\in B(x^*,\\g), \\,t\\in[0,T]$, are described using the corresponding gradient representation associated with flow and Hamilton-jacobi equations.","authors_text":"Constantin Varsan, Saima Parveen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-08T10:38:31Z","title":"Gradient flows with jumps associated with nonlinear Hamilton-Jacobi equations with jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1741","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":"sha256:9b571310f6a26e6c16a7ecc9f79b11431695abf9d840513408ca4661d67896b2","target":"record","created_at":"2026-05-18T04:00:37Z","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":"c8ccbfef5a0eafe292e5676d233342fba3bc03e610c4fa85674c023a81271254","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-08T10:38:31Z","title_canon_sha256":"c6a71bfedc5dd27ba0f26d393936d7cd74de93b4a7e5a57af3ba436df61e0361"},"schema_version":"1.0","source":{"id":"1203.1741","kind":"arxiv","version":1}},"canonical_sha256":"73bb924f6f1d15a9f7cee92c1c14eaebbf5785fabee436481090727ac64390e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73bb924f6f1d15a9f7cee92c1c14eaebbf5785fabee436481090727ac64390e9","first_computed_at":"2026-05-18T04:00:37.134680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:37.134680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PRdDZfVej2W3DWXd0Zc0B4Z+L/apmveMA/YNIeGC21ShGLbmMNbYGdyXVSKdRrqHb5eWf5C4b4GpKQeY9kcABw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:37.135256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b571310f6a26e6c16a7ecc9f79b11431695abf9d840513408ca4661d67896b2","sha256:6f35994b39e19dccbfafab29761e37c57b9d3ce1a4828cba494920ee5172ffa2"],"state_sha256":"49d8ed28a798de3b6ef8ddf62a9da0539a31c2d54a43da883fdbdbb046d9fd27"}