{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VBWZ4DNVA24ZTHBJDLWJMXT25X","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":"375f7abad101124b567e12c0ed6ad06358759cb36fbdc2a48c4fd07f644d4b6e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-03T21:03:09Z","title_canon_sha256":"72bb3121e21cc3c4d7f954e32f12d72e838ce877d3651a18c9ff12689367f92b"},"schema_version":"1.0","source":{"id":"1703.01339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01339","created_at":"2026-05-18T00:49:31Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01339v1","created_at":"2026-05-18T00:49:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01339","created_at":"2026-05-18T00:49:31Z"},{"alias_kind":"pith_short_12","alias_value":"VBWZ4DNVA24Z","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VBWZ4DNVA24ZTHBJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VBWZ4DNV","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:f31829367621e1bbebc7b10181720b3790413b25b8410ac72fb2307495d7e793","target":"graph","created_at":"2026-05-18T00:49:31Z","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 consider the dynamical system \\begin{equation*}\\left\\{ \\begin{array}{ll} v(t)\\in\\partial\\phi(x(t))\\\\ \\lambda\\dot x(t) + \\dot v(t) + v(t) + \\nabla \\psi(x(t))=0, \\end{array}\\right.\\end{equation*} where $\\phi:\\R^n\\to\\R\\cup\\{+\\infty\\}$ is a proper, convex and lower semicontinuous function, $\\psi:\\R^n\\to\\R$ is a (possibly nonconvex) smooth function and $\\lambda>0$ is a parameter which controls the velocity. We show that the set of limit points of the trajectory $x$ is contained in the set of critical points of the objective function $\\phi+\\psi$, which is here seen as the set of the zeros of its ","authors_text":"Ern\\\"o Robert Csetnek, Radu Ioan Bot","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-03T21:03:09Z","title":"Newton-like dynamics associated to nonconvex optimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01339","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":"sha256:9a1b6b0fd2a375b3a99317c5cd8308522b9aae9065af0371dce8dce1fc1e7638","target":"record","created_at":"2026-05-18T00:49:31Z","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":"375f7abad101124b567e12c0ed6ad06358759cb36fbdc2a48c4fd07f644d4b6e","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-03T21:03:09Z","title_canon_sha256":"72bb3121e21cc3c4d7f954e32f12d72e838ce877d3651a18c9ff12689367f92b"},"schema_version":"1.0","source":{"id":"1703.01339","kind":"arxiv","version":1}},"canonical_sha256":"a86d9e0db506b9999c291aec965e7aedfcae263f96e0a40d716414c50672af04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a86d9e0db506b9999c291aec965e7aedfcae263f96e0a40d716414c50672af04","first_computed_at":"2026-05-18T00:49:31.061238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:31.061238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1EZEs5uqCXY8ar3W3arciHak4ass0/4Xk/BeY7oIkpAHNf06Z50hSRNYrrDltTt16ppWjdBeh1GtGz47S8c8Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:31.061819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a1b6b0fd2a375b3a99317c5cd8308522b9aae9065af0371dce8dce1fc1e7638","sha256:f31829367621e1bbebc7b10181720b3790413b25b8410ac72fb2307495d7e793"],"state_sha256":"fee6e13678b2ad79d6ec58c3dff0c9608e1014f7d586c87a34dc0af7a9722c1b"}