{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CPQ6YI4MHCTOALUUANLPYCF3O7","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":"2a2a8d8c50cb6a43d1707fe52ec992c5452eff93cca8ceeda5abde6618bb7d7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-16T17:26:26Z","title_canon_sha256":"68c286f11783da2defa624806ffe191afb21c370d1c8bdd004035ae9695134aa"},"schema_version":"1.0","source":{"id":"1207.3736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3736","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3736v1","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3736","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"CPQ6YI4MHCTO","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CPQ6YI4MHCTOALUU","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CPQ6YI4M","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:accf65b268900813a8820a30f75f70a402b844a69703c04a1c64f948f8e2ffa0","target":"graph","created_at":"2026-05-18T01:56:17Z","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":"A linear system $\\dot x = Ax$, $A \\in \\mathbb{R}^{n \\times n}$, $x \\in \\mathbb{R}^n$, with $\\mathrm{rk} A = n-1$, has a one-dimensional center manifold $E^c = \\{v \\in \\mathbb{R}^n : Av=0\\}$. If a differential equation $\\dot x = f(x)$ has a one-dimensional center manifold $W^c$ at an equilibrium $x^*$ then $E^c$ is tangential to $W^c$ with $A = Df(x^*)$ and for stability of $W^c$ it is necessary that $A$ has no spectrum in $\\mathbb{C}^+$, i.e.\\ if $A$ is symmetric, it has to be negative semi-definite.\n  We establish a graph theoretical approach to characterize semi-definiteness. Using spanning ","authors_text":"Anne-Ly Do, Jeremias Epperlein, Stefan Siegmund, Thilo gross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-16T17:26:26Z","title":"Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3736","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:acd5fd1c04f395bf2726940c36ed7db727fa18df2a5bae61c9bafefdbeb56acd","target":"record","created_at":"2026-05-18T01:56:17Z","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":"2a2a8d8c50cb6a43d1707fe52ec992c5452eff93cca8ceeda5abde6618bb7d7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-16T17:26:26Z","title_canon_sha256":"68c286f11783da2defa624806ffe191afb21c370d1c8bdd004035ae9695134aa"},"schema_version":"1.0","source":{"id":"1207.3736","kind":"arxiv","version":1}},"canonical_sha256":"13e1ec238c38a6e02e940356fc08bb77f306c146d91c536cd939062da7c53977","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13e1ec238c38a6e02e940356fc08bb77f306c146d91c536cd939062da7c53977","first_computed_at":"2026-05-18T01:56:17.934698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:17.934698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V+nqS/kA4XbbYKo2rEo0lD7uALbHuWOwYzP9hffI5FPafgOsRUEJ3VZXU9KVvLKgO9z+hWJeLa5jPoo/iSSWBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:17.935244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acd5fd1c04f395bf2726940c36ed7db727fa18df2a5bae61c9bafefdbeb56acd","sha256:accf65b268900813a8820a30f75f70a402b844a69703c04a1c64f948f8e2ffa0"],"state_sha256":"b42d4936df0468d8c9db4ea774bae7034043741af2ca5d9f278d2b9c4d7b681e"}