{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QB5TC4VKLFRCNOHBSFIWSDW25B","short_pith_number":"pith:QB5TC4VK","schema_version":"1.0","canonical_sha256":"807b3172aa596226b8e19151690edae86e96bfe7a4e1f4a9e33ffe5bb76d4ed5","source":{"kind":"arxiv","id":"1207.5699","version":1},"attestation_state":"computed","paper":{"title":"Signature stability analysis for networks of coupled dynamical systems with Hermitian Jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.DS","authors_text":"Anne-Ly Do, Jeremias Epperlein, Stefano Boccaletti, Stefan Siegmund, Thilo gross","submitted_at":"2012-07-24T13:44:34Z","abstract_excerpt":"The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what conditions a complex network of microscopic dynamical units has to meet to permit stationary macroscopic dynamics, such as stable equilibria or phase-locked states. We present an analytical approach which is based on a graphical notation that allows rewriting Jacobi's signature criterion in an interpretable form. The derived conditions pertain to topological structures on all scales, ranging from individual nodes to"},"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":"1207.5699","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-24T13:44:34Z","cross_cats_sorted":["nlin.AO"],"title_canon_sha256":"8c1ecdf1cd8ce6e4c75614bddd5cdceecb94ac9387c7922d0975b0058f03af34","abstract_canon_sha256":"a5472b521f272beaae83004f371da026782e7cf2fce677272e39c1643f25f06f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:11.595101Z","signature_b64":"HkEP8FIjSF0ZzYd3N/e26i+I6tsHQiXBx9gjaw4JCD55pO4VnOwAugd/sJO95XB2u4PRb90BxL62c2AvBtjdCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"807b3172aa596226b8e19151690edae86e96bfe7a4e1f4a9e33ffe5bb76d4ed5","last_reissued_at":"2026-05-18T03:50:11.594615Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:11.594615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Signature stability analysis for networks of coupled dynamical systems with Hermitian Jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.DS","authors_text":"Anne-Ly Do, Jeremias Epperlein, Stefano Boccaletti, Stefan Siegmund, Thilo gross","submitted_at":"2012-07-24T13:44:34Z","abstract_excerpt":"The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what conditions a complex network of microscopic dynamical units has to meet to permit stationary macroscopic dynamics, such as stable equilibria or phase-locked states. We present an analytical approach which is based on a graphical notation that allows rewriting Jacobi's signature criterion in an interpretable form. The derived conditions pertain to topological structures on all scales, ranging from individual nodes to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5699","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":"1207.5699","created_at":"2026-05-18T03:50:11.594693+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5699v1","created_at":"2026-05-18T03:50:11.594693+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5699","created_at":"2026-05-18T03:50:11.594693+00:00"},{"alias_kind":"pith_short_12","alias_value":"QB5TC4VKLFRC","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QB5TC4VKLFRCNOHB","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QB5TC4VK","created_at":"2026-05-18T12:27:18.751474+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/QB5TC4VKLFRCNOHBSFIWSDW25B","json":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B.json","graph_json":"https://pith.science/api/pith-number/QB5TC4VKLFRCNOHBSFIWSDW25B/graph.json","events_json":"https://pith.science/api/pith-number/QB5TC4VKLFRCNOHBSFIWSDW25B/events.json","paper":"https://pith.science/paper/QB5TC4VK"},"agent_actions":{"view_html":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B","download_json":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B.json","view_paper":"https://pith.science/paper/QB5TC4VK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5699&json=true","fetch_graph":"https://pith.science/api/pith-number/QB5TC4VKLFRCNOHBSFIWSDW25B/graph.json","fetch_events":"https://pith.science/api/pith-number/QB5TC4VKLFRCNOHBSFIWSDW25B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/action/storage_attestation","attest_author":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/action/author_attestation","sign_citation":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/action/citation_signature","submit_replication":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/action/replication_record"}},"created_at":"2026-05-18T03:50:11.594693+00:00","updated_at":"2026-05-18T03:50:11.594693+00:00"}