{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QB5TC4VKLFRCNOHBSFIWSDW25B","short_pith_number":"pith:QB5TC4VK","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"},"canonical_sha256":"807b3172aa596226b8e19151690edae86e96bfe7a4e1f4a9e33ffe5bb76d4ed5","source":{"kind":"arxiv","id":"1207.5699","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5699","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5699v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5699","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"QB5TC4VKLFRC","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QB5TC4VKLFRCNOHB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QB5TC4VK","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QB5TC4VKLFRCNOHBSFIWSDW25B","target":"record","payload":{"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"},"canonical_sha256":"807b3172aa596226b8e19151690edae86e96bfe7a4e1f4a9e33ffe5bb76d4ed5","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"},"source_kind":"arxiv","source_id":"1207.5699","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":"2026-05-18T03:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dk0eYcY1AuoyKpxHg2FC+LCeM9+uE9HbhFa5xHwZrd3oUmk7YP/fQZK9NsjdMUiLJPnit+rVOKcuzOR9aV0cAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:01:29.151953Z"},"content_sha256":"07d46f93464b1bf6efa4434d186740fa1b3c5635247c5c65b5c74befa6b65d5e","schema_version":"1.0","event_id":"sha256:07d46f93464b1bf6efa4434d186740fa1b3c5635247c5c65b5c74befa6b65d5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QB5TC4VKLFRCNOHBSFIWSDW25B","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTmRM/2mwW+1k7ApuoCSPOmHgjtsOnl1Gr2JYCiy8QAesIhnBnoiMMzesjar+yd+SJU9WsHJeVH6kRXvP9DKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:01:29.152401Z"},"content_sha256":"505386a82b20d436386a0f04928a1dd0346f6986710a751650a0c636b7a5df68","schema_version":"1.0","event_id":"sha256:505386a82b20d436386a0f04928a1dd0346f6986710a751650a0c636b7a5df68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/bundle.json","state_url":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/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":"2026-05-28T07:01:29Z","links":{"resolver":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B","bundle":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/bundle.json","state":"https://pith.science/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QB5TC4VKLFRCNOHBSFIWSDW25B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QB5TC4VKLFRCNOHBSFIWSDW25B","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":"a5472b521f272beaae83004f371da026782e7cf2fce677272e39c1643f25f06f","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-24T13:44:34Z","title_canon_sha256":"8c1ecdf1cd8ce6e4c75614bddd5cdceecb94ac9387c7922d0975b0058f03af34"},"schema_version":"1.0","source":{"id":"1207.5699","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5699","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5699v1","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5699","created_at":"2026-05-18T03:50:11Z"},{"alias_kind":"pith_short_12","alias_value":"QB5TC4VKLFRC","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QB5TC4VKLFRCNOHB","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QB5TC4VK","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:505386a82b20d436386a0f04928a1dd0346f6986710a751650a0c636b7a5df68","target":"graph","created_at":"2026-05-18T03:50:11Z","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":"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","authors_text":"Anne-Ly Do, Jeremias Epperlein, Stefano Boccaletti, Stefan Siegmund, Thilo gross","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-24T13:44:34Z","title":"Signature stability analysis for networks of coupled dynamical systems with Hermitian Jacobian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5699","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":"sha256:07d46f93464b1bf6efa4434d186740fa1b3c5635247c5c65b5c74befa6b65d5e","target":"record","created_at":"2026-05-18T03:50:11Z","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":"a5472b521f272beaae83004f371da026782e7cf2fce677272e39c1643f25f06f","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-07-24T13:44:34Z","title_canon_sha256":"8c1ecdf1cd8ce6e4c75614bddd5cdceecb94ac9387c7922d0975b0058f03af34"},"schema_version":"1.0","source":{"id":"1207.5699","kind":"arxiv","version":1}},"canonical_sha256":"807b3172aa596226b8e19151690edae86e96bfe7a4e1f4a9e33ffe5bb76d4ed5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"807b3172aa596226b8e19151690edae86e96bfe7a4e1f4a9e33ffe5bb76d4ed5","first_computed_at":"2026-05-18T03:50:11.594615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:11.594615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HkEP8FIjSF0ZzYd3N/e26i+I6tsHQiXBx9gjaw4JCD55pO4VnOwAugd/sJO95XB2u4PRb90BxL62c2AvBtjdCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:11.595101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5699","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07d46f93464b1bf6efa4434d186740fa1b3c5635247c5c65b5c74befa6b65d5e","sha256:505386a82b20d436386a0f04928a1dd0346f6986710a751650a0c636b7a5df68"],"state_sha256":"e75b615749721cdaee8d1d75ae43a8a04a58904fe4d43a5b682513f525b1ef9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zADr2EZwoDih5Qgoj/ocHfZLrPHhrhvfQmbtyhqwUCBucm18Cu+3XS9Ygsri7f6PAxyWHhNcerUIBjJG0Z2Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:01:29.154605Z","bundle_sha256":"f8869f465437dfdee51394dcb11303e8d2c12ba8f1e85bfe88b31f320784b9ac"}}