{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VA2OJGTNGD3EFRAM3E3RRUCX2Y","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":"1a4f81252503e30eab5681622a69a1257299edb5fad08fcc7c56a4cc9f5e3665","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-02-04T15:20:33Z","title_canon_sha256":"dba10197d8cf1e90bda9e63ff37b45c77049d2736eb5b491ab14b879f7b253f1"},"schema_version":"1.0","source":{"id":"1402.0760","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0760","created_at":"2026-05-18T02:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0760v2","created_at":"2026-05-18T02:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0760","created_at":"2026-05-18T02:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"VA2OJGTNGD3E","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"VA2OJGTNGD3EFRAM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"VA2OJGTN","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:f211a90428abb59356a6d893315f0ce78888afafcaee68ac9ccbe4e9fa129ae5","target":"graph","created_at":"2026-05-18T02:46:12Z","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 theory of pattern formation in reaction-diffusion systems is extended to the case of a directed network. Due to the structure of the network Laplacian of the scrutinised system, the dispersion relation has both real and imaginary parts, at variance with the conventional case for a symmetric network. It is found that the homogeneous fixed point can become unstable due to the topology of the network, resulting in a new class of instabilities which cannot be induced on undirected graphs. Results from a linear stability analysis allow the instability region to be analytically traced. Numerical","authors_text":"Duccio Fanelli, Francesco Saverio Pavone, Joseph D. Challenger, Leonardo Sacconi, Malbor Asllani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-02-04T15:20:33Z","title":"Topology-driven instabilities: the theory of pattern formation on directed networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0760","kind":"arxiv","version":2},"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:fa6a188aa60759bb19faa7d112f50e8ccdf8b1b668a9d29071b81426acf8701b","target":"record","created_at":"2026-05-18T02:46:12Z","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":"1a4f81252503e30eab5681622a69a1257299edb5fad08fcc7c56a4cc9f5e3665","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-02-04T15:20:33Z","title_canon_sha256":"dba10197d8cf1e90bda9e63ff37b45c77049d2736eb5b491ab14b879f7b253f1"},"schema_version":"1.0","source":{"id":"1402.0760","kind":"arxiv","version":2}},"canonical_sha256":"a834e49a6d30f642c40cd93718d057d6167f96d17251fed43edf2cf85f98422e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a834e49a6d30f642c40cd93718d057d6167f96d17251fed43edf2cf85f98422e","first_computed_at":"2026-05-18T02:46:12.821502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:12.821502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XGPUEacOi5QHoN+/GnoYDi9U2NtPprPUX3FEUDh7NDr/X4EFJMDI1gFhjaXygA+OKBDY8nLGA8ZO7xF9kgc2Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:12.822171Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0760","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa6a188aa60759bb19faa7d112f50e8ccdf8b1b668a9d29071b81426acf8701b","sha256:f211a90428abb59356a6d893315f0ce78888afafcaee68ac9ccbe4e9fa129ae5"],"state_sha256":"1fb57a45e4464a57489bc04cf86a88aa88acf936b933812f486b8cd81c4e1459"}