{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VA2OJGTNGD3EFRAM3E3RRUCX2Y","short_pith_number":"pith:VA2OJGTN","schema_version":"1.0","canonical_sha256":"a834e49a6d30f642c40cd93718d057d6167f96d17251fed43edf2cf85f98422e","source":{"kind":"arxiv","id":"1402.0760","version":2},"attestation_state":"computed","paper":{"title":"Topology-driven instabilities: the theory of pattern formation on directed networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Duccio Fanelli, Francesco Saverio Pavone, Joseph D. Challenger, Leonardo Sacconi, Malbor Asllani","submitted_at":"2014-02-04T15:20:33Z","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"},"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":"1402.0760","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2014-02-04T15:20:33Z","cross_cats_sorted":[],"title_canon_sha256":"dba10197d8cf1e90bda9e63ff37b45c77049d2736eb5b491ab14b879f7b253f1","abstract_canon_sha256":"1a4f81252503e30eab5681622a69a1257299edb5fad08fcc7c56a4cc9f5e3665"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:12.822171Z","signature_b64":"XGPUEacOi5QHoN+/GnoYDi9U2NtPprPUX3FEUDh7NDr/X4EFJMDI1gFhjaXygA+OKBDY8nLGA8ZO7xF9kgc2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a834e49a6d30f642c40cd93718d057d6167f96d17251fed43edf2cf85f98422e","last_reissued_at":"2026-05-18T02:46:12.821502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:12.821502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology-driven instabilities: the theory of pattern formation on directed networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Duccio Fanelli, Francesco Saverio Pavone, Joseph D. Challenger, Leonardo Sacconi, Malbor Asllani","submitted_at":"2014-02-04T15:20:33Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0760","kind":"arxiv","version":2},"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":"1402.0760","created_at":"2026-05-18T02:46:12.821602+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0760v2","created_at":"2026-05-18T02:46:12.821602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0760","created_at":"2026-05-18T02:46:12.821602+00:00"},{"alias_kind":"pith_short_12","alias_value":"VA2OJGTNGD3E","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VA2OJGTNGD3EFRAM","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VA2OJGTN","created_at":"2026-05-18T12:28:52.271510+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/VA2OJGTNGD3EFRAM3E3RRUCX2Y","json":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y.json","graph_json":"https://pith.science/api/pith-number/VA2OJGTNGD3EFRAM3E3RRUCX2Y/graph.json","events_json":"https://pith.science/api/pith-number/VA2OJGTNGD3EFRAM3E3RRUCX2Y/events.json","paper":"https://pith.science/paper/VA2OJGTN"},"agent_actions":{"view_html":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y","download_json":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y.json","view_paper":"https://pith.science/paper/VA2OJGTN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0760&json=true","fetch_graph":"https://pith.science/api/pith-number/VA2OJGTNGD3EFRAM3E3RRUCX2Y/graph.json","fetch_events":"https://pith.science/api/pith-number/VA2OJGTNGD3EFRAM3E3RRUCX2Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y/action/storage_attestation","attest_author":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y/action/author_attestation","sign_citation":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y/action/citation_signature","submit_replication":"https://pith.science/pith/VA2OJGTNGD3EFRAM3E3RRUCX2Y/action/replication_record"}},"created_at":"2026-05-18T02:46:12.821602+00:00","updated_at":"2026-05-18T02:46:12.821602+00:00"}