{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SULKTHRG2X6ISP2MTE2CPRQPJL","short_pith_number":"pith:SULKTHRG","schema_version":"1.0","canonical_sha256":"9516a99e26d5fc893f4c993427c60f4acc3f774af61cecc2cb7a2186aa70c701","source":{"kind":"arxiv","id":"1603.07122","version":1},"attestation_state":"computed","paper":{"title":"Pattern formation in a two-component reaction-diffusion system with delayed processes on a network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ben Lauwens, Duccio Fanelli, Julien Petit, Malbor Asllani, Timoteo Carletti","submitted_at":"2016-03-23T10:24:03Z","abstract_excerpt":"Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overc"},"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":"1603.07122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-23T10:24:03Z","cross_cats_sorted":[],"title_canon_sha256":"db98dfc73e77dae60b97f5de99210eb979eef87a813d922eee075bb618660270","abstract_canon_sha256":"216819032754704731798e85ec93e968ab9b656fd990100ad8f01d648230c91d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:06.216863Z","signature_b64":"t4QN8BwZgvZPxaaSJtsS5Mi8cJ2eZamzTyrFFZtLhrEBx7OGEc+FU98nQq5qv1MYLEIn0FXLBxIe2GkuN+caCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9516a99e26d5fc893f4c993427c60f4acc3f774af61cecc2cb7a2186aa70c701","last_reissued_at":"2026-05-18T01:10:06.216435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:06.216435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pattern formation in a two-component reaction-diffusion system with delayed processes on a network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ben Lauwens, Duccio Fanelli, Julien Petit, Malbor Asllani, Timoteo Carletti","submitted_at":"2016-03-23T10:24:03Z","abstract_excerpt":"Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07122","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":"1603.07122","created_at":"2026-05-18T01:10:06.216505+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.07122v1","created_at":"2026-05-18T01:10:06.216505+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07122","created_at":"2026-05-18T01:10:06.216505+00:00"},{"alias_kind":"pith_short_12","alias_value":"SULKTHRG2X6I","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SULKTHRG2X6ISP2M","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SULKTHRG","created_at":"2026-05-18T12:30:44.179134+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/SULKTHRG2X6ISP2MTE2CPRQPJL","json":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL.json","graph_json":"https://pith.science/api/pith-number/SULKTHRG2X6ISP2MTE2CPRQPJL/graph.json","events_json":"https://pith.science/api/pith-number/SULKTHRG2X6ISP2MTE2CPRQPJL/events.json","paper":"https://pith.science/paper/SULKTHRG"},"agent_actions":{"view_html":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL","download_json":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL.json","view_paper":"https://pith.science/paper/SULKTHRG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.07122&json=true","fetch_graph":"https://pith.science/api/pith-number/SULKTHRG2X6ISP2MTE2CPRQPJL/graph.json","fetch_events":"https://pith.science/api/pith-number/SULKTHRG2X6ISP2MTE2CPRQPJL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL/action/storage_attestation","attest_author":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL/action/author_attestation","sign_citation":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL/action/citation_signature","submit_replication":"https://pith.science/pith/SULKTHRG2X6ISP2MTE2CPRQPJL/action/replication_record"}},"created_at":"2026-05-18T01:10:06.216505+00:00","updated_at":"2026-05-18T01:10:06.216505+00:00"}