{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AMNIMDDGWQBU7PZPD76SDQ4WNM","short_pith_number":"pith:AMNIMDDG","schema_version":"1.0","canonical_sha256":"031a860c66b4034fbf2f1ffd21c3966b2d3ff55264b0589cd76b880abfc59d8a","source":{"kind":"arxiv","id":"1403.3585","version":1},"attestation_state":"computed","paper":{"title":"Pattern formation in systems with multiple delayed feedbacks","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.AO","nlin.CD","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Giovanni Giacomelli, Serhiy Yanchuk","submitted_at":"2014-03-14T14:18:22Z","abstract_excerpt":"Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behaviour in the case of two delays is shown to ''encode'' two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the att"},"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":"1403.3585","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"nlin.PS","submitted_at":"2014-03-14T14:18:22Z","cross_cats_sorted":["math-ph","math.MP","nlin.AO","nlin.CD","physics.optics"],"title_canon_sha256":"09794861a85eb194dc742275baa8384fae6fb74b710a1ad5446c861302d8b809","abstract_canon_sha256":"b6768243e69804fff3656b54a160a2cd9bb4ed2e6faf28e371ebcf9bb84a2429"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:01.131428Z","signature_b64":"zQn+B4vz6d4p7+VesXY485e+0UY7CoASSpgJ6R+pbYIDOxxiO8WQD65bD+irc23TS5C5BPWaq2T4GDXeMj93Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"031a860c66b4034fbf2f1ffd21c3966b2d3ff55264b0589cd76b880abfc59d8a","last_reissued_at":"2026-05-18T01:44:01.130815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:01.130815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pattern formation in systems with multiple delayed feedbacks","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.AO","nlin.CD","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Giovanni Giacomelli, Serhiy Yanchuk","submitted_at":"2014-03-14T14:18:22Z","abstract_excerpt":"Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long time delays, and using a suitable space-time representation we uncover features otherwise hidden in their temporal dynamics. The behaviour in the case of two delays is shown to ''encode'' two-dimensional spiral defects and defects turbulence. A multiple scale analysis sets the equivalence to a complex Ginzburg-Landau equation, and a novel criterium for the att"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3585","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":"1403.3585","created_at":"2026-05-18T01:44:01.130918+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.3585v1","created_at":"2026-05-18T01:44:01.130918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3585","created_at":"2026-05-18T01:44:01.130918+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMNIMDDGWQBU","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMNIMDDGWQBU7PZP","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMNIMDDG","created_at":"2026-05-18T12:28:19.803747+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/AMNIMDDGWQBU7PZPD76SDQ4WNM","json":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM.json","graph_json":"https://pith.science/api/pith-number/AMNIMDDGWQBU7PZPD76SDQ4WNM/graph.json","events_json":"https://pith.science/api/pith-number/AMNIMDDGWQBU7PZPD76SDQ4WNM/events.json","paper":"https://pith.science/paper/AMNIMDDG"},"agent_actions":{"view_html":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM","download_json":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM.json","view_paper":"https://pith.science/paper/AMNIMDDG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.3585&json=true","fetch_graph":"https://pith.science/api/pith-number/AMNIMDDGWQBU7PZPD76SDQ4WNM/graph.json","fetch_events":"https://pith.science/api/pith-number/AMNIMDDGWQBU7PZPD76SDQ4WNM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM/action/storage_attestation","attest_author":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM/action/author_attestation","sign_citation":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM/action/citation_signature","submit_replication":"https://pith.science/pith/AMNIMDDGWQBU7PZPD76SDQ4WNM/action/replication_record"}},"created_at":"2026-05-18T01:44:01.130918+00:00","updated_at":"2026-05-18T01:44:01.130918+00:00"}