{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RN5X6UQDYVXEUFI4BVSVA6PRTQ","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":"3d31d3490d7af7dd4cf405debc1b9984869ba327742f8b66cb633396226e3793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-11T15:16:43Z","title_canon_sha256":"15aecb6d14dd44ebafe9822f4cc82d38b64c9dcbfac3f102993059d73ed4ce0d"},"schema_version":"1.0","source":{"id":"1810.05072","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05072","created_at":"2026-05-17T23:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05072v1","created_at":"2026-05-17T23:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05072","created_at":"2026-05-17T23:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"RN5X6UQDYVXE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RN5X6UQDYVXEUFI4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RN5X6UQD","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:8f8bbfd34ef2f6d7dbe35285593d46d93c41a8f3fbddb188a043728a5f3c1ed2","target":"graph","created_at":"2026-05-17T23:57:39Z","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 Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator model. By using numerical continuation methods in two spatial dimensions, we establish a bifurcation diagram showing the emergence of localized spots. We characterize the transition from a single spot to an extended pattern in the form of squares. In the second part, we incorporate delayed feedback control and show that delayed feedback can induce ","authors_text":"Bilal Kostet, Etienne Averlant, Felix Tabbert, Giorgio Sonnino, Krassimir Panajotov, Mustapha Tlidi, Ren\\'e Rojas, Svetlana V. Gurevich, Tobias Frohoff-H\\\"ulsmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-11T15:16:43Z","title":"Stationary localized structures and the effect of the delayed feedback in the Brusselator model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05072","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":"sha256:0bc9a9f6dbcd0cf669719f0f6bfe9e356ba451136e4d3364b5d6369d2a2e04b6","target":"record","created_at":"2026-05-17T23:57:39Z","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":"3d31d3490d7af7dd4cf405debc1b9984869ba327742f8b66cb633396226e3793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-11T15:16:43Z","title_canon_sha256":"15aecb6d14dd44ebafe9822f4cc82d38b64c9dcbfac3f102993059d73ed4ce0d"},"schema_version":"1.0","source":{"id":"1810.05072","kind":"arxiv","version":1}},"canonical_sha256":"8b7b7f5203c56e4a151c0d655079f19c19afd61b87b314e07f9f7e1872c85b4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b7b7f5203c56e4a151c0d655079f19c19afd61b87b314e07f9f7e1872c85b4c","first_computed_at":"2026-05-17T23:57:39.709640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:39.709640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iqIO87a1bG+x1BwWOVnbevMjxuukDgfaC5oBwJX/5jbYvC27R8XHLgGFSrjEzs2yMxM2A+8YFuErjjl4q7LhCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:39.710151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05072","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bc9a9f6dbcd0cf669719f0f6bfe9e356ba451136e4d3364b5d6369d2a2e04b6","sha256:8f8bbfd34ef2f6d7dbe35285593d46d93c41a8f3fbddb188a043728a5f3c1ed2"],"state_sha256":"ff1713dc93d7f6f478ad5f4ca99aa359a32a64c175286a966730a439a0894b3c"}