{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BXW6ZASFHT77I5WZJLM5FG7S26","short_pith_number":"pith:BXW6ZASF","schema_version":"1.0","canonical_sha256":"0dedec82453cfff476d94ad9d29bf2d7905d1f0326d44b7665f03ae9b346fd74","source":{"kind":"arxiv","id":"1804.04537","version":1},"attestation_state":"computed","paper":{"title":"Fejer Polynomials and Control of Nonlinear Discrete Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Stokolos, Anatolii Korenovskyi, Anna Khamitova, Dmitriy Dmitrishin, Paul Hagelstein","submitted_at":"2018-04-12T14:37:39Z","abstract_excerpt":"We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of a differentiable function $f: \\mathbb{R}\\rightarrow\\mathbb{R}$ of the form $$x(k+1) = f(x(k)) + u(k)$$ where $$u(k) = (a_1 - 1)f(x(k)) + a_2 f(x(k-T)) + \\cdots + a_N f(x(k-(N-1)T))\\;,$$ with $a_1 + \\cdots + a_N = 1$. Following an approach of Morg\\\"ul, we associate to each periodic orbit of $f$, $N \\in \\mathbb{N}$, and $a_1,\\ldots,a_N$ an explicit polynomial "},"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":"1804.04537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-12T14:37:39Z","cross_cats_sorted":[],"title_canon_sha256":"f19e08b76c3d05b17a1a15480695a8128c4c56b85af26ba410ce4636e6cefb80","abstract_canon_sha256":"674c95ac265365fa9265a9870ad015b4a4e3969fea200cd63f75da9c4a7aceb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:37.303761Z","signature_b64":"ei4EPuF8sp6knOoVzLs9cXzRNbp7meaRAXfylfUnJm5aqQZP95DDa0GYvumcuRIp1ieU5KyU+3smtX+hQNMIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dedec82453cfff476d94ad9d29bf2d7905d1f0326d44b7665f03ae9b346fd74","last_reissued_at":"2026-05-18T00:18:37.303178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:37.303178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fejer Polynomials and Control of Nonlinear Discrete Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Stokolos, Anatolii Korenovskyi, Anna Khamitova, Dmitriy Dmitrishin, Paul Hagelstein","submitted_at":"2018-04-12T14:37:39Z","abstract_excerpt":"We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of a differentiable function $f: \\mathbb{R}\\rightarrow\\mathbb{R}$ of the form $$x(k+1) = f(x(k)) + u(k)$$ where $$u(k) = (a_1 - 1)f(x(k)) + a_2 f(x(k-T)) + \\cdots + a_N f(x(k-(N-1)T))\\;,$$ with $a_1 + \\cdots + a_N = 1$. Following an approach of Morg\\\"ul, we associate to each periodic orbit of $f$, $N \\in \\mathbb{N}$, and $a_1,\\ldots,a_N$ an explicit polynomial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04537","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":"1804.04537","created_at":"2026-05-18T00:18:37.303271+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.04537v1","created_at":"2026-05-18T00:18:37.303271+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04537","created_at":"2026-05-18T00:18:37.303271+00:00"},{"alias_kind":"pith_short_12","alias_value":"BXW6ZASFHT77","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BXW6ZASFHT77I5WZ","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BXW6ZASF","created_at":"2026-05-18T12:32:16.446611+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/BXW6ZASFHT77I5WZJLM5FG7S26","json":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26.json","graph_json":"https://pith.science/api/pith-number/BXW6ZASFHT77I5WZJLM5FG7S26/graph.json","events_json":"https://pith.science/api/pith-number/BXW6ZASFHT77I5WZJLM5FG7S26/events.json","paper":"https://pith.science/paper/BXW6ZASF"},"agent_actions":{"view_html":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26","download_json":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26.json","view_paper":"https://pith.science/paper/BXW6ZASF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.04537&json=true","fetch_graph":"https://pith.science/api/pith-number/BXW6ZASFHT77I5WZJLM5FG7S26/graph.json","fetch_events":"https://pith.science/api/pith-number/BXW6ZASFHT77I5WZJLM5FG7S26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26/action/storage_attestation","attest_author":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26/action/author_attestation","sign_citation":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26/action/citation_signature","submit_replication":"https://pith.science/pith/BXW6ZASFHT77I5WZJLM5FG7S26/action/replication_record"}},"created_at":"2026-05-18T00:18:37.303271+00:00","updated_at":"2026-05-18T00:18:37.303271+00:00"}