{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AIGK4QX2RFP5YTDLKHZ4OTRJJX","short_pith_number":"pith:AIGK4QX2","schema_version":"1.0","canonical_sha256":"020cae42fa895fdc4c6b51f3c74e294dd9bf60941fcc7b826726e0236b98bf0a","source":{"kind":"arxiv","id":"1503.08241","version":2},"attestation_state":"computed","paper":{"title":"Stability of Hopf bifurcations in Time-delayed fully-connected PLL networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\'Atila Madureira Bueno, Diego Paolo Ferruzzo Correa, Jos\\'e Roberto Castilho Piqueira","submitted_at":"2015-03-27T23:34:27Z","abstract_excerpt":"Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the solutions in the parameter space for a network of Phase-Locked Loop oscillators was studied in \\textit{Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators}. Communications in Nonlinear Science and Numerical Simulation, Elsevier BV, Volume 22, Issues 1-3, May 2015, Pages 793-820, where the existence of Hopf bifu"},"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":"1503.08241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-27T23:34:27Z","cross_cats_sorted":[],"title_canon_sha256":"bf6bad88ff432acfaef6e29a87ecc789494cccdaaa34e457d7e8110ac0ebb051","abstract_canon_sha256":"dbf176c9de663027ab9cbb6a3568a343635fe1f17f5f0c0da80bcf1398b4fe90"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.002133Z","signature_b64":"WIzLhDBhhuVuGgzsKuVQ2hcfQzz/9byAkeR6czVQeWWuTbun3bQbkhVhTPUtDxAWtsgyrcVbfcbfUxvi5PedAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"020cae42fa895fdc4c6b51f3c74e294dd9bf60941fcc7b826726e0236b98bf0a","last_reissued_at":"2026-05-18T02:17:33.001593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.001593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of Hopf bifurcations in Time-delayed fully-connected PLL networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"\\'Atila Madureira Bueno, Diego Paolo Ferruzzo Correa, Jos\\'e Roberto Castilho Piqueira","submitted_at":"2015-03-27T23:34:27Z","abstract_excerpt":"Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the solutions in the parameter space for a network of Phase-Locked Loop oscillators was studied in \\textit{Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators}. Communications in Nonlinear Science and Numerical Simulation, Elsevier BV, Volume 22, Issues 1-3, May 2015, Pages 793-820, where the existence of Hopf bifu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08241","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":"1503.08241","created_at":"2026-05-18T02:17:33.001678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08241v2","created_at":"2026-05-18T02:17:33.001678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08241","created_at":"2026-05-18T02:17:33.001678+00:00"},{"alias_kind":"pith_short_12","alias_value":"AIGK4QX2RFP5","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AIGK4QX2RFP5YTDL","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AIGK4QX2","created_at":"2026-05-18T12:29:10.953037+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/AIGK4QX2RFP5YTDLKHZ4OTRJJX","json":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX.json","graph_json":"https://pith.science/api/pith-number/AIGK4QX2RFP5YTDLKHZ4OTRJJX/graph.json","events_json":"https://pith.science/api/pith-number/AIGK4QX2RFP5YTDLKHZ4OTRJJX/events.json","paper":"https://pith.science/paper/AIGK4QX2"},"agent_actions":{"view_html":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX","download_json":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX.json","view_paper":"https://pith.science/paper/AIGK4QX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08241&json=true","fetch_graph":"https://pith.science/api/pith-number/AIGK4QX2RFP5YTDLKHZ4OTRJJX/graph.json","fetch_events":"https://pith.science/api/pith-number/AIGK4QX2RFP5YTDLKHZ4OTRJJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX/action/storage_attestation","attest_author":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX/action/author_attestation","sign_citation":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX/action/citation_signature","submit_replication":"https://pith.science/pith/AIGK4QX2RFP5YTDLKHZ4OTRJJX/action/replication_record"}},"created_at":"2026-05-18T02:17:33.001678+00:00","updated_at":"2026-05-18T02:17:33.001678+00:00"}