{"paper":{"title":"Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Orthogonal polynomials on the unit circle enable low-dimensional reduction for globally coupled phase oscillators with multiharmonic couplings.","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Kai Tokunaga","submitted_at":"2026-04-16T04:36:04Z","abstract_excerpt":"Low-dimensional reduction theories such as the Ott-Antonsen ansatz have played a crucial role in the study of populations of coupled oscillators. However, most of these theories apply only to models in which the interaction is described by a single harmonic component, limiting their use in more realistic oscillator models. Using the theory of orthogonal polynomials on the unit circle (OPUC), we develop a low-dimensional reduction theory for populations of globally coupled phase oscillators with multiharmonic coupling. We show theoretically and numerically that it is exact for uniformly rotatin"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"by employing the theory of orthogonal polynomials on the unit circle (OPUC), we construct a framework that enables low-dimensional reduction for populations of globally coupled phase oscillators with multiharmonic coupling.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the OPUC theory applies directly and yields a valid low-dimensional reduction for arbitrary multiharmonic coupling functions without requiring additional restrictions on the oscillator frequencies or coupling strengths.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A low-dimensional reduction framework for multiharmonic globally coupled phase oscillators is constructed using OPUC theory.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Orthogonal polynomials on the unit circle enable low-dimensional reduction for globally coupled phase oscillators with multiharmonic couplings.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a57b8b247e1c609f92e0ec2cf2433ce10418627157073ddf3add4f2610278c1c"},"source":{"id":"2604.14611","kind":"arxiv","version":2},"verdict":{"id":"886a19d2-fa32-4596-8aea-f454d1ffa01e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T10:04:16.027609Z","strongest_claim":"by employing the theory of orthogonal polynomials on the unit circle (OPUC), we construct a framework that enables low-dimensional reduction for populations of globally coupled phase oscillators with multiharmonic coupling.","one_line_summary":"A low-dimensional reduction framework for multiharmonic globally coupled phase oscillators is constructed using OPUC theory.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the OPUC theory applies directly and yields a valid low-dimensional reduction for arbitrary multiharmonic coupling functions without requiring additional restrictions on the oscillator frequencies or coupling strengths.","pith_extraction_headline":"Orthogonal polynomials on the unit circle enable low-dimensional reduction for globally coupled phase oscillators with multiharmonic couplings."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.14611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}