{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TNKNGHSL42TN72LUOTDUUTAIF2","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":"ed11921bbb2a592204ebe8d1cc9293be0b35b86dab896e9f1a4e8932aa5118cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2026-04-16T04:36:04Z","title_canon_sha256":"6d9ed77ac4337827a2485e2b96a76a9059bc47d5073e99fc3d358edf298c7b83"},"schema_version":"1.0","source":{"id":"2604.14611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.14611","created_at":"2026-06-02T01:03:47Z"},{"alias_kind":"arxiv_version","alias_value":"2604.14611v2","created_at":"2026-06-02T01:03:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.14611","created_at":"2026-06-02T01:03:47Z"},{"alias_kind":"pith_short_12","alias_value":"TNKNGHSL42TN","created_at":"2026-06-02T01:03:47Z"},{"alias_kind":"pith_short_16","alias_value":"TNKNGHSL42TN72LU","created_at":"2026-06-02T01:03:47Z"},{"alias_kind":"pith_short_8","alias_value":"TNKNGHSL","created_at":"2026-06-02T01:03:47Z"}],"graph_snapshots":[{"event_id":"sha256:60c8094202d9faf567a23e137772e37aa681efcc4d5be0cea5827ab41eae70c8","target":"graph","created_at":"2026-06-02T01:03:47Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A low-dimensional reduction framework for multiharmonic globally coupled phase oscillators is constructed using OPUC theory."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Orthogonal polynomials on the unit circle enable low-dimensional reduction for globally coupled phase oscillators with multiharmonic couplings."}],"snapshot_sha256":"a57b8b247e1c609f92e0ec2cf2433ce10418627157073ddf3add4f2610278c1c"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.14611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Kai Tokunaga","cross_cats":[],"headline":"Orthogonal polynomials on the unit circle enable low-dimensional reduction for globally coupled phase oscillators with multiharmonic couplings.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2026-04-16T04:36:04Z","title":"Low-Dimensional Reduction Theory for Populations of Globally Coupled Phase Oscillators with Multiharmonic Coupling: A Method Based on OPUC Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.14611","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T10:04:16.027609Z","id":"886a19d2-fa32-4596-8aea-f454d1ffa01e","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Orthogonal polynomials on the unit circle enable low-dimensional reduction for globally coupled phase oscillators with multiharmonic couplings.","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.","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."}},"verdict_id":"886a19d2-fa32-4596-8aea-f454d1ffa01e"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47f4e4c620c1a2c008fe3f92c4c5f2f65624ac13e412d9b50d7c7c74c4fcce0c","target":"record","created_at":"2026-06-02T01:03:47Z","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":"ed11921bbb2a592204ebe8d1cc9293be0b35b86dab896e9f1a4e8932aa5118cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2026-04-16T04:36:04Z","title_canon_sha256":"6d9ed77ac4337827a2485e2b96a76a9059bc47d5073e99fc3d358edf298c7b83"},"schema_version":"1.0","source":{"id":"2604.14611","kind":"arxiv","version":2}},"canonical_sha256":"9b54d31e4be6a6dfe97474c74a4c082ebf89e8d270b500bd51dd9edfec88b04f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b54d31e4be6a6dfe97474c74a4c082ebf89e8d270b500bd51dd9edfec88b04f","first_computed_at":"2026-06-02T01:03:47.059205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:47.059205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9O52fCYX2acTdwBYdA+lLADyDbF60FMV5eH/LaYBQnfllXUIxLmSKQOi3K2ShUZxGDtprAup8B9nuYWZm6IfAA==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:47.059750Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.14611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f4e4c620c1a2c008fe3f92c4c5f2f65624ac13e412d9b50d7c7c74c4fcce0c","sha256:60c8094202d9faf567a23e137772e37aa681efcc4d5be0cea5827ab41eae70c8"],"state_sha256":"755da693bccc86e13015478be441df16603992b9e1bfb862949b2da1f6c950d1"}