{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4PR4PNV5LF5PJGBV7HYIYI6AMJ","short_pith_number":"pith:4PR4PNV5","schema_version":"1.0","canonical_sha256":"e3e3c7b6bd597af49835f9f08c23c0625c7ec3c74788af1e9b62f14cd93dbc89","source":{"kind":"arxiv","id":"1412.0666","version":2},"attestation_state":"computed","paper":{"title":"Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.AG","math.DS","math.MP"],"primary_cat":"nlin.CD","authors_text":"Dhagash Mehta, Florian D\\\"orfler, Jonathan D. Hauenstein, Noah Daleo","submitted_at":"2014-12-01T21:00:10Z","abstract_excerpt":"Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find all of the equilibria for various choices of coupling constants K, natural frequencies, and on different graphs. We note that for even modest sizes (N ~ 10-20), the number of equilibria is already more than 100,000. We analyze the stability of each computed equilibrium as well as the configuration of angles. Our exploration of the equilibrium landscape leads "},"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":"1412.0666","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-12-01T21:00:10Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.AG","math.DS","math.MP"],"title_canon_sha256":"c4e7537bcf0a3baee2e89222dc7c5db837737be7b8cd0452f5cb3684a2c0bdf1","abstract_canon_sha256":"8ddf044a9158acbaaaa678919981d4ef1c63417c8e3a13b62bd21ed44ed54a21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:08.073513Z","signature_b64":"Jf521LcEIhmsAGS6EeOxtZT5lnwKy75i6m7kuYc96X1CnIeFr8hpGQ2H8fF2sjXGPMn0uTAtF9BScyCvQH7xAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3e3c7b6bd597af49835f9f08c23c0625c7ec3c74788af1e9b62f14cd93dbc89","last_reissued_at":"2026-05-18T02:04:08.072855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:08.072855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.AG","math.DS","math.MP"],"primary_cat":"nlin.CD","authors_text":"Dhagash Mehta, Florian D\\\"orfler, Jonathan D. Hauenstein, Noah Daleo","submitted_at":"2014-12-01T21:00:10Z","abstract_excerpt":"Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an algebraic geometry problem and use numerical methods to find all of the equilibria for various choices of coupling constants K, natural frequencies, and on different graphs. We note that for even modest sizes (N ~ 10-20), the number of equilibria is already more than 100,000. We analyze the stability of each computed equilibrium as well as the configuration of angles. Our exploration of the equilibrium landscape leads "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0666","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":"1412.0666","created_at":"2026-05-18T02:04:08.072963+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.0666v2","created_at":"2026-05-18T02:04:08.072963+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0666","created_at":"2026-05-18T02:04:08.072963+00:00"},{"alias_kind":"pith_short_12","alias_value":"4PR4PNV5LF5P","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4PR4PNV5LF5PJGBV","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4PR4PNV5","created_at":"2026-05-18T12:28:14.216126+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/4PR4PNV5LF5PJGBV7HYIYI6AMJ","json":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ.json","graph_json":"https://pith.science/api/pith-number/4PR4PNV5LF5PJGBV7HYIYI6AMJ/graph.json","events_json":"https://pith.science/api/pith-number/4PR4PNV5LF5PJGBV7HYIYI6AMJ/events.json","paper":"https://pith.science/paper/4PR4PNV5"},"agent_actions":{"view_html":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ","download_json":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ.json","view_paper":"https://pith.science/paper/4PR4PNV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.0666&json=true","fetch_graph":"https://pith.science/api/pith-number/4PR4PNV5LF5PJGBV7HYIYI6AMJ/graph.json","fetch_events":"https://pith.science/api/pith-number/4PR4PNV5LF5PJGBV7HYIYI6AMJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ/action/storage_attestation","attest_author":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ/action/author_attestation","sign_citation":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ/action/citation_signature","submit_replication":"https://pith.science/pith/4PR4PNV5LF5PJGBV7HYIYI6AMJ/action/replication_record"}},"created_at":"2026-05-18T02:04:08.072963+00:00","updated_at":"2026-05-18T02:04:08.072963+00:00"}