{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WD5F5USLGCPEWOACA2Q6MHS2XQ","short_pith_number":"pith:WD5F5USL","schema_version":"1.0","canonical_sha256":"b0fa5ed24b309e4b380206a1e61e5abc1e0ae90b9de8e777adfb97ec7da814fa","source":{"kind":"arxiv","id":"1009.6004","version":3},"attestation_state":"computed","paper":{"title":"Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Bulbul Chakraborty, Michael Giver, Zahera Jabeen","submitted_at":"2010-09-29T20:58:46Z","abstract_excerpt":"Recent experiments in one and two-dimensional microfluidic arrays of droplets containing Belousov -Zhabotinsky reactants show a rich variety of spatial patterns [J. Phys. Chem. Lett. 1, 1241-1246 (2010)]. The dominant coupling between these droplets is inhibitory. Motivated by this experimental system, we study repulsively coupled Kuramoto oscillators with nearest neighbor interactions, on a linear chain as well as a ring in one dimension, and on a triangular lattice in two dimensions. In one dimension, we show using linear stability analysis as well as numerical study, that the stable phase p"},"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":"1009.6004","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2010-09-29T20:58:46Z","cross_cats_sorted":[],"title_canon_sha256":"8e954b3b69dfd1845db1c40933660799faa36023b7906dce8c9178cc469104f7","abstract_canon_sha256":"75ec87a38a2f90b046a889223c9860f1deefcb9a24a7057ed54fccb0ef7536db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:48.038637Z","signature_b64":"YBjeKvUh5gOLTPNoz9ntYfLm24o+9xFlYr/UCmF9weN6TEZpN4iFuz26J2iod1w/O/Gu8rbC0yByofe5CW5sAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0fa5ed24b309e4b380206a1e61e5abc1e0ae90b9de8e777adfb97ec7da814fa","last_reissued_at":"2026-05-18T02:23:48.037966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:48.037966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Bulbul Chakraborty, Michael Giver, Zahera Jabeen","submitted_at":"2010-09-29T20:58:46Z","abstract_excerpt":"Recent experiments in one and two-dimensional microfluidic arrays of droplets containing Belousov -Zhabotinsky reactants show a rich variety of spatial patterns [J. Phys. Chem. Lett. 1, 1241-1246 (2010)]. The dominant coupling between these droplets is inhibitory. Motivated by this experimental system, we study repulsively coupled Kuramoto oscillators with nearest neighbor interactions, on a linear chain as well as a ring in one dimension, and on a triangular lattice in two dimensions. In one dimension, we show using linear stability analysis as well as numerical study, that the stable phase p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.6004","kind":"arxiv","version":3},"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":"1009.6004","created_at":"2026-05-18T02:23:48.038081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.6004v3","created_at":"2026-05-18T02:23:48.038081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.6004","created_at":"2026-05-18T02:23:48.038081+00:00"},{"alias_kind":"pith_short_12","alias_value":"WD5F5USLGCPE","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"WD5F5USLGCPEWOAC","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"WD5F5USL","created_at":"2026-05-18T12:26:15.391820+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/WD5F5USLGCPEWOACA2Q6MHS2XQ","json":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ.json","graph_json":"https://pith.science/api/pith-number/WD5F5USLGCPEWOACA2Q6MHS2XQ/graph.json","events_json":"https://pith.science/api/pith-number/WD5F5USLGCPEWOACA2Q6MHS2XQ/events.json","paper":"https://pith.science/paper/WD5F5USL"},"agent_actions":{"view_html":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ","download_json":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ.json","view_paper":"https://pith.science/paper/WD5F5USL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.6004&json=true","fetch_graph":"https://pith.science/api/pith-number/WD5F5USLGCPEWOACA2Q6MHS2XQ/graph.json","fetch_events":"https://pith.science/api/pith-number/WD5F5USLGCPEWOACA2Q6MHS2XQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ/action/storage_attestation","attest_author":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ/action/author_attestation","sign_citation":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ/action/citation_signature","submit_replication":"https://pith.science/pith/WD5F5USLGCPEWOACA2Q6MHS2XQ/action/replication_record"}},"created_at":"2026-05-18T02:23:48.038081+00:00","updated_at":"2026-05-18T02:23:48.038081+00:00"}