{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YYHODSXIA7POWWAP3CDOCIGHFA","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":"a5d3256cccd60b05afa1fb84eaef1757cd7d27f8a8e1fbb29149029078b77463","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2026-05-15T05:26:32Z","title_canon_sha256":"8a7f32cf42bed50b94aee8f28a55f9bf2bc5a75bb996a224015fe8453d4ca589"},"schema_version":"1.0","source":{"id":"2605.15628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15628","created_at":"2026-05-20T00:01:08Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15628v1","created_at":"2026-05-20T00:01:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15628","created_at":"2026-05-20T00:01:08Z"},{"alias_kind":"pith_short_12","alias_value":"YYHODSXIA7PO","created_at":"2026-05-20T00:01:08Z"},{"alias_kind":"pith_short_16","alias_value":"YYHODSXIA7POWWAP","created_at":"2026-05-20T00:01:08Z"},{"alias_kind":"pith_short_8","alias_value":"YYHODSXI","created_at":"2026-05-20T00:01:08Z"}],"graph_snapshots":[{"event_id":"sha256:dc8c89ec5ea55478b5d7ac9550ffbf2075e59cae6c83706732d14aaea5437231","target":"graph","created_at":"2026-05-20T00:01:08Z","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":"In the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2π/n."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The coupling function is assumed to be piecewise linear, nonlocal, repulsive, and to include a fixed phase lag; if the functional form or the nonlocality range changes, the reported phase-difference rule and stability regions may not hold."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Nonlocal repulsive coupling produces multi-cluster chimeras with antiphase or splay synchronized clusters that differ by 2π/n, in contrast to attractive coupling, as shown by numerics, stability analysis, and Ott-Antonsen reduction."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Phase oscillators with repulsive nonlocal coupling form multi-cluster chimeras where synchronized clusters differ by 2π/n."}],"snapshot_sha256":"4ba8e6fee79a5175b32fbe446caf994f47b1df1475e284110836beb6eed780d7"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"68bdc9a4241d22552f070903ce109692c89d475e40e43d5b762c2325b0581ebe"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T19:34:34.311424Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T18:31:25.154098Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T18:31:18.807370Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:41:56.029845Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.15628/integrity.json","findings":[],"snapshot_sha256":"b0ebff8f81a240d8fb8a9cc59aace85e354210ed8dfc5d87f7f589ff58c304cb","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Local repulsive coupling tend to a desynchronize ensembles of globally coupled oscillators, but when the repulsive coupling is nonlocal, multi-cluster chimeras can result. In this case, several groups of synchronized oscillators (the so-called clusters) are formed, and these coexist with a set of desynchronized oscillators. For phase oscillators on a ring with nonlocal piecewise linear repulsive coupling that also involves a phase lag, we find that in the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive ","authors_text":"Ayushi Saxena, Ram Ramaswamy, Sangeeta Rani Ujjwal","cross_cats":[],"headline":"Phase oscillators with repulsive nonlocal coupling form multi-cluster chimeras where synchronized clusters differ by 2π/n.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2026-05-15T05:26:32Z","title":"Multi-cluster chimeras in phase oscillators with repulsive nonlocal coupling"},"references":{"count":58,"internal_anchors":0,"resolved_work":58,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"G(x) -a a a a x FIG","work_id":"491439bc-6255-485e-843f-11ed8e938aac","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"inverted Mexican- hat","work_id":"18bb5b81-ab47-4ab2-beef-6ae5143e5e2b","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"The interplay of the coupling function and the phase lag parameter α gives rise to various states","work_id":"dd9a53cf-434b-43a4-9d7d-909481258ee0","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"2(i)-(xxii)), for instance, Fig","work_id":"0e248615-e0c7-401a-ad90-41a464428e5f","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Therefore, the phase of the ith oscillator will evolve ac- cording to the following equation: ∂φ i ∂t = N∑ j=1 Gij sin(φ j − φ i − α )","work_id":"908453c5-af03-4503-b66a-d21b7d097c0b","year":null}],"snapshot_sha256":"55d0197f304c598e9fe04287c1615e8a86332516c5077dc6ea29fbfebdda2025"},"source":{"id":"2605.15628","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:21:26.817232Z","id":"a81c4632-f2e5-4285-ac36-b23d8157309b","model_set":{"reader":"grok-4.3"},"one_line_summary":"Nonlocal repulsive coupling produces multi-cluster chimeras with antiphase or splay synchronized clusters that differ by 2π/n, in contrast to attractive coupling, as shown by numerics, stability analysis, and Ott-Antonsen reduction.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Phase oscillators with repulsive nonlocal coupling form multi-cluster chimeras where synchronized clusters differ by 2π/n.","strongest_claim":"In the multi-cluster chimera state the synchronized clusters are either antiphase or in splay with respect to each other, namely the n consecutive synchronized clusters differ in phase by 2π/n.","weakest_assumption":"The coupling function is assumed to be piecewise linear, nonlocal, repulsive, and to include a fixed phase lag; if the functional form or the nonlocality range changes, the reported phase-difference rule and stability regions may not hold."}},"verdict_id":"a81c4632-f2e5-4285-ac36-b23d8157309b"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fa07bebda7651204e93784570c424509eeeeacdf7408ca2ec85cbf86996e697c","target":"record","created_at":"2026-05-20T00:01:08Z","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":"a5d3256cccd60b05afa1fb84eaef1757cd7d27f8a8e1fbb29149029078b77463","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2026-05-15T05:26:32Z","title_canon_sha256":"8a7f32cf42bed50b94aee8f28a55f9bf2bc5a75bb996a224015fe8453d4ca589"},"schema_version":"1.0","source":{"id":"2605.15628","kind":"arxiv","version":1}},"canonical_sha256":"c60ee1cae807deeb580fd886e120c7283f1c9696bf58a487c7c4b17c28d8fd98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c60ee1cae807deeb580fd886e120c7283f1c9696bf58a487c7c4b17c28d8fd98","first_computed_at":"2026-05-20T00:01:08.921639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:08.921639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/9ZdztKpPnhNGwoZy9cxStUPRinzuRNbEd/0Tv8FWmz3Z72pkM8+SvrLuwSBH0G3Lhixs3NbBWwf9nNIJONBDA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:08.922479Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa07bebda7651204e93784570c424509eeeeacdf7408ca2ec85cbf86996e697c","sha256:dc8c89ec5ea55478b5d7ac9550ffbf2075e59cae6c83706732d14aaea5437231"],"state_sha256":"56be1bc3775c60a6311b02df39fcb001060f8c0abed5babff5c79c53c3265593"}