{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:M2Q5WFO6RETMNNZXPSMIHIANP3","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":"a7bbd2e18b69edbd780ef52749e4884745f15948db4a3770e3a8b0b871118ae9","cross_cats_sorted":["math.FA","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-01T23:51:31Z","title_canon_sha256":"594ec5e4e74a52af60a6d75198a63135aec6136f408ab690cf61b6fb27b0806d"},"schema_version":"1.0","source":{"id":"1706.00524","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00524","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00524v2","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00524","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"M2Q5WFO6RETM","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"M2Q5WFO6RETMNNZX","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"M2Q5WFO6","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:657fdac9eef3737206885ca4837eaafbe0fac9cc8d727ff5aec1f3e7064b1943","target":"graph","created_at":"2026-05-17T23:59:53Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a viscous eikonal equation that is known to describe the phase modulation of traveling waves in reaction-diffusion systems. We show the existence of a branch of target pattern solutions that bifurcates from the spatially homogeneous state when $\\varepsilon$, the strength of the inhomogeneity, is nonzero and we also show that these target patterns have an asym","authors_text":"Gabriela Jaramillo, Shankar Venkataramani","cross_cats":["math.FA","nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-01T23:51:31Z","title":"Target Patterns in a 2-D Array of Oscillators with Nonlocal Coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00524","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:482b92bb3e1df1280a4874dc3256eba59f124ab9fc3ee6f9728d25d7afc639a4","target":"record","created_at":"2026-05-17T23:59:53Z","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":"a7bbd2e18b69edbd780ef52749e4884745f15948db4a3770e3a8b0b871118ae9","cross_cats_sorted":["math.FA","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-01T23:51:31Z","title_canon_sha256":"594ec5e4e74a52af60a6d75198a63135aec6136f408ab690cf61b6fb27b0806d"},"schema_version":"1.0","source":{"id":"1706.00524","kind":"arxiv","version":2}},"canonical_sha256":"66a1db15de8926c6b7377c9883a00d7efd4bbfeefdebd6d0091c71224acaee10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66a1db15de8926c6b7377c9883a00d7efd4bbfeefdebd6d0091c71224acaee10","first_computed_at":"2026-05-17T23:59:53.833790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:53.833790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nU8mkswtdFSBo34IIDYIiTRypHMkMs7aNjDmIhSVaQFDex1m5WfquMfYM0/K8YCdF/mCOIOMng+Npp+6Cq/1BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:53.834326Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00524","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:482b92bb3e1df1280a4874dc3256eba59f124ab9fc3ee6f9728d25d7afc639a4","sha256:657fdac9eef3737206885ca4837eaafbe0fac9cc8d727ff5aec1f3e7064b1943"],"state_sha256":"e319a6f04b63487cf076a989c8c2fab40fc9b8974f409716dece5f70c9ce663c"}