{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O64P2CYRKEST5CP3TE2JZ42DVG","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":"b7e8abd2fcc927a8afc593941050bba29cb5440c48e249d00516a9458d87da75","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-11T18:26:54Z","title_canon_sha256":"8abe2c8fa475627e00814ee39adb1fbebb66b8a9e3edb0a0d44a1e783ae97ce1"},"schema_version":"1.0","source":{"id":"1802.03787","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03787","created_at":"2026-07-05T04:27:02Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03787v3","created_at":"2026-07-05T04:27:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03787","created_at":"2026-07-05T04:27:02Z"},{"alias_kind":"pith_short_12","alias_value":"O64P2CYRKEST","created_at":"2026-07-05T04:27:02Z"},{"alias_kind":"pith_short_16","alias_value":"O64P2CYRKEST5CP3","created_at":"2026-07-05T04:27:02Z"},{"alias_kind":"pith_short_8","alias_value":"O64P2CYR","created_at":"2026-07-05T04:27:02Z"}],"graph_snapshots":[{"event_id":"sha256:4071a0363c39076095a7dfe15c54050a27aab9b19e362ed264d9a99ee10d7032","target":"graph","created_at":"2026-07-05T04:27:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1802.03787/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to that for the nonlocal diffusion equation on a unit interval, as the graph size tends to infinity. We improve our earlier results in [Arch. Ration. Mech. Anal., 21 (2014), pp. 781--803] and extend them to a larger class of graphs, which includes directed and undirected, sparse and dense, random and deterministic graphs.\n  There are three main ingredients of ","authors_text":"Georgi S. Medvedev","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-11T18:26:54Z","title":"The continuum limit of the Kuramoto model on sparse random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03787","kind":"arxiv","version":3},"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":"sha256:0e802fa022869f6dd401a6763a70a1f0acfaef229c039c9ebadd21102c273846","target":"record","created_at":"2026-07-05T04:27:02Z","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":"b7e8abd2fcc927a8afc593941050bba29cb5440c48e249d00516a9458d87da75","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-02-11T18:26:54Z","title_canon_sha256":"8abe2c8fa475627e00814ee39adb1fbebb66b8a9e3edb0a0d44a1e783ae97ce1"},"schema_version":"1.0","source":{"id":"1802.03787","kind":"arxiv","version":3}},"canonical_sha256":"77b8fd0b1151253e89fb99349cf343a9ae345f1c3f693718ef2303d312eeef32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77b8fd0b1151253e89fb99349cf343a9ae345f1c3f693718ef2303d312eeef32","first_computed_at":"2026-07-05T04:27:02.326599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:27:02.326599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJv4h1cU5OnYDziuqi7E1jY2czL54H58xgLrCGT0B+3Ry5GVga1w7Q3e1qXrbMTVNz//c9471ke/vLZ8gP9SCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:27:02.327053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03787","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e802fa022869f6dd401a6763a70a1f0acfaef229c039c9ebadd21102c273846","sha256:4071a0363c39076095a7dfe15c54050a27aab9b19e362ed264d9a99ee10d7032"],"state_sha256":"f9284aae3462adeb71269588c2dcfafc4a4de778a2f8a38db03e0a440c6f32c6"}