{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:K6UJ2QD74YMC4NPAGGFPZOIU7Q","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":"bbc902a2fd826bf5fd641e27828d313814f66e43a84e9918a34fe1a072ccd37c","cross_cats_sorted":["math.DS","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2013-02-23T14:30:52Z","title_canon_sha256":"3d07bee3f1d4ca97c26dc46a4c6ea203de1a8649f51da965ff15e7d6e7896096"},"schema_version":"1.0","source":{"id":"1302.5804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5804","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5804v3","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5804","created_at":"2026-05-18T03:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"K6UJ2QD74YMC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K6UJ2QD74YMC4NPA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K6UJ2QD7","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:fcc221f3773ba060446c0d55569fc3696e1a911e0168c74042ccd73c6017c381","target":"graph","created_at":"2026-05-18T03:06:32Z","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 use the combination of ideas and results from the theory of graph limits and nonlinear evolution equations to provide a rigorous mathematical justification for taking continuum limit for certain nonlocally coupled networks and to extend this method to cover many complex networks, for which it has not been applied before. Specifically, for dynamical networks on convergent sequences of simple and weighted graphs, we prove convergence of solutions of the initial-value problems for discrete models to those of the limiting continuous equations. In addition, for sequences of simple graphs converg","authors_text":"Georgi S. Medvedev","cross_cats":["math.DS","q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2013-02-23T14:30:52Z","title":"The nonlinear heat equation on dense graphs and graph limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5804","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":"sha256:299fa562be57133486db2793141f8bcae32985c58fe014f9b80070f242182b1e","target":"record","created_at":"2026-05-18T03:06:32Z","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":"bbc902a2fd826bf5fd641e27828d313814f66e43a84e9918a34fe1a072ccd37c","cross_cats_sorted":["math.DS","q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2013-02-23T14:30:52Z","title_canon_sha256":"3d07bee3f1d4ca97c26dc46a4c6ea203de1a8649f51da965ff15e7d6e7896096"},"schema_version":"1.0","source":{"id":"1302.5804","kind":"arxiv","version":3}},"canonical_sha256":"57a89d407fe6182e35e0318afcb914fc32b76225b27aa0350c92dac6be667ca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57a89d407fe6182e35e0318afcb914fc32b76225b27aa0350c92dac6be667ca7","first_computed_at":"2026-05-18T03:06:32.772253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:32.772253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0h6Id3MM3G3Ka6ViONx2GMl3XM94vH+upsZm6Hxo+ZBKUju4utXAPLyqIr6eoIczqQHry8UsyBFq9ufXNyk4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:32.772665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:299fa562be57133486db2793141f8bcae32985c58fe014f9b80070f242182b1e","sha256:fcc221f3773ba060446c0d55569fc3696e1a911e0168c74042ccd73c6017c381"],"state_sha256":"e44e8a04e206f35cb5d18da63229d0e04ccd438cf04e2741bf7fa1b0c6dfb3e0"}