{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LGVCGUKIJXQIGAZB6FEWVJDIFK","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":"075e42ad551c9f6501c89508591c5b83795f431f27279ccde063e221f6d2c7d6","cross_cats_sorted":["math.AP","q-bio.NC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-09-10T08:29:49Z","title_canon_sha256":"512ee15157df134c56484ad3e02cc95c7e2ca685b4d3fa9aac3bbb2791f9d283"},"schema_version":"1.0","source":{"id":"2409.06325","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.06325","created_at":"2026-07-05T10:45:11Z"},{"alias_kind":"arxiv_version","alias_value":"2409.06325v3","created_at":"2026-07-05T10:45:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.06325","created_at":"2026-07-05T10:45:11Z"},{"alias_kind":"pith_short_12","alias_value":"LGVCGUKIJXQI","created_at":"2026-07-05T10:45:11Z"},{"alias_kind":"pith_short_16","alias_value":"LGVCGUKIJXQIGAZB","created_at":"2026-07-05T10:45:11Z"},{"alias_kind":"pith_short_8","alias_value":"LGVCGUKI","created_at":"2026-07-05T10:45:11Z"}],"graph_snapshots":[{"event_id":"sha256:c4f4b9614de581346c11285911a5d3a9c1384d7d860915cf15251ca9ff1ae5e4","target":"graph","created_at":"2026-07-05T10:45:11Z","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/2409.06325/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dynamics of spatially-structured networks of $N$ interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does synaptic weight scaling suffice, by itself, to guarantee the convergence of network dynamics to a deterministic population equation, even when networks are not assumed to be homogeneous or spatially structured? In this work, we consider networks of stochastic integrate-and-fire neurons with arbitrary synaptic weights satisfying a $O(1/N)$ scaling condition. Borrow","authors_text":"Datong Zhou, Pierre-Emmanuel Jabin, Valentin Schmutz","cross_cats":["math.AP","q-bio.NC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-09-10T08:29:49Z","title":"Dense networks of integrate-and-fire neurons: Spatially-extended mean-field limit of the empirical measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.06325","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:cbd1f4440158a03e2150de393ff747929e40eba688bca793a794c99e36fc360f","target":"record","created_at":"2026-07-05T10:45:11Z","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":"075e42ad551c9f6501c89508591c5b83795f431f27279ccde063e221f6d2c7d6","cross_cats_sorted":["math.AP","q-bio.NC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.PR","submitted_at":"2024-09-10T08:29:49Z","title_canon_sha256":"512ee15157df134c56484ad3e02cc95c7e2ca685b4d3fa9aac3bbb2791f9d283"},"schema_version":"1.0","source":{"id":"2409.06325","kind":"arxiv","version":3}},"canonical_sha256":"59aa2351484de0830321f1496aa4682ab944232fb5226bd9c44c32698d5eac40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59aa2351484de0830321f1496aa4682ab944232fb5226bd9c44c32698d5eac40","first_computed_at":"2026-07-05T10:45:11.434369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:45:11.434369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"esytMW2rFHnUjHnxuk2jnzBxYJ8hFYh/L+vKSMV+QX9w3AXOqUHIF0JTzLI5fGZTjFH3pawX321nPq7u625vDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:45:11.434872Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.06325","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbd1f4440158a03e2150de393ff747929e40eba688bca793a794c99e36fc360f","sha256:c4f4b9614de581346c11285911a5d3a9c1384d7d860915cf15251ca9ff1ae5e4"],"state_sha256":"a57fe38a515f1c8893b1e7734c62707150fdee7792048d47203e91e655d3ab19"}