{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LXY4LOABXOFEDTRXS62ICVXUAT","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":"b532ab4b96db9a315d50b5e4bfded38da8a9bd0d1db510b3a15611f4703f46f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T22:15:42Z","title_canon_sha256":"6486ba9358c3b31397f5ccd554d7bb05f4e5b23e49e09c225b5dd986e5f605f8"},"schema_version":"1.0","source":{"id":"1902.03504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03504","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03504v1","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03504","created_at":"2026-05-17T23:54:20Z"},{"alias_kind":"pith_short_12","alias_value":"LXY4LOABXOFE","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LXY4LOABXOFEDTRX","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LXY4LOAB","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:dd92468261f37bbf436ecd07b515dca540da6ff17beb7a7472a37866c6488ce8","target":"graph","created_at":"2026-05-17T23:54:20Z","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":"Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying assumptions, such as considering models in the thermodynamic mean-field limit. In the thermodynamic mean-field limit, an infinite number of neurons interact via vanishingly small interactions, thereby erasing the finite size of interactions. To better capture the finite-size effects of interactions, we propose to analyze the activity of neural networks in the re","authors_text":"Fran\\c{c}ois Baccelli, Thibaud Taillefumier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T22:15:42Z","title":"Replica-mean-field limits for intensity-based neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03504","kind":"arxiv","version":1},"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":"sha256:08a5bcc897ca318c6f097c920b73787a4ef67434dacf2c04b161d0d479a88af6","target":"record","created_at":"2026-05-17T23:54:20Z","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":"b532ab4b96db9a315d50b5e4bfded38da8a9bd0d1db510b3a15611f4703f46f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-02-09T22:15:42Z","title_canon_sha256":"6486ba9358c3b31397f5ccd554d7bb05f4e5b23e49e09c225b5dd986e5f605f8"},"schema_version":"1.0","source":{"id":"1902.03504","kind":"arxiv","version":1}},"canonical_sha256":"5df1c5b801bb8a41ce3797b48156f404cec8a70eb3dcef7200e7feac9cafacae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5df1c5b801bb8a41ce3797b48156f404cec8a70eb3dcef7200e7feac9cafacae","first_computed_at":"2026-05-17T23:54:20.634777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:20.634777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X0eJcbbnNM/87SpCbnJ+c2trNBZn1JISIe1jq/nV72Iq3u7C5KTuswNDSxsSa+3MfY+UDqqozqmUGoB7qUSLCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:20.635365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a5bcc897ca318c6f097c920b73787a4ef67434dacf2c04b161d0d479a88af6","sha256:dd92468261f37bbf436ecd07b515dca540da6ff17beb7a7472a37866c6488ce8"],"state_sha256":"f86ebd5a7b03e8f52733c19b4201e6897207bfdd141e33847321c415a0fb2fe6"}