{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4OVDV4WSA3GU3BCDDNQI4FBTBB","short_pith_number":"pith:4OVDV4WS","schema_version":"1.0","canonical_sha256":"e3aa3af2d206cd4d84431b608e1433086150958f6c5dbfab134d5dc119d03254","source":{"kind":"arxiv","id":"1904.12798","version":1},"attestation_state":"computed","paper":{"title":"Mathematical studies of the dynamics of finite-size binary neural networks: A review of recent progress","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"q-bio.NC","authors_text":"Diego Fasoli, Stefano Panzeri","submitted_at":"2019-04-29T16:21:39Z","abstract_excerpt":"Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological networks have finite size, and many of them, such as microscopic circuits in invertebrates, are composed only of a few tens of neurons. Thus, it is important to be able to extend to small-size networks our ability to study analytically neural dynamics. Analytical solutions of the dynamics of finite-size neural networks have remained elusive for many decades, beca"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1904.12798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2019-04-29T16:21:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5df25d9662a913bc49b71a782f9d433b461458ef1480c0e87f8e980cc1057235","abstract_canon_sha256":"441e8e1773cdaa20733c061f90e65ceb8d03561e456674f3e0cf38e7c1ec6a26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:32.233501Z","signature_b64":"Jqgx4uAyGSMK1SqWZKt4/V6AOY5WVHJQsJ69SIQ2T/I1f6BTP6R09UJ3L0668g1XizqnHNeYhu/1Kv7sgutSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3aa3af2d206cd4d84431b608e1433086150958f6c5dbfab134d5dc119d03254","last_reissued_at":"2026-05-17T23:47:32.232967Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:32.232967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mathematical studies of the dynamics of finite-size binary neural networks: A review of recent progress","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"q-bio.NC","authors_text":"Diego Fasoli, Stefano Panzeri","submitted_at":"2019-04-29T16:21:39Z","abstract_excerpt":"Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological networks have finite size, and many of them, such as microscopic circuits in invertebrates, are composed only of a few tens of neurons. Thus, it is important to be able to extend to small-size networks our ability to study analytically neural dynamics. Analytical solutions of the dynamics of finite-size neural networks have remained elusive for many decades, beca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12798","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.12798","created_at":"2026-05-17T23:47:32.233049+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.12798v1","created_at":"2026-05-17T23:47:32.233049+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12798","created_at":"2026-05-17T23:47:32.233049+00:00"},{"alias_kind":"pith_short_12","alias_value":"4OVDV4WSA3GU","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4OVDV4WSA3GU3BCD","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4OVDV4WS","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB","json":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB.json","graph_json":"https://pith.science/api/pith-number/4OVDV4WSA3GU3BCDDNQI4FBTBB/graph.json","events_json":"https://pith.science/api/pith-number/4OVDV4WSA3GU3BCDDNQI4FBTBB/events.json","paper":"https://pith.science/paper/4OVDV4WS"},"agent_actions":{"view_html":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB","download_json":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB.json","view_paper":"https://pith.science/paper/4OVDV4WS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.12798&json=true","fetch_graph":"https://pith.science/api/pith-number/4OVDV4WSA3GU3BCDDNQI4FBTBB/graph.json","fetch_events":"https://pith.science/api/pith-number/4OVDV4WSA3GU3BCDDNQI4FBTBB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB/action/storage_attestation","attest_author":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB/action/author_attestation","sign_citation":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB/action/citation_signature","submit_replication":"https://pith.science/pith/4OVDV4WSA3GU3BCDDNQI4FBTBB/action/replication_record"}},"created_at":"2026-05-17T23:47:32.233049+00:00","updated_at":"2026-05-17T23:47:32.233049+00:00"}