{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:L5PTFTVDGXDL4UIEIYB2XJ72WU","short_pith_number":"pith:L5PTFTVD","canonical_record":{"source":{"id":"2408.12540","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-22T16:53:46Z","cross_cats_sorted":["math.DS","q-bio.NC"],"title_canon_sha256":"9995b7b563dbdc78d096e9bad4e9d4c6823ece72949fc3d572ff6bbe2acda755","abstract_canon_sha256":"f38e26131dcbd8f2c4159f4efd01d135d814dc65fad47dd61268fc34d239c4a1"},"schema_version":"1.0"},"canonical_sha256":"5f5f32cea335c6be51044603aba7fab51e57325eb168f8ed992674408a84f8c7","source":{"kind":"arxiv","id":"2408.12540","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12540","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12540v2","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12540","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"pith_short_12","alias_value":"L5PTFTVDGXDL","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"pith_short_16","alias_value":"L5PTFTVDGXDL4UIE","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"pith_short_8","alias_value":"L5PTFTVD","created_at":"2026-07-05T11:58:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:L5PTFTVDGXDL4UIEIYB2XJ72WU","target":"record","payload":{"canonical_record":{"source":{"id":"2408.12540","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-22T16:53:46Z","cross_cats_sorted":["math.DS","q-bio.NC"],"title_canon_sha256":"9995b7b563dbdc78d096e9bad4e9d4c6823ece72949fc3d572ff6bbe2acda755","abstract_canon_sha256":"f38e26131dcbd8f2c4159f4efd01d135d814dc65fad47dd61268fc34d239c4a1"},"schema_version":"1.0"},"canonical_sha256":"5f5f32cea335c6be51044603aba7fab51e57325eb168f8ed992674408a84f8c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:58:20.137693Z","signature_b64":"EXHnrhIcXCVV8vZ5C/rlgv0/kYd/ZuNy2VG3Pbg85xgV1NtSCE7w5ahv645CyjvRAiZ6MXZ4VYDz4VUE947cBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f5f32cea335c6be51044603aba7fab51e57325eb168f8ed992674408a84f8c7","last_reissued_at":"2026-07-05T11:58:20.137242Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:58:20.137242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.12540","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:58:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxgwfkDm1OfBWvEcwXIftSNWO+xnhYCq60P/xJGi+viwz8M9ZtySZUJ7nIz/833vgBHFjEvdwkkK9anOWhZvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:44:06.172509Z"},"content_sha256":"2fb7e4b298201f4b8fe657954383b1387280346c74029711cc56a182ee4f6eec","schema_version":"1.0","event_id":"sha256:2fb7e4b298201f4b8fe657954383b1387280346c74029711cc56a182ee4f6eec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:L5PTFTVDGXDL4UIEIYB2XJ72WU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","q-bio.NC"],"primary_cat":"math.PR","authors_text":"Daniele Avitabile, James MacLaurin","submitted_at":"2024-08-22T16:53:46Z","abstract_excerpt":"We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as control parameter the diffusivity strength of the afferent white noise on each neuro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12540","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.12540/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:58:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5LXgf4C5fwAOjr9jFvWMCa/IczpVJ69iG7eLI3pr2jDOAznLY4VBNDV2fVZyihp3HBjABXeIwLiK34wlCcaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:44:06.173073Z"},"content_sha256":"c1d1612a44ecbc17eb495960ad810bd45393a59bd09a00ebdb3248175fba224f","schema_version":"1.0","event_id":"sha256:c1d1612a44ecbc17eb495960ad810bd45393a59bd09a00ebdb3248175fba224f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU/bundle.json","state_url":"https://pith.science/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T08:44:06Z","links":{"resolver":"https://pith.science/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU","bundle":"https://pith.science/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU/bundle.json","state":"https://pith.science/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5PTFTVDGXDL4UIEIYB2XJ72WU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:L5PTFTVDGXDL4UIEIYB2XJ72WU","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":"f38e26131dcbd8f2c4159f4efd01d135d814dc65fad47dd61268fc34d239c4a1","cross_cats_sorted":["math.DS","q-bio.NC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-22T16:53:46Z","title_canon_sha256":"9995b7b563dbdc78d096e9bad4e9d4c6823ece72949fc3d572ff6bbe2acda755"},"schema_version":"1.0","source":{"id":"2408.12540","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.12540","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"arxiv_version","alias_value":"2408.12540v2","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.12540","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"pith_short_12","alias_value":"L5PTFTVDGXDL","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"pith_short_16","alias_value":"L5PTFTVDGXDL4UIE","created_at":"2026-07-05T11:58:20Z"},{"alias_kind":"pith_short_8","alias_value":"L5PTFTVD","created_at":"2026-07-05T11:58:20Z"}],"graph_snapshots":[{"event_id":"sha256:c1d1612a44ecbc17eb495960ad810bd45393a59bd09a00ebdb3248175fba224f","target":"graph","created_at":"2026-07-05T11:58:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.12540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting systems are the mean and variance of neuronal activity. We select networks whose mean-field equations are tractable and we perform a bifurcation analysis using as control parameter the diffusivity strength of the afferent white noise on each neuro","authors_text":"Daniele Avitabile, James MacLaurin","cross_cats":["math.DS","q-bio.NC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-22T16:53:46Z","title":"Neural Fields and Noise-Induced Patterns in Neurons on Large Disordered Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.12540","kind":"arxiv","version":2},"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":"sha256:2fb7e4b298201f4b8fe657954383b1387280346c74029711cc56a182ee4f6eec","target":"record","created_at":"2026-07-05T11:58:20Z","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":"f38e26131dcbd8f2c4159f4efd01d135d814dc65fad47dd61268fc34d239c4a1","cross_cats_sorted":["math.DS","q-bio.NC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-22T16:53:46Z","title_canon_sha256":"9995b7b563dbdc78d096e9bad4e9d4c6823ece72949fc3d572ff6bbe2acda755"},"schema_version":"1.0","source":{"id":"2408.12540","kind":"arxiv","version":2}},"canonical_sha256":"5f5f32cea335c6be51044603aba7fab51e57325eb168f8ed992674408a84f8c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f5f32cea335c6be51044603aba7fab51e57325eb168f8ed992674408a84f8c7","first_computed_at":"2026-07-05T11:58:20.137242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:58:20.137242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EXHnrhIcXCVV8vZ5C/rlgv0/kYd/ZuNy2VG3Pbg85xgV1NtSCE7w5ahv645CyjvRAiZ6MXZ4VYDz4VUE947cBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:58:20.137693Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.12540","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fb7e4b298201f4b8fe657954383b1387280346c74029711cc56a182ee4f6eec","sha256:c1d1612a44ecbc17eb495960ad810bd45393a59bd09a00ebdb3248175fba224f"],"state_sha256":"0da462ee4ca79767630e29ca43b8f7fe3da26027f50c9b45a62d337aff663a88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQdKBJb7IOpNqaDIuuGDtVMz8+WD+0VzbI6GXPXMmIqsuTnXrAdOYAV07OHBVGVPREssEtZ2ift92O9l3KL4Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T08:44:06.177493Z","bundle_sha256":"2d36333e81dabf5f0bbf5e6098a6faec4c245bbb2655218633a886de9070c9aa"}}