{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RFMPKAXRHFMNNF3YDD7TIOHKBJ","short_pith_number":"pith:RFMPKAXR","canonical_record":{"source":{"id":"1402.3555","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-02-14T19:33:39Z","cross_cats_sorted":[],"title_canon_sha256":"6f86b5fb4167da223bf1d2bf8a197fdc4070462aafa129b3fa123cdf85d8e106","abstract_canon_sha256":"000d4088d087c30b6fdb244983736153022477d9ec6ac41e3e60c52a1ef4ac4d"},"schema_version":"1.0"},"canonical_sha256":"8958f502f13958d6977818ff3438ea0a5e22dd38bd4d21ec4509f39ca20b958a","source":{"kind":"arxiv","id":"1402.3555","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3555","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3555v4","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3555","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"RFMPKAXRHFMN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RFMPKAXRHFMNNF3Y","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RFMPKAXR","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RFMPKAXRHFMNNF3YDD7TIOHKBJ","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3555","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-02-14T19:33:39Z","cross_cats_sorted":[],"title_canon_sha256":"6f86b5fb4167da223bf1d2bf8a197fdc4070462aafa129b3fa123cdf85d8e106","abstract_canon_sha256":"000d4088d087c30b6fdb244983736153022477d9ec6ac41e3e60c52a1ef4ac4d"},"schema_version":"1.0"},"canonical_sha256":"8958f502f13958d6977818ff3438ea0a5e22dd38bd4d21ec4509f39ca20b958a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:46.743689Z","signature_b64":"wdaVgkt8V/jsGoo7NftiJtrzWtAaQoxXDAwvhXPBrNExUVAiIQ+a3LVoKhebdrhNbAwl/dkGKkBDKRbci9lGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8958f502f13958d6977818ff3438ea0a5e22dd38bd4d21ec4509f39ca20b958a","last_reissued_at":"2026-05-18T01:31:46.743310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:46.743310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3555","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7PHj7bAROM3wJmHBufPBVyRaSLI39znV5rB/La+Z9MhwpMlKHyerILg3eH1HtC9AKFlp/YYBgAXbr1oO4ILAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T00:50:08.530660Z"},"content_sha256":"a8d7c4183b99f05d3b70d0230eb87823d34e1e7803c3fec205bbd90804786ce2","schema_version":"1.0","event_id":"sha256:a8d7c4183b99f05d3b70d0230eb87823d34e1e7803c3fec205bbd90804786ce2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RFMPKAXRHFMNNF3YDD7TIOHKBJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular graphs maximize the variability of random neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Gilles Wainrib, Mathieu Galtier","submitted_at":"2014-02-14T19:33:39Z","abstract_excerpt":"In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on a combination of a classical mean-field theory originally developed in the context of dynamical spin-glass models, and the heterogeneous mean-field theory developed to study epidemic propagation on graphs. Our main result is that, surprisingly, increasing the variance of the in-degree distribution does not result in a more variable dynamical behavior, but on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3555","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIgoRnJ1Tazh0OVnFjrLL2Z08WAzdsrbT36jylIxOp4f/wjpsX1k0WkiUET8V6PWhhieVNpDCHL8MSTe5GapBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T00:50:08.531015Z"},"content_sha256":"f4f68cafe550ba729775ad1d42656847d5d7f2b52c8f23f058358487c8d37810","schema_version":"1.0","event_id":"sha256:f4f68cafe550ba729775ad1d42656847d5d7f2b52c8f23f058358487c8d37810"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ/bundle.json","state_url":"https://pith.science/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ/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":"2026-07-02T00:50:08Z","links":{"resolver":"https://pith.science/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ","bundle":"https://pith.science/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ/bundle.json","state":"https://pith.science/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RFMPKAXRHFMNNF3YDD7TIOHKBJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RFMPKAXRHFMNNF3YDD7TIOHKBJ","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":"000d4088d087c30b6fdb244983736153022477d9ec6ac41e3e60c52a1ef4ac4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-02-14T19:33:39Z","title_canon_sha256":"6f86b5fb4167da223bf1d2bf8a197fdc4070462aafa129b3fa123cdf85d8e106"},"schema_version":"1.0","source":{"id":"1402.3555","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3555","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3555v4","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3555","created_at":"2026-05-18T01:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"RFMPKAXRHFMN","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RFMPKAXRHFMNNF3Y","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RFMPKAXR","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f4f68cafe550ba729775ad1d42656847d5d7f2b52c8f23f058358487c8d37810","target":"graph","created_at":"2026-05-18T01:31:46Z","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":"In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on a combination of a classical mean-field theory originally developed in the context of dynamical spin-glass models, and the heterogeneous mean-field theory developed to study epidemic propagation on graphs. Our main result is that, surprisingly, increasing the variance of the in-degree distribution does not result in a more variable dynamical behavior, but on","authors_text":"Gilles Wainrib, Mathieu Galtier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-02-14T19:33:39Z","title":"Regular graphs maximize the variability of random neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3555","kind":"arxiv","version":4},"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:a8d7c4183b99f05d3b70d0230eb87823d34e1e7803c3fec205bbd90804786ce2","target":"record","created_at":"2026-05-18T01:31:46Z","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":"000d4088d087c30b6fdb244983736153022477d9ec6ac41e3e60c52a1ef4ac4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2014-02-14T19:33:39Z","title_canon_sha256":"6f86b5fb4167da223bf1d2bf8a197fdc4070462aafa129b3fa123cdf85d8e106"},"schema_version":"1.0","source":{"id":"1402.3555","kind":"arxiv","version":4}},"canonical_sha256":"8958f502f13958d6977818ff3438ea0a5e22dd38bd4d21ec4509f39ca20b958a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8958f502f13958d6977818ff3438ea0a5e22dd38bd4d21ec4509f39ca20b958a","first_computed_at":"2026-05-18T01:31:46.743310Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:46.743310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wdaVgkt8V/jsGoo7NftiJtrzWtAaQoxXDAwvhXPBrNExUVAiIQ+a3LVoKhebdrhNbAwl/dkGKkBDKRbci9lGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:46.743689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3555","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8d7c4183b99f05d3b70d0230eb87823d34e1e7803c3fec205bbd90804786ce2","sha256:f4f68cafe550ba729775ad1d42656847d5d7f2b52c8f23f058358487c8d37810"],"state_sha256":"b2b877cc1617f738e89d17cb853eb8c16ff2c2c860f8ae11774c70188de038e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pAMjLwIT9IP2jlKnOojp3p7iqkz26AnmInfNdYQCKj7F8OYVdVjodnOl73pQBscbG8J5FPBeyRblMR+PWAHxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T00:50:08.533481Z","bundle_sha256":"e981eaa63b00b1460a5e040d88158179da1e3966655c0ba54ae4e64f3f153cc7"}}