{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NW5X6VM3PFFO5CW7B3W6DZ2Q3A","short_pith_number":"pith:NW5X6VM3","canonical_record":{"source":{"id":"1002.4993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-02-26T14:03:01Z","cross_cats_sorted":[],"title_canon_sha256":"118876ea891c491da43b98bc249334793cd828aa113496119bb7e0488bca312f","abstract_canon_sha256":"7e44a8eeaf92ee5aa9d2b1f130eb20bc6ab9113e2672f8525b6815a7c0d3b19d"},"schema_version":"1.0"},"canonical_sha256":"6dbb7f559b794aee8adf0eede1e750d81d9f3ad6f8bf8cbcf07075cc8f89e67e","source":{"kind":"arxiv","id":"1002.4993","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4993","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4993v1","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4993","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"NW5X6VM3PFFO","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NW5X6VM3PFFO5CW7","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NW5X6VM3","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NW5X6VM3PFFO5CW7B3W6DZ2Q3A","target":"record","payload":{"canonical_record":{"source":{"id":"1002.4993","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-02-26T14:03:01Z","cross_cats_sorted":[],"title_canon_sha256":"118876ea891c491da43b98bc249334793cd828aa113496119bb7e0488bca312f","abstract_canon_sha256":"7e44a8eeaf92ee5aa9d2b1f130eb20bc6ab9113e2672f8525b6815a7c0d3b19d"},"schema_version":"1.0"},"canonical_sha256":"6dbb7f559b794aee8adf0eede1e750d81d9f3ad6f8bf8cbcf07075cc8f89e67e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:31.327496Z","signature_b64":"O7TzCivXSOT1NIqwdwh+FuI141OflKC3Yo4Bs2AP6yMDdqUOoUHa8QhlXKN2xUPgn1kczixu1xEWrJwIBW0sBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dbb7f559b794aee8adf0eede1e750d81d9f3ad6f8bf8cbcf07075cc8f89e67e","last_reissued_at":"2026-05-18T04:04:31.326821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:31.326821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.4993","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8SpFTfxtJmY3sr59W9ZGhzuKe4pkfT6Ez1seRQxzYrwFiXjkHCFUdYyLttEcxRMIyDRta+sswrasVHXtxxvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:24:28.190685Z"},"content_sha256":"0eb17337910726c293db9ed330c4d3ba69768a30451466169eae493625520634","schema_version":"1.0","event_id":"sha256:0eb17337910726c293db9ed330c4d3ba69768a30451466169eae493625520634"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NW5X6VM3PFFO5CW7B3W6DZ2Q3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Collective oscillations in disordered neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Alessandro Torcini, Antonio Politi, Roberto Livi, Simona Olmi","submitted_at":"2010-02-26T14:03:01Z","abstract_excerpt":"We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O.V. Popovych at al., Phys. Rev. E 71} 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N going to infinite, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4993","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QkFQEvoVcxXtMVfSZRaTfOZa4IdegDZ4ng4tMRLLcza5IeGQ7v2+aKtgbw1p1lp2gIg3sqN0fuM3hvA6yO0GBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:24:28.191027Z"},"content_sha256":"aeaee496ccd03e388d4d525f38a32051e98d6f9facf2eaa1ed049edc874935e1","schema_version":"1.0","event_id":"sha256:aeaee496ccd03e388d4d525f38a32051e98d6f9facf2eaa1ed049edc874935e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A/bundle.json","state_url":"https://pith.science/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A/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":"2026-06-01T21:24:28Z","links":{"resolver":"https://pith.science/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A","bundle":"https://pith.science/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A/bundle.json","state":"https://pith.science/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NW5X6VM3PFFO5CW7B3W6DZ2Q3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NW5X6VM3PFFO5CW7B3W6DZ2Q3A","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":"7e44a8eeaf92ee5aa9d2b1f130eb20bc6ab9113e2672f8525b6815a7c0d3b19d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-02-26T14:03:01Z","title_canon_sha256":"118876ea891c491da43b98bc249334793cd828aa113496119bb7e0488bca312f"},"schema_version":"1.0","source":{"id":"1002.4993","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4993","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4993v1","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4993","created_at":"2026-05-18T04:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"NW5X6VM3PFFO","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NW5X6VM3PFFO5CW7","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NW5X6VM3","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:aeaee496ccd03e388d4d525f38a32051e98d6f9facf2eaa1ed049edc874935e1","target":"graph","created_at":"2026-05-18T04:04:31Z","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":"We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O.V. Popovych at al., Phys. Rev. E 71} 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N going to infinite, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to tha","authors_text":"Alessandro Torcini, Antonio Politi, Roberto Livi, Simona Olmi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-02-26T14:03:01Z","title":"Collective oscillations in disordered neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4993","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":"sha256:0eb17337910726c293db9ed330c4d3ba69768a30451466169eae493625520634","target":"record","created_at":"2026-05-18T04:04:31Z","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":"7e44a8eeaf92ee5aa9d2b1f130eb20bc6ab9113e2672f8525b6815a7c0d3b19d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-02-26T14:03:01Z","title_canon_sha256":"118876ea891c491da43b98bc249334793cd828aa113496119bb7e0488bca312f"},"schema_version":"1.0","source":{"id":"1002.4993","kind":"arxiv","version":1}},"canonical_sha256":"6dbb7f559b794aee8adf0eede1e750d81d9f3ad6f8bf8cbcf07075cc8f89e67e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dbb7f559b794aee8adf0eede1e750d81d9f3ad6f8bf8cbcf07075cc8f89e67e","first_computed_at":"2026-05-18T04:04:31.326821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:31.326821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O7TzCivXSOT1NIqwdwh+FuI141OflKC3Yo4Bs2AP6yMDdqUOoUHa8QhlXKN2xUPgn1kczixu1xEWrJwIBW0sBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:31.327496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4993","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0eb17337910726c293db9ed330c4d3ba69768a30451466169eae493625520634","sha256:aeaee496ccd03e388d4d525f38a32051e98d6f9facf2eaa1ed049edc874935e1"],"state_sha256":"b8b8595bf318731926059c9c3b1543bc9a0b198869bfda9af5fef4a74f40449d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z2vLK7uIAQFSlAqLQ9qS948dYKwU4vH50V0W1hGjvxpgUr2qU3YCBmcLKLiACGgo4W56Ay/Jacv9gm/yhtYJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:24:28.192957Z","bundle_sha256":"32afae606ad57aa6acc78567c12b3212a20ed3c47b847f8e7a7fe6940c54ff6b"}}