{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:P743PMBXK5FDYONNHV7F7ZAS3O","short_pith_number":"pith:P743PMBX","canonical_record":{"source":{"id":"2006.02427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2020-06-03T17:55:43Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"ef56b3ddbe011caaa92898d7eebc92e3e871fb3de58755f1bc24cb1930339d8f","abstract_canon_sha256":"0b5beadd21c3bd74c474bb64a53a1ef7d40c8c1b2642c8c672b0884edc4db26a"},"schema_version":"1.0"},"canonical_sha256":"7ff9b7b037574a3c39ad3d7e5fe412db8cb7b014831197293e5576886fae72ab","source":{"kind":"arxiv","id":"2006.02427","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02427","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02427v1","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02427","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"pith_short_12","alias_value":"P743PMBXK5FD","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"pith_short_16","alias_value":"P743PMBXK5FDYONN","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"pith_short_8","alias_value":"P743PMBX","created_at":"2026-07-05T01:07:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:P743PMBXK5FDYONNHV7F7ZAS3O","target":"record","payload":{"canonical_record":{"source":{"id":"2006.02427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2020-06-03T17:55:43Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"ef56b3ddbe011caaa92898d7eebc92e3e871fb3de58755f1bc24cb1930339d8f","abstract_canon_sha256":"0b5beadd21c3bd74c474bb64a53a1ef7d40c8c1b2642c8c672b0884edc4db26a"},"schema_version":"1.0"},"canonical_sha256":"7ff9b7b037574a3c39ad3d7e5fe412db8cb7b014831197293e5576886fae72ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:46.611992Z","signature_b64":"W1dwWRujxEFW83pgkt+nibMr5RVOrcgUdnvgcwfQw3WdHdDpFrM4fcJpwXyhryQRy7xew/1Dt3G2E9b6KUBiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ff9b7b037574a3c39ad3d7e5fe412db8cb7b014831197293e5576886fae72ab","last_reissued_at":"2026-07-05T01:07:46.611477Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:46.611477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.02427","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":"2026-07-05T01:07:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"puwAy1+wv8FzM65tQs3tlYW8p1WNID38LMK8SUF9BYn/eCcQV+OopjRt9ekt4t5x43bShnNOzQE8JgHYHMY6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T17:39:48.581325Z"},"content_sha256":"67717358e7665f8a013bcd21a4551df3cf1e7267713e5029a3c5d16c728371a9","schema_version":"1.0","event_id":"sha256:67717358e7665f8a013bcd21a4551df3cf1e7267713e5029a3c5d16c728371a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:P743PMBXK5FDYONNHV7F7ZAS3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lyapunov spectra of chaotic recurrent neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"nlin.CD","authors_text":"Fred Wolf, L.F. Abbott, Rainer Engelken","submitted_at":"2020-06-03T17:55:43Z","abstract_excerpt":"Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of incoming information streams. In dissipative systems, chaotic dynamics takes place on a subset of phase space of reduced dimensionality and is organized by a complex tangle of stable, neutral and unstable manifolds. Key topological invariants of this phase space structure such as attractor dimension, and Kolmogorov-Sinai entropy so far remained elusive.\n  Her"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.02427/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":"2026-07-05T01:07:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCB/BORwUdjIxwgWGXThQ7J++WF4MpRZRlVA+GK9L6mEfpvht1nxLbGzTttT83gbjWWhsPcZ/vC3IbEeT40ABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T17:39:48.582239Z"},"content_sha256":"2e97e51f24397760e2a8d7ec96082f89a487e1b760bfcde57f75a784fec34f63","schema_version":"1.0","event_id":"sha256:2e97e51f24397760e2a8d7ec96082f89a487e1b760bfcde57f75a784fec34f63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P743PMBXK5FDYONNHV7F7ZAS3O/bundle.json","state_url":"https://pith.science/pith/P743PMBXK5FDYONNHV7F7ZAS3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P743PMBXK5FDYONNHV7F7ZAS3O/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":"2026-08-07T17:39:48Z","links":{"resolver":"https://pith.science/pith/P743PMBXK5FDYONNHV7F7ZAS3O","bundle":"https://pith.science/pith/P743PMBXK5FDYONNHV7F7ZAS3O/bundle.json","state":"https://pith.science/pith/P743PMBXK5FDYONNHV7F7ZAS3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P743PMBXK5FDYONNHV7F7ZAS3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:P743PMBXK5FDYONNHV7F7ZAS3O","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":"0b5beadd21c3bd74c474bb64a53a1ef7d40c8c1b2642c8c672b0884edc4db26a","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2020-06-03T17:55:43Z","title_canon_sha256":"ef56b3ddbe011caaa92898d7eebc92e3e871fb3de58755f1bc24cb1930339d8f"},"schema_version":"1.0","source":{"id":"2006.02427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.02427","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"arxiv_version","alias_value":"2006.02427v1","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.02427","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"pith_short_12","alias_value":"P743PMBXK5FD","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"pith_short_16","alias_value":"P743PMBXK5FDYONN","created_at":"2026-07-05T01:07:46Z"},{"alias_kind":"pith_short_8","alias_value":"P743PMBX","created_at":"2026-07-05T01:07:46Z"}],"graph_snapshots":[{"event_id":"sha256:2e97e51f24397760e2a8d7ec96082f89a487e1b760bfcde57f75a784fec34f63","target":"graph","created_at":"2026-07-05T01:07:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2006.02427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of incoming information streams. In dissipative systems, chaotic dynamics takes place on a subset of phase space of reduced dimensionality and is organized by a complex tangle of stable, neutral and unstable manifolds. Key topological invariants of this phase space structure such as attractor dimension, and Kolmogorov-Sinai entropy so far remained elusive.\n  Her","authors_text":"Fred Wolf, L.F. Abbott, Rainer Engelken","cross_cats":["q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2020-06-03T17:55:43Z","title":"Lyapunov spectra of chaotic recurrent neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.02427","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":"sha256:67717358e7665f8a013bcd21a4551df3cf1e7267713e5029a3c5d16c728371a9","target":"record","created_at":"2026-07-05T01:07:46Z","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":"0b5beadd21c3bd74c474bb64a53a1ef7d40c8c1b2642c8c672b0884edc4db26a","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2020-06-03T17:55:43Z","title_canon_sha256":"ef56b3ddbe011caaa92898d7eebc92e3e871fb3de58755f1bc24cb1930339d8f"},"schema_version":"1.0","source":{"id":"2006.02427","kind":"arxiv","version":1}},"canonical_sha256":"7ff9b7b037574a3c39ad3d7e5fe412db8cb7b014831197293e5576886fae72ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff9b7b037574a3c39ad3d7e5fe412db8cb7b014831197293e5576886fae72ab","first_computed_at":"2026-07-05T01:07:46.611477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:07:46.611477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W1dwWRujxEFW83pgkt+nibMr5RVOrcgUdnvgcwfQw3WdHdDpFrM4fcJpwXyhryQRy7xew/1Dt3G2E9b6KUBiDg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:07:46.611992Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.02427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67717358e7665f8a013bcd21a4551df3cf1e7267713e5029a3c5d16c728371a9","sha256:2e97e51f24397760e2a8d7ec96082f89a487e1b760bfcde57f75a784fec34f63"],"state_sha256":"849bbed7633899c6b1a1f699539d4f0b1e142dfe91020a1cb9e3df5a85a723ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6yFQizCp5n51ZFHXdUrHiHFv8BGYpdO8FYlyaf3Jcs5LHGHZeL4dBevtybajQ8RybAbRtTzyK+mOidqvDZglAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T17:39:48.588042Z","bundle_sha256":"e0396f695d7a8956a3034d70ec53d27b4fc7a6ba23fa2c8ec9f35dc3cf3c1268"}}