{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:IVBAEHAJ3QQH5NPM5DJTENGJWL","short_pith_number":"pith:IVBAEHAJ","canonical_record":{"source":{"id":"2107.03402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-07-07T18:00:03Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG"],"title_canon_sha256":"654cb68133dbdf4ac769ebb37317624dee6872c627b144710d0d4940d878c3bc","abstract_canon_sha256":"be728dcf2a82036f994e7cf6994b765c47707900155b2e5bfc6de0f715234baf"},"schema_version":"1.0"},"canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","source":{"kind":"arxiv","id":"2107.03402","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03402","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03402v1","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03402","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"IVBAEHAJ3QQH","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"pith_short_16","alias_value":"IVBAEHAJ3QQH5NPM","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"pith_short_8","alias_value":"IVBAEHAJ","created_at":"2026-07-05T02:56:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:IVBAEHAJ3QQH5NPM5DJTENGJWL","target":"record","payload":{"canonical_record":{"source":{"id":"2107.03402","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-07-07T18:00:03Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG"],"title_canon_sha256":"654cb68133dbdf4ac769ebb37317624dee6872c627b144710d0d4940d878c3bc","abstract_canon_sha256":"be728dcf2a82036f994e7cf6994b765c47707900155b2e5bfc6de0f715234baf"},"schema_version":"1.0"},"canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:56:05.613593Z","signature_b64":"Wlhx/LQRsInlO7ZmNfD/OG2YOxjSz0LrsrBvOfWT/D50TSfbGVayuS2XOnUyQ49C2dbw3BdOO/sVNWi/V4a/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","last_reissued_at":"2026-07-05T02:56:05.612852Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:56:05.612852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.03402","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":"2026-07-05T02:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HkLuWiqWEOcHyHC+XzQbpLzkIgdAIAE0lIuMmi+LO2RH8o22gb0W/WprU22Lf+daceE7ZuaYZbv063oaZgG+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:56.858826Z"},"content_sha256":"b0e22d7143d0b564098b64b4297312c66c7ffffcb05182854cdd1d80d8a7880d","schema_version":"1.0","event_id":"sha256:b0e22d7143d0b564098b64b4297312c66c7ffffcb05182854cdd1d80d8a7880d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:IVBAEHAJ3QQH5NPM5DJTENGJWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-organized criticality in neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG"],"primary_cat":"cond-mat.stat-mech","authors_text":"Mikhail I. Katsnelson, Tom Westerhout, Vitaly Vanchurin","submitted_at":"2021-07-07T18:00:03Z","abstract_excerpt":"We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales. Our results suggest that the scale invariance observed in many physica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03402","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/2107.03402/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":"2026-07-05T02:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y4F5pMzL8i3gqyMelsN33HXwjaa6U+6yhqVS+2BbTtrFE4g4aVP3AsrXmtbDgOp1NL0chnFKY0+MF6KwTd4wAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T12:31:56.859317Z"},"content_sha256":"2956744404b71dc245d3dd03962bee239f8534d513d1aa1cf891b5162d86daae","schema_version":"1.0","event_id":"sha256:2956744404b71dc245d3dd03962bee239f8534d513d1aa1cf891b5162d86daae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/bundle.json","state_url":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/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":"2026-08-08T12:31:56Z","links":{"resolver":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL","bundle":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/bundle.json","state":"https://pith.science/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVBAEHAJ3QQH5NPM5DJTENGJWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:IVBAEHAJ3QQH5NPM5DJTENGJWL","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":"be728dcf2a82036f994e7cf6994b765c47707900155b2e5bfc6de0f715234baf","cross_cats_sorted":["cond-mat.dis-nn","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-07-07T18:00:03Z","title_canon_sha256":"654cb68133dbdf4ac769ebb37317624dee6872c627b144710d0d4940d878c3bc"},"schema_version":"1.0","source":{"id":"2107.03402","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.03402","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"2107.03402v1","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.03402","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"IVBAEHAJ3QQH","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"pith_short_16","alias_value":"IVBAEHAJ3QQH5NPM","created_at":"2026-07-05T02:56:05Z"},{"alias_kind":"pith_short_8","alias_value":"IVBAEHAJ","created_at":"2026-07-05T02:56:05Z"}],"graph_snapshots":[{"event_id":"sha256:2956744404b71dc245d3dd03962bee239f8534d513d1aa1cf891b5162d86daae","target":"graph","created_at":"2026-07-05T02:56:05Z","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/2107.03402/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly driven towards stochastic equilibrium and trainable variables are slowly driven towards learning equilibrium described by a scale-invariant distribution on a wide range of scales. Our results suggest that the scale invariance observed in many physica","authors_text":"Mikhail I. Katsnelson, Tom Westerhout, Vitaly Vanchurin","cross_cats":["cond-mat.dis-nn","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-07-07T18:00:03Z","title":"Self-organized criticality in neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03402","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:b0e22d7143d0b564098b64b4297312c66c7ffffcb05182854cdd1d80d8a7880d","target":"record","created_at":"2026-07-05T02:56:05Z","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":"be728dcf2a82036f994e7cf6994b765c47707900155b2e5bfc6de0f715234baf","cross_cats_sorted":["cond-mat.dis-nn","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-07-07T18:00:03Z","title_canon_sha256":"654cb68133dbdf4ac769ebb37317624dee6872c627b144710d0d4940d878c3bc"},"schema_version":"1.0","source":{"id":"2107.03402","kind":"arxiv","version":1}},"canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4542021c09dc207eb5ece8d33234c9b2c2351df4d6e43abb9eee3326270eedae","first_computed_at":"2026-07-05T02:56:05.612852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:56:05.612852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wlhx/LQRsInlO7ZmNfD/OG2YOxjSz0LrsrBvOfWT/D50TSfbGVayuS2XOnUyQ49C2dbw3BdOO/sVNWi/V4a/Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:56:05.613593Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.03402","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0e22d7143d0b564098b64b4297312c66c7ffffcb05182854cdd1d80d8a7880d","sha256:2956744404b71dc245d3dd03962bee239f8534d513d1aa1cf891b5162d86daae"],"state_sha256":"ad316d417936ef212c7826306954e62f8f0229ebc9f643e3545744254d44174b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QheiL+XjogURASNgvE+xjhJvnnDgqJ6xoIHrCtxbHypmu/uS7IdZm2/4BtL3nND/fI040OWk2LNOqf3FMYUiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T12:31:56.862962Z","bundle_sha256":"ce16331aa9da7c76ea03ca8b851ad9a44505abd3796783df0dbd2439929dca3f"}}