{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3W64S2M3E37RTI23F3ZVOVWIGC","short_pith_number":"pith:3W64S2M3","canonical_record":{"source":{"id":"1509.02546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-08T20:30:14Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"944d46351d4ed28cb46c275c1ab29d9677370af0e50d6109b18ecf5934e52be7","abstract_canon_sha256":"2caeb8f4022d77168f9057f83d38946edb20ce7549577c6c60049dead6d71219"},"schema_version":"1.0"},"canonical_sha256":"ddbdc9699b26ff19a35b2ef35756c8309e1e7a16d4e8e4f6473ddce3eb4077f4","source":{"kind":"arxiv","id":"1509.02546","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02546","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02546v1","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02546","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"3W64S2M3E37R","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3W64S2M3E37RTI23","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3W64S2M3","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3W64S2M3E37RTI23F3ZVOVWIGC","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-08T20:30:14Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"944d46351d4ed28cb46c275c1ab29d9677370af0e50d6109b18ecf5934e52be7","abstract_canon_sha256":"2caeb8f4022d77168f9057f83d38946edb20ce7549577c6c60049dead6d71219"},"schema_version":"1.0"},"canonical_sha256":"ddbdc9699b26ff19a35b2ef35756c8309e1e7a16d4e8e4f6473ddce3eb4077f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:13.121699Z","signature_b64":"KaWK+EGNPzGHNq3Yz7p3sbCDJoaqogynUi5VkdOMTt5zEY36Elw1rvraFB2qPivWhHcioGczvXY4Oq/By6xNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddbdc9699b26ff19a35b2ef35756c8309e1e7a16d4e8e4f6473ddce3eb4077f4","last_reissued_at":"2026-05-18T01:21:13.121006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:13.121006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02546","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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wd+zASPP8LYY7aYQjDfSyaDMrIhkeT0RBkmeSp+zumkv+DX0K2PJPMNx3zsRNbXXC6tkfXd6N/tmQqbxP5plAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:28:03.814506Z"},"content_sha256":"ca68be1fe26010b6251467b81b3ba9d429327e4b7b0337192c8e7a2b6e1ae07b","schema_version":"1.0","event_id":"sha256:ca68be1fe26010b6251467b81b3ba9d429327e4b7b0337192c8e7a2b6e1ae07b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3W64S2M3E37RTI23F3ZVOVWIGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the low dimensional dynamics of structured random networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"cond-mat.dis-nn","authors_text":"David Renfrew, Johnatan Aljadeff, Marina Vegu\\'e, Tatyana O. Sharpee","submitted_at":"2015-09-08T20:30:14Z","abstract_excerpt":"Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network connectivity structure and its low dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and post-synaptic neurons through a sufficiently smooth function $g$ of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02546","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":"2026-05-18T01:21:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMh+bDqFuTQyTfyoTBHny02r86/uK7qriaApr/wyD232zBowpfRs6lTB0eI8qE8ZVSOJB2awXGHgAq6fzSQfCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:28:03.815107Z"},"content_sha256":"4ecd5bc26cbd74c9645bfdaaca69a2987510af3b8060450bb40a22e7b6c07899","schema_version":"1.0","event_id":"sha256:4ecd5bc26cbd74c9645bfdaaca69a2987510af3b8060450bb40a22e7b6c07899"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3W64S2M3E37RTI23F3ZVOVWIGC/bundle.json","state_url":"https://pith.science/pith/3W64S2M3E37RTI23F3ZVOVWIGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3W64S2M3E37RTI23F3ZVOVWIGC/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":"2026-05-31T00:28:03Z","links":{"resolver":"https://pith.science/pith/3W64S2M3E37RTI23F3ZVOVWIGC","bundle":"https://pith.science/pith/3W64S2M3E37RTI23F3ZVOVWIGC/bundle.json","state":"https://pith.science/pith/3W64S2M3E37RTI23F3ZVOVWIGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3W64S2M3E37RTI23F3ZVOVWIGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3W64S2M3E37RTI23F3ZVOVWIGC","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":"2caeb8f4022d77168f9057f83d38946edb20ce7549577c6c60049dead6d71219","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-08T20:30:14Z","title_canon_sha256":"944d46351d4ed28cb46c275c1ab29d9677370af0e50d6109b18ecf5934e52be7"},"schema_version":"1.0","source":{"id":"1509.02546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02546","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02546v1","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02546","created_at":"2026-05-18T01:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"3W64S2M3E37R","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3W64S2M3E37RTI23","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3W64S2M3","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:4ecd5bc26cbd74c9645bfdaaca69a2987510af3b8060450bb40a22e7b6c07899","target":"graph","created_at":"2026-05-18T01:21:13Z","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":"Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network connectivity structure and its low dimensional dynamics. Each connection in the network is a random number with mean 0 and variance that depends on pre- and post-synaptic neurons through a sufficiently smooth function $g$ of their identities. We find that these networks undergo a phase transition from a silent to a chaotic state at a critical point we derive ","authors_text":"David Renfrew, Johnatan Aljadeff, Marina Vegu\\'e, Tatyana O. Sharpee","cross_cats":["q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-08T20:30:14Z","title":"On the low dimensional dynamics of structured random networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02546","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:ca68be1fe26010b6251467b81b3ba9d429327e4b7b0337192c8e7a2b6e1ae07b","target":"record","created_at":"2026-05-18T01:21:13Z","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":"2caeb8f4022d77168f9057f83d38946edb20ce7549577c6c60049dead6d71219","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2015-09-08T20:30:14Z","title_canon_sha256":"944d46351d4ed28cb46c275c1ab29d9677370af0e50d6109b18ecf5934e52be7"},"schema_version":"1.0","source":{"id":"1509.02546","kind":"arxiv","version":1}},"canonical_sha256":"ddbdc9699b26ff19a35b2ef35756c8309e1e7a16d4e8e4f6473ddce3eb4077f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddbdc9699b26ff19a35b2ef35756c8309e1e7a16d4e8e4f6473ddce3eb4077f4","first_computed_at":"2026-05-18T01:21:13.121006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:13.121006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KaWK+EGNPzGHNq3Yz7p3sbCDJoaqogynUi5VkdOMTt5zEY36Elw1rvraFB2qPivWhHcioGczvXY4Oq/By6xNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:13.121699Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca68be1fe26010b6251467b81b3ba9d429327e4b7b0337192c8e7a2b6e1ae07b","sha256:4ecd5bc26cbd74c9645bfdaaca69a2987510af3b8060450bb40a22e7b6c07899"],"state_sha256":"b7966cc210084c7286d01118c31a12f96f02cf6312fcf4aea936c882b7911fa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9cWDgID/7qNBQ40BSNUrm9ManMsd6uV1DHDLU0kQLmjCRzj8Oe2UpudzXa9KHCA8zfEAbLQSR/EYB5wc+6JuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:28:03.818503Z","bundle_sha256":"8fb31b931faf16903e95e2083492572f4d32e1cf2049a74be9922046f449b707"}}