{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7IBIAJQF5HVX5YCMNLHT6ILTWX","short_pith_number":"pith:7IBIAJQF","canonical_record":{"source":{"id":"1212.3549","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2012-12-14T18:06:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"e1857b30f56524e5e963e7a8178694d55f011e6a9cec8c9326b3b909842d9c53","abstract_canon_sha256":"5405b73b954db62eceef98e1da5ef85c39dc45b3e24ef2827614b56640363acf"},"schema_version":"1.0"},"canonical_sha256":"fa02802605e9eb7ee04c6acf3f2173b5f29227153cfb2e3356c412c9652ab5b9","source":{"kind":"arxiv","id":"1212.3549","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3549","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3549v4","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3549","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"pith_short_12","alias_value":"7IBIAJQF5HVX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7IBIAJQF5HVX5YCM","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7IBIAJQF","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7IBIAJQF5HVX5YCMNLHT6ILTWX","target":"record","payload":{"canonical_record":{"source":{"id":"1212.3549","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2012-12-14T18:06:38Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"e1857b30f56524e5e963e7a8178694d55f011e6a9cec8c9326b3b909842d9c53","abstract_canon_sha256":"5405b73b954db62eceef98e1da5ef85c39dc45b3e24ef2827614b56640363acf"},"schema_version":"1.0"},"canonical_sha256":"fa02802605e9eb7ee04c6acf3f2173b5f29227153cfb2e3356c412c9652ab5b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:30.987987Z","signature_b64":"NGLUoCORkph9QyJu6f2qMsj9WyYb9yS3W8uhbcaMKdomQQmSKRbunLhALnf9Pcil3papIIVKJM65w+lV2YuNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa02802605e9eb7ee04c6acf3f2173b5f29227153cfb2e3356c412c9652ab5b9","last_reissued_at":"2026-05-18T01:24:30.987348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:30.987348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.3549","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":"2026-05-18T01:24:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XN5kSXWeXZar1ZQNjOZppkM8LF2oYzjIliYm1NkN3qBxNCEdhTafIZn4XqT4QFOgEytj98flZt/CCIBX5NVqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:45:08.433712Z"},"content_sha256":"328fdccdcf9f31dd519efbfb2b60952c4301ddd5a421cd3d6657546e0803a2e3","schema_version":"1.0","event_id":"sha256:328fdccdcf9f31dd519efbfb2b60952c4301ddd5a421cd3d6657546e0803a2e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7IBIAJQF5HVX5YCMNLHT6ILTWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Input nonlinearities can shape beyond-pairwise correlations and improve information transmission by neural populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.NC","authors_text":"Eric Shea-Brown, Joel Zylberberg","submitted_at":"2012-12-14T18:06:38Z","abstract_excerpt":"While recent recordings from neural populations show beyond-pairwise, or higher-order correlations (HOC), we have little understanding of how HOC arise from network interactions and of how they impact encoded information. Here, we show that input nonlinearities imply HOC in spin-glass-type statistical models. We then discuss one such model with parameterized pairwise- and higher-order interactions, revealing conditions under which beyond-pairwise interactions increase the mutual information between a given stimulus type and the population responses. For jointly Gaussian stimuli, coding perform"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3549","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":"2026-05-18T01:24:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NgBhl19S9/2XruDfmF5cSbs0GORaw/DPd3QRdBBJyOkESkOzWCv/to4F+i5Pfm9+exraPrardkIV2q3as2X6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T06:45:08.434053Z"},"content_sha256":"82b1fdcca400123f6be3ef02bf7725aa7e921e63ad09cd9a8f2601f6a8c5d215","schema_version":"1.0","event_id":"sha256:82b1fdcca400123f6be3ef02bf7725aa7e921e63ad09cd9a8f2601f6a8c5d215"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX/bundle.json","state_url":"https://pith.science/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX/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":"2026-06-29T06:45:08Z","links":{"resolver":"https://pith.science/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX","bundle":"https://pith.science/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX/bundle.json","state":"https://pith.science/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IBIAJQF5HVX5YCMNLHT6ILTWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7IBIAJQF5HVX5YCMNLHT6ILTWX","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":"5405b73b954db62eceef98e1da5ef85c39dc45b3e24ef2827614b56640363acf","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2012-12-14T18:06:38Z","title_canon_sha256":"e1857b30f56524e5e963e7a8178694d55f011e6a9cec8c9326b3b909842d9c53"},"schema_version":"1.0","source":{"id":"1212.3549","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3549","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3549v4","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3549","created_at":"2026-05-18T01:24:30Z"},{"alias_kind":"pith_short_12","alias_value":"7IBIAJQF5HVX","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7IBIAJQF5HVX5YCM","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7IBIAJQF","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:82b1fdcca400123f6be3ef02bf7725aa7e921e63ad09cd9a8f2601f6a8c5d215","target":"graph","created_at":"2026-05-18T01:24:30Z","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":"While recent recordings from neural populations show beyond-pairwise, or higher-order correlations (HOC), we have little understanding of how HOC arise from network interactions and of how they impact encoded information. Here, we show that input nonlinearities imply HOC in spin-glass-type statistical models. We then discuss one such model with parameterized pairwise- and higher-order interactions, revealing conditions under which beyond-pairwise interactions increase the mutual information between a given stimulus type and the population responses. For jointly Gaussian stimuli, coding perform","authors_text":"Eric Shea-Brown, Joel Zylberberg","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2012-12-14T18:06:38Z","title":"Input nonlinearities can shape beyond-pairwise correlations and improve information transmission by neural populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3549","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":"sha256:328fdccdcf9f31dd519efbfb2b60952c4301ddd5a421cd3d6657546e0803a2e3","target":"record","created_at":"2026-05-18T01:24:30Z","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":"5405b73b954db62eceef98e1da5ef85c39dc45b3e24ef2827614b56640363acf","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.NC","submitted_at":"2012-12-14T18:06:38Z","title_canon_sha256":"e1857b30f56524e5e963e7a8178694d55f011e6a9cec8c9326b3b909842d9c53"},"schema_version":"1.0","source":{"id":"1212.3549","kind":"arxiv","version":4}},"canonical_sha256":"fa02802605e9eb7ee04c6acf3f2173b5f29227153cfb2e3356c412c9652ab5b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa02802605e9eb7ee04c6acf3f2173b5f29227153cfb2e3356c412c9652ab5b9","first_computed_at":"2026-05-18T01:24:30.987348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:30.987348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGLUoCORkph9QyJu6f2qMsj9WyYb9yS3W8uhbcaMKdomQQmSKRbunLhALnf9Pcil3papIIVKJM65w+lV2YuNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:30.987987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3549","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:328fdccdcf9f31dd519efbfb2b60952c4301ddd5a421cd3d6657546e0803a2e3","sha256:82b1fdcca400123f6be3ef02bf7725aa7e921e63ad09cd9a8f2601f6a8c5d215"],"state_sha256":"71fbaf94a45176435ca8e54e7e3b5d8575225b3077426538d66f26c847f3c2f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hp7pvNMORHon70sxZszOlUBRgE9MqEMESow0h/K3AkkW3i0yBUD0Uvj8ZoQZ6Qy/QTzjHF8q+5CQSB2iyxzoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T06:45:08.435920Z","bundle_sha256":"bd963cd70a81f825e7515fccd04d97344700fe3f85b9863f389345f636580428"}}