{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6VFJ3CIRCD7XNSQTMDFUAZ5RVX","short_pith_number":"pith:6VFJ3CIR","canonical_record":{"source":{"id":"1003.3270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-16T22:58:43Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"0c81e83e73c4d076fc735bb0f32fc5809d6732e3b0461ab9d8280e61c9cfbcaf","abstract_canon_sha256":"bd81fa8b41ec1ce8465d0d967582aebfb8471802860f365135be88c799c19777"},"schema_version":"1.0"},"canonical_sha256":"f54a9d891110ff76ca1360cb4067b1ade958fa11c30cabb6b1a71917db978111","source":{"kind":"arxiv","id":"1003.3270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3270","created_at":"2026-05-18T02:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3270v1","created_at":"2026-05-18T02:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3270","created_at":"2026-05-18T02:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"6VFJ3CIRCD7X","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6VFJ3CIRCD7XNSQT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6VFJ3CIR","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6VFJ3CIRCD7XNSQTMDFUAZ5RVX","target":"record","payload":{"canonical_record":{"source":{"id":"1003.3270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-16T22:58:43Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"0c81e83e73c4d076fc735bb0f32fc5809d6732e3b0461ab9d8280e61c9cfbcaf","abstract_canon_sha256":"bd81fa8b41ec1ce8465d0d967582aebfb8471802860f365135be88c799c19777"},"schema_version":"1.0"},"canonical_sha256":"f54a9d891110ff76ca1360cb4067b1ade958fa11c30cabb6b1a71917db978111","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:33.067370Z","signature_b64":"LW1rBX4+4Lq+OQ28sJHVMogY9SxIhQlIFHNsI8IDQYktqWwmtO/sCkFP/TDQ4xtr5p63k0ytCt+dUUcKUMiTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f54a9d891110ff76ca1360cb4067b1ade958fa11c30cabb6b1a71917db978111","last_reissued_at":"2026-05-18T02:08:33.066658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:33.066658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.3270","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":"2026-05-18T02:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N07czLRR1J2D3T6/GpzSi6kZ1k+08h8XnZEBOrg/5f6t3owYzfNjkyYjCU3rL7W2mwMunRiDHxHeh/jZcdSUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:56:25.196244Z"},"content_sha256":"9cce623849e74e05a88d3f44027d95f24ac250f0bd66e47e3064d2673152d4f2","schema_version":"1.0","event_id":"sha256:9cce623849e74e05a88d3f44027d95f24ac250f0bd66e47e3064d2673152d4f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6VFJ3CIRCD7XNSQTMDFUAZ5RVX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A geometrical approach to nonlinear perturbations in relativistic cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"David Langlois, Filippo Vernizzi","submitted_at":"2010-03-16T22:58:43Z","abstract_excerpt":"We give a pedagogical  review of  a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to  cosmological fluids,  we  define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a  nonlinear description in terms of  adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to  easily obtain equations up to second, third  and higher orders."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3270","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":"2026-05-18T02:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6S4IG4mekXZVasK6mXm2z08k1jHDSoALC2WQQakht+ruLQmDoybvF9rU/VZ87B37CjnGTMZpq6SY8HGZoqVRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:56:25.196917Z"},"content_sha256":"cdf70c55f508062c74da12e4d3d22728549dcd18ef59e30e75c858f75a4398c9","schema_version":"1.0","event_id":"sha256:cdf70c55f508062c74da12e4d3d22728549dcd18ef59e30e75c858f75a4398c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX/bundle.json","state_url":"https://pith.science/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX/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":"2026-05-26T05:56:25Z","links":{"resolver":"https://pith.science/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX","bundle":"https://pith.science/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX/bundle.json","state":"https://pith.science/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VFJ3CIRCD7XNSQTMDFUAZ5RVX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6VFJ3CIRCD7XNSQTMDFUAZ5RVX","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":"bd81fa8b41ec1ce8465d0d967582aebfb8471802860f365135be88c799c19777","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-16T22:58:43Z","title_canon_sha256":"0c81e83e73c4d076fc735bb0f32fc5809d6732e3b0461ab9d8280e61c9cfbcaf"},"schema_version":"1.0","source":{"id":"1003.3270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3270","created_at":"2026-05-18T02:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3270v1","created_at":"2026-05-18T02:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3270","created_at":"2026-05-18T02:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"6VFJ3CIRCD7X","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6VFJ3CIRCD7XNSQT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6VFJ3CIR","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:cdf70c55f508062c74da12e4d3d22728549dcd18ef59e30e75c858f75a4398c9","target":"graph","created_at":"2026-05-18T02:08:33Z","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 give a pedagogical  review of  a covariant and fully non-perturbative approach to study nonlinear perturbations in cosmology. In the first part, devoted to  cosmological fluids,  we  define a nonlinear extension of the uniform-density curvature perturbation and derive its evolution equation. In the second part, we focus our attention on multiple scalar fields and present a  nonlinear description in terms of  adiabatic and entropy perturbations. In both cases, we show how the formalism presented here enables one to  easily obtain equations up to second, third  and higher orders.","authors_text":"David Langlois, Filippo Vernizzi","cross_cats":["gr-qc","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-16T22:58:43Z","title":"A geometrical approach to nonlinear perturbations in relativistic cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3270","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":"sha256:9cce623849e74e05a88d3f44027d95f24ac250f0bd66e47e3064d2673152d4f2","target":"record","created_at":"2026-05-18T02:08:33Z","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":"bd81fa8b41ec1ce8465d0d967582aebfb8471802860f365135be88c799c19777","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2010-03-16T22:58:43Z","title_canon_sha256":"0c81e83e73c4d076fc735bb0f32fc5809d6732e3b0461ab9d8280e61c9cfbcaf"},"schema_version":"1.0","source":{"id":"1003.3270","kind":"arxiv","version":1}},"canonical_sha256":"f54a9d891110ff76ca1360cb4067b1ade958fa11c30cabb6b1a71917db978111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f54a9d891110ff76ca1360cb4067b1ade958fa11c30cabb6b1a71917db978111","first_computed_at":"2026-05-18T02:08:33.066658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:33.066658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LW1rBX4+4Lq+OQ28sJHVMogY9SxIhQlIFHNsI8IDQYktqWwmtO/sCkFP/TDQ4xtr5p63k0ytCt+dUUcKUMiTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:33.067370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cce623849e74e05a88d3f44027d95f24ac250f0bd66e47e3064d2673152d4f2","sha256:cdf70c55f508062c74da12e4d3d22728549dcd18ef59e30e75c858f75a4398c9"],"state_sha256":"0d186d9349b6d6c4432edb27d8c248dbfc322021b0166b540542001a0592e0f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIM3eri5VjuurssXvbY5QWnZ8sd9/REsCPyiZmIxfIShh1+mp0h0IVtFirQWCKgWVk6curEYOVCVPFg8okKUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:56:25.199809Z","bundle_sha256":"b896ba8877d0f6c26081f4d55b4da9aaae6eee23d17c1319139aa125d8e9c337"}}