{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:AXEIOVJSPUUFLDVXEQCG5QEEBW","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":"aa77e487d0aa07bc5920c56cc4d298da0efca7059946fa45259837300fe3bf33","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1993-11-17T15:53:13Z","title_canon_sha256":"d40a9d460a8c89de3e2bb4914e4dc577f2a7b497ae3fe7d58db6521721d74234"},"schema_version":"1.0","source":{"id":"astro-ph/9311041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9311041","created_at":"2026-05-18T04:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9311041v1","created_at":"2026-05-18T04:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9311041","created_at":"2026-05-18T04:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"AXEIOVJSPUUF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"AXEIOVJSPUUFLDVX","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"AXEIOVJS","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:bda1655abaf9759cc21123de87ca6e0cbe4b5a8e35a60c3b6c79c964068844a7","target":"graph","created_at":"2026-05-18T04:33:50Z","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":"After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbati","authors_text":"Ruth Durrer","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1993-11-17T15:53:13Z","title":"Gauge Invariant Cosmological Perturbation Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9311041","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":"sha256:9b173097340f53e3d043b20483ac9f420c318b11a013dbf6cd5b8141a0fbe876","target":"record","created_at":"2026-05-18T04:33:50Z","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":"aa77e487d0aa07bc5920c56cc4d298da0efca7059946fa45259837300fe3bf33","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1993-11-17T15:53:13Z","title_canon_sha256":"d40a9d460a8c89de3e2bb4914e4dc577f2a7b497ae3fe7d58db6521721d74234"},"schema_version":"1.0","source":{"id":"astro-ph/9311041","kind":"arxiv","version":1}},"canonical_sha256":"05c88755327d28558eb724046ec0840dbe0b68cc73a50c388ea30e6cb5925fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05c88755327d28558eb724046ec0840dbe0b68cc73a50c388ea30e6cb5925fcc","first_computed_at":"2026-05-18T04:33:50.514564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:50.514564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fTV8t3B2fT5APstulpV456Rowtg1Fbe4BFVVpzVbylWbeuukpAZprd1z8wXPgDCOr/YIVIZBbmGxGIUft7ASAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:50.515135Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9311041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b173097340f53e3d043b20483ac9f420c318b11a013dbf6cd5b8141a0fbe876","sha256:bda1655abaf9759cc21123de87ca6e0cbe4b5a8e35a60c3b6c79c964068844a7"],"state_sha256":"47cb6ac87b82a700056a37cf28f68cf314a0f86c2596213b31f8c0cf2f5d6eb2"}