{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:52SYJOJHN7N2IPNGGUCKQAK7YA","short_pith_number":"pith:52SYJOJH","canonical_record":{"source":{"id":"0804.3276","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-04-21T13:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"0d3e528f9946698f4e67d8e88e5380158e85db354e48c1370ede62e0453f32b2","abstract_canon_sha256":"aa33a3c4ac869c8ff8015b0f2d00be397eeaec9219305092606372bf726c1424"},"schema_version":"1.0"},"canonical_sha256":"eea584b9276fdba43da63504a8015fc02b21d962fefefdeecc8ba185b16e62ed","source":{"kind":"arxiv","id":"0804.3276","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.3276","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"0804.3276v2","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.3276","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"52SYJOJHN7N2","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"pith_short_16","alias_value":"52SYJOJHN7N2IPNG","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"pith_short_8","alias_value":"52SYJOJH","created_at":"2026-07-04T15:44:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:52SYJOJHN7N2IPNGGUCKQAK7YA","target":"record","payload":{"canonical_record":{"source":{"id":"0804.3276","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-04-21T13:05:48Z","cross_cats_sorted":[],"title_canon_sha256":"0d3e528f9946698f4e67d8e88e5380158e85db354e48c1370ede62e0453f32b2","abstract_canon_sha256":"aa33a3c4ac869c8ff8015b0f2d00be397eeaec9219305092606372bf726c1424"},"schema_version":"1.0"},"canonical_sha256":"eea584b9276fdba43da63504a8015fc02b21d962fefefdeecc8ba185b16e62ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:44:47.807021Z","signature_b64":"c1qnx1yhoaNQocM1k6ptrvsufVqv799jYe5A5ESHzqZUNKY0GH2Rrhp+H/14rPb9tqUSGC3VdZXJ5+icM6WZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eea584b9276fdba43da63504a8015fc02b21d962fefefdeecc8ba185b16e62ed","last_reissued_at":"2026-07-04T15:44:47.806627Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:44:47.806627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0804.3276","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6eqFAPwCSRIEcUuiKy3U5pl2iaDKBncDOtqQVYttknIcOdoeJy/dXWTSbECdgAIBnyZR4IvtYsZnj/uVVS1kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T19:18:24.309358Z"},"content_sha256":"d41a0a5fff097a030eb0dcbbcd23f3b485dc4106419a74583e7ac5f1f967ef20","schema_version":"1.0","event_id":"sha256:d41a0a5fff097a030eb0dcbbcd23f3b485dc4106419a74583e7ac5f1f967ef20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:52SYJOJHN7N2IPNGGUCKQAK7YA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Concise Introduction to Perturbation Theory in Cosmology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"David R. Matravers, Karim A. Malik","submitted_at":"2008-04-21T13:05:48Z","abstract_excerpt":"We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3276","kind":"arxiv","version":2},"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/0804.3276/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":"2026-07-04T15:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZhQDKIpGV8jer8kYJ0s+bBz7nWnsLJmvlMs3W6RZmEklpFFlSeJjf311KlAcdeSKu9prxZAQNt+kn2Z9UEnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T19:18:24.309859Z"},"content_sha256":"44a1d7a058cd2efa38e306cecf26e25719b5e81bf11de937392cd4dda5156d17","schema_version":"1.0","event_id":"sha256:44a1d7a058cd2efa38e306cecf26e25719b5e81bf11de937392cd4dda5156d17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52SYJOJHN7N2IPNGGUCKQAK7YA/bundle.json","state_url":"https://pith.science/pith/52SYJOJHN7N2IPNGGUCKQAK7YA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52SYJOJHN7N2IPNGGUCKQAK7YA/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":"2026-08-07T19:18:24Z","links":{"resolver":"https://pith.science/pith/52SYJOJHN7N2IPNGGUCKQAK7YA","bundle":"https://pith.science/pith/52SYJOJHN7N2IPNGGUCKQAK7YA/bundle.json","state":"https://pith.science/pith/52SYJOJHN7N2IPNGGUCKQAK7YA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52SYJOJHN7N2IPNGGUCKQAK7YA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:52SYJOJHN7N2IPNGGUCKQAK7YA","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":"aa33a3c4ac869c8ff8015b0f2d00be397eeaec9219305092606372bf726c1424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-04-21T13:05:48Z","title_canon_sha256":"0d3e528f9946698f4e67d8e88e5380158e85db354e48c1370ede62e0453f32b2"},"schema_version":"1.0","source":{"id":"0804.3276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.3276","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"0804.3276v2","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.3276","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"52SYJOJHN7N2","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"pith_short_16","alias_value":"52SYJOJHN7N2IPNG","created_at":"2026-07-04T15:44:47Z"},{"alias_kind":"pith_short_8","alias_value":"52SYJOJH","created_at":"2026-07-04T15:44:47Z"}],"graph_snapshots":[{"event_id":"sha256:44a1d7a058cd2efa38e306cecf26e25719b5e81bf11de937392cd4dda5156d17","target":"graph","created_at":"2026-07-04T15:44:47Z","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/0804.3276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a concise, self-contained introduction to perturbation theory in cosmology at linear and second order, striking a balance between mathematical rigour and usability. In particular we discuss gauge issues and the active and passive approach to calculating gauge transformations. We also construct gauge-invariant variables, including the second order tensor perturbation on uniform curvature hypersurfaces.","authors_text":"David R. Matravers, Karim A. Malik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-04-21T13:05:48Z","title":"A Concise Introduction to Perturbation Theory in Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3276","kind":"arxiv","version":2},"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:d41a0a5fff097a030eb0dcbbcd23f3b485dc4106419a74583e7ac5f1f967ef20","target":"record","created_at":"2026-07-04T15:44:47Z","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":"aa33a3c4ac869c8ff8015b0f2d00be397eeaec9219305092606372bf726c1424","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-04-21T13:05:48Z","title_canon_sha256":"0d3e528f9946698f4e67d8e88e5380158e85db354e48c1370ede62e0453f32b2"},"schema_version":"1.0","source":{"id":"0804.3276","kind":"arxiv","version":2}},"canonical_sha256":"eea584b9276fdba43da63504a8015fc02b21d962fefefdeecc8ba185b16e62ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eea584b9276fdba43da63504a8015fc02b21d962fefefdeecc8ba185b16e62ed","first_computed_at":"2026-07-04T15:44:47.806627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:44:47.806627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c1qnx1yhoaNQocM1k6ptrvsufVqv799jYe5A5ESHzqZUNKY0GH2Rrhp+H/14rPb9tqUSGC3VdZXJ5+icM6WZDw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:44:47.807021Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.3276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d41a0a5fff097a030eb0dcbbcd23f3b485dc4106419a74583e7ac5f1f967ef20","sha256:44a1d7a058cd2efa38e306cecf26e25719b5e81bf11de937392cd4dda5156d17"],"state_sha256":"10cf387d75bf9df296bf131e46a8bd9291c0301d947d9e9860ce140b3cb82b73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HVKM97QhlouDO6UK3thYcxcgs6ZBZBv/oRZD55LDtMnPVZhkwt/oq0SPLOGkd3GaE5+PAClcXN9Cow3m2sBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T19:18:24.313612Z","bundle_sha256":"f27803a5747e8a767366ef198b0a46fa5fe8af6f234c2fcdfe858702bce0b691"}}