{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:GMC6JWZ53EICL3ZHA2W76OZYJR","short_pith_number":"pith:GMC6JWZ5","canonical_record":{"source":{"id":"astro-ph/0505236","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2005-05-11T21:24:05Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"8257c5393744ae2999c8e6d831a7ee5a5992fb77eee3aca877121ac3c95afe0c","abstract_canon_sha256":"6ac8cc8de1325f9b6fc227a02fb10e000b1add717ba6e040dbab194739e369c7"},"schema_version":"1.0"},"canonical_sha256":"3305e4db3dd91025ef2706adff3b384c74b98e9bb0c4d7cce0025a7b5ec6fb96","source":{"kind":"arxiv","id":"astro-ph/0505236","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0505236","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0505236v1","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0505236","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"pith_short_12","alias_value":"GMC6JWZ53EIC","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"pith_short_16","alias_value":"GMC6JWZ53EICL3ZH","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"pith_short_8","alias_value":"GMC6JWZ5","created_at":"2026-07-04T16:52:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:GMC6JWZ53EICL3ZHA2W76OZYJR","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0505236","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2005-05-11T21:24:05Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"8257c5393744ae2999c8e6d831a7ee5a5992fb77eee3aca877121ac3c95afe0c","abstract_canon_sha256":"6ac8cc8de1325f9b6fc227a02fb10e000b1add717ba6e040dbab194739e369c7"},"schema_version":"1.0"},"canonical_sha256":"3305e4db3dd91025ef2706adff3b384c74b98e9bb0c4d7cce0025a7b5ec6fb96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:52:21.918030Z","signature_b64":"C2Y8GPTj8CDuXolUrUOfPm0zvPoyLxAinIxTTcwE00+gGg/a/4fFPCex1dnfPzMdXkQIHGmYhcnxgvQwrvQpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3305e4db3dd91025ef2706adff3b384c74b98e9bb0c4d7cce0025a7b5ec6fb96","last_reissued_at":"2026-07-04T16:52:21.917694Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:52:21.917694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0505236","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":"2026-07-04T16:52:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uj+/SECaWe2SJv2hNF1v1MdylMI6IcPJ0hLtn/t1OhKsnSUthjqSUuml6vsE1yEi9lPAmqFTtZAkYD5TgAMxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:49:09.329607Z"},"content_sha256":"43c252e9ca71af89ac3c64f3ea511cc487d3e3669b7671dc37c20843a195be25","schema_version":"1.0","event_id":"sha256:43c252e9ca71af89ac3c64f3ea511cc487d3e3669b7671dc37c20843a195be25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:GMC6JWZ53EICL3ZHA2W76OZYJR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Effects of Gravitational Back-Reaction on Cosmological Perturbations","license":"","headline":"","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph","authors_text":"Patrick Martineau, Robert Brandenberger","submitted_at":"2005-05-11T21:24:05Z","abstract_excerpt":"Because of the non-linearity of the Einstein equations, the cosmological fluctuations which are generated during inflation on a wide range of wavelengths do not evolve independently. In particular, to second order in perturbation theory, the first order fluctuations back-react both on the background geometry and on the perturbations themselves. I this paper, the gravitational back-reaction of long wavelength (super-Hubble) scalar metric fluctuations on the perturbations themselves is investigated for a large class of inflationary models. Specifically, the equations describing the evolution of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0505236","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/0505236/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":"2026-07-04T16:52:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sD7wD2OMLPc4RJosE7TfJaJs1sHvz6FDYBd27tHu+Yfg3b06IIwsB3cwWAoIzYmUfsp3OzIHE6dQgnP5+CbZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T08:49:09.330488Z"},"content_sha256":"f4741a1c9d2f4a10c2208e492872a90978f460162d2666ba964d92255eb915f2","schema_version":"1.0","event_id":"sha256:f4741a1c9d2f4a10c2208e492872a90978f460162d2666ba964d92255eb915f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GMC6JWZ53EICL3ZHA2W76OZYJR/bundle.json","state_url":"https://pith.science/pith/GMC6JWZ53EICL3ZHA2W76OZYJR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GMC6JWZ53EICL3ZHA2W76OZYJR/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":"2026-08-17T08:49:09Z","links":{"resolver":"https://pith.science/pith/GMC6JWZ53EICL3ZHA2W76OZYJR","bundle":"https://pith.science/pith/GMC6JWZ53EICL3ZHA2W76OZYJR/bundle.json","state":"https://pith.science/pith/GMC6JWZ53EICL3ZHA2W76OZYJR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GMC6JWZ53EICL3ZHA2W76OZYJR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:GMC6JWZ53EICL3ZHA2W76OZYJR","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":"6ac8cc8de1325f9b6fc227a02fb10e000b1add717ba6e040dbab194739e369c7","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"2005-05-11T21:24:05Z","title_canon_sha256":"8257c5393744ae2999c8e6d831a7ee5a5992fb77eee3aca877121ac3c95afe0c"},"schema_version":"1.0","source":{"id":"astro-ph/0505236","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0505236","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0505236v1","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0505236","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"pith_short_12","alias_value":"GMC6JWZ53EIC","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"pith_short_16","alias_value":"GMC6JWZ53EICL3ZH","created_at":"2026-07-04T16:52:21Z"},{"alias_kind":"pith_short_8","alias_value":"GMC6JWZ5","created_at":"2026-07-04T16:52:21Z"}],"graph_snapshots":[{"event_id":"sha256:f4741a1c9d2f4a10c2208e492872a90978f460162d2666ba964d92255eb915f2","target":"graph","created_at":"2026-07-04T16:52:21Z","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/astro-ph/0505236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Because of the non-linearity of the Einstein equations, the cosmological fluctuations which are generated during inflation on a wide range of wavelengths do not evolve independently. In particular, to second order in perturbation theory, the first order fluctuations back-react both on the background geometry and on the perturbations themselves. I this paper, the gravitational back-reaction of long wavelength (super-Hubble) scalar metric fluctuations on the perturbations themselves is investigated for a large class of inflationary models. Specifically, the equations describing the evolution of ","authors_text":"Patrick Martineau, Robert Brandenberger","cross_cats":["gr-qc","hep-ph","hep-th"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2005-05-11T21:24:05Z","title":"The Effects of Gravitational Back-Reaction on Cosmological Perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0505236","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":"sha256:43c252e9ca71af89ac3c64f3ea511cc487d3e3669b7671dc37c20843a195be25","target":"record","created_at":"2026-07-04T16:52:21Z","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":"6ac8cc8de1325f9b6fc227a02fb10e000b1add717ba6e040dbab194739e369c7","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"2005-05-11T21:24:05Z","title_canon_sha256":"8257c5393744ae2999c8e6d831a7ee5a5992fb77eee3aca877121ac3c95afe0c"},"schema_version":"1.0","source":{"id":"astro-ph/0505236","kind":"arxiv","version":1}},"canonical_sha256":"3305e4db3dd91025ef2706adff3b384c74b98e9bb0c4d7cce0025a7b5ec6fb96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3305e4db3dd91025ef2706adff3b384c74b98e9bb0c4d7cce0025a7b5ec6fb96","first_computed_at":"2026-07-04T16:52:21.917694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:52:21.917694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C2Y8GPTj8CDuXolUrUOfPm0zvPoyLxAinIxTTcwE00+gGg/a/4fFPCex1dnfPzMdXkQIHGmYhcnxgvQwrvQpDg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:52:21.918030Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0505236","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43c252e9ca71af89ac3c64f3ea511cc487d3e3669b7671dc37c20843a195be25","sha256:f4741a1c9d2f4a10c2208e492872a90978f460162d2666ba964d92255eb915f2"],"state_sha256":"7cc2e2f7238503745aeeae42c8972f4ef2080dd411e19e8fa3a1766ca689c059"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZhyUbzoAIYuMFHG/bvknaVisLlfY5T1Rp4J8NchArGpy7o2VX0DYwmneM86YSD4Vve7whkJA7ZYqDCAj7dmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T08:49:09.338368Z","bundle_sha256":"c92bfd635380d851a7b26c2bbf19db0e42800bf0ca44665b7f27ad253b71f341"}}