{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:GOAT6GWWRCIYVIPNU6CVV6WSGO","short_pith_number":"pith:GOAT6GWW","canonical_record":{"source":{"id":"0801.1667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-01-10T21:00:04Z","cross_cats_sorted":["astro-ph","gr-qc"],"title_canon_sha256":"ab9b0db451c1addc5694eb60efb235e72608785ecc65a8512b111b21fc08f476","abstract_canon_sha256":"be3ca4a39978dad5e835b180bec605b28bbbc8753931d055b1696709a9b5c0aa"},"schema_version":"1.0"},"canonical_sha256":"33813f1ad688918aa1eda7855afad233817e095a00426507b42c283a16d1bcff","source":{"kind":"arxiv","id":"0801.1667","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1667","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1667v2","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1667","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"GOAT6GWWRCIY","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"GOAT6GWWRCIYVIPN","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"GOAT6GWW","created_at":"2026-07-04T15:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:GOAT6GWWRCIYVIPNU6CVV6WSGO","target":"record","payload":{"canonical_record":{"source":{"id":"0801.1667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-01-10T21:00:04Z","cross_cats_sorted":["astro-ph","gr-qc"],"title_canon_sha256":"ab9b0db451c1addc5694eb60efb235e72608785ecc65a8512b111b21fc08f476","abstract_canon_sha256":"be3ca4a39978dad5e835b180bec605b28bbbc8753931d055b1696709a9b5c0aa"},"schema_version":"1.0"},"canonical_sha256":"33813f1ad688918aa1eda7855afad233817e095a00426507b42c283a16d1bcff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:30:53.216611Z","signature_b64":"cV/CnZU9AihKxd/oONcb9hXiGfkgry9RJV4ugB3eAAWUgUhqCueHYrSh1wpYZ3h/ejjdD8AtiyD1c1qSbTsYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33813f1ad688918aa1eda7855afad233817e095a00426507b42c283a16d1bcff","last_reissued_at":"2026-07-04T15:30:53.216208Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:30:53.216208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.1667","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":"2026-07-04T15:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhcPgmUJwjcwHMcl3WwFVYgCZkLAehEzGdUr6dNuKZ5mCpY6wjYhQQlSer5gZiQ1R0IuwjqKM0XFNzWFOMYbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T02:48:17.819571Z"},"content_sha256":"1f8e866ef4776ac3149a5528118a931504dd709241a76627083d9a1799711ba2","schema_version":"1.0","event_id":"sha256:1f8e866ef4776ac3149a5528118a931504dd709241a76627083d9a1799711ba2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:GOAT6GWWRCIYVIPNU6CVV6WSGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised perturbation equations in bouncing cosmologies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph","gr-qc"],"primary_cat":"hep-th","authors_text":"Antonio Cardoso, David Wands","submitted_at":"2008-01-10T21:00:04Z","abstract_excerpt":"We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalised gravity, applicable to non-singular cosmological models including a bounce from collapse to expansion in the very early universe. We present the general form for the perturbation equations which follows from requiring that the inhomogeneous universe on large scales obeys the same local equations as the homogeneous Friedmann-Robertson-Walker background cosmology (the separate universes approach). In a pseudo-longitudinal gauge this becomes a homogeneous second-order differential equation for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1667","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/0801.1667/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":"2026-07-04T15:30:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xPvpzB2KTDWzgvNR9ypxS39cLZrg+el6YXP1IhIj9VQZMmxbeCxBpFge3+k56VYeXhxMP+cONAPiO2Ca7KaSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T02:48:17.819929Z"},"content_sha256":"657b0b0fe294adcc625bd3278f6904973473ae026bdba9e7c30535bea578fe7b","schema_version":"1.0","event_id":"sha256:657b0b0fe294adcc625bd3278f6904973473ae026bdba9e7c30535bea578fe7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO/bundle.json","state_url":"https://pith.science/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO/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":"2026-07-22T02:48:17Z","links":{"resolver":"https://pith.science/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO","bundle":"https://pith.science/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO/bundle.json","state":"https://pith.science/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOAT6GWWRCIYVIPNU6CVV6WSGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GOAT6GWWRCIYVIPNU6CVV6WSGO","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":"be3ca4a39978dad5e835b180bec605b28bbbc8753931d055b1696709a9b5c0aa","cross_cats_sorted":["astro-ph","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-01-10T21:00:04Z","title_canon_sha256":"ab9b0db451c1addc5694eb60efb235e72608785ecc65a8512b111b21fc08f476"},"schema_version":"1.0","source":{"id":"0801.1667","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.1667","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"arxiv_version","alias_value":"0801.1667v2","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.1667","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"pith_short_12","alias_value":"GOAT6GWWRCIY","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"GOAT6GWWRCIYVIPN","created_at":"2026-07-04T15:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"GOAT6GWW","created_at":"2026-07-04T15:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:657b0b0fe294adcc625bd3278f6904973473ae026bdba9e7c30535bea578fe7b","target":"graph","created_at":"2026-07-04T15:30:53Z","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/0801.1667/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider linear perturbation equations for long-wavelength scalar metric perturbations in generalised gravity, applicable to non-singular cosmological models including a bounce from collapse to expansion in the very early universe. We present the general form for the perturbation equations which follows from requiring that the inhomogeneous universe on large scales obeys the same local equations as the homogeneous Friedmann-Robertson-Walker background cosmology (the separate universes approach). In a pseudo-longitudinal gauge this becomes a homogeneous second-order differential equation for","authors_text":"Antonio Cardoso, David Wands","cross_cats":["astro-ph","gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-01-10T21:00:04Z","title":"Generalised perturbation equations in bouncing cosmologies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.1667","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":"sha256:1f8e866ef4776ac3149a5528118a931504dd709241a76627083d9a1799711ba2","target":"record","created_at":"2026-07-04T15:30:53Z","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":"be3ca4a39978dad5e835b180bec605b28bbbc8753931d055b1696709a9b5c0aa","cross_cats_sorted":["astro-ph","gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-01-10T21:00:04Z","title_canon_sha256":"ab9b0db451c1addc5694eb60efb235e72608785ecc65a8512b111b21fc08f476"},"schema_version":"1.0","source":{"id":"0801.1667","kind":"arxiv","version":2}},"canonical_sha256":"33813f1ad688918aa1eda7855afad233817e095a00426507b42c283a16d1bcff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33813f1ad688918aa1eda7855afad233817e095a00426507b42c283a16d1bcff","first_computed_at":"2026-07-04T15:30:53.216208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:30:53.216208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cV/CnZU9AihKxd/oONcb9hXiGfkgry9RJV4ugB3eAAWUgUhqCueHYrSh1wpYZ3h/ejjdD8AtiyD1c1qSbTsYAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:30:53.216611Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.1667","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f8e866ef4776ac3149a5528118a931504dd709241a76627083d9a1799711ba2","sha256:657b0b0fe294adcc625bd3278f6904973473ae026bdba9e7c30535bea578fe7b"],"state_sha256":"ceae2796cd9d21c91a3f3eed777499098cc17ed2605daff6649c3c25c6a761d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLUC+zdbkkb3PUJZoylPlA4vX4H7fE6xQxhXeuUxRNq/QI1AdL3es4SLn3dtD7/hWjTG7fpm9GBSNnPqeCHsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T02:48:17.821952Z","bundle_sha256":"bf4583dddb0b70fed5fc35ec7277c473af75f35f26664087951e220dd405ad5d"}}