{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:A26RFWW7TOF4L2HIJK7FNQKSBM","short_pith_number":"pith:A26RFWW7","canonical_record":{"source":{"id":"0712.1291","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2007-12-08T16:53:40Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"dcd5a9a21497d98ccbad21164bf0d0f1f5da2d582758899681b95f80c84ab7ad","abstract_canon_sha256":"3861971959adc82b6fadf9790d20c02329ddc02da680b0112b9c3b658b89e687"},"schema_version":"1.0"},"canonical_sha256":"06bd12dadf9b8bc5e8e84abe56c1520b3645cd672a2c8591cb710db6beb6adcb","source":{"kind":"arxiv","id":"0712.1291","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1291","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1291v2","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1291","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"A26RFWW7TOF4","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"A26RFWW7TOF4L2HI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"A26RFWW7","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:A26RFWW7TOF4L2HIJK7FNQKSBM","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1291","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2007-12-08T16:53:40Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"dcd5a9a21497d98ccbad21164bf0d0f1f5da2d582758899681b95f80c84ab7ad","abstract_canon_sha256":"3861971959adc82b6fadf9790d20c02329ddc02da680b0112b9c3b658b89e687"},"schema_version":"1.0"},"canonical_sha256":"06bd12dadf9b8bc5e8e84abe56c1520b3645cd672a2c8591cb710db6beb6adcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:26.582694Z","signature_b64":"HAwZ99Aq+MSqPeGzMSo4rfJc6x7ph/eT6d7KSDEAChpMkHOuEKtuWwwp8Kq/Hrlp3aHXU712hOu7ZhiCnGBfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06bd12dadf9b8bc5e8e84abe56c1520b3645cd672a2c8591cb710db6beb6adcb","last_reissued_at":"2026-05-18T02:43:26.581952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:26.581952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1291","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":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OjhmaKb9m1MdqZgiJSEzV2XAS7aMZM9p2HkkXjSiHbaBYrauOdrWbzJwbaQd/vZWjbi3UERWrBL2ExbbwysUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:15:21.005218Z"},"content_sha256":"2fb6b6c63f6ea2139200cf9d8cb444d73761b0b2b4c14954c6b3f52257bd1d23","schema_version":"1.0","event_id":"sha256:2fb6b6c63f6ea2139200cf9d8cb444d73761b0b2b4c14954c6b3f52257bd1d23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:A26RFWW7TOF4L2HIJK7FNQKSBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second Order Gravitational Effects on CMB Temperature Anisotropy in Lambda dominated flat universes","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph","authors_text":"Kaiki Taro Inoue, Kenji Tomita","submitted_at":"2007-12-08T16:53:40Z","abstract_excerpt":"We study second order gravitational effects of local inhomogeneities on the cosmic microwave background radiation in flat universes with matter and a cosmological constant $\\Lambda$. We find that the general relativistic correction to the Newtonian approximation is negligible at second order provided that the size of the inhomogeneous region is sufficiently smaller than the horizon scale. For a spherically symmetric top-hat type quasi-linear perturbation, the first order temperature fluctuation corresponding to the linear integrated Sachs-Wolfe (ISW) effect is enhanced(suppressed) by the secon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1291","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":""},"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":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PreY5Rdy//7p5jGWKi9GkhNb9ZAkoYLXOr0WwjvBHv3Xaw40sBuaO8wBb8GahauZMeCqDqUcAy3S06CU6hXxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:15:21.005589Z"},"content_sha256":"83b007b8242f39c09427eba649acd153c90bdc44d3f49bc575a9b5eefda31673","schema_version":"1.0","event_id":"sha256:83b007b8242f39c09427eba649acd153c90bdc44d3f49bc575a9b5eefda31673"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A26RFWW7TOF4L2HIJK7FNQKSBM/bundle.json","state_url":"https://pith.science/pith/A26RFWW7TOF4L2HIJK7FNQKSBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A26RFWW7TOF4L2HIJK7FNQKSBM/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":"2026-05-27T23:15:21Z","links":{"resolver":"https://pith.science/pith/A26RFWW7TOF4L2HIJK7FNQKSBM","bundle":"https://pith.science/pith/A26RFWW7TOF4L2HIJK7FNQKSBM/bundle.json","state":"https://pith.science/pith/A26RFWW7TOF4L2HIJK7FNQKSBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A26RFWW7TOF4L2HIJK7FNQKSBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:A26RFWW7TOF4L2HIJK7FNQKSBM","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":"3861971959adc82b6fadf9790d20c02329ddc02da680b0112b9c3b658b89e687","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"astro-ph","submitted_at":"2007-12-08T16:53:40Z","title_canon_sha256":"dcd5a9a21497d98ccbad21164bf0d0f1f5da2d582758899681b95f80c84ab7ad"},"schema_version":"1.0","source":{"id":"0712.1291","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1291","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1291v2","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1291","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"A26RFWW7TOF4","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"A26RFWW7TOF4L2HI","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"A26RFWW7","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:83b007b8242f39c09427eba649acd153c90bdc44d3f49bc575a9b5eefda31673","target":"graph","created_at":"2026-05-18T02:43:26Z","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 study second order gravitational effects of local inhomogeneities on the cosmic microwave background radiation in flat universes with matter and a cosmological constant $\\Lambda$. We find that the general relativistic correction to the Newtonian approximation is negligible at second order provided that the size of the inhomogeneous region is sufficiently smaller than the horizon scale. For a spherically symmetric top-hat type quasi-linear perturbation, the first order temperature fluctuation corresponding to the linear integrated Sachs-Wolfe (ISW) effect is enhanced(suppressed) by the secon","authors_text":"Kaiki Taro Inoue, Kenji Tomita","cross_cats":["gr-qc"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2007-12-08T16:53:40Z","title":"Second Order Gravitational Effects on CMB Temperature Anisotropy in Lambda dominated flat universes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1291","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":"sha256:2fb6b6c63f6ea2139200cf9d8cb444d73761b0b2b4c14954c6b3f52257bd1d23","target":"record","created_at":"2026-05-18T02:43:26Z","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":"3861971959adc82b6fadf9790d20c02329ddc02da680b0112b9c3b658b89e687","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"astro-ph","submitted_at":"2007-12-08T16:53:40Z","title_canon_sha256":"dcd5a9a21497d98ccbad21164bf0d0f1f5da2d582758899681b95f80c84ab7ad"},"schema_version":"1.0","source":{"id":"0712.1291","kind":"arxiv","version":2}},"canonical_sha256":"06bd12dadf9b8bc5e8e84abe56c1520b3645cd672a2c8591cb710db6beb6adcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06bd12dadf9b8bc5e8e84abe56c1520b3645cd672a2c8591cb710db6beb6adcb","first_computed_at":"2026-05-18T02:43:26.581952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:26.581952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HAwZ99Aq+MSqPeGzMSo4rfJc6x7ph/eT6d7KSDEAChpMkHOuEKtuWwwp8Kq/Hrlp3aHXU712hOu7ZhiCnGBfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:26.582694Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1291","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2fb6b6c63f6ea2139200cf9d8cb444d73761b0b2b4c14954c6b3f52257bd1d23","sha256:83b007b8242f39c09427eba649acd153c90bdc44d3f49bc575a9b5eefda31673"],"state_sha256":"ba20540ec7fd3e165fc83a9e9e3757eb05d144d145cbba3aba76e7653d4f2118"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHylR25bqsT0SnHMxIKVKlM/rSm4XdZrb5HWfDXjwNvWpguRbEuH5mBcXaEXdGvo94o1KyqHdNwMSaJ2Fou9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:15:21.007759Z","bundle_sha256":"65aa35b670dff0525b53b480a9db8cc1d6693e4e947f328edb03ce3339569aa6"}}