{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:RT72WF2JVEX5BQ44UTIK4MB6VO","short_pith_number":"pith:RT72WF2J","canonical_record":{"source":{"id":"0808.2689","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-20T04:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"a1415fc743735634467b5d1a7add1be5222b67e9432903ab5b92db755a9e430e","abstract_canon_sha256":"de5cb0b6ffba03a026b23456e167e1cc385570e1eb25c1549f3ac9dac83fd584"},"schema_version":"1.0"},"canonical_sha256":"8cffab1749a92fd0c39ca4d0ae303eab869746bb6d1fd84c91c14143021ad234","source":{"kind":"arxiv","id":"0808.2689","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2689","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2689v4","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2689","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"RT72WF2JVEX5","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"pith_short_16","alias_value":"RT72WF2JVEX5BQ44","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"pith_short_8","alias_value":"RT72WF2J","created_at":"2026-07-04T17:12:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:RT72WF2JVEX5BQ44UTIK4MB6VO","target":"record","payload":{"canonical_record":{"source":{"id":"0808.2689","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-20T04:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"a1415fc743735634467b5d1a7add1be5222b67e9432903ab5b92db755a9e430e","abstract_canon_sha256":"de5cb0b6ffba03a026b23456e167e1cc385570e1eb25c1549f3ac9dac83fd584"},"schema_version":"1.0"},"canonical_sha256":"8cffab1749a92fd0c39ca4d0ae303eab869746bb6d1fd84c91c14143021ad234","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:12:24.835645Z","signature_b64":"wBapBlCIcU/zJCxm3S+LEQqKk2oVDckkiKeKPjQQEp00hIl9vqIwX42/9hLKw9HoO2KfiXoMerSoq4TEhA2WDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cffab1749a92fd0c39ca4d0ae303eab869746bb6d1fd84c91c14143021ad234","last_reissued_at":"2026-07-04T17:12:24.835298Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:12:24.835298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.2689","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywQ0HWDGD65tJwoq4fuKG7Lgbtwi/pTIUfOArz74zGUfkkfDgtNBWAWdCz3ykoaDdZHkoywt7gTJJO5bc3vTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:02:29.392330Z"},"content_sha256":"2138c70df8bdb5056d1f5fea1ad894b9a5f1e3ec758b008674127cc95b770b37","schema_version":"1.0","event_id":"sha256:2138c70df8bdb5056d1f5fea1ad894b9a5f1e3ec758b008674127cc95b770b37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:RT72WF2JVEX5BQ44UTIK4MB6VO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the dangers of using the growth equation on large scales in the Newtonian gauge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"James B. Dent, Sourish Dutta","submitted_at":"2008-08-20T04:37:15Z","abstract_excerpt":"We examine the accuracy of the growth equation $\\ddot{\\delta} + 2H\\dot{\\delta} - 4\\pi G\\rho\\delta = 0$, which is ubiquitous in the cosmological literature, in the context of the Newtonian gauge. By comparing the growth predicted by this equation to a numerical solution of the linearized Einstein equations in the $\\Lambda$CDM scenario, we show that while this equation is a reliable approximation on small scales ($k\\gtrsim $h Mpc$^{-1}$), it can be disastrously inaccurate ($\\sim 10^4% $) on larger scales in this gauge. We propose a modified version of the growth equation for the Newtonian gauge,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2689","kind":"arxiv","version":4},"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/0808.2689/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":"2026-07-04T17:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YLNg8aa7x1TdQKp4Bs41Hh9qAUfrr7IVxP7kSF9Mf6Kcl0i35/99X8GcKqjPkJoReSVtLdvSlVz0zMlniI7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T04:02:29.392864Z"},"content_sha256":"296fa1d26300dc6ec16ab3e89798cdf4ddebbaa50bb04c34db9cbfdad3909c44","schema_version":"1.0","event_id":"sha256:296fa1d26300dc6ec16ab3e89798cdf4ddebbaa50bb04c34db9cbfdad3909c44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RT72WF2JVEX5BQ44UTIK4MB6VO/bundle.json","state_url":"https://pith.science/pith/RT72WF2JVEX5BQ44UTIK4MB6VO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RT72WF2JVEX5BQ44UTIK4MB6VO/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":"2026-08-05T04:02:29Z","links":{"resolver":"https://pith.science/pith/RT72WF2JVEX5BQ44UTIK4MB6VO","bundle":"https://pith.science/pith/RT72WF2JVEX5BQ44UTIK4MB6VO/bundle.json","state":"https://pith.science/pith/RT72WF2JVEX5BQ44UTIK4MB6VO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RT72WF2JVEX5BQ44UTIK4MB6VO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:RT72WF2JVEX5BQ44UTIK4MB6VO","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":"de5cb0b6ffba03a026b23456e167e1cc385570e1eb25c1549f3ac9dac83fd584","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-20T04:37:15Z","title_canon_sha256":"a1415fc743735634467b5d1a7add1be5222b67e9432903ab5b92db755a9e430e"},"schema_version":"1.0","source":{"id":"0808.2689","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2689","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2689v4","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2689","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"RT72WF2JVEX5","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"pith_short_16","alias_value":"RT72WF2JVEX5BQ44","created_at":"2026-07-04T17:12:24Z"},{"alias_kind":"pith_short_8","alias_value":"RT72WF2J","created_at":"2026-07-04T17:12:24Z"}],"graph_snapshots":[{"event_id":"sha256:296fa1d26300dc6ec16ab3e89798cdf4ddebbaa50bb04c34db9cbfdad3909c44","target":"graph","created_at":"2026-07-04T17:12:24Z","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/0808.2689/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We examine the accuracy of the growth equation $\\ddot{\\delta} + 2H\\dot{\\delta} - 4\\pi G\\rho\\delta = 0$, which is ubiquitous in the cosmological literature, in the context of the Newtonian gauge. By comparing the growth predicted by this equation to a numerical solution of the linearized Einstein equations in the $\\Lambda$CDM scenario, we show that while this equation is a reliable approximation on small scales ($k\\gtrsim $h Mpc$^{-1}$), it can be disastrously inaccurate ($\\sim 10^4% $) on larger scales in this gauge. We propose a modified version of the growth equation for the Newtonian gauge,","authors_text":"James B. Dent, Sourish Dutta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-20T04:37:15Z","title":"On the dangers of using the growth equation on large scales in the Newtonian gauge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2689","kind":"arxiv","version":4},"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":"sha256:2138c70df8bdb5056d1f5fea1ad894b9a5f1e3ec758b008674127cc95b770b37","target":"record","created_at":"2026-07-04T17:12:24Z","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":"de5cb0b6ffba03a026b23456e167e1cc385570e1eb25c1549f3ac9dac83fd584","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-08-20T04:37:15Z","title_canon_sha256":"a1415fc743735634467b5d1a7add1be5222b67e9432903ab5b92db755a9e430e"},"schema_version":"1.0","source":{"id":"0808.2689","kind":"arxiv","version":4}},"canonical_sha256":"8cffab1749a92fd0c39ca4d0ae303eab869746bb6d1fd84c91c14143021ad234","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cffab1749a92fd0c39ca4d0ae303eab869746bb6d1fd84c91c14143021ad234","first_computed_at":"2026-07-04T17:12:24.835298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:12:24.835298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wBapBlCIcU/zJCxm3S+LEQqKk2oVDckkiKeKPjQQEp00hIl9vqIwX42/9hLKw9HoO2KfiXoMerSoq4TEhA2WDA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:12:24.835645Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2689","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2138c70df8bdb5056d1f5fea1ad894b9a5f1e3ec758b008674127cc95b770b37","sha256:296fa1d26300dc6ec16ab3e89798cdf4ddebbaa50bb04c34db9cbfdad3909c44"],"state_sha256":"54da54d95a996283573456cd3461ee303da90fb05524e18d1e3f04f3b6b8b852"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ve1itznsYBGlX/6TmejjcltLwcyYvDFJqMcHReA08TEotzyRST8+zy3pMGfiTsGTjAs9tc+peTdeF8TDF6voDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T04:02:29.398020Z","bundle_sha256":"2c9849b7421d425884361d378bc3c23262f899a293c570b56e1212650633a712"}}