{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J46A2DLWCK46CLHXF75RNT7WXQ","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":"99ebdd633211327604dceafd278a792f2f257e2d2d31ccdf1290e44c498fae47","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-06T17:09:43Z","title_canon_sha256":"34070acf3f921aefc729419561524718de62adf97082e188a401045995b072de"},"schema_version":"1.0","source":{"id":"1312.1929","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1929","created_at":"2026-05-18T01:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1929v2","created_at":"2026-05-18T01:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1929","created_at":"2026-05-18T01:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"J46A2DLWCK46","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J46A2DLWCK46CLHX","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J46A2DLW","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:e4316d1cd04f9ecf1034057eee66f088ddcc7bf95d30784878158e380a785625","target":"graph","created_at":"2026-05-18T01:45:57Z","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":"In this paper we present four simple expressions for the relativistic first and second order fractional density perturbations for $\\Lambda$CDM cosmologies in different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. A distinctive feature of our approach is the use of a canonical set of quadratic differential expressions involving an arbitrary spatial function, the so-called comoving curvature perturbation, to describe the spatial dependence, which enables us to unify, simplify and extend previous seemingly disparate results. The simple structure of the expressions ","authors_text":"Claes Uggla, John Wainwright","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-06T17:09:43Z","title":"Simple expressions for second order density perturbations in standard cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1929","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:b3f6fc37e7c4db33a90ebe1ad442552a6ec4b6b64468b70ffb2ad5a8c05db2de","target":"record","created_at":"2026-05-18T01:45:57Z","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":"99ebdd633211327604dceafd278a792f2f257e2d2d31ccdf1290e44c498fae47","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-12-06T17:09:43Z","title_canon_sha256":"34070acf3f921aefc729419561524718de62adf97082e188a401045995b072de"},"schema_version":"1.0","source":{"id":"1312.1929","kind":"arxiv","version":2}},"canonical_sha256":"4f3c0d0d7612b9e12cf72ffb16cff6bc2d5b5b4317c19e146a56211ad6fb9a9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f3c0d0d7612b9e12cf72ffb16cff6bc2d5b5b4317c19e146a56211ad6fb9a9a","first_computed_at":"2026-05-18T01:45:57.771259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:57.771259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2kE1nX+hc00/UVEpY/7kKAGreTQToyT3c7A2IrTp0liK4Rk2o8DXikHxfj4HOaBW306fijYNlqh+duEB3hNVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:57.771703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1929","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3f6fc37e7c4db33a90ebe1ad442552a6ec4b6b64468b70ffb2ad5a8c05db2de","sha256:e4316d1cd04f9ecf1034057eee66f088ddcc7bf95d30784878158e380a785625"],"state_sha256":"fd1999d559efff8e54e8754e868d6539095465f44574a926029dbf53203bc179"}