{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:L2CXVGERQI2PCUHZIZLD6AUEDL","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":"ae61953dadcb72a527c49da7e69b95dffc0a5773593a51bb45415fb825e2b823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-05-14T19:46:12Z","title_canon_sha256":"e9a6e61e09155f4f3a1aeed129f81167fa1b9b2f8e56591837c32e7c1a5bb057"},"schema_version":"1.0","source":{"id":"1305.3261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3261","created_at":"2026-05-18T01:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3261v2","created_at":"2026-05-18T01:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3261","created_at":"2026-05-18T01:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"L2CXVGERQI2P","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"L2CXVGERQI2PCUHZ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"L2CXVGER","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:85d3ab19a2f64bb06a3f89d550757fc13034f45abd2ea7860d7155ae6a5e521a","target":"graph","created_at":"2026-05-18T01:50:02Z","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":"This paper presents the linearised Boltzmann equation for photons for scalar, vector and tensor perturbations in flat, open and closed FLRW cosmologies. We show that E- and B-mode polarisation for all types can be computed using only a single hierarchy. This was previously shown explicitly for tensor modes in flat cosmologies but not for vectors, and not for non-flat cosmologies.","authors_text":"Julien Lesgourgues, Thomas Tram","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-05-14T19:46:12Z","title":"Optimal polarisation equations in FLRW universes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3261","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":"sha256:1dcdd1a0bd73d2dcd212298d2347d83b915968187e6e7ff8f2566a52ad8ea9f0","target":"record","created_at":"2026-05-18T01:50:02Z","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":"ae61953dadcb72a527c49da7e69b95dffc0a5773593a51bb45415fb825e2b823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-05-14T19:46:12Z","title_canon_sha256":"e9a6e61e09155f4f3a1aeed129f81167fa1b9b2f8e56591837c32e7c1a5bb057"},"schema_version":"1.0","source":{"id":"1305.3261","kind":"arxiv","version":2}},"canonical_sha256":"5e857a98918234f150f946563f02841ad058fa507be13010dfe40f884ff2ee4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e857a98918234f150f946563f02841ad058fa507be13010dfe40f884ff2ee4a","first_computed_at":"2026-05-18T01:50:02.111939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:02.111939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rBNgEh1qCoQBL8yhqXotd3OiyDZZ731UGHNUA7TjpqX1r85a9SSofye3FagX90rSj3PYLEMfKGAxifFMoFKOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:02.112597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dcdd1a0bd73d2dcd212298d2347d83b915968187e6e7ff8f2566a52ad8ea9f0","sha256:85d3ab19a2f64bb06a3f89d550757fc13034f45abd2ea7860d7155ae6a5e521a"],"state_sha256":"b65a34bbce7b2a56d8526dcf195ed5fe4b8fca2458fd4cff46d5eecae510ecb3"}