{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HLJUXRLUVMHD2EKREZBL27YBVF","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":"ae0e17a049336b989b5c14e804a01b88db81fa2a25049da4fa406bdc16ccb5ff","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-04-01T09:18:46Z","title_canon_sha256":"52e1a27db971c0e38af299be1c39576ba08aa6db1e2440c868864de8120fab20"},"schema_version":"1.0","source":{"id":"1304.0315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0315","created_at":"2026-05-18T01:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0315v1","created_at":"2026-05-18T01:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0315","created_at":"2026-05-18T01:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"HLJUXRLUVMHD","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HLJUXRLUVMHD2EKR","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HLJUXRLU","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:9cac5cbd32917d77e65eec5a4de0e807a6bfa62e3f1a5a35cf4c1037976c3edd","target":"graph","created_at":"2026-05-18T01:50:50Z","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 investigate sets of random variables that can be arranged sequentially such that a given variable only depends conditionally on its immediate predecessor. For such sets, we show that the full joint probability distribution may be expressed exclusively in terms of uni- and bivariate marginals. Under the assumption that the CMB power spectrum likelihood only exhibits correlations within a banded multipole range, \\Delta l, we apply this expression to two outstanding problems in CMB likelihood analysis. First, we derive a statistically well-defined hybrid likelihood estimator, merging two indep","authors_text":"D. S. Seljebotn, E. Gjerl{\\o}w, G. Huey, G. Rocha, H. K. Eriksen, I. K. Wehus, J. B. Jewell, K. M. G\\'orski, K. Mikkelsen, S. K. N{\\ae}ss","cross_cats":["astro-ph.IM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-04-01T09:18:46Z","title":"CMB likelihood approximation for banded probability distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0315","kind":"arxiv","version":1},"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":"sha256:7ee53fc032152b33bbf9b40138bd1eb018e2e941e07cef6fa6370a0971076b52","target":"record","created_at":"2026-05-18T01:50:50Z","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":"ae0e17a049336b989b5c14e804a01b88db81fa2a25049da4fa406bdc16ccb5ff","cross_cats_sorted":["astro-ph.IM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-04-01T09:18:46Z","title_canon_sha256":"52e1a27db971c0e38af299be1c39576ba08aa6db1e2440c868864de8120fab20"},"schema_version":"1.0","source":{"id":"1304.0315","kind":"arxiv","version":1}},"canonical_sha256":"3ad34bc574ab0e3d11512642bd7f01a967d72c988dd0867cbbd607b61ef813fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ad34bc574ab0e3d11512642bd7f01a967d72c988dd0867cbbd607b61ef813fa","first_computed_at":"2026-05-18T01:50:50.584496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:50:50.584496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wT313Zk5/KTzq2lykzacQFodtTVnJuPo/gD8ahaWqYk3YhLKlFRUVc/vBvcCSvWnbGM6rlu5QBKLWB2PzOnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:50:50.585174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ee53fc032152b33bbf9b40138bd1eb018e2e941e07cef6fa6370a0971076b52","sha256:9cac5cbd32917d77e65eec5a4de0e807a6bfa62e3f1a5a35cf4c1037976c3edd"],"state_sha256":"c290a7265d31ebeab9c3fe982e2075afd41d555ed3db39fb2192077ba37dc471"}