{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ACPHUX5Y6R5RHIEE733NCLZ32I","short_pith_number":"pith:ACPHUX5Y","schema_version":"1.0","canonical_sha256":"009e7a5fb8f47b13a084fef6d12f3bd2033a2b1dcd9630ea2e43cec19df44978","source":{"kind":"arxiv","id":"1105.3672","version":2},"attestation_state":"computed","paper":{"title":"Constrained probability distributions of correlation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"astro-ph.CO","authors_text":"David Keitel, Peter Schneider","submitted_at":"2011-05-18T16:02:25Z","abstract_excerpt":"Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation. However, this has been shown to be insufficient.\n  Aims: For the case of Gaussian random fields, we search for an exact probability distribution of correlation functions, which could improve the accuracy of future data analyses.\n  Methods: We use a fully analytic approach, first expanding the random field in its Fourier modes, and then calculating the charac"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1105.3672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2011-05-18T16:02:25Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"2783e4f662d8f74ae67b8a98eb67185d437431ffbdafc5c9fec568b69e02d1c3","abstract_canon_sha256":"005b9c87eeae702c9163e1ea3a506f9be609b88f5c0bf337e35475f4d7f3c75a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:39.526440Z","signature_b64":"1OIpPNII2ylBAeBgCyCOwkl+nq+ICcNyRi6VyVfScOaEnHhkYMMa/HNKWNt1JJDge+xVnzrz9hgZcqZzKaMRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"009e7a5fb8f47b13a084fef6d12f3bd2033a2b1dcd9630ea2e43cec19df44978","last_reissued_at":"2026-05-18T04:11:39.525828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:39.525828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constrained probability distributions of correlation functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"astro-ph.CO","authors_text":"David Keitel, Peter Schneider","submitted_at":"2011-05-18T16:02:25Z","abstract_excerpt":"Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation. However, this has been shown to be insufficient.\n  Aims: For the case of Gaussian random fields, we search for an exact probability distribution of correlation functions, which could improve the accuracy of future data analyses.\n  Methods: We use a fully analytic approach, first expanding the random field in its Fourier modes, and then calculating the charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3672","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1105.3672","created_at":"2026-05-18T04:11:39.525922+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.3672v2","created_at":"2026-05-18T04:11:39.525922+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3672","created_at":"2026-05-18T04:11:39.525922+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACPHUX5Y6R5R","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACPHUX5Y6R5RHIEE","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACPHUX5Y","created_at":"2026-05-18T12:26:24.575870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I","json":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I.json","graph_json":"https://pith.science/api/pith-number/ACPHUX5Y6R5RHIEE733NCLZ32I/graph.json","events_json":"https://pith.science/api/pith-number/ACPHUX5Y6R5RHIEE733NCLZ32I/events.json","paper":"https://pith.science/paper/ACPHUX5Y"},"agent_actions":{"view_html":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I","download_json":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I.json","view_paper":"https://pith.science/paper/ACPHUX5Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.3672&json=true","fetch_graph":"https://pith.science/api/pith-number/ACPHUX5Y6R5RHIEE733NCLZ32I/graph.json","fetch_events":"https://pith.science/api/pith-number/ACPHUX5Y6R5RHIEE733NCLZ32I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I/action/storage_attestation","attest_author":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I/action/author_attestation","sign_citation":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I/action/citation_signature","submit_replication":"https://pith.science/pith/ACPHUX5Y6R5RHIEE733NCLZ32I/action/replication_record"}},"created_at":"2026-05-18T04:11:39.525922+00:00","updated_at":"2026-05-18T04:11:39.525922+00:00"}