{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SIBS4IYGIZTYIUHRAY3IU2JCWF","short_pith_number":"pith:SIBS4IYG","schema_version":"1.0","canonical_sha256":"92032e230646678450f106368a6922b146cd225cdad0108226cd8fe58af55322","source":{"kind":"arxiv","id":"1506.00705","version":2},"attestation_state":"computed","paper":{"title":"New Geometric Representations of the CMB 2pcf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Andre L. Froes, Armando Bernui, Glenn D. Starkman, Thiago S. Pereira","submitted_at":"2015-06-01T23:29:07Z","abstract_excerpt":"When searching for deviations of statistical isotropy in CMB, a popular strategy is to write the two-point correlation function (2pcf) as the most general function of four spherical angles (i.e., two unit vectors) in the celestial sphere. Then, using a basis of bipolar spherical harmonics, statistical anisotropy will show up if and only if any coefficient of the expansion with non-trivial bipolar momentum is detected -- although this detection will not in general elucidate the origin of the anisotropy. In this work we show that two new sets of four angles and basis functions exist which comple"},"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":"1506.00705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2015-06-01T23:29:07Z","cross_cats_sorted":[],"title_canon_sha256":"513e77fd535a626aa9d275db5490f1254ea8454d20a9db1afcf0ac8cc41526c5","abstract_canon_sha256":"c91467bee77d25f33367ba0feb429355a7515c7207b7c65982e375d6135878e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:29.916186Z","signature_b64":"2FkkAOOJWNdpBBtLYl/1OzVpKbDPc6MNgrWX8Wjkge/rFaWJuTg7N/xvBeixD23J/H3v4SlOn8b4RN71ugRRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92032e230646678450f106368a6922b146cd225cdad0108226cd8fe58af55322","last_reissued_at":"2026-05-18T01:35:29.915644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:29.915644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New Geometric Representations of the CMB 2pcf","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Andre L. Froes, Armando Bernui, Glenn D. Starkman, Thiago S. Pereira","submitted_at":"2015-06-01T23:29:07Z","abstract_excerpt":"When searching for deviations of statistical isotropy in CMB, a popular strategy is to write the two-point correlation function (2pcf) as the most general function of four spherical angles (i.e., two unit vectors) in the celestial sphere. Then, using a basis of bipolar spherical harmonics, statistical anisotropy will show up if and only if any coefficient of the expansion with non-trivial bipolar momentum is detected -- although this detection will not in general elucidate the origin of the anisotropy. In this work we show that two new sets of four angles and basis functions exist which comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00705","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":"1506.00705","created_at":"2026-05-18T01:35:29.915722+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.00705v2","created_at":"2026-05-18T01:35:29.915722+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00705","created_at":"2026-05-18T01:35:29.915722+00:00"},{"alias_kind":"pith_short_12","alias_value":"SIBS4IYGIZTY","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SIBS4IYGIZTYIUHR","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SIBS4IYG","created_at":"2026-05-18T12:29:42.218222+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/SIBS4IYGIZTYIUHRAY3IU2JCWF","json":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF.json","graph_json":"https://pith.science/api/pith-number/SIBS4IYGIZTYIUHRAY3IU2JCWF/graph.json","events_json":"https://pith.science/api/pith-number/SIBS4IYGIZTYIUHRAY3IU2JCWF/events.json","paper":"https://pith.science/paper/SIBS4IYG"},"agent_actions":{"view_html":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF","download_json":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF.json","view_paper":"https://pith.science/paper/SIBS4IYG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.00705&json=true","fetch_graph":"https://pith.science/api/pith-number/SIBS4IYGIZTYIUHRAY3IU2JCWF/graph.json","fetch_events":"https://pith.science/api/pith-number/SIBS4IYGIZTYIUHRAY3IU2JCWF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF/action/storage_attestation","attest_author":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF/action/author_attestation","sign_citation":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF/action/citation_signature","submit_replication":"https://pith.science/pith/SIBS4IYGIZTYIUHRAY3IU2JCWF/action/replication_record"}},"created_at":"2026-05-18T01:35:29.915722+00:00","updated_at":"2026-05-18T01:35:29.915722+00:00"}