{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:WN6H7NGFFXZOBKVZMI4ESZ4X4S","short_pith_number":"pith:WN6H7NGF","schema_version":"1.0","canonical_sha256":"b37c7fb4c52df2e0aab96238496797e4aeec8f065b2b4028410d066c8b689d54","source":{"kind":"arxiv","id":"2111.15427","version":1},"attestation_state":"computed","paper":{"title":"Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the $\\texttt{NPIPE}$ and $\\texttt{FFP10}$ data releases","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"astro-ph.CO","authors_text":"Pratyush Pranav","submitted_at":"2021-11-30T14:17:17Z","abstract_excerpt":"We present a multi-scale topological analysis of the temperature fluctuation maps from the NPIPE and FFP10 datasets, invoking relative homology to account for the analysis in the presence of masks. For the topological components, we detect a $2.96\\sigma$ deviation between the observations and simulations at $N = 128, FWHM = 80'$, for the FFP10 dataset. For the topological loops, we observe a high deviation between the observation and simulations in the number of loops at $FWHM = 320'$, at a low dimensionless threshold $\\nu = -2.5$, for the NPIPE dataset. Under a Gaussian assumption, this would"},"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":"2111.15427","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2021-11-30T14:17:17Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"d6348e1e5162f5b00eca779988074dd6c52090455a0c507383ca90f449ada649","abstract_canon_sha256":"cc74d757769c81414a0bfa15650113cd38a2e9f400617af2e4889dfea2ac14ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:05:15.115623Z","signature_b64":"3S5zfNFbQwRDdJB3ti9dVU87okkXSsSWeJbTigvtkZmWFOx7tCHFCJLITlZmJSL9cROv2tXit9ynNBfVhUrtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b37c7fb4c52df2e0aab96238496797e4aeec8f065b2b4028410d066c8b689d54","last_reissued_at":"2026-07-05T04:05:15.115269Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:05:15.115269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the $\\texttt{NPIPE}$ and $\\texttt{FFP10}$ data releases","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"astro-ph.CO","authors_text":"Pratyush Pranav","submitted_at":"2021-11-30T14:17:17Z","abstract_excerpt":"We present a multi-scale topological analysis of the temperature fluctuation maps from the NPIPE and FFP10 datasets, invoking relative homology to account for the analysis in the presence of masks. For the topological components, we detect a $2.96\\sigma$ deviation between the observations and simulations at $N = 128, FWHM = 80'$, for the FFP10 dataset. For the topological loops, we observe a high deviation between the observation and simulations in the number of loops at $FWHM = 320'$, at a low dimensionless threshold $\\nu = -2.5$, for the NPIPE dataset. Under a Gaussian assumption, this would"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.15427","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.15427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2111.15427","created_at":"2026-07-05T04:05:15.115325+00:00"},{"alias_kind":"arxiv_version","alias_value":"2111.15427v1","created_at":"2026-07-05T04:05:15.115325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.15427","created_at":"2026-07-05T04:05:15.115325+00:00"},{"alias_kind":"pith_short_12","alias_value":"WN6H7NGFFXZO","created_at":"2026-07-05T04:05:15.115325+00:00"},{"alias_kind":"pith_short_16","alias_value":"WN6H7NGFFXZOBKVZ","created_at":"2026-07-05T04:05:15.115325+00:00"},{"alias_kind":"pith_short_8","alias_value":"WN6H7NGF","created_at":"2026-07-05T04:05:15.115325+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.06255","citing_title":"On the statistical nature of Betti numbers and Euler characteristic of smooth random fields","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S","json":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S.json","graph_json":"https://pith.science/api/pith-number/WN6H7NGFFXZOBKVZMI4ESZ4X4S/graph.json","events_json":"https://pith.science/api/pith-number/WN6H7NGFFXZOBKVZMI4ESZ4X4S/events.json","paper":"https://pith.science/paper/WN6H7NGF"},"agent_actions":{"view_html":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S","download_json":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S.json","view_paper":"https://pith.science/paper/WN6H7NGF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2111.15427&json=true","fetch_graph":"https://pith.science/api/pith-number/WN6H7NGFFXZOBKVZMI4ESZ4X4S/graph.json","fetch_events":"https://pith.science/api/pith-number/WN6H7NGFFXZOBKVZMI4ESZ4X4S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S/action/storage_attestation","attest_author":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S/action/author_attestation","sign_citation":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S/action/citation_signature","submit_replication":"https://pith.science/pith/WN6H7NGFFXZOBKVZMI4ESZ4X4S/action/replication_record"}},"created_at":"2026-07-05T04:05:15.115325+00:00","updated_at":"2026-07-05T04:05:15.115325+00:00"}