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We show that, for several natural ideals $\\mathcal{I}$, $x$ computes a list of $\\mathcal{I}$ if and only if it computes a function dominating all the functions in $\\mathcal{I}$. On the other hand, we provide reals which are $\\mathsf{HYP}$-strongly null engulfing (and hence $\\mathsf{HYP}$-dominating, by results of Greenberg, Kuyper and Turetsky) but which cann"},"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":"2605.21194","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2026-05-20T13:56:42Z","cross_cats_sorted":[],"title_canon_sha256":"dc29627029b4debf5c7241203d2d92ac4219060c618a8318c8bf4a5786944586","abstract_canon_sha256":"b3781fabb42738efbf6c54a5856c79ed717bac24f9ca62766a2f9108c6f3154e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:42.822873Z","signature_b64":"AZ/sp7GOhq3sdj3zvdVIFNxob5cgMbAYxNC/CYV75Msf0OW4PiQXvktRN5eNJp3LrBRR1YjDGUsToR5fMQHvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4d9652ee0fabba50a9c1705fbd985afc56e47333bf7c7fb62e1a40745eb6959","last_reissued_at":"2026-05-21T01:05:42.822244Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:42.822244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Listing the hyperarithmetical functions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gian Marco Osso, Isabella Scott, Joseph S. 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