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Also, assuming $\\operatorname{add}(\\mathcal{N}) = \\mathfrak{c}$, we prove $\\operatorname{cof}(\\mathcal{UN}) = \\mathfrak{d}_\\mathfrak{c}$ by adapting Yorioka's technique. Moreover, we prove the consistency of $\\operatorname{add}(\\mathcal{UN}) < \\operatorname{cov}(\\mathcal{UN}) < \\operatorname{non}(\\mathcal{UN}) < \\operatorname{cof}(\\"},"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":"2607.12936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-07-14T16:09:33Z","cross_cats_sorted":[],"title_canon_sha256":"fca386a045add3fa2cd1250703abcbf07ce34c211b9179ec340906cc7a7da35f","abstract_canon_sha256":"04b187d1de7f35b649e0160d68460593a345763090880bb155c8effde30e4c54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:22:26.092970Z","signature_b64":"ezntII78BpQ9uJBpig/a9xm0rvZxlgEnsUEdgl3Id+QlDmCNngRw7oVRevJAA3S7MyanUy3VeqlOPDo2+M7cDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"428821e05933fd8926dd66debab91b89f5c9edcc20396e389fa75e47e172c1e4","last_reissued_at":"2026-07-15T01:22:26.092128Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:22:26.092128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cardinal invariants on universally null sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Tatsuya Goto","submitted_at":"2026-07-14T16:09:33Z","abstract_excerpt":"We investigate the cardinal invariants on universally null sets. 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