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We find conditions under which, for given metric space $X$, there is a class $\\mathfrak{M}$ of metric spaces such that $X$ is minimal $\\mathfrak{M}$-universal. We generalize the notion of minimal $\\mathfrak{M}$-universal metric space to notion of minimal $\\mathfrak{M}$-universal class of metric spaces and prove the uniqueness, up to an isomorphism, for these classe"},"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":"1503.00667","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-03-02T19:22:08Z","cross_cats_sorted":[],"title_canon_sha256":"c02ca14adf3e1291515dd9b74bccd8dff71bd2e875a3ee39379766e8c91a0e06","abstract_canon_sha256":"3ee8d416e712fb96e6eb293f5f66c75ce99136c8135ac1c461611a43931425f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:40.347067Z","signature_b64":"rXn5590eILRJXimZwFhOQgqDh6iVwApu5aYveEiM3T/KsgrlygN+01/GsQ3uBsHGHmHu3dSdYqXhKeEytdzNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ad7788a852e91aa0eaaca864dc27caf5680eb565878b55cf500aeacff64c53d","last_reissued_at":"2026-05-18T02:18:40.346296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:40.346296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal universal metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"E. 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