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We prove separation results for these constants. In particular, concerning the constants $\\beta_{\\mathrm{TSP}}^d$, $\\beta_{\\mathrm{MST}}^d$, $\\beta_{\\mathrm{MM}}^d$, and $\\beta_{\\mathrm{TF}}^d$ from the asymptotic formulas for the minimum length TSP, spanning tree"},"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":"1501.01944","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-01-08T20:15:00Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"0238e246b6af719843f2166709497794b7a8c9f499a74d808d9f332160b35ee3","abstract_canon_sha256":"0f6fe473fa9e661878acc829694628d41903ae90c1b3f332c49230ca87abcdb4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:55.035255Z","signature_b64":"sCkT6AW0cIPnPRV47NQJJqBCk4XRMKhc0ISXgriCLR9yHlIHOYQdrf3+b0Mk6Yk7z8b96gpAaDtKCyPR7pS4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9b16732c49718a5d97fffe427b463abd8b93bfa0e520d1e9e6d3666aaa9648b","last_reissued_at":"2026-05-18T02:03:55.034583Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:55.034583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separating subadditive Euclidean functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.PR","authors_text":"Alan Frieze, Wesley Pegden","submitted_at":"2015-01-08T20:15:00Z","abstract_excerpt":"If we are given $n$ random points in the hypercube $[0,1]^d$, then the minimum length of a Traveling Salesperson Tour through the points, the minimum length of a spanning tree, and the minimum length of a matching, etc., are known to be asymptotically $\\beta n^{\\frac{d-1}{d}}$ a.s., where $\\beta$ is an absolute constant in each case. We prove separation results for these constants. 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