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Saff, concerning the form of the dominant term (as $N\\to \\infty$) of the $N$-point Riesz $d$-polarization constant for an infinite compact subset $A$ of a $d$-dimensional $C^{1}$-manifold embedded in $\\mathbb{R}^{m}$ ($d\\leq m$). Moreover, if we assume further that the $d$-dimensional Hausdorff measure of $A$ is positive, we show that any asymptotically optimal sequence of $N$-point configurations for the $N$-point $d$-polarization problem on $A$ is asymptotically uniformly distributed with respect to $\\mathcal H_d|_A$."},"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":"1307.1160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-07-03T21:14:20Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3992f2be38f317c9ac61b7b1e3ad6562defecada4b731c28f2afc072a439d389","abstract_canon_sha256":"843244d13ce76af7aa421a2e40bbd5fc51581ec525c211d26d3e7decd09b4708"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:14.550679Z","signature_b64":"0OiU3GLdG+XYnIUp3rIcqvIgIzH1jJGNeUovGij/Nnq2bYewWCMmZCYS4Y+64j6ouiw14SzX9IjzHreHMTS0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f64becb6161deae88328c8bcd719c29522e04925077e6784e3c35d4a559e2e76","last_reissued_at":"2026-05-18T03:19:14.550208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:14.550208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of discrete Riesz $d$-polarization on subsets of $d$-dimensional manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"N. Bosuwan, S. V. Borodachov","submitted_at":"2013-07-03T21:14:20Z","abstract_excerpt":"We prove a conjecture of T. Erd\\'{e}lyi and E.B. Saff, concerning the form of the dominant term (as $N\\to \\infty$) of the $N$-point Riesz $d$-polarization constant for an infinite compact subset $A$ of a $d$-dimensional $C^{1}$-manifold embedded in $\\mathbb{R}^{m}$ ($d\\leq m$). 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