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For any algorithm and time horizon $T$ exceeding an explicit threshold, the worst-case expected regret over the RKHS-ball $\\|f\\|_{\\Hil_{k_\\nu}}\\!\\le\\!B$ satisfies \\begin{multline*} \\E[R_T(f)]\\;\\ge\\;c_*(d,\\nu)\\,B^{d/(2\\nu+d)}\\,\\sigma_n^{2\\nu/(2\\nu+d)} \\\\ \\cdot\\,\\vol_g(\\M)^{\\nu/(2\\nu+d)}\\,T^{(\\nu+d)/(2\\nu+d)}(\\log T)^{\\nu/(2\\nu+d)}. \\end{multline*} The exponent "},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.13524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2026-05-13T13:38:29Z","cross_cats_sorted":[],"title_canon_sha256":"c4a2e3746dce5160c35e1445a86352c0bd46eff5b84d2032583603c187056fa4","abstract_canon_sha256":"7d5ab8315f10f536e82e7446c92142f34870925f8636df5524f7fc07d31724d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:24.333497Z","signature_b64":"GMqOgieKgTtJuJYs89u4nya8mzunrX3NeoOJva5loVdbmzi0EkgZYqIinQrFGimFKbXjgFhwCX1dRpNwMorjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33f04096e9775e0a26b15a4909e509d3fcb284c3f3ae96a688fcab4c65c63e83","last_reissued_at":"2026-05-18T02:44:24.333071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:24.333071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Manifold-Aware Information Gain and Lower Bounds for Gaussian-Process Bandits on Riemannian Quotient Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A regret lower bound for Gaussian-process bandits on Riemannian manifolds includes an explicit factor of the manifold volume raised to the power ν/(2ν+d).","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Changsheng Chen, Ning Xie, Yuriy Dorn","submitted_at":"2026-05-13T13:38:29Z","abstract_excerpt":"We prove a regret lower bound for Gaussian-process bandits on a smooth compact Riemannian manifold $\\M$ of dimension $d$ with intrinsic Mat\\'ern-$\\nu$ kernel ($\\nu>d/2$) that exposes how the geometry of the arm space enters the constant. 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