| The cost of preserving the affine error bound | statement | theorem Y.1 | arxiv |
| Expected risk in terms of conditional variance | statement | theorem G.1 | arxiv |
| Unknown variance and original distance | statement | corollary 6.2 | arxiv |
| An exact competitive factor on the two-law family | statement | theorem V.3 | arxiv |
| Unknown population smoothness | statement | corollary L.6 | arxiv |
| A local accelerated variance benchmark | statement | corollary V.4 | arxiv |
| Forward radial secant | statement | lemma M.1 | arxiv |
| Biased vector energy and inner products | statement | lemma M.3 | arxiv |
| Anchor-radius second moment | statement | lemma R.1 | arxiv |
| Target-linked protected corruption budgets | statement | corollary N.4 | arxiv |
| Ball smoothing | statement | lemma B.1 | arxiv |
| Bounded value corruption | statement | theorem F.2 | arxiv |
| Moments and corruption of the symmetric estimate | statement | lemma B.2 | arxiv |
| Nonsymmetric directional endpoints | statement | proposition B.3 | arxiv |
| A local second-moment benchmark | statement | corollary V.5 | arxiv |
| The offset-controller potential | statement | lemma Q.1 | arxiv |
| A finite sample cannot bound an unknown variance uniformly | statement | proposition H.1 | arxiv |
| Trajectory-sensitive risk | statement | theorem W.3 | arxiv |
| Unknown nonsmooth regularity | statement | corollary L.7 | arxiv |
| Relative-function moments | statement | lemma S.1 | arxiv |
| Local charge and reciprocal moments | statement | lemma K.5 | arxiv |
| Protected coefficient and target drift | statement | lemma M.5 | arxiv |
| A necessary additional adaptation price | statement | corollary S.6 | arxiv |
| Robust records under finite second moments | statement | lemma T.1 | arxiv |
| Observed radial smoothing | statement | theorem J.1 | arxiv |
| A sufficient corruption allowance | statement | corollary M.8 | arxiv |
| Batch sizes fixed before sampling | statement | corollary 4.1 | arxiv |
| Joint smoothing and a radial affine model | statement | lemma K.1 | arxiv |
| Accelerated bounds with adaptive smoothing | statement | theorem 5.1 | arxiv |
| Expected error from rejected trials | statement | proposition S.3 | arxiv |
| Joint anchor moment refinement | statement | theorem R.4 | arxiv |
| Weighted variance on the actual trajectory | statement | corollary W.4 | arxiv |
| Curvature under adaptive thresholds | statement | lemma L.3 | arxiv |
| Corruption-protected adaptive smoothing | statement | theorem M.6 | arxiv |
| Reciprocal radii and geometric references | statement | lemma L.2 | arxiv |
| Exact-record scalar backtracking | statement | theorem S.4 | arxiv |
| Exact worst-case ratio of the adaptive batch rule | statement | proposition G.3 | arxiv |
| Expected fixed-objective comparator potential | statement | theorem E.1 | arxiv |
| Work under spatial corruption | statement | theorem Z.3 | arxiv |
| Ambiguity in uncorrupted smoothing bias | statement | proposition Z.5 | arxiv |
| Protected observed radii | statement | theorem W.1 | arxiv |
| A trial cap chosen before sampling for ball smoothing | statement | corollary T.5 | arxiv |
| Exponential work requirement | statement | corollary Z.4 | arxiv |
| Exact-gradient accelerated comparator bound | statement | corollary D.2 | arxiv |
| Guarantee with a selected search radius | statement | theorem 6.1 | arxiv |
| Stages, values and admissible corruption | statement | corollary W.2 | arxiv |
| An adjacent-scale paired diagnostic | statement | proposition B.4 | arxiv |
| A supplied initial coefficient | statement | corollary V.6 | arxiv |
| Fixed-radius moment localization | statement | theorem R.3 | arxiv |
| Protected radius and exact resource bounds | statement | lemma M.2 | arxiv |
| Log-free sufficient clean budgets | statement | corollary N.3 | arxiv |
| Risk under spatial corruption | statement | theorem K.6 | arxiv |
| Saturated startup and clipping price | statement | lemma R.2 | arxiv |
| The certification scale under a supplied moment cap | statement | theorem U.3 | arxiv |
| A common-curvature family | statement | lemma V.1 | arxiv |
| A rare-curvature original-distance obstruction | statement | theorem S.5 | arxiv |
| Local radial potential | statement | theorem K.4 | arxiv |
| Sampling costs and monotone radii | statement | lemma I.1 | arxiv |
| Adaptive certification cost on the common history | statement | theorem U.1 | arxiv |
| Expected risk with confidence bounds | statement | theorem T.4 | arxiv |
| Adaptive batch guarantee | statement | theorem 4.2 | arxiv |
| A radius from the iteration budget | statement | corollary C.3 | arxiv |
| Protected local charge | statement | lemma M.4 | arxiv |
| Protected bias budget | statement | corollary M.7 | arxiv |
| An exact curved trajectory | statement | proposition R.7 | arxiv |
| No finite upper confidence bound without a moment bound | statement | corollary U.2 | arxiv |
| Clean coefficient and diagnostic scales | statement | lemma N.1 | arxiv |
| Sampling costs of radial selection | statement | lemma K.3 | arxiv |
| Accelerated potential | statement | theorem C.1 | arxiv |
| A universal cross-instance risk relation | statement | theorem V.2 | arxiv |
| Accounting and diagnostic moments | statement | lemma L.1 | arxiv |
| Hidden-direction geometry | statement | proposition Z.2 | arxiv |
| Ball smoothing and minimizer distance | statement | proposition X.1 | arxiv |
| Fixed-objective trajectory potential | statement | theorem D.1 | arxiv |
| Scalar coefficient growth | statement | lemma C.2 | arxiv |
| Original stationary distance | statement | corollary R.5 | arxiv |
| Fixed batch sizes | statement | corollary G.2 | arxiv |
| Radial mean and second moment | statement | lemma K.2 | arxiv |
| Absorbing a reference chosen before sampling | statement | corollary R.6 | arxiv |
| Sum of the executed trial weights | statement | lemma T.2 | arxiv |
| Spherical hiding | statement | lemma Z.1 | arxiv |
| Noise at a fixed pair budget | statement | corollary W.5 | arxiv |
| Target-linked clean initialization | statement | theorem N.2 | arxiv |
| Drift at radius reexpansions | statement | lemma L.4 | arxiv |
| Failure of comparator-only curvature transfer | statement | corollary R.8 | arxiv |
| Smooth populations | statement | proposition I.3 | arxiv |
| Collapse beyond the radial corruption margin | statement | proposition K.7 | arxiv |
| Pre-step acceleration on a simultaneous error event | statement | theorem T.3 | arxiv |
| A simultaneous threshold guarantee | statement | theorem L.5 | arxiv |
| Secant-curvature growth | statement | lemma I.2 | arxiv |
| Conditional fixed-radius geometry | statement | lemma P.1 | arxiv |
| The cost of the relaxed affine error guarantee | statement | theorem P.3 | arxiv |
| The required stochastic error multiplier | statement | corollary Y.2 | arxiv |
| A uniform noise multiplier | statement | corollary P.2 | arxiv |
| Original-comparator accepted-trial potential | statement | theorem S.2 | arxiv |
| Controlling the initialization error | statement | corollary 5.2 | arxiv |
| Adaptive batch sample counts | statement | lemma F.1 | arxiv |
