| Fixed-design four-component decomposition | statement | lemma C.3 | arxiv |
| Integrated query and weight bounds | statement | lemma C.16 | arxiv |
| Automatic quadratic curvature | statement | proposition B.2 | arxiv |
| Measurable approximate minimizer | statement | proposition B.4 | arxiv |
| Coercivity | statement | proposition B.3 | arxiv |
| Conditional second-moment lifting | statement | lemma C.11 | arxiv |
| Argmin inversion for approximate minimizers | statement | lemma C.23 | arxiv |
| Derived stability of the centered labeled covariance | statement | lemma C.15 | arxiv |
| Hilbert responses: fractional source and noise | statement | proposition C.1 | arxiv |
| Regularized covariance and empirical-centering stability | statement | lemma C.7 | arxiv |
| Centered RKHS realization | statement | proposition B.1 | arxiv |
| Uniform linear escape | statement | lemma C.22 | arxiv |
| A Fourier kernel satisfying the spectral conditions | example | example B.1 | arxiv |
| Empirical eigenvalue comparability | statement | lemma C.8 | arxiv |
| Finite second moment | definition | definition B.3 | arxiv |
| Relative PCA control of the empirically centered projector | statement | lemma C.13 | arxiv |
| $L^2$ conditional response-noise bound | statement | lemma C.17 | arxiv |
| Hadamard space | definition | definition B.2 | arxiv |
| Relative spectral stability | statement | proposition C.4 | arxiv |
| Normalized-contrast oracle inequality | statement | theorem C.1 | arxiv |
| Basic spectral stability | statement | proposition C.3 | arxiv |
| A BHV contrast in the closure but outside the RKHS | example | example B.2 | arxiv |
| Exact geodesic prediction mixing | statement | proposition E.1 | arxiv |
| Propagation of the fractional-source residual | statement | lemma C.19 | arxiv |
| G9HZ0XTNWM | statement | corollary 2.1 | arxiv |
| PH at balanced cutoffs | statement | corollary 3.1 | arxiv |
| Spectral expansion in the fixed closure | statement | lemma C.1 | arxiv |
| JHTSW42883 | statement | theorem 2.2 | arxiv |
| An abstract entropy sufficient condition for general metric responses | statement | proposition C.2 | arxiv |
| Uniform fractional-source truncation | statement | lemma C.2 | arxiv |
| Leading-side PCA excess bound | statement | lemma C.12 | arxiv |
| Proper metric space | statement | corollary B.1 | arxiv |
| Ridge bias in the learned subspace | statement | lemma C.21 | arxiv |
| Fitted representation residual | statement | lemma C.20 | arxiv |
| Positive definite kernel and RKHS | definition | definition B.1 | arxiv |
| Polynomial rate for a Hilbert-valued source | statement | corollary C.1 | arxiv |
| Normalized squared-distance algebra | statement | lemma B.1 | arxiv |
| Consequences of the cross-boundary polynomial spectrum | statement | lemma C.4 | arxiv |
| R2ACSH5V20 | statement | theorem 2.1 | arxiv |
| Moment bounds for fixed spectral transforms | statement | lemma C.6 | arxiv |
| Empirical cutoff separation and weighted good events | statement | lemma C.9 | arxiv |
| Labeled means and covariance | statement | lemma C.14 | arxiv |
| Stability of the two-level hybrid | statement | theorem 3.1 | arxiv |
| Ridge-leverage stability | statement | lemma C.10 | arxiv |
| Hilbert-valued stability of the fitted smoother | statement | lemma C.18 | arxiv |
| Consequences of the tuning regime | statement | lemma C.5 | arxiv |
| Hilbert space | statement | corollary B.2 | arxiv |
