| Exact divergence of truncation | statement | lemma 1 | arxiv |
| Isotropic rates on the same retained subspace | statement | proposition 3 | arxiv |
| Davis-Kahan subspace perturbation | statement | lemma 13 | arxiv |
| Convergence on the retained coordinates | statement | theorem 3 | arxiv |
| Gaussian sample covariance concentration | statement | lemma 11 | arxiv |
| Forward second moment bound | statement | lemma 5 | arxiv |
| Continuous broken power law | definition | definition 2 | arxiv |
| Trace-dependent TV convergence | statement | theorem 6 | arxiv |
| Data processing for TV | statement | lemma 4 | arxiv |
| Top-$K$ TV bound | statement | corollary 2 | arxiv |
| $\bLambda$-weighted score perturbation, $\kappa$-dependent version | statement | lemma 10 | arxiv |
| End-to-end complexity | statement | theorem 4 | arxiv |
| Empirical-coordinate covariance perturbation | statement | lemma 17 | arxiv |
| Smoothed Gaussian reconstruction, empirical basis and rates, oracle score | statement | theorem 7 | arxiv |
| Score perturbation for a diagonal OU step | statement | lemma 9 | arxiv |
| Fisher bound from score regularity | statement | lemma 6 | arxiv |
| $\bLambda$-weighted forward movement bound | statement | lemma 8 | arxiv |
| Forward movement bound | statement | lemma 7 | arxiv |
| TV convergence, dimension-dependent warm-up | statement | theorem 5 | arxiv |
| Decoupling of data collection and sampling | statement | theorem 8 | arxiv |
| Minimum empirical rate stability | statement | lemma 16 | arxiv |
| Envelope of a broken power law | statement | proposition 5 | arxiv |
| Trace bounds under Wiener-gain rates and power-law decay | statement | lemma 2 | arxiv |
| Cost of spectral truncation | statement | theorem 1 | arxiv |
| Truncation error for general data | statement | proposition 1 | arxiv |
| Correction to the Gaussian reference score | statement | proposition 2 | arxiv |
| Trace-aware one-step score perturbation | statement | corollary 3 | arxiv |
| Weyl eigenvalue stability | statement | lemma 12 | arxiv |
| Mixture lifting of the Gaussian bound | statement | proposition 4 | arxiv |
| Lipschitz stability of Wiener gain | statement | lemma 14 | arxiv |
| $\sigma$-explicit active error, Gaussian case | statement | lemma 3 | arxiv |
| Trace perturbation bounds | statement | lemma 15 | arxiv |
| Truncating at the noise level is not enough | statement | corollary 1 | arxiv |
| Truncated samplers | definition | definition 1 | arxiv |
| Number of retained directions | statement | theorem 2 | arxiv |
