| Scalar scale-Gaussian decomposition | statement | lemma D.1 | arxiv |
| Randomized methods on a Gaussian target | statement | proposition 6.2 | arxiv |
| Bias accumulation at a reference law | statement | lemma 3.3 | arxiv |
| Numerical hypocoercive contraction | statement | proposition 4.2 | arxiv |
| Exponential midpoint upper bound | statement | theorem 4.1 | arxiv |
| Uniform multiplier bound for sectorial operators | statement | lemma E.1 | arxiv |
| Stationary affine recursion with a bounded perturbation | statement | lemma C.3 | arxiv |
| Stationary bias and iteration lower bounds, informal | statement | theorem 1.2 | arxiv |
| Randomized overdamped lower bounds on a Gaussian target | statement | proposition 6.1 | arxiv |
| Mean error in a modulated block | statement | lemma C.4 | arxiv |
| RLMC radial lower bound on a Gaussian target | statement | proposition D.4 | arxiv |
| Conditional mean bound | statement | lemma A.3 | arxiv |
| Heun upper bound | statement | theorem 3.1 | arxiv |
| Wasserstein lower bound for Gaussian scale perturbations | statement | lemma D.3 | arxiv |
| PLMC lower bound on a Gaussian target | statement | proposition D.5 | arxiv |
| Condition number lower bound for Heun | statement | theorem 5.2 | arxiv |
| Short-time stability in \(\dot H^{-1}\ | statement | lemma B.1 | arxiv |
| One-step error at stationarity | statement | proposition 4.3 | arxiv |
| Transport bound for a random displacement | statement | lemma B.5 | arxiv |
| Deterministic midpoint guarantees, informal | statement | theorem 1.1 | arxiv |
| Covariance fluctuations before stationarity | statement | lemma D.8 | arxiv |
| Contractivity of the Heun kernel | statement | proposition 3.2 | arxiv |
| PULMC conditional covariance fluctuations | statement | lemma D.7 | arxiv |
| Gaussian convolution inequality | statement | lemma A.10 | arxiv |
| Displacement estimates | statement | lemma A.1 | arxiv |
| Gaussian lower bound for Heun | statement | proposition C.2 | arxiv |
| Invariant distribution bias | statement | proposition A.13 | arxiv |
| Second moment of the corrected local error | statement | lemma A.2 | arxiv |
| \(\W_2\) estimate for one auxiliary step | statement | lemma A.12 | arxiv |
| Malliavin--Stein kernel estimate | statement | lemma A.4 | arxiv |
| Conditional \(\mathfrak{S}_4\) derivative | statement | proposition A.6 | arxiv |
| Conditional covariance fluctuations | statement | lemma D.6 | arxiv |
| Local differential estimates | statement | lemma B.2 | arxiv |
| Matrix scale-Gaussian decomposition | statement | lemma D.2 | arxiv |
| Oscillatory expectation change for Heun | statement | lemma C.1 | arxiv |
| Contraction estimates for the Witten semigroup | statement | lemma A.7 | arxiv |
| Heun lower bounds on an oscillatory target | statement | proposition 5.1 | arxiv |
| Corrector derivative | statement | lemma A.5 | arxiv |
| Iteration lower bounds for all midpoint methods | statement | corollary 6.3 | arxiv |
| Second action of the adjoint generator | statement | lemma B.3 | arxiv |
| \(\dot H^{-1}\) estimate for the weighted divergence | statement | proposition B.4 | arxiv |
| Exponential midpoint on a Gaussian target | statement | proposition 5.3 | arxiv |
| Dimension-free analyticity on \(L^4(\pi;\mathfrak{S}_4)\ | statement | lemma A.8 | arxiv |
| Uniform \(\mathfrak{S}_4\) Witten--Laplacian multiplier | statement | lemma A.9 | arxiv |
