| Invariance and refresh dissipation | statement | lemma 9 | arxiv |
| Finite compiler at a fixed step size | statement | proposition 8 | arxiv |
| Closed weak-gradient smoothing | statement | lemma 10 | arxiv |
| Implementable flux half-turn | statement | theorem 2 | arxiv |
| Mode certificate and deterministic cap | statement | lemma 19 | arxiv |
| Dyadic operator comparison | statement | lemma 5 | arxiv |
| Clock cap | statement | lemma 20 | arxiv |
| Ideal \(L^2\) contraction | statement | proposition 6 | arxiv |
| Global half-turn estimate | statement | proposition 7 | arxiv |
| Quadratic-baseline refinement | statement | corollary 3 | arxiv |
| Random-center and path accounting | statement | lemma 24 | arxiv |
| Outer-reflection geometry | statement | lemma 11 | arxiv |
| Implementable persistent sampler | statement | theorem 4 | arxiv |
| Ideal persistent contraction | statement | proposition 11 | arxiv |
| Shifted-reference transfer | statement | lemma 18 | arxiv |
| One-step energy decay | statement | lemma 6 | arxiv |
| Stationary rate tail and clock coupling | statement | lemma 7 | arxiv |
| Affine evolution | statement | lemma 2 | arxiv |
| Logarithmic work truncation | statement | lemma 22 | arxiv |
| Affine approximation after reflection | statement | lemma 4 | arxiv |
| General warmness budget | statement | corollary 1 | arxiv |
| Ideal flux contraction | statement | theorem 1 | arxiv |
| Unit-circle resolvent bound | statement | lemma 14 | arxiv |
| Fixed-reference validity | statement | proposition 4 | arxiv |
| Conditional invariance | statement | proposition 3 | arxiv |
| Approximate RGO | statement | proposition 12 | arxiv |
| Controlled transfer errors | statement | corollary 2 | arxiv |
| Position--momentum transfer | statement | proposition 10 | arxiv |
| Localized conditional geometry | statement | lemma 1 | arxiv |
| P9T06WDTGR | definition | definition | arxiv |
| Affine approximation after reflection | statement | lemma 12 | arxiv |
| Warm path comparison | statement | lemma 16 | arxiv |
| Approximate RGO | statement | proposition 9 | arxiv |
| Fixed-reference validity | statement | lemma 8 | arxiv |
| Affine local compiler | statement | lemma 21 | arxiv |
| Finite posterior interfaces | statement | proposition 13 | arxiv |
| Conditional invariance and reversibility | statement | proposition 2 | arxiv |
| Exactness of the framework | statement | proposition 1 | arxiv |
| Shifted-Gaussian comparison | statement | lemma 17 | arxiv |
| Exact proximal warmification | statement | lemma 23 | arxiv |
| Observable localization | statement | lemma 26 | arxiv |
| Warm-start removal | statement | theorem 5 | arxiv |
| Capped reflected finalizer | statement | proposition 14 | arxiv |
| Approximate quarter rotation | statement | lemma 13 | arxiv |
| Ideal persistent contraction | statement | theorem 3 | arxiv |
| Outer-reflection geometry | statement | lemma 3 | arxiv |
| Unit-circle bound implies geometric decay | statement | lemma 15 | arxiv |
| Finite approximation of the coarse path | statement | lemma 25 | arxiv |
| Implementation theorem | statement | theorem 6 | arxiv |
| Conditional affine half-turn | statement | proposition 5 | arxiv |
