| Continuous-depth convergence from averaged margins | statement | theorem 4.2 | arxiv |
| Quantitative trajectory bounds | statement | proposition C.4 | arxiv |
| Mean-field conservation law | definition | definition B.2 | arxiv |
| Hyperbolic isotropy | definition | definition E.1 | arxiv |
| Reduced phase dynamics | statement | proposition E.5 | arxiv |
| Global full phase flow | statement | proposition C.22 | arxiv |
| Global convergence from a positive support gap | statement | theorem 3.1 | arxiv |
| Fixed trace and predictor, arbitrarily slow escape | example | example C.9 | arxiv |
| Conditional phase-energy decay | statement | lemma C.24 | arxiv |
| Conformal symplectic isotropy | definition | definition E.4 | arxiv |
| A stepsize fixed before sampling | statement | corollary C.18 | arxiv |
| Conformal phase conservation laws | statement | proposition 5.1 | arxiv |
| Tightened conditional energy decay | statement | proposition C.27 | arxiv |
| Transported support and accumulated defect | statement | lemma C.14 | arxiv |
| Explicit rate used in the figures | statement | corollary C.29 | arxiv |
| Covariance closure and conservation laws | statement | proposition 2.1 | arxiv |
| Predictor-only intrinsic equation | statement | proposition E.2 | arxiv |
| Two-scale white initialization | statement | corollary 5.3 | arxiv |
| Finite-depth convergence from conserved layer margins | statement | theorem 4.1 | arxiv |
| Adjustable rate budgets | statement | proposition C.17 | arxiv |
| The Gaussian initial-error cost | statement | proposition C.13 | arxiv |
| Covariance support margins and gap | definition | definition 2.2 | arxiv |
| Coercivity prevents covariance collapse | statement | proposition C.6 | arxiv |
| Global bootstrap with the correct prefactor | statement | corollary C.30 | arxiv |
| Global linear rate from a phase-energy certificate | statement | theorem 5.2 | arxiv |
| Second-moment closure | statement | proposition B.1 | arxiv |
| Conditional hidden-block criterion | statement | lemma C.5 | arxiv |
| Marcotte-style covariance-level completeness | statement | corollary D.2 | arxiv |
| High-probability finite-width convergence | statement | theorem C.12 | arxiv |
| Transported lower bounds | statement | proposition 2.3 | arxiv |
| Minimum-energy lift of a covariance velocity | statement | proposition C.25 | arxiv |
| Large-position-scale certificate asymptotics | statement | proposition C.31 | arxiv |
| Isotropic Gaussian sampling can lose the support gap | example | example C.11 | arxiv |
| Optimal rate within the Lyapunov bounds | statement | proposition C.28 | arxiv |
| Fundamental mean-field laws | statement | proposition B.3 | arxiv |
| Finite width preserves the population rate | statement | corollary 3.4 | arxiv |
| Identical position covariance and covariance derivative, arbitrarily large energy | example | example C.26 | arxiv |
| Relative initialization stability | statement | theorem C.10 | arxiv |
| General covariance coordinates | statement | proposition C.23 | arxiv |
| Smooth PL consequences | statement | lemma C.1 | arxiv |
| Split fields generate \(\mathfrak o(d_u,d_v)\ | statement | proposition D.1 | arxiv |
| Descent with unequal hidden lower bounds | statement | lemma C.15 | arxiv |
| Small-step global convergence of factor descent | statement | theorem 3.6 | arxiv |
