| Independent trajectories | definition | definition G.8 | arxiv |
| Rate under SGC | statement | corollary K.7 | arxiv |
| Few rounds | statement | theorem J.11 | arxiv |
| Variational inequality | definition | definition 2.1 | arxiv |
| Exact quadratics | statement | lemma N.1 | arxiv |
| Local extragradient with averaging | definition | definition G.4 | arxiv |
| An explicit uniform asymptotic | statement | theorem B.2 | arxiv |
| Matching bounds for large sample smoothness | statement | corollary 5.6 | arxiv |
| The two schedules for every budget | statement | lemma I.1 | arxiv |
| A depth lower bound in dimension quadratic in depth | statement | corollary E.6 | arxiv |
| One switch | statement | theorem K.6 | arxiv |
| Affine minimax risks | definition | definition 3.2 | arxiv |
| Operator energy of one round | statement | lemma G.5 | arxiv |
| Monotone VI under SGC | statement | theorem 4.1 | arxiv |
| Pooled gradients and local solves | statement | theorem M.1 | arxiv |
| Composite gap | definition | definition 5.2 | arxiv |
| Clipped chain | statement | lemma J.3 | arxiv |
| Affine minimax rate under mixed noise | statement | theorem 3.4 | arxiv |
| Polynomial representation of batched queries | statement | lemma E.2 | arxiv |
| Lipschitz bound along a segment | statement | lemma K.1 | arxiv |
| Intermittent communication | definition | definition 2.4 | arxiv |
| Gap criteria | definition | definition 2.9 | arxiv |
| Gap of one trajectory | statement | theorem F.1 | arxiv |
| Two schedules | statement | proposition L.3 | arxiv |
| Monotone VIs under mixed noise | statement | theorem 4.2 | arxiv |
| Strongly monotone chain | statement | lemma H.9 | arxiv |
| Monotone VIs under mixed noise | statement | corollary J.8 | arxiv |
| Root of the strongly monotone chain | statement | lemma J.9 | arxiv |
| A uniform Gaussian projection bound | statement | lemma E.4 | arxiv |
| Lower bound for any success probability | statement | theorem J.6 | arxiv |
| Exponential scale | statement | corollary H.11 | arxiv |
| All budgets | statement | theorem F.2 | arxiv |
| A weighted bound on Chebyshev nodes | statement | lemma E.3 | arxiv |
| Lower bound on the number of rounds | statement | corollary J.13 | arxiv |
| Gaussian observations and adaptive transcripts | statement | lemma C.1 | arxiv |
| Projected extragradient step | statement | lemma K.2 | arxiv |
| Averaging absorbs the relative noise | statement | lemma G.6 | arxiv |
| Number of rounds up to worker logarithms | statement | corollary J.14 | arxiv |
| A variant with a uniform variance bound | statement | lemma M.2 | arxiv |
| Lower bound under SGC | statement | lemma G.2 | arxiv |
| Affine minimax rate under SGC | statement | theorem 3.3 | arxiv |
| Independent trajectories under mixed noise | statement | lemma G.9 | arxiv |
| Robust chain | statement | lemma H.3 | arxiv |
| Distance lower bound | statement | theorem H.10 | arxiv |
| Gap on a hidden cube | statement | lemma J.4 | arxiv |
| Variance of smooth convex samples | statement | lemma L.1 | arxiv |
| Residual under arbitrary Gaussian polynomial information | statement | proposition E.5 | arxiv |
| Masked quadratics | statement | theorem N.2 | arxiv |
| Root noise | statement | lemma N.3 | arxiv |
| Accelerated mirror-prox | statement | theorem L.2 | arxiv |
| Localization of a saddle function | statement | lemma H.5 | arxiv |
| Flat edge | statement | lemma H.2 | arxiv |
| Statistical lower bound | statement | lemma G.11 | arxiv |
| Comparison with the nonlinear upper bound | statement | lemma B.3 | arxiv |
| Gap of the affine chain | statement | lemma H.1 | arxiv |
| One stage | statement | lemma K.4 | arxiv |
| The admissible horizon | statement | lemma G.7 | arxiv |
| Strongly monotone VIs under mixed noise | statement | theorem 4.3 | arxiv |
| Clipped edge | statement | lemma J.2 | arxiv |
| \revision{Sequential local updates and parallel minibatching | statement | theorem 5.3 | arxiv |
| Upper bound under mixed noise | statement | corollary G.10 | arxiv |
| Extragradient identity | statement | lemma D.1 | arxiv |
| Number of rounds | statement | corollary I.4 | arxiv |
| Statistical lower bound | statement | proposition J.1 | arxiv |
| Restarts | statement | theorem K.5 | arxiv |
| Simulation by exact batches | statement | lemma G.1 | arxiv |
| One pooled gradient | statement | lemma M.3 | arxiv |
| Hiding | statement | lemma H.6 | arxiv |
| Hiding for the boundary-edge oracle | statement | lemma J.5 | arxiv |
| Statistical lower bound for the distance | statement | lemma I.3 | arxiv |
| Interpolation without strong growth | statement | proposition L.4 | arxiv |
| Median of block means | statement | lemma K.3 | arxiv |
| Generalized smoothness under SGC | statement | corollary 4.5 | arxiv |
| Saddle and Minty gaps under SGC | statement | theorem H.8 | arxiv |
| Lower bound after $N$ rounds | statement | theorem J.12 | arxiv |
| Distance to the root | statement | proposition F.4 | arxiv |
| Expected extragradient step | statement | lemma D.2 | arxiv |
| Minty gap under SGC | statement | theorem H.7 | arxiv |
| Hiding with a prescribed chain length | statement | lemma J.10 | arxiv |
| Elementary bounds | statement | lemma B.1 | arxiv |
| Localization of an operator | statement | lemma H.4 | arxiv |
| A scalar recursion with two phases | statement | lemma F.3 | arxiv |
| SGC | statement | corollary F.5 | arxiv |
| Composite minimax risk | definition | definition 5.4 | arxiv |
| Local calls and noise | statement | corollary J.7 | arxiv |
| General composite lower bound | statement | theorem 5.5 | arxiv |
| Serial phase followed by common queries | statement | theorem I.2 | arxiv |
| Sampling lower bound with an exact component | statement | theorem N.4 | arxiv |
| Serial and common-query bounds | statement | lemma G.3 | arxiv |
| Batched matrix-query algorithm | definition | definition E.1 | arxiv |
