| Probability of failure of localization | statement | lemma 7.20 | arxiv |
| Expectation of level increments | statement | lemma 7.4 | arxiv |
| Overlap and interaction between inserted points | statement | lemma 5.6 | arxiv |
| Functional CLT | statement | theorem 2.4 | arxiv |
| Moment bound for the cover time | statement | corollary 3.5 | arxiv |
| 33NMDX1VWB | statement | lemma C.1 | arxiv |
| Tail bound for the cover time | statement | proposition 3.3 | arxiv |
| 46TF48XPXJ | statement | lemma A.1 | arxiv |
| 4GS4ZF2A0N | statement | lemma 6.2 | arxiv |
| Boundary characterization of the cover time | statement | lemma 3.2 | arxiv |
| 63KYEZ509N | statement | lemma 4.3 | arxiv |
| 6C79EF432Q | statement | lemma 7.17 | arxiv |
| Geometry of the truncated cell | statement | lemma 3.1 | arxiv |
| Expectation of weighted level increments | statement | lemma 7.13 | arxiv |
| Covariance term | statement | proposition 5.2 | arxiv |
| Measure of intersections of cube envelopes | statement | lemma D.3 | arxiv |
| Univariate normal approximation | statement | theorem 2.1 | arxiv |
| Tail bound for the maximum cover time in a cube | statement | lemma D.4 | arxiv |
| Covariance asymptotics | statement | theorem 2.2 | arxiv |
| D8YHSZSTJC | statement | theorem 6.5 | arxiv |
| Fourth-moment bound for weighted increments | statement | proposition 7.12 | arxiv |
| Moments of weighted block scores | statement | lemma 7.18 | arxiv |
| Interaction between the inserted points | statement | proposition 5.1 | arxiv |
| Cumulant decomposition across a partition | statement | lemma 7.7 | arxiv |
| Davydov reduction | statement | proposition 7.1 | arxiv |
| Overlap bound for deterministic extremality regions | statement | lemma D.2 | arxiv |
| Cumulant bound | statement | proposition 7.3 | arxiv |
| KGAWD07B5W | statement | lemma 6.3 | arxiv |
| Bounds for overlap and boundary terms | statement | proposition 5.4 | arxiv |
| Deterministic localization for extremality | statement | lemma D.1 | arxiv |
| Extension of , Lemma 5.5 | statement | lemma C.2 | arxiv |
| Multivariate normal approximation | statement | theorem 2.3 | arxiv |
| RPTNEZA61R | statement | proposition 4.2 | arxiv |
| RTH4ZEY5SC | statement | lemma 6.6 | arxiv |
| Maximum cover time among contributing points | definition | definition 7.16 | arxiv |
| Localization and resampling on a fixed region | statement | lemma 5.5 | arxiv |
| Comparison of configurations that agree locally | statement | lemma D.7 | arxiv |
| Translation bound for the observation window | statement | lemma 5.3 | arxiv |
| Covariance bound for products of block scores | statement | lemma 7.8 | arxiv |
| Variance bound for \(\tilde G_n\ | statement | proposition 7.2 | arxiv |
| Cube envelopes | definition | definition 7.14 | arxiv |
| WTB6QJ70X7 | statement | theorem 6.1 | arxiv |
| Covariance decay for products of weighted block scores | statement | lemma 7.19 | arxiv |
| X9FZ8RQM84 | statement | lemma 6.4 | arxiv |
| Variance bound for weighted increments | statement | proposition 7.10 | arxiv |
| Weighted Davydov reduction | statement | proposition 7.9 | arxiv |
| Y94G84E735 | statement | proposition 4.1 | arxiv |
| Fourth cumulant bound for weighted increments | statement | proposition 7.11 | arxiv |
| YHQ6JYQSN7 | statement | lemma 3.6 | arxiv |
| Lattice shell bound | statement | lemma 7.5 | arxiv |
| Tail of a cube envelope outside a fixed neighborhood | statement | lemma D.6 | arxiv |
| Shell counting for labeled quadruples | statement | lemma 7.6 | arxiv |
| Approximation by conditioning on a bounded region | statement | lemma 7.21 | arxiv |
| Envelope domination | statement | lemma 7.15 | arxiv |
| Palm moment for an inserted generator | statement | lemma D.5 | arxiv |
