| Attainment of the global minimum | statement | lemma 4.2 | arxiv |
| Isoduality and reciprocal scales | statement | lemma 3.7 | arxiv |
| The full-fibre stationarity identity | statement | proposition 4.5 | arxiv |
| Comparison at extreme scales | statement | proposition 3.13 | arxiv |
| A moment bound near the identity | statement | lemma 3.4 | arxiv |
| A projected Fourier lower bound | statement | lemma 4.6 | arxiv |
| Determinant separation | statement | theorem 2.1 | arxiv |
| A scalar lower-bound alternative | statement | lemma 4.8 | arxiv |
| Comparison at stationary pairs | statement | theorem 4.1 | arxiv |
| First variations and the shortest-vector moment | statement | lemma 4.3 | arxiv |
| Finite covering criterion | statement | lemma A.4 | arxiv |
| Local comparison at $D_4$ | statement | theorem 3.1 | arxiv |
| The higher-shell moment estimate | statement | lemma 3.5 | arxiv |
| Reference energy and moment bounds | statement | lemma 3.9 | arxiv |
| Compactness of reduced forms | statement | lemma 2.2 | arxiv |
| Uniform auxiliary estimates | statement | theorem A.1 | arxiv |
| Comparison near $A_4$ | statement | proposition 3.10 | arxiv |
| Uniform properties of the auxiliary family | statement | lemma 4.7 | arxiv |
| Minima of 4d theta function | statement | theorem 1.1 | arxiv |
| The projected lattice and its fibres | statement | lemma 4.4 | arxiv |
| The $A_4$ tangent determinant | statement | lemma 2.4 | arxiv |
| Exclusion by a short vector | statement | proposition 3.12 | arxiv |
| An exponential bound from two moments | statement | lemma 3.3 | arxiv |
| The root-shell moment estimate | statement | lemma 3.6 | arxiv |
| Uniform truncation bounds | statement | lemma A.3 | arxiv |
| Length bound away from the perfect forms | statement | corollary 3.11 | arxiv |
| Compact theta sublevels and smooth dependence | statement | lemma 3.8 | arxiv |
| Localization of the remaining pairs | statement | corollary 3.14 | arxiv |
| Positive Gaussian mixtures | statement | corollary 5.1 | arxiv |
| Short-vector auxiliary polynomials | statement | lemma A.2 | arxiv |
| The $D_4$ tangent section | statement | lemma 2.3 | arxiv |
| Projected endpoint polynomials | statement | lemma B.2 | arxiv |
| Minima of 4d Epstein zeta function | statement | theorem 1.2 | arxiv |
| Short-vector endpoint polynomials | statement | lemma B.1 | arxiv |
| Shell moment identities | statement | lemma 3.2 | arxiv |
