| Positive-depth quadratic saving | statement | lemma 16.1 | arxiv |
| Part II: the nonsaturated regime | statement | theorem 2.3 | arxiv |
| Outer actions and factor systems | statement | lemma 17.4 | arxiv |
| Nonminimal endpoint spaces | statement | proposition 11.1 | arxiv |
| Agreement from selected relations | statement | proposition 6.9 | arxiv |
| Higman's lower-bound construction | statement | lemma 15.6 | arxiv |
| Row basis at a unique hollowing matrix | statement | lemma 11.7 | arxiv |
| Second-layer defect | statement | lemma 7.2 | arxiv |
| Uniform and saturated isotropic estimates | statement | lemma 9.2 | arxiv |
| Recovery at the current excess | statement | corollary 6.8 | arxiv |
| 7TKVCAZP3S | statement | proposition 5.4 | arxiv |
| Commutators of matched pairs | statement | proposition 6.4 | arxiv |
| One-excess estimate | statement | proposition 6.10 | arxiv |
| 996A0B1F83 | statement | corollary 6.3 | arxiv |
| Intermediate uniform upper bound | statement | theorem 1.4 | arxiv |
| Reed--Muller support | statement | lemma 11.11 | arxiv |
| Positive-excess relation bound | statement | corollary 6.11 | arxiv |
| Refined saturated optimization | statement | lemma 7.3 | arxiv |
| BRZTFPGY22 | statement | theorem 1.1 | arxiv |
| First-difference theorem | statement | theorem 6.6 | arxiv |
| CKQ6P7PWF5 | statement | proposition 6.2 | arxiv |
| Minimal endpoint spaces | statement | proposition 11.4 | arxiv |
| Adjacent-order growth | statement | corollary 14.2 | arxiv |
| Concentration in Frattini class $2$ | statement | theorem 1.3 | arxiv |
| DEV400165B | statement | proposition 11.5 | arxiv |
| Power-relation count | statement | lemma 7.1 | arxiv |
| The kernel of the Frattini action | statement | lemma 17.3 | arxiv |
| E9NKXZMNKY | statement | proposition 17.5 | arxiv |
| Minimum dimension | statement | lemma 10.1 | arxiv |
| Determinant constraint | statement | proposition 11.10 | arxiv |
| FN684DWHT5 | statement | proposition 16.3 | arxiv |
| An odd first generator | statement | lemma 17.2 | arxiv |
| Multiplicity across the power-word fibres | statement | lemma 15.3 | arxiv |
| Fourier transform of the invertible-matrix indicator | statement | lemma 11.13 | arxiv |
| Prescribing the core centralizer | statement | lemma 15.4 | arxiv |
| Retaining the defining commutator identities | statement | corollary 6.12 | arxiv |
| Coefficient maps | statement | lemma 11.9 | arxiv |
| H3KWSXJWBG | statement | theorem 2.1 | arxiv |
| Relative graded determination | statement | lemma 5.2 | arxiv |
| HYYY3T7WR9 | statement | proposition 5.1 | arxiv |
| Part I: the saturated regime | statement | theorem 2.2 | arxiv |
| JTQNMANV5T | statement | theorem 14.1 | arxiv |
| Rank bound for unique hollowing forms | statement | proposition 11.3 | arxiv |
| Universal finite-field estimates | statement | lemma 4.1 | arxiv |
| Isotropic count via the radical | statement | lemma 9.1 | arxiv |
| Endpoint absorption | statement | lemma 12.1 | arxiv |
| Sims rank versus faithfulness and hollowing | statement | proposition 8.1 | arxiv |
| Large odd parts | statement | proposition 18.3 | arxiv |
| M4NXX9JSDF | statement | lemma 15.2 | arxiv |
| Perturbed $h$-spaces | statement | lemma 11.8 | arxiv |
| Counting hollowing spaces away from the binary endpoint | statement | proposition 10.2 | arxiv |
| MW9996B529 | statement | proposition 15.5 | arxiv |
| Bounded odd parts | statement | corollary 18.2 | arxiv |
| Recovery in the second layer | statement | lemma 6.7 | arxiv |
| Fixed-breadth relation bound | statement | proposition 6.1 | arxiv |
| An arbitrary fixed balance coefficient | statement | lemma 15.1 | arxiv |
| Bounded second-layer rank | statement | lemma 12.2 | arxiv |
| Domination by $2$-groups of class $2$ | statement | theorem 1.2 | arxiv |
| Commutator comparison using Sims lifts | statement | proposition 6.5 | arxiv |
| SP3KDWVMSA | statement | proposition 5.3 | arxiv |
| SRRHKZD5HB | statement | theorem 17.1 | arxiv |
| Trace representation of $b(u,-)$ | statement | lemma 11.14 | arxiv |
| The cumulative cutoff | statement | proposition 18.1 | arxiv |
| W1QJGGFV2Q | statement | theorem 13.2 | arxiv |
| WHFYWVDDGY | statement | corollary 18.4 | arxiv |
| Presentation-parameter ledger | statement | proposition 13.1 | arxiv |
| Fourier bound for $R_u(X_0)$ | statement | proposition 11.15 | arxiv |
| Fibre kernel bound | statement | proposition 11.12 | arxiv |
| Unique hollowing forms of minimally hollowing spaces | statement | proposition 11.2 | arxiv |
| YEPN5N7X9Q | statement | proposition 16.2 | arxiv |
