| Degenerate stratum | statement | theorem 2.11 | arxiv |
| Wild-inertia criterion for finite monodromy, every $n$ | statement | proposition 2.50 | arxiv |
| Purity of the middle-extension cohomology on a curve | statement | lemma 1.12 | arxiv |
| Decoupling of moment degree from family dimension | statement | lemma 2.112 | arxiv |
| Case (C): the exact exceptional set | statement | proposition 2.46 | arxiv |
| Alternative direct-classification route | statement | theorem 2.76 | arxiv |
| Fourth moment | statement | theorem 2.25 | arxiv |
| $n=127$: a moment criterion, uniform in $p$ | statement | theorem 2.58 | arxiv |
| Two-pair stratum in arbitrary fixed dimension | statement | lemma 2.13 | arxiv |
| Unipotence on the fibres at the boundary | statement | lemma 2.88 | arxiv |
| 2TCCZF43E9 | statement | corollary 2.67 | arxiv |
| A closure criterion for case (C | statement | corollary 2.54 | arxiv |
| A binomial gap | statement | lemma 2.101 | arxiv |
| The boundary fibre at $t=0$ | statement | lemma 1.9 | arxiv |
| Generic contribution in fixed dimension | statement | proposition 2.111 | arxiv |
| 59SSQ3MZ7S | definition | definition | arxiv |
| Independence of scalar pullbacks | statement | proposition 2.62 | arxiv |
| Diagonal stratum | statement | theorem 2.9 | arxiv |
| Lissit\'e, purity, rank, and the trace relation | statement | theorem 1.14 | arxiv |
| Reductivity, all $n$ | statement | proposition 2.31 | arxiv |
| A second derivation of the sixth-moment lower bound | statement | proposition 2.69 | arxiv |
| Degenerate stratum in arbitrary fixed dimension | statement | lemma 2.113 | arxiv |
| Projective-ray estimate | statement | lemma 2.110 | arxiv |
| $n=127$: a sharp local criterion | statement | theorem 2.56 | arxiv |
| Excluding the two dimension-$10$ Table I exceptions | statement | proposition 2.43 | arxiv |
| The unipotent blocks at the boundary | statement | proposition 2.94 | arxiv |
| Cohomology of the $t$-line | statement | proposition 1.8 | arxiv |
| Kloosterman factorisation | statement | lemma 1.5 | arxiv |
| Finite determinant and finite scalars | statement | proposition 2.100 | arxiv |
| Exact conductor of the top-weight sheaf | statement | theorem 2.98 | arxiv |
| 850AAFV0J2 | statement | corollary 2.7 | arxiv |
| 8CF6JJKGHF | statement | proposition 2.82 | arxiv |
| The three non-$\SL$ cases all force finite monodromy | statement | proposition 2.35 | arxiv |
| Conductor of an arbitrary irreducible construction | statement | corollary 2.107 | arxiv |
| Tameness at the coordinate boundary | statement | proposition 2.90 | arxiv |
| Two-pair stratum | statement | theorem 2.12 | arxiv |
| Why the fourth moment alone does not decide case (C | statement | proposition 2.59 | arxiv |
| AQ0GAFNAEH | statement | proposition 2.79 | arxiv |
| Tame constraint on finite monodromy | statement | proposition 2.49 | arxiv |
| Diagonal evaluation | statement | lemma 2.4 | arxiv |
| Rojas--Le\'on product rule, specialized form | statement | theorem 2.93 | arxiv |
| The nine lines | statement | proposition 2.16 | arxiv |
| Conductor constancy and lissit\'e for the relative punctured line | statement | lemma 1.11 | arxiv |
| Why the case-(C) range resists elementary factorisation | statement | proposition 2.47 | arxiv |
| The complement of $\Gm^4$ | statement | lemma 2.24 | arxiv |
| Boundary degeneration | statement | proposition 2.86 | arxiv |
| Larsen's alternative, with the needed proof | statement | theorem 2.28 | arxiv |
| Geometric monodromy | statement | theorem 2.81 | arxiv |
| Katz's moment principle, with proof | statement | theorem 2.27 | arxiv |
| A binomial identity | statement | lemma 2.95 | arxiv |
| Integrating the Lagrange multiplier | statement | lemma 1.10 | arxiv |
| A self-contained ray determinant obstruction | statement | proposition 2.42 | arxiv |
| Guralnick--Tiep | statement | theorem 2.33 | arxiv |
| EDYRVWD30J | statement | lemma 2.15 | arxiv |
| Fixed spaces in the extraspecial normaliser are small | statement | proposition 2.53 | arxiv |
| Purity of middle convolution | statement | lemma 2.96 | arxiv |
| The hypothetical extraspecial group is pinned down | statement | proposition 2.51 | arxiv |
| F87VKV34E9 | statement | proposition 2.78 | arxiv |
| The sixth moment of $\SL_N$ | statement | lemma 2.63 | arxiv |
| Unequal breaks | statement | lemma 1.6 | arxiv |
| Case (D) is closed for \emph{every} $n$ | statement | proposition 2.37 | arxiv |
| GQGTV0ZPZ2 | statement | theorem 2.3 | arxiv |
| Two-factor local convolution at the origin | statement | lemma 1.1 | arxiv |
| Independent cohomological bound on the generic stratum | statement | proposition 2.22 | arxiv |
| Geometric semisimplicity of a pure lisse sheaf | statement | lemma 2.29 | arxiv |
| Quadratic stationary phase for the Kloosterman phase | statement | lemma 1.2 | arxiv |
| A characteristic-free criterion at the boundary divisor | statement | theorem 2.72 | arxiv |
| KSWSV1871X | statement | lemma 2.8 | arxiv |
| The complement of $\Gm^n$, all moments | statement | lemma 2.64 | arxiv |
| The clean dichotomy | statement | corollary 2.36 | arxiv |
| Non-self-duality, unconditional and non-circular | statement | corollary 2.32 | arxiv |
| Scalar pullbacks of $\Kl$ are pairwise non-isomorphic, even up to twist | statement | lemma 2.61 | arxiv |
| MKFTW94YDA | statement | lemma 2.18 | arxiv |
| Clebsch--Gordan multiplicities | statement | lemma 1.7 | arxiv |
| $n=127$, by congruence | statement | theorem 2.74 | arxiv |
| Bounds in the degenerate lower-dimensional fibres | statement | corollary 1.15 | arxiv |
| Case (B) is closed for \emph{every} $n$ in the unitary family | statement | proposition 2.38 | arxiv |
| Higher moments explode in the extraspecial case | statement | proposition 2.57 | arxiv |
| PSNY1XDQ1Z | statement | lemma 2.20 | arxiv |
| The interpolation route is unavailable | statement | proposition 2.70 | arxiv |
| The two factors are admissible | statement | lemma 2.92 | arxiv |
| The sixth moment | statement | theorem 2.66 | arxiv |
| Exact diagonal contribution to the fourth moment | statement | lemma 2.5 | arxiv |
| All dimensions in the scope of this article | statement | corollary 2.103 | arxiv |
| QNNEXNJ5WG | statement | proposition 2.80 | arxiv |
| Local Fourier transform in the slope-$<1$ range | statement | theorem 2.89 | arxiv |
| An exact Pocklington certificate for $r(127)$ | statement | lemma 2.45 | arxiv |
| Uniformity in $q$ | statement | lemma 2.23 | arxiv |
| Euler characteristic on a coordinate line | statement | theorem 2.87 | arxiv |
| Boundary unipotence and infinitude | statement | proposition 2.99 | arxiv |
| Fourth moment, general $n$ | statement | theorem 2.114 | arxiv |
| The two surviving case-(B) collisions are self-dual, hence excluded | statement | proposition 2.39 | arxiv |
| No twisted self-duality | statement | proposition 2.84 | arxiv |
| TG64N7JHBD | statement | lemma 2.14 | arxiv |
| Case (C) forces a congruence on $p$ | statement | proposition 2.52 | arxiv |
| A $2$-adic obstruction for the $q=3$ symplectic family | statement | proposition 2.40 | arxiv |
| The middle convolution is $\mathcal W_n$ on the line | statement | proposition 2.97 | arxiv |
| The rank-two Kloosterman local calculation | statement | theorem 1.3 | arxiv |
| Alternative weight-gap proof of infinitude | statement | theorem 2.102 | arxiv |
| WG91KEMX7V | statement | proposition 2.19 | arxiv |
| Excision and the top-weight quotient | statement | proposition 1.13 | arxiv |
| Geometric monodromy of the rank-two Kloosterman sheaf | statement | proposition 1.4 | arxiv |
| Case (D) at $n=5$ | statement | proposition 2.44 | arxiv |
| The family is a multiplicative convolution | statement | lemma 2.91 | arxiv |
| Tame dimension from the smallest break | statement | lemma 2.55 | arxiv |
| YTF9J3PK4J | statement | lemma 2.17 | arxiv |
| Non-self-duality | statement | proposition 2.83 | arxiv |
| Conductor of the symmetric powers | statement | corollary 2.106 | arxiv |
| Connected geometric monodromy | statement | theorem 2.116 | arxiv |
| Generic stratum: sharp projective-ray bound | statement | theorem 2.21 | arxiv |
