| Normalized tilted Fourier integral | statement | lemma 6.16 | arxiv |
| Quadratic lower-tail bound over $\R$ and $\C$ | statement | theorem 1.3 | arxiv |
| Complex projection and geometric estimates | statement | lemma 7.1 | arxiv |
| Original and reference observation laws | definition | definition 6.1 | arxiv |
| Singular-value energy and small-value count | statement | lemma 6.13 | arxiv |
| Pointwise density bound with coordinate-weight error | statement | lemma 6.15 | arxiv |
| Delete concentrated coordinates after the queries | definition | definition 6.6 | arxiv |
| Smooth Gaussian replacement and score | statement | lemma 2.3 | arxiv |
| Complex good-core border probability | statement | proposition 7.6 | arxiv |
| The reference for a fixed candidate | definition | definition 6.3 | arxiv |
| Annealed flat-sphere asymptotics | statement | lemma 2.7 | arxiv |
| Gaussian border bound in terms of Hessenberg links | statement | lemma 5.6 | arxiv |
| Coarse and weighted observation comparison | statement | theorem 6.2 | arxiv |
| Coordinate-volume loss | definition | definition 6.8 | arxiv |
| Evaluation determinant and choice of nodes | statement | lemma 5.10 | arxiv |
| Complex observation comparison | statement | theorem 7.3 | arxiv |
| Few deletions suffice to flatten the queries | statement | proposition 6.7 | arxiv |
| Canonical projection bound | statement | lemma 6.11 | arxiv |
| Two-stage border negative moment | statement | lemma 5.11 | arxiv |
| Sequential Gaussian coupling | statement | lemma 6.17 | arxiv |
| Regularized bulk events | statement | lemma 2.2 | arxiv |
| Two-dimensional tilt and projection bounds | statement | lemma 7.2 | arxiv |
| Prefix and suffix evaluation matrices | definition | definition 5.9 | arxiv |
| Triangular coupling | statement | lemma 2.4 | arxiv |
| Original-law weighted links | statement | proposition 5.2 | arxiv |
| Full spectral-radius large deviation principle | statement | theorem 1.6 | arxiv |
| Exact reconstruction and the comparison inputs | statement | lemma 6.4 | arxiv |
| Matching upper-tail rates | statement | theorem 1.2 | arxiv |
| Volume loss for independent columns | statement | lemma 6.9 | arxiv |
| Gaussian power-moment asymptotics | statement | corollary 3.4 | arxiv |
| Inverse Gram moments | statement | corollary 6.12 | arxiv |
| Universal lower bound for upper deviations | statement | theorem 1.1 | arxiv |
| A nilpotent core with strong links | example | example 5.4 | arxiv |
| Gaussian third moments and a random variance sum | statement | lemma 6.18 | arxiv |
| Convex concentration for independent blocks | statement | lemma 2.1 | arxiv |
| Hessenberg cofactor factorization | statement | lemma 5.8 | arxiv |
| Entropy gain for the observation likelihood | statement | lemma 6.19 | arxiv |
| Arnoldi queries of the core | definition | definition 5.1 | arxiv |
| Annealed full-sphere bound | statement | lemma 3.1 | arxiv |
| Original-law complex links | statement | proposition 7.4 | arxiv |
| Local eigenvalue deviations in the complex exterior | statement | theorem 1.7 | arxiv |
| Gaussian inverse moments for conjugate-paired values | statement | lemma 5.7 | arxiv |
| Mixed reference links | statement | lemma 6.5 | arxiv |
| Conditional real Schur distribution | statement | fact 3.2 | arxiv |
| Conditional Schur power bound | statement | lemma 3.3 | arxiv |
| Spherical integral identity and bounds | statement | lemma 2.6 | arxiv |
| Good-core border probability | statement | proposition 5.3 | arxiv |
| Hessenberg form of the core | statement | fact 5.5 | arxiv |
| Capped coordinate-weight exponential moment | statement | lemma 6.10 | arxiv |
| Complex Gaussian inverse determinants | statement | lemma 7.5 | arxiv |
| Exact observation likelihood | statement | lemma 6.14 | arxiv |
