| Geodesic convexity of both inverse terms | statement | corollary 5.7 | arxiv |
| Centered variational problem and capacity | statement | theorem 11.2 | arxiv |
| Exact identity on normalized triples | statement | proposition 4.1 | arxiv |
| $\mathcal C$ maps geodesics to geodesics | statement | lemma 5.4 | arxiv |
| 3FNSF5NXT7 | problem | problem 1 | arxiv |
| Boundary values are invertible | statement | lemma 9.6 | arxiv |
| Perron--Frobenius description of the feasible set | statement | lemma 5.1 | arxiv |
| Geodesic log-convexity of the normalized covariance | statement | lemma 5.5 | arxiv |
| Unitary normalizer | definition | definition 6.1 | arxiv |
| Inverse of a shifted operator geodesic | statement | lemma 5.6 | arxiv |
| Limit of the regularized normalizers | statement | proposition 9.2 | arxiv |
| Centered problem and capacity | statement | theorem 1.4 | arxiv |
| Real and imaginary parts of the balanced Dyson equation | statement | lemma 6.4 | arxiv |
| 64E5HSHXKC | problem | problem 4 | arxiv |
| Eliminating the multiplier enforces feasibility | statement | proposition 5.2 | arxiv |
| Characterization of the value $-\infty$ | statement | corollary 8.2 | arxiv |
| Attainment at nondegenerate regular points | statement | corollary 9.3 | arxiv |
| Location of the minimizer | statement | proposition 9.4 | arxiv |
| Local regularity at non-atomic points | statement | theorem B.3 | arxiv |
| BMMYMAZHBP | problem | problem 2 | arxiv |
| The regularized partial supremum | statement | proposition 7.1 | arxiv |
| Balanced Dyson equations | statement | corollary 6.5 | arxiv |
| Mai--Speicher formula | statement | corollary 11.3 | arxiv |
| Unitary normalization and strict feasibility | statement | lemma 7.2 | arxiv |
| Capacity of a doubly stochastic map | statement | lemma 11.1 | arxiv |
| Local Puiseux control | statement | lemma B.1 | arxiv |
| $pUp$ factorization | statement | lemma 6.2 | arxiv |
| JE8JSVB6E5 | problem | problem 5 | arxiv |
| Geodesic Hessian of $F_z$ | statement | proposition 5.8 | arxiv |
| Real-axis variational identity | statement | theorem 8.1 | arxiv |
| Radial approximation of boundary values | statement | lemma 5.3 | arxiv |
| Closed determinant identity | statement | theorem 3.1 | arxiv |
| First variation of the regularized objective | statement | proposition 7.3 | arxiv |
| Nondegenerate regular point | definition | definition 1.2 | arxiv |
| Attainment at a positive definite cluster point | statement | proposition 9.1 | arxiv |
| Attainment at nondegenerate regular points | statement | theorem 1.3 | arxiv |
| Variational formula at every real point | statement | theorem 1.1 | arxiv |
| Atoms and the exponent one | statement | lemma B.2 | arxiv |
| Degenerate points filling the support | example | example 9.8 | arxiv |
| Brown measure of matrix-valued semicircular elements | statement | corollary 1.5 | arxiv |
| Regularized variational identity | statement | theorem 7.5 | arxiv |
| Brown measure of matrix-valued semicircular elements | statement | corollary 10.1 | arxiv |
| Geodesic convexity | statement | corollary 7.4 | arxiv |
| ZH37007X2M | problem | problem 3 | arxiv |
