| Finite branched continued fractions | statement | corollary 2.10 | arxiv |
| Compatibility of the finite Metelmann factorizations | statement | lemma 2.18 | arxiv |
| A semi-infinite obstruction from inverse entries | statement | corollary 2.19 | arxiv |
| Generating functions for the full Toeplitz class | statement | theorem 3.2 | arxiv |
| Behavior of all density entries at zero | statement | theorem 3.19 | arxiv |
| Density near the endpoints | statement | proposition 3.11 | arxiv |
| Refactorization of a fixed lower product, row by row | statement | lemma 2.4 | arxiv |
| Spectral transition and first-return formulas | statement | proposition 4.2 | arxiv |
| Finite-section PBFs, global obstruction, and norm approximation | statement | theorem 2.17 | arxiv |
| Finite BTP equals PBF | statement | theorem 2.6 | arxiv |
| Initial parameters for all positive factorizations | statement | proposition 2.7 | arxiv |
| Centering and the upper spectral endpoint | statement | proposition 4.3 | arxiv |
| Toeplitz characterization and global PBF | statement | theorem 2.36 | arxiv |
| Inverse minors and a uniform bound | statement | lemma 2.22 | arxiv |
| Approximation by perturbing an initial block | statement | theorem 2.31 | arxiv |
| A determinant formula for one-factor extraction | statement | lemma 2.24 | arxiv |
| A conservative positive harmonic transform | statement | proposition 4.4 | arxiv |
| Finite root formula for the resolvent | statement | theorem 3.7 | arxiv |
| The criterion for arbitrary lower and upper bandwidths | statement | corollary 2.26 | arxiv |
| Eventually constant Metelmann parameters | statement | proposition 2.29 | arxiv |
| Application of the spectral Favard theorem | statement | corollary 3.4 | arxiv |
| Jacobi fractions for the inverse-minor ratios | statement | proposition 2.23 | arxiv |
| H05F0X1TBN | statement | theorem 3.13 | arxiv |
| PBF implies BTP, recalled | statement | proposition 2.1 | arxiv |
| $\tau$-Vandermonde--Pfaff convolution | statement | lemma 3.21 | arxiv |
| Upper endpoint | statement | proposition 3.20 | arxiv |
| Classical oscillation and spectrum | statement | corollary 2.3 | arxiv |
| Positive upper--lower exchange | statement | lemma 2.35 | arxiv |
| Orthogonality of mixed type for every ordered partition of roots | statement | corollary 3.6 | arxiv |
| NQSS5H7HC0 | statement | lemma 3.17 | arxiv |
| Essential spectrum and an initial resolvent block | statement | proposition 2.33 | arxiv |
| Root separation and a support bound | statement | theorem 3.8 | arxiv |
| Finite coefficient formulas | statement | corollary 3.3 | arxiv |
| Global positive factorization in arbitrary lower bandwidth | statement | theorem 2.25 | arxiv |
| QZVNJVSAM0 | statement | theorem 3.15 | arxiv |
| Binomial specialization | statement | corollary 3.14 | arxiv |
| Algebraic rank-one measure | statement | theorem 3.9 | arxiv |
| Factorization and polynomials for geometrically spaced roots | statement | proposition 3.22 | arxiv |
| Metelmann characterization, recalled | statement | proposition 2.2 | arxiv |
| Determining successive factors by linear recurrences | statement | proposition 2.9 | arxiv |
| Killed Poisson-binomial walks | statement | proposition 4.1 | arxiv |
| The initial-condition matrices and their inverses | statement | lemma 3.1 | arxiv |
| Strictly decreasing inverse-entry bounds | statement | proposition 2.15 | arxiv |
| XPVQBN0HMW | statement | proposition 3.12 | arxiv |
| Change of factorization and normalization | statement | corollary 3.5 | arxiv |
| Explicit algebraic measure for the deformation | statement | corollary 3.23 | arxiv |
| Algebraic matrix weight | statement | theorem 3.18 | arxiv |
