| The gain of a Jacobi matrix | statement | theorem 2.2 | arxiv |
| Exactness at a self-consistent reference | statement | proposition 5 | arxiv |
| The calibration constant | statement | lemma 9 | arxiv |
| Ground state | statement | theorem 3.1 | arxiv |
| Green energy of the Chebyshev fiber | statement | theorem 1.1 | arxiv |
| One measure for all filters | statement | theorem 3.3 | arxiv |
| Dual certificates bound the energy | statement | theorem 3.6 | arxiv |
| Continuity of the comparison filters | statement | lemma 13 | arxiv |
| Polynomial translation | statement | lemma 23 | arxiv |
| Cubic conjugate | statement | lemma 15 | arxiv |
| The centering lift | statement | theorem A.1 | arxiv |
| Quadrature | statement | lemma 20 | arxiv |
| Derivatives of the primal family | statement | proposition 13 | arxiv |
| Regularity of the comparison density | statement | lemma 10 | arxiv |
| Near-optimality of the sine--Jacobi method | statement | theorem 1.2 | arxiv |
| Exact base identity | statement | proposition 4 | arxiv |
| Removing a cubic zero | statement | lemma 22 | arxiv |
| Properties of the sine density | statement | proposition 2 | arxiv |
| Two cancellation identities | statement | lemma 17 | arxiv |
| Transfer of an admissible certificate | statement | theorem E.1 | arxiv |
| Uniform spectral transfer | statement | theorem 2.4 | arxiv |
| Computed values for the primal certificate | statement | proposition 11 | arxiv |
| Spectral values of a symmetric density | statement | lemma 14 | arxiv |
| The sine--Jacobi matrices | statement | theorem 2.5 | arxiv |
| Dual certificate | definition | definition 7 | arxiv |
| Recurrences and Jacobi matrices | statement | theorem 2.1 | arxiv |
| Comparison density | definition | definition 6 | arxiv |
| Upper bounds on a box | statement | lemma 24 | arxiv |
| Pointwise criterion | statement | theorem 3.5 | arxiv |
| The positive cubic root | statement | lemma 19 | arxiv |
| Parametrization of the state region | statement | lemma 8 | arxiv |
| Gradients of the observations | statement | lemma 26 | arxiv |
| Green factorization | statement | lemma 3 | arxiv |
| Signed comparisons | statement | theorem 3.4 | arxiv |
| Jet recurrences | statement | lemma 18 | arxiv |
| States | definition | definition 5 | arxiv |
| Densities with a prescribed ground parameter | statement | theorem 5.1 | arxiv |
| A finite sum for the sine energy | statement | lemma 7 | arxiv |
| No locally sharp $C^1$ bound from finitely many observations | statement | theorem 6.1 | arxiv |
| Feature operators | statement | lemma 4 | arxiv |
| Calibration | definition | definition 4 | arxiv |
| Observations and the relaxed class | definition | definition 3 | arxiv |
| Contact potential | statement | theorem 3.2 | arxiv |
| Admissibility and value | definition | definition 8 | arxiv |
| The state region | statement | proposition 7 | arxiv |
| Right filters | statement | lemma 11 | arxiv |
| Uniform bound for the sine diagonal | statement | lemma 6 | arxiv |
| Comparison with a comparison profile | statement | lemma 12 | arxiv |
| Derivative of the terminal residual | statement | lemma 2 | arxiv |
| The certified constant | statement | corollary 2 | arxiv |
| Primal certificates define feasible densities | statement | theorem 5.2 | arxiv |
| Integrating the residual | statement | proposition 8 | arxiv |
| Computed values for $\Theta_{\mathrm{cert}}$ | statement | proposition 9 | arxiv |
| Symmetric perturbations | statement | corollary 1 | arxiv |
| The sine density | definition | definition 2 | arxiv |
| The sine energy | statement | proposition 10 | arxiv |
| Exponential representation | statement | proposition 1 | arxiv |
| Spectral identities of the fiber | statement | lemma 1 | arxiv |
| The range of three filters | statement | proposition 12 | arxiv |
| Terminal-exact recurrences and their gain | definition | definition 1 | arxiv |
| A feasible density below the sine energy | statement | corollary 3 | arxiv |
| The continuum sine kernel | statement | lemma 5 | arxiv |
| Comparison profiles | definition | definition 10 | arxiv |
| Primal certificate | definition | definition 9 | arxiv |
| Y9M86WYG0M | statement | theorem 2.3 | arxiv |
| The normalized criterion | statement | lemma 16 | arxiv |
| A one-determinant lower bound | statement | proposition 6 | arxiv |
| Exact feasibility by contraction | statement | lemma 25 | arxiv |
| A validated flow step | statement | lemma 21 | arxiv |
| Filters | statement | proposition 3 | arxiv |
