| Confinement | statement | lemma F.8 | arxiv |
| The field | statement | lemma C.1 | arxiv |
| The dual function | statement | lemma A.9 | arxiv |
| Radial Schur complement | statement | lemma E.7 | arxiv |
| Spectral gap and inverse at a strictly stable profile | statement | lemma D.2 | arxiv |
| Annealed upper bound for SUSY states | statement | proposition E.18 | arxiv |
| The variational gap at equilibrium | statement | lemma 6.3 | arxiv |
| The Hessian bulk at localized points | statement | proposition 4.2 | arxiv |
| A monotone glued coefficient gains nothing | statement | lemma 3.4 | arxiv |
| The index window cannot be widened | statement | proposition D.15 | arxiv |
| Every level is regular | statement | proposition A.11 | arxiv |
| Expected marked count | statement | lemma E.15 | arxiv |
| Standing estimates | statement | corollary F.9 | arxiv |
| Fractional moments for convex mixtures | statement | proposition 2.9 | arxiv |
| Band step | statement | lemma 2.7 | arxiv |
| Regularity at the contact set | statement | lemma A.14 | arxiv |
| The TAP correction | statement | lemma D.5 | arxiv |
| Capped diagonal | statement | corollary D.8 | arxiv |
| Reflected Pastur laws | statement | lemma 4.1 | arxiv |
| Gradient and one-sided Hessians of the TAP function | statement | lemma D.7 | arxiv |
| Gap exclusion | statement | lemma F.7 | arxiv |
| The perturbed terminal | statement | lemma B.5 | arxiv |
| Values at the selected data | statement | lemma E.11 | arxiv |
| Comparison of covariances | statement | lemma G.5 | arxiv |
| Spectral facts | statement | lemma E.19 | arxiv |
| Upper band | statement | proposition 2.2 | arxiv |
| Measurable majorant | statement | corollary B.7 | arxiv |
| Constrained minimizers | statement | lemma A.10 | arxiv |
| Diagonals in shrinking windows | statement | lemma E.24 | arxiv |
| Onsager shift | statement | lemma B.2 | arxiv |
| Test functions | statement | lemma B.8 | arxiv |
| An annealed determinant bound without a spectral gap | statement | lemma E.25 | arxiv |
| Pure even covariances | statement | proposition G.3 | arxiv |
| Under every tilt | statement | corollary 2.3 | arxiv |
| Field-law tilt | statement | lemma E.3 | arxiv |
| The upper tail of the TAP maximum | statement | proposition C.6 | arxiv |
| Stability | statement | lemma A.5 | arxiv |
| Uniformity under bounded tilts | statement | lemma D.10 | arxiv |
| AP8TFY3SQ2 | definition | definition | arxiv |
| A second route to the fractional-moment formula | statement | corollary G.4 | arxiv |
| Uniform spectral estimate | statement | lemma D.11 | arxiv |
| Jets and their stability | statement | lemma F.3 | arxiv |
| Cascade domination | statement | lemma B.3 | arxiv |
| Window facts | statement | lemma E.22 | arxiv |
| Order parameters of near-optimal states | statement | proposition 4.5 | arxiv |
| Stability in the order parameter | statement | lemma D.6 | arxiv |
| TAP values at small self-overlap | statement | lemma C.9 | arxiv |
| The obstacle is minimal at the origin | statement | lemma 6.2 | arxiv |
| The edge of the bulk | statement | lemma 4.3 | arxiv |
| Marginal first contacts near criticality | statement | proposition F.1 | arxiv |
| Conditional third derivatives | statement | lemma E.8 | arxiv |
| Positive overlap of near-maximizers | statement | proposition C.8 | arxiv |
| Conditional block representation | statement | lemma E.6 | arxiv |
| Critical points of the fixed TAP function | statement | proposition E.1 | arxiv |
| Retained states are subexponentially many given existence | statement | proposition E.26 | arxiv |
| Energy shift | statement | lemma E.4 | arxiv |
| Marked Kac--Rice formula | statement | lemma E.12 | arxiv |
| Near-minimizers of the band problem | statement | lemma D.14 | arxiv |
| Ramsey multiplicity | statement | lemma 2.6 | arxiv |
| Class preservation and regularity | statement | lemma A.1 | arxiv |
| The perturbed models | statement | lemma G.6 | arxiv |
| Inverse fields up to the boundary | statement | lemma E.5 | arxiv |
| Spherical code | statement | lemma E.16 | arxiv |
| Lower band | statement | proposition 2.1 | arxiv |
| Two estimates near the critical pair | statement | lemma F.5 | arxiv |
| Relaxed variational gap | statement | proposition 3.3 | arxiv |
| Rate of the selected data | statement | lemma E.14 | arxiv |
| The band theorem at every exponential rate | statement | lemma 2.5 | arxiv |
| First-order conditions at equilibrium | statement | lemma 6.1 | arxiv |
| Strict Hessian bound around a conditioned critical point | statement | proposition E.9 | arxiv |
| The fixed order parameter is nearly optimal near a contact | statement | corollary D.13 | arxiv |
| The Hessian of the Gaussian field | statement | lemma D.3 | arxiv |
| The perturbing field | statement | lemma G.7 | arxiv |
| A priori bounds | statement | lemma C.2 | arxiv |
| The marks | statement | lemma E.13 | arxiv |
| Logarithmic potential at the edge | statement | lemma E.21 | arxiv |
| Measurable coefficients | statement | lemma A.7 | arxiv |
| Logarithmic law of large numbers | statement | lemma E.20 | arxiv |
| The first contact | statement | lemma E.2 | arxiv |
| Terminal sandwich | statement | lemma A.4 | arxiv |
| Perturbed Fenchel terminal values | statement | lemma A.8 | arxiv |
| Separation of retained points | statement | lemma E.17 | arxiv |
| Tangent bound | statement | lemma B.9 | arxiv |
| Contact conditions | statement | lemma F.6 | arxiv |
| The band problem at a contact | statement | lemma D.12 | arxiv |
| Shifted Poisson points with independent marks | statement | lemma B.1 | arxiv |
| Conditional comparison and a quadratic gap | statement | lemma E.10 | arxiv |
| The constrained minimizer and its obstacle | statement | lemma 3.1 | arxiv |
| Glued comparison on a sphere or a shell | statement | proposition 3.2 | arxiv |
| Bulk marginality at degenerate contacts | statement | corollary 4.8 | arxiv |
| Continuity, attainment and interiority | statement | lemma C.3 | arxiv |
| Exact criticality | statement | lemma C.4 | arxiv |
| Coefficient sandwich | statement | lemma A.3 | arxiv |
| Annealed count of SUSY states | statement | proposition 5.3 | arxiv |
| Index form of the bulk | statement | proposition 4.6 | arxiv |
| Every contact is marginal | statement | lemma 5.4 | arxiv |
| SUSY states | definition | definition 5.2 | arxiv |
| Structure of the conditional Hessian | statement | lemma E.23 | arxiv |
| Calculus of $\Gamma$ | statement | lemma F.4 | arxiv |
| Guerra's bound for fractional moments | statement | lemma G.1 | arxiv |
| The edge hypothesis for the Parisi variables | statement | lemma D.9 | arxiv |
| Auffinger--Chen process and verification | statement | lemma A.2 | arxiv |
| Approximation by step data | statement | lemma B.6 | arxiv |
| Gaussian comparison and the resolvent equation | statement | lemma D.1 | arxiv |
| The Parisi functional on step coefficients | statement | corollary A.6 | arxiv |
