| Symmetric output from a larger nonsymmetric input | statement | corollary 14.13 | arxiv |
| Nutz--Wang--Zhang inputs | statement | proposition 11.23 | arxiv |
| One Gaussian event for every unitarily invariant norm | statement | theorem 1.8 | arxiv |
| Simultaneous singular-value domination | statement | lemma 8.4 | arxiv |
| Exact fixed-reference extraction | statement | theorem 14.6 | arxiv |
| An extreme coupling on two circles | statement | lemma 11.10 | arxiv |
| The score under coordinate rearrangement | statement | theorem 19.7 | arxiv |
| Explicit nonproduct energy gap | statement | theorem 20.4 | arxiv |
| Bounded differences in full convex order | statement | theorem 4.16 | arxiv |
| An infinite release with bounded conditional information cost | statement | theorem 28.16 | arxiv |
| Sharp Gaussian reference for Haar frames | statement | corollary 22.11 | arxiv |
| Conditionally atomless data | statement | corollary 29.2 | arxiv |
| Recovery by compact interior competitors | statement | lemma 17.7 | arxiv |
| Realization of permitted directing means | statement | theorem 24.8 | arxiv |
| L\'evy-reference realization | statement | theorem 17.24 | arxiv |
| Exponential score moments on bounded supports | statement | proposition 19.22 | arxiv |
| Strict improvement by an endpoint perturbation | statement | proposition 3.15 | arxiv |
| Compactness of the admissible laws | statement | lemma 19.4 | arxiv |
| Explicit dimension-comparable estimate | statement | proposition 9.9 | arxiv |
| A singular source with infinite source mutual information | example | example 28.26 | arxiv |
| Limits of conditional kernels | statement | lemma 11.16 | arxiv |
| Backward Monge density with a common parameter | statement | theorem 11.6 | arxiv |
| Counting and equal-trace subsampling | statement | corollary 7.11 | arxiv |
| Wiener space | statement | corollary 14.17 | arxiv |
| Compact densities with matching score marginals | statement | theorem 19.15 | arxiv |
| Joint matrix and scalar balancing | statement | theorem 7.5 | arxiv |
| Exact criterion for cosine optimality | statement | theorem 20.3 | arxiv |
| Adaptive bounded variables and a Poisson reference | statement | theorem 4.7 | arxiv |
| Logarithmic radius formula | statement | proposition D.1 | arxiv |
| An independent component gives a dimension-free gap | statement | corollary 26.6 | arxiv |
| Sharp comparison for bounded martingale increments | statement | corollary 4.11 | arxiv |
| A uniform distance from compact Gaussian operators | statement | corollary 13.12 | arxiv |
| Full posterior entropy identity | statement | theorem 23.8 | arxiv |
| Scaled adjacent boxes | statement | corollary 5.7 | arxiv |
| 34FVYJZ3GB | statement | theorem 27.2 | arxiv |
| A linear conditional eigenvalue with full support | statement | proposition 25.3 | arxiv |
| Finite initial law and full conditional communication | statement | lemma 16.6 | arxiv |
| Every exponent strictly between zero and one | example | example 23.22 | arxiv |
| 3713MFWHRV | statement | lemma D.2 | arxiv |
| Finite balanced-tree endpoint | statement | theorem 5.13 | arxiv |
| Akbas--Sra interpolation estimate | statement | lemma 8.8 | arxiv |
| Quadrature with hard feature constraints | statement | theorem 6.6 | arxiv |
| Conditional maximal coupling | statement | lemma 28.1 | arxiv |
| A vector regression from field symmetries | statement | lemma 23.11 | arxiv |
| Inhomogeneous vector balancing | statement | corollary 19.18 | arxiv |
| Deterministic garbling after strict attenuation | statement | theorem 30.3 | arxiv |
| Deterministic realization of the joint signing law | statement | corollary 10.5 | arxiv |
| Common-noise stability of optimal maps | statement | lemma 18.22 | arxiv |
| A continuous cost with no deterministic minimizer | example | example 10.13 | arxiv |
| Binary utility and Bayes error | statement | corollary 26.9 | arxiv |
| Greatest full-data private releases | statement | theorem 1.13 | arxiv |
| Retained body under a first-moment score hypothesis | statement | theorem 19.1 | arxiv |
| 41NCGWGJWQ | statement | theorem 22.6 | arxiv |
| Two Gaussian summands are insufficient | statement | proposition 15.12 | arxiv |
| Gaussian endpoint and nonattainment | statement | theorem 28.13 | arxiv |
| 452J0C6SFE | statement | lemma 30.6 | arxiv |
| An exact non-Gaussian convolution model | example | example 17.27 | arxiv |
| Gaussian chords in a star-shaped set | statement | lemma 15.17 | arxiv |
| Convex support retained for the whole path | statement | corollary 15.14 | arxiv |
| Bounded-time Skorokhod embedding | statement | corollary 15.13 | arxiv |
| Sharp Gaussian scale | statement | proposition 14.3 | arxiv |
| Local realization of conditional means | statement | lemma 10.8 | arxiv |
| Continuity of maximal covariance | statement | lemma 17.5 | arxiv |
| 4HKANVBW6J | statement | lemma 2.2 | arxiv |
| Three-point convex combinations with dilation two | statement | corollary 15.10 | arxiv |
| Strict terminal inflation | statement | corollary 17.25 | arxiv |
| Compactness and positive curvature | statement | lemma 18.3 | arxiv |
| Sharp calibration of the universal reference | statement | theorem 20.11 | arxiv |
| Strict attenuation can be necessary for an exact output law | example | example 30.4 | arxiv |
| The bounded joint reference | statement | theorem 2.6 | arxiv |
| Symmetric matrices and spectrahedra | statement | corollary 9.8 | arxiv |
| Unbiased Marcinkiewicz--Zygmund discretization | statement | corollary 7.15 | arxiv |
| Uniform compactness after Gaussian smoothing | statement | lemma 18.14 | arxiv |
| Ellipsoidal Gaussian references | statement | corollary 4.12 | arxiv |
| 54QCJFAYBV | statement | proposition 30.19 | arxiv |
| Hermite eigenfunctions and the Gaussian power spectrum | statement | corollary 13.7 | arxiv |
| Rectangular real and complex matrices | statement | corollary 8.14 | arxiv |
| A common conditional support | statement | lemma 17.4 | arxiv |
| Five summands below half Gaussian mass | statement | theorem 1.5 | arxiv |
| Exact references and a local stationary obstruction | statement | theorem 25.6 | arxiv |
| Both marginals and the driving law | statement | corollary 1.11 | arxiv |
| Outer approximation of the weighted eigenvalue | statement | lemma 21.3 | arxiv |
| Local conditional information cost | statement | theorem 26.10 | arxiv |
| Grouping refined labels | statement | lemma 30.10 | arxiv |
| One prescribed-mean law for every Schatten norm | statement | theorem 1.7 | arxiv |
| 610HZEPTN3 | statement | lemma 24.3 | arxiv |
| Top-gap version for a finite alphabet | statement | proposition 23.25 | arxiv |
| Complete empirical-mean limit set | statement | theorem 24.6 | arxiv |
| The two observation models have different greatest elements | statement | corollary 29.15 | arxiv |
| Contact normalization | statement | lemma 9.4 | arxiv |
| 6J5DMKYFMT | statement | theorem 26.1 | arxiv |
| Refinement completion | statement | theorem 30.9 | arxiv |
| Solid sets | statement | corollary 14.14 | arxiv |
| Conditional Gaussian residuals at stopping times | statement | theorem 15.6 | arxiv |
| Smooth finite-family obstruction | statement | theorem 30.20 | arxiv |
| Fair PSD partition input | statement | lemma 7.9 | arxiv |
| Sharp entropy deficit at the Gaussian endpoint | statement | theorem 1.3 | arxiv |
| 759J56PB01 | statement | theorem 27.6 | arxiv |
| Gaussian rounding on an integral base polyhedron | statement | theorem 5.4 | arxiv |
| Unique finite partition and quantitative complementarity | statement | theorem 19.11 | arxiv |
| Explicit counts above Gaussian mass one half | statement | corollary 15.11 | arxiv |
| Complementary bases at a midpoint | statement | lemma 5.8 | arxiv |
| A coupling to one repeated bit | statement | corollary 24.10 | arxiv |
| Exponential convergence on a bounded trajectory | statement | proposition 18.12 | arxiv |
| A distribution-free Gaussian channel | statement | theorem 20.9 | arxiv |
| Smooth indistinguishability | statement | corollary 31.11 | arxiv |
| Gaussian comparison for adaptive increments | statement | theorem 4.8 | arxiv |
| Irreducibility is the exact criterion for positive references | statement | proposition 17.15 | arxiv |
| A general sharp quadratic height inequality | statement | theorem 3.12 | arxiv |
| 7SVBTSJJM9 | statement | theorem 24.1 | arxiv |
| Backward Monge realization of a discrete target | statement | corollary 10.2 | arxiv |
| Quadratic dual rigidity | statement | theorem 12.2 | arxiv |
| A common radial profile | statement | theorem 19.14 | arxiv |
| Hua--Song--Tudose | statement | theorem 14.9 | arxiv |
| Compact elliptic diffusions from deterministic stationary maps | statement | theorem 13.15 | arxiv |
| Universal finite potentials and the $q$-Bass existence criterion | statement | theorem 17.12 | arxiv |
| The cycle transportation value | statement | lemma 30.11 | arxiv |
| Exact comparison for a fixed singular-value orbit | statement | theorem 22.10 | arxiv |
| Dyadic reconstruction | statement | theorem 19.9 | arxiv |
| Optimal discrepancy--Gaussian tradeoff | statement | theorem 1.2 | arxiv |
| Parity of the inverse | statement | proposition 31.9 | arxiv |
| Directional and distributional inverses | statement | lemma 31.2 | arxiv |
| Approximate cyclic comparisons | statement | lemma 30.13 | arxiv |
| Coupling the marginals | statement | theorem 6.5 | arxiv |
| Fixed-terminal stability under conditional means and contraction | statement | theorem 16.3 | arxiv |
| Gaussian simplex frontier to second order | statement | theorem 23.26 | arxiv |
| Coordinate rounding | statement | theorem 2.1 | arxiv |
| average score to exact product calibration | statement | theorem 23.13 | arxiv |
| Adaptive covariance completion | statement | lemma 5.9 | arxiv |
| Positive anticommutator factorization | statement | lemma 8.3 | arxiv |
| Reference stability | statement | theorem 17.17 | arxiv |
| Gaussian projection | statement | proposition 3.1 | arxiv |
| Compact inputs at the mass endpoint | statement | corollary 14.11 | arxiv |
| Deterministic conditional correction | statement | lemma 28.7 | arxiv |
| Every positive input mass | statement | corollary 15.21 | arxiv |
| 9FDXF54FZF | statement | corollary 30.7 | arxiv |
| 9FZTFCJV9A | statement | proposition A.2 | arxiv |
| Smooth covariance-preserving privacy instability | statement | theorem 28.19 | arxiv |
| Unrestricted curvature-controlled contraction and deficit | statement | theorem 17.19 | arxiv |
| 9WRQEFRX1F | statement | corollary 24.5 | arxiv |
| Exponential Bass flow in every dimension | statement | theorem 18.9 | arxiv |
| Uniform integrability with fixed marginals | statement | lemma 11.24 | arxiv |
| Arbitrarily small inflation of an atomless reference | statement | corollary 11.4 | arxiv |
| The exact two-step transition | statement | corollary 27.4 | arxiv |
| Every symmetric scalar source | statement | corollary 23.3 | arxiv |
| Exact output law and prescribed moment attenuation | statement | theorem 10.11 | arxiv |
| Coisometry and information contraction | statement | proposition 13.9 | arxiv |
| Uniform continuity at exact privacy | statement | theorem 28.3 | arxiv |
| The Smirnov--Vershynin Fisher-information capacity | statement | corollary 20.7 | arxiv |
| Interior coercivity | statement | lemma 18.15 | arxiv |
| Simultaneous rounding in arbitrary matrix dimension | statement | theorem 8.12 | arxiv |
| Beck--Fiala with a complete reference | statement | corollary 3.9 | arxiv |
| Directional entropy measurements determine a vector law | statement | corollary 23.19 | arxiv |
| One Gaussian event for every unitarily invariant norm | statement | theorem 8.2 | arxiv |
| Exact replica entropy identity | statement | theorem 3.4 | arxiv |
| Stability of the optimal martingale coupling | statement | corollary 18.25 | arxiv |
| Exact entropy rate | statement | corollary 24.7 | arxiv |
| History-indexed kernels and finite horizons | statement | corollary 11.15 | arxiv |
| Global product-reference entropy frontier | statement | theorem 23.1 | arxiv |
| AXGJXV5JAP | statement | theorem 26.2 | arxiv |
| Upper-quantile submeasure | statement | lemma 11.20 | arxiv |
| Cost approximation under the supermartingale constraint | statement | corollary 11.26 | arxiv |
| Conditional attainment | statement | theorem 17.8 | arxiv |
| An a posteriori primal--dual certificate | statement | corollary 16.11 | arxiv |
| BEK934B7QP | statement | theorem 22.3 | arxiv |
| A whole Brownian history encoded in its later Gaussian reference | statement | corollary 13.2 | arxiv |
| Affine rounding | statement | corollary 2.3 | arxiv |
| The spectral limit for arbitrary joint references | statement | theorem 20.10 | arxiv |
| Linear-size refinement witness | statement | theorem 30.12 | arxiv |
| Canonical source tests | statement | corollary 30.17 | arxiv |
| BMWVWDMV1P | statement | lemma 6.2 | arxiv |
| Boundary atoms with at most $2^q$ queries | statement | theorem 31.5 | arxiv |
| Fivefold Gaussian convexity below half mass | statement | theorem 15.16 | arxiv |
| Every finite logarithmic zero-budget value | statement | corollary 28.21 | arxiv |
| A gap above zero | statement | theorem 23.23 | arxiv |
| Exact reverse randomness and failure at the endpoint | statement | corollary 11.12 | arxiv |
| BTS8N8BBRG | statement | theorem 27.11 | arxiv |
| Gaussian optimality for the quadratic coefficient | statement | theorem 3.13 | arxiv |
| Mixed weighted products | statement | theorem 21.1 | arxiv |
| Exact feasible correlation polytope | statement | lemma 26.7 | arxiv |
| Duality before the nondegeneracy assumption | statement | proposition 17.3 | arxiv |
| Four-wise independence bounds the diagonal radius | statement | proposition 19.16 | arxiv |
| A smooth positive minorant | statement | lemma 18.2 | arxiv |
| A multidimensional second-variation bound | statement | lemma 18.6 | arxiv |
| A bounded Bass measure | statement | proposition 18.16 | arxiv |
| Directional backward Monge density | statement | theorem 11.21 | arxiv |
| Gaussian and log-concave thresholds | statement | corollary 14.7 | arxiv |
| Extension across the chamber boundary | statement | lemma 31.3 | arxiv |
| What the full-support mixture preserves | statement | proposition 25.1 | arxiv |
| Spectral minimax | statement | theorem 20.2 | arxiv |
| Outward dilation and an exact product component | statement | lemma 11.14 | arxiv |
| CKSFTR7GXD | statement | proposition 24.2 | arxiv |
| Positive families of asymptotically optimal reference laws | statement | theorem 23.16 | arxiv |
| CM2EZK6X8Q | statement | corollary 3.2 | arxiv |
| Exact Gaussian integer rounding | statement | theorem 4.9 | arxiv |
| Posterior covariance matrices | statement | corollary 29.11 | arxiv |
| Identification from accumulating entropy scales | statement | theorem 23.17 | arxiv |
| Diagonal reference from any linear code | statement | theorem 22.5 | arxiv |
| Hard discrepancy at a near-endpoint Gaussian scale | statement | theorem 3.14 | arxiv |
| Feasible sets and continuous or weak costs | statement | corollary 11.17 | arxiv |
| The whole signing law and a canonical reference | statement | corollary 16.18 | arxiv |
| Extraction of a convex subset | statement | proposition 14.4 | arxiv |
| Simultaneous-exchange rounding | statement | theorem 5.1 | arxiv |
| Contraction of the canonical conditional maps | statement | theorem 16.1 | arxiv |
| A finite reference cannot match a nonatomic one locally | statement | corollary 23.18 | arxiv |
| One subgradient representation for arbitrary references | statement | theorem 17.2 | arxiv |
| Optimal Gaussian comparison for cut signs | statement | theorem 22.12 | arxiv |
| One calibrated law with an energy-dependent entropy deficit | statement | theorem 3.3 | arxiv |
| Regularity of the matrix reference; Akbas--Sra | statement | lemma 9.5 | arxiv |
| Gaussian convex median inequality | statement | lemma 14.1 | arxiv |
| Exact augmentation of a fixed joint law | statement | theorem 26.3 | arxiv |
| Private refinement | statement | lemma 29.10 | arxiv |
| Dyadic thinning with prescribed marginals | statement | theorem 7.10 | arxiv |
| The half-measure level of extraction is sharp | statement | proposition 14.5 | arxiv |
| Exact all-alphabet characterization | statement | corollary 28.15 | arxiv |
| Bernoulli to Poisson | statement | lemma 4.5 | arxiv |
| Conditional inequalities at stopping times | statement | theorem 16.14 | arxiv |
| Green's Gaussian product-space problem | statement | corollary 14.18 | arxiv |
| Finite-alphabet utility loss | statement | lemma 28.2 | arxiv |
| Sharp information cost with a fourth-order certificate | statement | theorem 26.5 | arxiv |
| Reis--Rothvoss: square matrices and the rectangular $p=2$ case | statement | corollary 3.17 | arxiv |
| Hard vector balancing in joint convex order | statement | theorem 1.1 | arxiv |
| Strict homothetic contractions | statement | theorem 11.3 | arxiv |
| Haar projectors | statement | corollary 22.9 | arxiv |
| A quantitative removal bound | statement | proposition 23.9 | arxiv |
| Threefold Gaussian convexity | statement | theorem 14.8 | arxiv |
| Matrix reference laws with inverse-square-root loss | statement | theorem 7.1 | arxiv |
| A conditional strengthening of Gaussian convex order | statement | corollary 15.7 | arxiv |
| Prediction of the entire private output | statement | corollary 28.17 | arxiv |
| Sharp inverse on the closed simplex | statement | theorem 31.7 | arxiv |
| Polyhedral approximation from the subdifferential | statement | lemma 30.14 | arxiv |
| A unique martingale with atomless components | statement | theorem 11.9 | arxiv |
| A whole signing law with exponentially calibrated reference | statement | corollary 18.26 | arxiv |
| L\'evy reference completion | statement | theorem 4.3 | arxiv |
| Optimal orders in the square case | statement | proposition 8.13 | arxiv |
| Simultaneous Schatten rounding | statement | theorem 8.1 | arxiv |
| FM0N75DBX6 | statement | lemma 19.2 | arxiv |
| Gaussian isoperimetry and transportation for the whole future path | statement | theorem 16.15 | arxiv |
| Hereditary variance small ball | statement | theorem 8.7 | arxiv |
| $W_\infty$ density for countable initial marginals | statement | theorem 10.3 | arxiv |
| Weighted three-set Gaussian convexity | statement | theorem 15.8 | arxiv |
| Exact finite-depth reference | statement | theorem 5.12 | arxiv |
| Fivefold Gaussian enlargement | statement | theorem 15.18 | arxiv |
| Infinite information and the Gaussian innovation | statement | corollary 29.5 | arxiv |
| FX24VGFR9E | statement | theorem 27.9 | arxiv |
| Periodic useful-data quantizers | statement | corollary 28.11 | arxiv |
| Attainment and an arbitrary entropy budget | statement | corollary 28.9 | arxiv |
| Heat martingale of a Lipschitz transport | statement | lemma 15.4 | arxiv |
| A robust Gaussian utility gap | statement | proposition 29.6 | arxiv |
| Residual rank formula | statement | lemma 5.6 | arxiv |
| The cycle formula | statement | lemma 31.1 | arxiv |
| Anisotropy and finite certificates | statement | corollary 14.12 | arxiv |
| The published higher-dimensional conjecture | statement | corollary 18.13 | arxiv |
| Sachdeva--Thudi--Zhao matrix partial coloring with exact mean | statement | theorem 7.4 | arxiv |
| Lipschitz dependence on the initial marginal | statement | proposition 18.20 | arxiv |
| A cubic comparison for the likelihood transform | statement | lemma A.3 | arxiv |
| Exact nonlocal Cheeger dual | statement | theorem 20.1 | arxiv |
| Sobolev score realization | statement | proposition 19.13 | arxiv |
| Shifted partial coloring, Reis--Rothvoss | statement | lemma 8.11 | arxiv |
| Permutation convex hulls | statement | lemma 22.7 | arxiv |
| Exponential convergence of the reference coupling | statement | theorem 18.24 | arxiv |
| A two-by-three simultaneous utility gap | statement | proposition 29.14 | arxiv |
| Reis's volume-ratio conjecture | statement | corollary 9.2 | arxiv |
| Subgradient recovery | statement | lemma 17.10 | arxiv |
| Supermartingale backward Monge density | statement | theorem 11.25 | arxiv |
| Bounds for the optimal action | statement | proposition 16.12 | arxiv |
| Noncommuting dimension and perturbation limits | statement | theorem 24.9 | arxiv |
| Equality of finite-moment weak transport infima | statement | theorem 10.12 | arxiv |
| Retention of the complete selected reference | statement | proposition 3.5 | arxiv |
| Four summands and higher output mass | statement | corollary 15.9 | arxiv |
| General-reference existence | statement | theorem 17.1 | arxiv |
| Threefold convexity in a Gaussian Banach space | statement | theorem 14.16 | arxiv |
| Functional inequalities for Lipschitz Gaussian images | statement | lemma 16.13 | arxiv |
| Scalar partition geometry | statement | lemma 23.7 | arxiv |
| Volume ratios of trace-class quotients | statement | theorem 9.1 | arxiv |
| Approximate simulation with the exact observation marginal | statement | theorem 30.22 | arxiv |
| Positive semidefinite partitions | statement | corollary 7.2 | arxiv |
| Arbitrarily small initial contraction | statement | corollary 16.8 | arxiv |
| Proximal iteration | statement | proposition 18.19 | arxiv |
| Exact finite dual | statement | proposition 19.10 | arxiv |
| A gap forced by conditional atoms | statement | theorem 28.14 | arxiv |
| JADJ6H0YSQ | statement | corollary 22.4 | arxiv |
| Forward stability and topology | statement | proposition 31.6 | arxiv |
| Gaussian private releases with no common upper bound | statement | theorem 29.4 | arxiv |
| A general driving reference for the entire signing law | statement | corollary 17.26 | arxiv |
| Entropy-extremizing laws with slow linear-block dynamics | statement | theorem 25.5 | arxiv |
| Zero-temperature averaged curvature | statement | lemma 18.7 | arxiv |
| Point processes with exact intensity and spectral control | statement | theorem 7.14 | arxiv |
| Half-integral points | statement | corollary 5.5 | arxiv |
| Atomless components with a forced backward bit | statement | theorem 1.9 | arxiv |
| The $p$-Cheeger bound and smooth trial densities | statement | lemma 21.4 | arxiv |
| All Gaussian contractions at every finite moment order | statement | theorem 13.5 | arxiv |
| Interior compactness | statement | lemma 17.6 | arxiv |
| Short resolution of the Gaussian conjecture | statement | corollary 28.6 | arxiv |
| Greatest full-data private releases | statement | theorem 29.1 | arxiv |
| Parisi normalization | statement | corollary 22.13 | arxiv |
| Privacy instability at every correlated Gaussian pair | statement | theorem 1.12 | arxiv |
| Rigidity at the universal endpoint | statement | proposition 4.13 | arxiv |
| Arbitrarily small reference inflation | statement | corollary 18.10 | arxiv |
| Weighted cycles, faces and endpoint laws | statement | corollary 31.8 | arxiv |
| Poisson comparison for unbiased PSD sparsifiers | statement | theorem 7.12 | arxiv |
| Volume of an operator-norm section | statement | proposition 9.7 | arxiv |
| MGG52MZW2A | statement | theorem 6.3 | arxiv |
| Posterior rigidity at the entropy frontier | statement | corollary 23.10 | arxiv |
| A Fourier criterion for zero-budget utility | statement | theorem 28.20 | arxiv |
| Optimal average score with a finite first moment | statement | theorem 23.12 | arxiv |
| Energy-sensitive simultaneous norm bounds | statement | theorem 3.16 | arxiv |
| Quantitative Blackwell recovery | statement | theorem 30.15 | arxiv |
| A smooth maximum and centered Gumbel noise | statement | lemma 23.27 | arxiv |
| Uniform output mass and the half-input endpoint | statement | corollary 15.19 | arxiv |
| Finite-reference calibration of the original signing law | statement | corollary 17.28 | arxiv |
| MY3NTXC6BR | statement | lemma 6.7 | arxiv |
| Same-driver diffusion stability | statement | corollary 16.10 | arxiv |
| Compact driving support and a one-point initial law | statement | proposition 17.13 | arxiv |
| Posterior covariance minorization | statement | lemma 18.5 | arxiv |
| Sharp endpoint deficit | statement | theorem 16.9 | arxiv |
| Anisotropic rectangles | statement | theorem 21.5 | arxiv |
| Bernoulli--Gaussian comparison | statement | lemma 4.10 | arxiv |
| Comparison with an arbitrary compact orbit | statement | theorem 22.1 | arxiv |
| Sharp diffuse expansion | statement | theorem D.4 | arxiv |
| A quantitative exactly private Gaussian output | statement | proposition 28.12 | arxiv |
| Dyadic rounding from hereditary Gaussian signing | statement | lemma 7.3 | arxiv |
| Trajectory comparison | statement | proposition 4.15 | arxiv |
| Conditional densities with retained curvature | statement | lemma 15.3 | arxiv |
| Pathwise covariance at one level | statement | proposition 5.11 | arxiv |
| Continuous variational realization | statement | theorem 17.23 | arxiv |
| Exact spectral data and all iterates | statement | corollary 13.4 | arxiv |
| Stationary Ornstein--Uhlenbeck limit | statement | theorem 13.14 | arxiv |
| Explicit odd-alphabet indistinguishability | statement | theorem 31.10 | arxiv |
| Talagrand convexity with the optimal three summands | statement | theorem 1.4 | arxiv |
| All mean-square private optimizers | statement | theorem 29.12 | arxiv |
| A five-state obstruction and its exact correction | statement | proposition 27.10 | arxiv |
| Quadratic exact complexity and linear approximate complexity | statement | corollary 27.12 | arxiv |
| Dimension-sensitive simultaneous Gaussian event | statement | corollary 8.9 | arxiv |
| Complete recovery from one fixed cycle | statement | theorem 31.4 | arxiv |
| A finite source recovers the complete Hamming curve | example | example 23.5 | arxiv |
| Number of affine-code components | statement | proposition 25.7 | arxiv |
| Passing uniform regularity and its deficit to the limit | statement | lemma 16.7 | arxiv |
| Sharp reference for a compact homogeneous orbit | statement | theorem 22.2 | arxiv |
| Unique extremizer and stability | statement | theorem 19.5 | arxiv |
| Entropy and the determinant of Fisher information | statement | lemma 9.6 | arxiv |
| QKHW3K80P9 | statement | corollary 30.2 | arxiv |
| Sixfold convexity and the high-mass profile | statement | corollary 15.20 | arxiv |
| Finite-dimensional interpolation by a deterministic map | statement | theorem 13.3 | arxiv |
| Degree-optimal canonical moment partitions | statement | theorem 12.1 | arxiv |
| Identification from fair-binary calibration | statement | theorem 30.1 | arxiv |
| Size of a decision witness | statement | corollary 30.16 | arxiv |
| Gaussian reference perturbation | statement | corollary 17.20 | arxiv |
| Adapted upper Hausdorff convergence fails | example | example 11.19 | arxiv |
| Column-covariance displacement ellipsoid | statement | corollary 19.20 | arxiv |
| The component-disintegration formulation | statement | corollary 11.11 | arxiv |
| Application to the same signing law | statement | corollary 15.15 | arxiv |
| A three-point integer window | statement | corollary 6.4 | arxiv |
| Fixed-step approximation of the full Gaussian process | statement | corollary 13.8 | arxiv |
| Simultaneous stability of endpoints and reference | statement | corollary 11.18 | arxiv |
| Sparse approximation of an arbitrary fair baseline | statement | corollary 27.7 | arxiv |
| The capacity reduction from disconnected components | statement | proposition 20.8 | arxiv |
| Horizontal zonoid retained by every stage | statement | theorem 19.19 | arxiv |
| An exact spectral dual | statement | proposition 20.6 | arxiv |
| Mean-independent uniform factor | statement | lemma 10.6 | arxiv |
| Equality of optimal transport values | statement | corollary 11.2 | arxiv |
| Strict Gaussian mass from a variance perturbation | statement | lemma 14.10 | arxiv |
| Finite heat spectra realized by a measure-preserving map | statement | theorem 21.6 | arxiv |
| Simultaneous scalar transport | statement | lemma 29.9 | arxiv |
| Backward Monge approximation in higher dimensions | statement | theorem 11.1 | arxiv |
| Completion with a deterministic convolution parameter | statement | theorem 4.1 | arxiv |
| Compact Gaussian hitting | statement | theorem 14.2 | arxiv |
| Uniform inward drift | statement | lemma 18.17 | arxiv |
| Akbas--Sra matrix small ball | statement | lemma 8.6 | arxiv |
| Three labels | example | example 23.28 | arxiv |
| Gradient and monotonicity | statement | lemma 18.11 | arxiv |
| Information amplification with one retained reference | statement | corollary 3.6 | arxiv |
| All-marginal adapted stability | statement | theorem 1.10 | arxiv |
| Strong operator approximation | statement | corollary 13.13 | arxiv |
| Projected gradient iteration | statement | corollary 18.23 | arxiv |
| SFJP9C3H70 | definition | definition 30.5 | arxiv |
| Weighted divergence certificate | statement | lemma 21.2 | arxiv |
| Products and the ball of prescribed volume | statement | theorem 20.13 | arxiv |
| First variation in the reference | statement | corollary 17.21 | arxiv |
| SPTS1BAZRR | statement | theorem 24.4 | arxiv |
| The universal half-mean factor is sharp | statement | proposition 27.5 | arxiv |
| Exact replica realization of fractional bin packing | statement | theorem 3.7 | arxiv |
| Quadratic prediction detects the greatest experiment | statement | theorem 29.3 | arxiv |
| SVDFDN786R | statement | lemma A.1 | arxiv |
| Greatest private experiment and posterior simplex | statement | proposition 28.25 | arxiv |
| A log-concave reference and two Gaussian summands | statement | theorem 16.20 | arxiv |
| Square-function estimates across the Schatten scale | statement | lemma 8.10 | arxiv |
| Determinant bound | statement | theorem 9.3 | arxiv |
| Terminal recovery away from shared component closures | statement | corollary 11.7 | arxiv |
| The scalar Gaussian envelopes | statement | lemma B.1 | arxiv |
| Common-coordinate families | statement | corollary 11.8 | arxiv |
| All-marginal adapted approximation | statement | theorem 11.13 | arxiv |
| One sampling law for all integrands | statement | theorem 1.6 | arxiv |
| Exact comparison for a fixed eigenvalue orbit | statement | theorem 22.8 | arxiv |
| Contraction from a Gaussian convolution | statement | lemma 16.4 | arxiv |
| A bounded-volatility realization | statement | theorem 15.1 | arxiv |
| Conditional moments and backward deterministic approximation | statement | theorem 10.7 | arxiv |
| A Gaussian-terminal obstruction to initial-state contraction | statement | proposition 16.19 | arxiv |
| Optimal realization for a specified reference martingale | statement | theorem 17.22 | arxiv |
| Unbiased spectral graph sparsification | statement | corollary 7.13 | arxiv |
| Explicit bounds and polynomial-size packing | statement | proposition 3.8 | arxiv |
| Power-law small values | statement | theorem 23.21 | arxiv |
| The binary exception | statement | proposition 30.18 | arxiv |
| Optimal utility of a fair perfectly private bit | statement | theorem 26.8 | arxiv |
| All-density first-order optimum | statement | theorem 20.12 | arxiv |
| Equal score moments and different sharp supports | statement | theorem 19.21 | arxiv |
| PSD partitions with prescribed scalar statistics | statement | corollary 7.6 | arxiv |
| Two directions with a common mixed derivative | example | example 20.5 | arxiv |
| Stationary exit with arbitrary memory | statement | lemma 25.2 | arxiv |
| Integral capacities and inequalities | statement | corollary 5.3 | arxiv |
| Spectral signing with bounded signed degrees | statement | corollary 7.8 | arxiv |
| A homothetic section in the signing polytope | statement | theorem 2.4 | arxiv |
| Strong convexity on generalized geodesics | statement | proposition 18.21 | arxiv |
| Stable reference budgets | statement | corollary 4.4 | arxiv |
| A deterministic optimizer for measurable costs | statement | theorem 10.4 | arxiv |
| No relaxation gap for directional transport | statement | corollary 11.22 | arxiv |
| One rank release for all monotone tasks | statement | corollary 29.8 | arxiv |
| Exact feasible outputs | statement | corollary 5.2 | arxiv |
| Why a finite potential cannot always be required | example | example 17.14 | arxiv |
| Linear objectives and an entropy-maximizing law | statement | corollary 2.5 | arxiv |
| Countable purification with prescribed moments | statement | theorem 10.1 | arxiv |
| Incomparable maximal private releases near a Gaussian | statement | theorem 28.24 | arxiv |
| First-moment section inequality | statement | theorem 19.8 | arxiv |
| Oscillating partitions | statement | lemma 28.10 | arxiv |
| The greatest posterior mean for a scalar task | statement | theorem 29.7 | arxiv |
| Strict concavity of maximal covariance | statement | lemma 16.2 | arxiv |
| Minimum support and lower-order R\'enyi entropies | statement | corollary 23.2 | arxiv |
| An exact half-square partition | example | example 19.12 | arxiv |
| Optimal proximal kernels | statement | corollary 16.16 | arxiv |
| Integer parameters and matrix references | example | example 4.2 | arxiv |
| Any fixed finite order of conditional moments | statement | corollary 13.1 | arxiv |
| An extremizing interval density | statement | corollary 19.6 | arxiv |
| Bounded decision rewards | statement | corollary 28.4 | arxiv |
| Matrix Spencer with Gaussian and information guarantees | statement | corollary 7.7 | arxiv |
| Exact multitime polynomial moments | statement | theorem 13.6 | arxiv |
| Singularity and the infinite-order endpoint | statement | proposition 13.11 | arxiv |
| A necessary inverse-square-root radius | statement | theorem 3.11 | arxiv |
| The information retained by an independent refinement | statement | proposition 30.8 | arxiv |
| Exactly calibrated cost--entropy asymptotics | statement | theorem 12.3 | arxiv |
| Full finite-output entropy under conditional atomlessness | statement | theorem 28.8 | arxiv |
| Uniform escape bound for local block updates | statement | theorem 25.4 | arxiv |
| One nondegenerate reference coupling suffices | statement | corollary 10.10 | arxiv |
| An exact covariance Laplacian | statement | proposition 5.14 | arxiv |
| Prescribed means and independent references | statement | theorem 6.1 | arxiv |
| A discontinuity in the Gaussian conditional-information budget | statement | corollary 28.18 | arxiv |
| A bounded score detects full affine span | statement | lemma 10.9 | arxiv |
| The sharp Gaussian entropy loss at the endpoint | statement | corollary 23.4 | arxiv |
| Sharp interval support | statement | theorem 19.3 | arxiv |
| Conditional realization with a parameter | statement | theorem 11.5 | arxiv |
| Brunn--Minkowski inequality for the reference energy | statement | theorem 20.14 | arxiv |
| Optimal references with linearly many exact product marginals | statement | corollary 23.14 | arxiv |
| All private channels factor through the modulo release | statement | theorem 28.23 | arxiv |
| Two Brownian completions | statement | lemma 15.5 | arxiv |
| Directional cosine radii | statement | theorem 19.17 | arxiv |
| Uniform central and tail expansion | statement | lemma D.3 | arxiv |
| Failure of both semicontinuity directions | statement | corollary 28.22 | arxiv |
| Nearly independent random coordinate blocks | statement | corollary 3.10 | arxiv |
| The ground-state reference law | statement | corollary 21.7 | arxiv |
| ZDGGQ500VR | statement | corollary 6.8 | arxiv |
| Finite-dimensional Gaussian approximation | statement | lemma 14.15 | arxiv |
| Lifting retains the entire old pair law | statement | theorem 27.3 | arxiv |
| The irreducible calculation | statement | lemma 16.5 | arxiv |
| A complete two-base Gaussian reference | statement | theorem 5.10 | arxiv |
| ZTH4TNA7HR | statement | theorem 27.1 | arxiv |
| Strong convexity under additive noise | statement | theorem 18.1 | arxiv |
| Gaussian convex order as a continuous-time condition | statement | corollary 15.2 | arxiv |
| Every next level is strict, with smooth densities | statement | corollary 30.21 | arxiv |
| Arbitrarily many exact Gaussian modes without hypercontractivity | statement | corollary 13.10 | arxiv |
