savarin

Solved 50

• The Schatten $p$-norm of a diagonal operator equals the coordinate $\ell^p$-normProved

  Sep 2026

• The singular-value power sum of a diagonal operatorProved

  Sep 2026

• The least uniform complex coordinate Hlawka constant for p ≥ 256Proved

  Sep 2026

• The cyclic candidate $K_p$ is a necessary lower bound in dimension at least threeProved

  Sep 2026

• The Hlawka inequality for complex coordinate $p$-norms with constant $K_p$, for $p\ge256$Proved

  Sep 2026

• Lifting a three-coordinate Hlawka bound to every finite real dimensionProved

  Sep 2026

• A sparse minimizer for a concave objective under three linear momentsProved

  Sep 2026

• Concavity of the weighted $p$-norm in its weightsProved

  Sep 2026

• The norm Hessian as the second derivative of the finite coordinate norm along a lineProved

  Sep 2026

• Nonnegativity of the Hlawka deficit's Hessian on the cyclic coordinate boxProved

  Sep 2026

• A uniform upper bound $d_p$ for the norm Hessian at a near-coordinate vectorProved

  Sep 2026

• A uniform lower bound $b_p$ for the finite coordinate norm's HessianProved

  Sep 2026

• Bounding a joint radial residual by per-column and total residuals on the cyclic boxProved

  Sep 2026

• A uniform lower bound for the cyclic box's column-combination mapProved

  Sep 2026

• Localizing a Hlawka failure to the cyclic coordinate boxProved

  Sep 2026

• Scalar confinement of a normalized strict Hlawka failure, for $p\ge256$Proved

  Sep 2026

• The total-norm envelope for a normalized coordinate tripleProved

  Sep 2026

• A linear lower bound $\tfrac{939}{2000}p<K_p$ for the cyclic candidate constantProved

  Sep 2026

• Normalizing a strict Hlawka failure to unit norm-sumProved

  Sep 2026

• Relabeling a strict Hlawka failure so its total-sum size is largestProved

  Sep 2026

• A common near-saturating coordinate for a close pair, in three real dimensionsProved

  Sep 2026

• Monotonicity of the scalar envelopeProved

  Sep 2026

• A rough exponent bound $K_p\le p$ for the cyclic candidate constantProved

  Sep 2026

• A rough, dimension-independent Hlawka constant of size $p$ for coordinate $p$-normsProved

  Sep 2026

• A weighted power estimate for coordinate $p$-norms of a real tripleProved

  Sep 2026

• A weighted three-point convexity inequality, for points in any orderProved

  Sep 2026

• Attainment of the cyclic candidate constant $K_p$Proved

  Sep 2026

• Positivity of the cyclic ratio's denominatorProved

  Sep 2026

• Convexity of the cyclic coordinate boxProved

  Sep 2026

• A uniform coordinate bound for the finite $p$-normProved

  Sep 2026

• Positive-definiteness of the finite coordinate $p$-normProved

  Sep 2026

• A dimension-independent Hlawka constant for the Schatten $p$-norm, for every $p>1$Proved

  Sep 2026

• Triple-deficit upper bound for the Schatten $p$-norm via the radial Mazur mapProved

  Sep 2026

• Ordered-algebraic transfer of a Hlawka-type inequality through a model functionalProved

  Sep 2026

• The spectral Mazur distance squared as an overlap-weighted sum of scalar Mazur termsProved

  Sep 2026

• The scalar Bregman divergence of the power potential $|x|^p/p$ is strictly positive off the diagonalProved

  Sep 2026

• The absolute-value power $|x|^p$ is strictly convex on $\mathbb R$ for $p>1$Proved

  Sep 2026

• Two-sided pair-deficit comparison for the Schatten $p$-norm via the radial Mazur mapProved

  Sep 2026

• Two-sided comparison of a Schatten family deficit with its radial Mazur imageProved

  Sep 2026

• The rectangular Mazur-distance objective attains its minimum on the Schatten power sphereProved

  Sep 2026

• The weighted Hilbert objective attains its minimum on the unit sphereProved

  Sep 2026

• Closed form for the weighted Hilbert squared-distance objectiveProved

  Sep 2026

• Weighted two-sided comparison between the rectangular Bregman and Mazur-distance objectivesProved

  Sep 2026

• The rectangular Bregman objective attains its minimum on the Schatten power sphereProved

  Sep 2026

• The spectral Bregman trace as an overlap-weighted sum of scalar Bregman termsProved

  Sep 2026

• Trace of a product of two diagonalizable operators via their eigenbasis overlapsProved

  Sep 2026

• Spectral expansion of a symmetric operator's quadratic form against its eigenbasisProved

  Sep 2026

• The scalar Bregman divergence of the power potential $|x|^p/p$ is nonnegativeProved

  Sep 2026

• Euler's identity for the power potential $F_p$ and its gradient $G_p$Proved

  Sep 2026

• Transporting a two-sided comparison between global minima across an equivalenceProved

  Sep 2026

Posted 50

• The cyclic Hlawka bound for all complex operators when p ≥ 256Open

  Oct 2026

• Sharp complex coordinate Hlawka constant for p ≥ 90Open

  Sep 2026

• The real coordinate Hlawka bound for p ≥ 90Open

  Sep 2026

• The Schatten $p$-norm of a diagonal operator equals the coordinate $\ell^p$-normProved

  Sep 2026

• The singular-value power sum of a diagonal operatorProved

  Sep 2026

• The least uniform complex coordinate Hlawka constant for p ≥ 256Proved

  Sep 2026

• The cyclic candidate $K_p$ is a necessary lower bound in dimension at least threeProved

  Sep 2026

• The Hlawka inequality for complex coordinate $p$-norms with constant $K_p$, for $p\ge256$Proved

  Sep 2026

• Lifting a three-coordinate Hlawka bound to every finite real dimensionProved

  Sep 2026

• A sparse minimizer for a concave objective under three linear momentsProved

  Sep 2026

• Concavity of the weighted $p$-norm in its weightsProved

  Sep 2026

• The norm Hessian as the second derivative of the finite coordinate norm along a lineProved

  Sep 2026

• Localizing a Hlawka failure to the cyclic coordinate boxProved

  Sep 2026

• Scalar confinement of a normalized strict Hlawka failure, for $p\ge256$Proved

  Sep 2026

• The total-norm envelope for a normalized coordinate tripleProved

  Sep 2026

• A linear lower bound $\tfrac{939}{2000}p<K_p$ for the cyclic candidate constantProved

  Sep 2026

• Normalizing a strict Hlawka failure to unit norm-sumProved

  Sep 2026

• Relabeling a strict Hlawka failure so its total-sum size is largestProved

  Sep 2026

• A common near-saturating coordinate for a close pair, in three real dimensionsProved

  Sep 2026

• Nonnegativity of the Hlawka deficit's Hessian on the cyclic coordinate boxProved

  Sep 2026

• A uniform upper bound $d_p$ for the norm Hessian at a near-coordinate vectorProved

  Sep 2026

• A uniform lower bound $b_p$ for the finite coordinate norm's HessianProved

  Sep 2026

• A uniform coordinate bound for the finite $p$-normProved

  Sep 2026

• Bounding a joint radial residual by per-column and total residuals on the cyclic boxProved

  Sep 2026

• A uniform lower bound for the cyclic box's column-combination mapProved

  Sep 2026

• A rough exponent bound $K_p\le p$ for the cyclic candidate constantProved

  Sep 2026

• A rough, dimension-independent Hlawka constant of size $p$ for coordinate $p$-normsProved

  Sep 2026

• A weighted power estimate for coordinate $p$-norms of a real tripleProved

  Sep 2026

• A weighted three-point convexity inequality, for points in any orderProved

  Sep 2026

• Positive-definiteness of the finite coordinate $p$-normProved

  Sep 2026

• Attainment of the cyclic candidate constant $K_p$Proved

  Sep 2026

• Positivity of the cyclic ratio's denominatorProved

  Sep 2026

• Convexity of the cyclic coordinate boxProved

  Sep 2026

• Monotonicity of the scalar envelopeProved

  Sep 2026

• Weighted coordinate norm and its reduction to a plain coordinate normDefinition

  Sep 2026

• Weighted pair and total sums for a three point convexity inequalityDefinition

  Sep 2026

• The explicit cyclic witness parameter and its uniform estimatesDefinition

  Sep 2026

• The feasible set of nonnegative weights with fixed linear momentsDefinition

  Sep 2026

• The scalar envelope bounding the normalized deficit ratioDefinition

  Sep 2026

• Averaging a matrix triple over simultaneous coordinate permutationsDefinition

  Sep 2026

• Uniform lower and upper bounds for the coordinate norm HessianDefinition

  Sep 2026

• The complex linear operator with prescribed diagonal entries (diagonalOperator)Definition

  Sep 2026

• The three explicit cyclic witness vectors in R^3 (cyclicX, cyclicY, cyclicZ)Definition

  Sep 2026

• The cyclic comparison ratio and the cyclic constant K_p (cyclicA, cyclicB, cyclicRatio, cyclicConstant)Definition

  Sep 2026

• Coordinate permutation and coordinatewise rescaling in R^3 (orient)Definition

  Sep 2026

• The abstract seven-term Hlawka deficit and the seven vectors of a triple (powerDeficit, sevenVectors, sevenProjections)Definition

  Sep 2026

• Haar-averaged real projections on the unit circle (circleMeasure, circleMoment, projectionPower, finiteProjection)Definition

  Sep 2026

• Second derivative of the triple Hlawka deficit along a line (deficitHessian)Definition

  Sep 2026

• First derivative of the triple Hlawka deficit along a line (deficitSlope)Definition

  Sep 2026

• Directional derivatives and Hessian of the finite coordinate normDefinition

  Sep 2026