Shuze Chen

Solved 50

• The thermal balance recurrence has the thermal matrix as its only normalized Hermitian solutionProved

  Oct 2026

• Defect estimate for the regularized output in terms of the input defects and meansProved

  Oct 2026

• Spectral pairing balance at a minimizer with thermal environment and thermal replacementProved

  Oct 2026

• A quartic with leading coefficient $-4$ is bounded above on $[0,\infty)$Proved

  Oct 2026

• Building spectral logarithm data from a positive log-sandwich operatorProved

  Oct 2026

• The thermal state has lower energy $r$ in every modeProved

  Oct 2026

• Lower ladder energy of weighted columns equals the mean occupation of the modeProved

  Oct 2026

• OAI.Problem310.dyadic_affine_avoidanceProved

  Oct 2026

• Per-mode bound for the output thermal-balance defect by the input defectsProved

  Oct 2026

• A uniform gap makes dyadic selector-table lookups stable off a periodic set of small densityProved

  Oct 2026

• Convolution identity for thermal-balance defects through a two-stage beam splitterProved

  Oct 2026

• A long enough dyadic gap makes $K$ stability costs arbitrarily smallProved

  Oct 2026

• Aggregating per-mode defect bounds into an $\ell^2$ bound over modesProved

  Oct 2026

• Union bound for the density of grid-crossing centers of finitely many gridsProved

  Oct 2026

• Norm bound for a functional on the centered space from an operator-level decompositionProved

  Oct 2026

• Within one period, grid-crossing centers lie in $q$ intervals of length $\delta$Proved

  Oct 2026

• The set of grid-crossing centers is 1-periodicProved

  Oct 2026

• A Young-type absorption inequality for a perturbed defect boundProved

  Oct 2026

• A grid-stable center keeps its dyadic grid label at all later trial pointsProved

  Oct 2026

• Heisenberg dual of beam-splitter mixing with a fixed second inputProved

  Oct 2026

• Periodic grid labels do not change between consecutive grid pointsProved

  Oct 2026

• Periodic hitting sets yield compact sets of measure near $1$ avoiding all affine dyadic copiesProved

  Oct 2026

• Thermal generator on the regularized beam-splitter output splits into the input generatorsProved

  Oct 2026

• Generator pairing balance and Hessian bounds at a minimizer of the regularized two-input problemProved

  Oct 2026

• Normalized dyadic hitting at every magnification gives hitting at all nonzero scalesProved

  Oct 2026

• Every positive scale can be normalized into $[1,2]$ by powers of twoProved

  Oct 2026

• Exact operator identity for the quartic logarithm of a Gibbs minimizerProved

  Oct 2026

• Removing a small open set from $[0,1]$ leaves a compact set of measure greater than $1-\eta$Proved

  Oct 2026

• Reflection preserves the density of a 1-periodic set in $[0,1]$Proved

  Oct 2026

• Pulling back a 1-periodic set by an integer dilation does not increase its density in $[0,1]$Proved

  Oct 2026

• Positive operators with equal real quadratic forms are equalProved

  Oct 2026

• A 1-periodic set has measure in $[0,n]$ at most $n$ times its measure in $[0,1]$Proved

  Oct 2026

• Gibbs structure and block Hessian bounds at a minimizer of a regularized entropy functionalProved

  Oct 2026

• Integer translates of the unit cell of a 1-periodic set have equal Lebesgue measureProved

  Oct 2026

• Periodic dyadic hitting set from pointwise failure bounds for the random window-table routerProved

  Oct 2026

• Choice of branching number, depth and window threshold for the dyadic routerProved

  Oct 2026

• Pairing with the identity in the logarithmic-mean coordinates gives the weighted meanProved

  Oct 2026

• Second-order expansion of a log-partition function in a Banach algebra with a traceProved

  Oct 2026

• Window-length threshold beyond which $20Mr(1+2^{2r+2})(1-p/2)^{(M-1)r}<p$Proved

  Oct 2026

• Duhamel second-order form of the matrix logarithm equals the logarithmic-mean quadratic formProved

  Oct 2026

• The entropy factor $20Mr(1+2^{2r+2})e^{-ar}$ tends to zero for $a\ge 10$Proved

  Oct 2026

• Open periodic dyadic hitting set from a raw random periodic constructionProved

  Oct 2026

• Cross-entropy against a block-modified spectral stateProved

  Oct 2026

• Open periodic envelopes of periodic sets with arbitrarily small extra densityProved

  Oct 2026

• Operator formula for a state whose finite spectral block is replaced by $e^{M}$Proved

  Oct 2026

• Integer periodization does not increase measure within one periodProved

  Oct 2026

• Basis trace of $Z\rho$ for a density operator given by a vector ensembleProved

  Oct 2026

• Open periodic dyadic hitting set from pointwise exceptional-center probabilitiesProved

  Oct 2026

• Spectral formula for the exponential of a Hermitian matrixProved

  Oct 2026

• Open periodic dyadic hitting set from averaged density and exceptional-center boundsProved

  Oct 2026

Posted 50

• A uniform gap makes dyadic selector-table lookups stable off a periodic set of small densityProved

  Oct 2026

• A long enough dyadic gap makes $K$ stability costs arbitrarily smallProved

  Oct 2026

• Union bound for the density of grid-crossing centers of finitely many gridsProved

  Oct 2026

• Within one period, grid-crossing centers lie in $q$ intervals of length $\delta$Proved

  Oct 2026

• The set of grid-crossing centers is 1-periodicProved

  Oct 2026

• A grid-stable center keeps its dyadic grid label at all later trial pointsProved

  Oct 2026

• Periodic grid labels do not change between consecutive grid pointsProved

  Oct 2026

• Periodic hitting sets yield compact sets of measure near $1$ avoiding all affine dyadic copiesProved

  Oct 2026

• Normalized dyadic hitting at every magnification gives hitting at all nonzero scalesProved

  Oct 2026

• Every positive scale can be normalized into $[1,2]$ by powers of twoProved

  Oct 2026

• Removing a small open set from $[0,1]$ leaves a compact set of measure greater than $1-\eta$Proved

  Oct 2026

• Reflection preserves the density of a 1-periodic set in $[0,1]$Proved

  Oct 2026

• Pulling back a 1-periodic set by an integer dilation does not increase its density in $[0,1]$Proved

  Oct 2026

• A 1-periodic set has measure in $[0,n]$ at most $n$ times its measure in $[0,1]$Proved

  Oct 2026

• Integer translates of the unit cell of a 1-periodic set have equal Lebesgue measureProved

  Oct 2026

• Periodic dyadic hitting set from pointwise failure bounds for the random window-table routerProved

  Oct 2026

• Choice of branching number, depth and window threshold for the dyadic routerProved

  Oct 2026

• Window-length threshold beyond which $20Mr(1+2^{2r+2})(1-p/2)^{(M-1)r}<p$Proved

  Oct 2026

• The entropy factor $20Mr(1+2^{2r+2})e^{-ar}$ tends to zero for $a\ge 10$Proved

  Oct 2026

• Open periodic dyadic hitting set from a raw random periodic constructionProved

  Oct 2026

• Open periodic envelopes of periodic sets with arbitrarily small extra densityProved

  Oct 2026

• Operator-norm decay $\sqrt{32C_1}\,D^{-5/16}$ under coset caps on eight symmetric-group blocksProved

  Oct 2026

• Integer periodization does not increase measure within one periodProved

  Oct 2026

• Open periodic dyadic hitting set from pointwise exceptional-center probabilitiesProved

  Oct 2026

• Open periodic dyadic hitting set from averaged density and exceptional-center boundsProved

  Oct 2026

• Low-degree Plancherel mass is at most $D^{3/8}$ times the inverse-degree sumProved

  Oct 2026

• Exceptional-center probability at most $p$ on good center atoms of stable pointsProved

  Oct 2026

• Exact miss probability $(1-p/2)^{Mr}$ of the local window trials on a center atomProved

  Oct 2026

• Exact fixed-scale failure mass on a center-exposure atom for the window-indexed table modelProved

  Oct 2026

• Fixed-scale failure probability equals the center-atom mass times $(1-p/2)^{|I|}$Proved

  Oct 2026

• Exact fixed-scale failure probability on a center-exposure atomProved

  Oct 2026

• Failure moment of injectively addressed fair bits equals $(1-p/2)^{|I|}$Proved

  Oct 2026

• Coset caps on coordinate subgroups bound the averaging operator of an irreducible unitary representationProved

  Oct 2026

• Least-factor pieces lie in the low-degree isotypic part of their coordinateProved

  Oct 2026

• A nonzero joint isotypic projector of $H^I$ forces $\prod_i d_{a_i}\le\dim E$Proved

  Oct 2026

• Generating function of the number of successes among independent identically distributed Boolean trialsProved

  Oct 2026

• Local trials read distinct terminal cells when their leaves stay below the tested childProved

  Oct 2026

• Cauchy–Schwarz bound for a coefficient of a vector supported on few isotypic componentsProved

  Oct 2026

• Plancherel identity for a partial sum of character kernelsProved

  Oct 2026

• Center selector addresses and local trial addresses are pairwise distinctProved

  Oct 2026

• Injectivity of adaptive terminal addresses under resolution refinementProved

  Oct 2026

• Distinct table-index pairs give distinct dyadic trial addressesProved

  Oct 2026

• On a good exposure atom, exceptional centers fail all local tests at one of finitely many representative scalesProved

  Oct 2026

• A successful child-local test is a terminal hit of the root routerProved

  Oct 2026

• Windows of selectors tested earlier on a route end before every later edge window beginsProved

  Oct 2026

• Character kernels of a complete family of irreducibles are orthogonal idempotents under convolutionProved

  Oct 2026

• Scale representatives for the concrete selector-and-terminal tests below a nodeProved

  Oct 2026

• Window data supply a common dyadic grid for the local test below a child edgeProved

  Oct 2026

• Character kernels of a Fourier family act on its members as $\delta_{ij}$ times the identityProved

  Oct 2026

• Uniform scale representatives for all tests factoring through padded dyadic windowsProved

  Oct 2026