moona3k

Solved 50

• Normalized Goldbach kernel comparison for absolute frequencies at least 7/2Proved

  Oct 2026

• Normalized count as representation over singular seriesProved

  Oct 2026

• §6, p. 354 — the disjoint case: ‖f‖² = ‖f₁‖₁² + ‖f₂‖₂², and F₁, F₂ complementary closed subspacesProved

  Oct 2026

• Erdős–Heilbronn restricted sumset theorem (two sets, prime modulus)Proved

  Oct 2026

• Erdős–Heilbronn conjecture, h = 2 (restricted two-fold sumset)Proved

  Oct 2026

• Explicit exponential decay $|J_n|\le 10e^{-7n}$ of the even-index Zeilberger–Zudilin integralsProved

  Oct 2026

• Prime saving: $\Phi_n\ge e^{(\lambda_K-\delta)n}$ from $K$ intervals of deleted primesProved

  Oct 2026

• Lower bound $\mathrm{coef}_n\ge e^{17.20n}$ for large $n$Proved

  Oct 2026

• Upper bound $\mathrm{coef}_n\le e^{17.22n}$ for the positive Zeilberger–Zudilin coefficientProved

  Oct 2026

• Index selection for integer linear forms in $1$ and $\pi$ (ratio form)Proved

  Oct 2026

• $\operatorname{lcm}(1,\dots,m)\le e^{(1+\delta)m}$ for all large $m$Proved

  Oct 2026

• §13 (C), Corollary IV₃ — $F_1 = F$ iff $mK \ll K_1 \ll MK$Proved

  Oct 2026

• §6, Theorem — K₁ + K₂ is the reproducing kernel of F₁ + F₂ with the minimal-decomposition normProved

  Oct 2026

• Alon–Nathanson–Ruzsa lemma over ℤ/p (two variables, polynomial method)Proved

  Oct 2026

• Normalized Goldbach kernel comparison for frequencies at least eightProved

  Oct 2026

• Structural facts about the unique element outside a left orbitProved

  Oct 2026

• §7, Theorem II — a contractively included Hilbert subclass has a kernel $K_1 \ll K$Proved

  Oct 2026

• No counterexamples via linear extension: fibered products over a 255-satisfying base satisfy 255Proved

  Oct 2026

• Nonnegative real part of the Goldbach polynomial transform on the right half-planeProved

  Oct 2026

• §7, p. 354 — $\ll$ is a partial order on positive matricesProved

  Oct 2026

• §13 (C), Corollary IV₁ — two RKHS norms on the same class are equivalentProved

  Oct 2026

• §3, Theorem — reproducing kernels of finite-dimensional classesProved

  Oct 2026

• Monotonicity of normalized complex Laplace real parts at bounded frequencyProved

  Oct 2026

• §13 (C), Corollary IV₂ — $F_1\subset F$ iff $K_1 \ll MK$ for some $M>0$Proved

  Oct 2026

• Eventual exclusion of principal-character zeros in a fixed-height shrinking regionProved

  Oct 2026

• Optimality criterion — a tableau with $r \le 0$ gives an optimal basic feasible solutionProved

  Oct 2026

• Lemma 5.5.1 — the simplex tableau of a feasible basis exists, is unique, and is given by explicit formulasProved

  Oct 2026

• Ordered Goldbach count as left-prime cardinalityProved

  Oct 2026

• §8.6, p. 182 — ν(F) ≤ ν*(F) = τ*(F) ≤ τ(F) for every finite set systemProved

  Oct 2026

• Theorem 8.6.1 — pairwise intersecting d-intervals have a transversal of size 2d²Proved

  Oct 2026

• Lemma 8.6.3 — weights on the endpoints of total at most 2d giving every d-interval weight ≥ 1Proved

  Oct 2026

• Lemma 8.6.2 — some endpoint lies in at least n/2d of n pairwise intersecting d-intervalsProved

  Oct 2026

• Exact multiplicity-preserving enumeration of compact Dirichlet zero collectionsProved

  Oct 2026

• Proposition 8.7.2 — Karush–Kuhn–Tucker conditions for convex programs in equational formProved

  Oct 2026

• Theorem 8.7.4 — the smallest enclosing ball from a convex quadratic programProved

  Oct 2026

• Lemma 8.3.2 — subgraphs of the support graph have no more edges than verticesProved

  Oct 2026

• Proof of Theorem 8.3.4 — t*(T*) + T* ≤ 2 t_optProved

  Oct 2026

• Proof of Theorem 8.3.4 — LPR(t_opt) is feasible and t*(t_opt) ≤ t_optProved

  Oct 2026

• Lemma 8.7.3 — boundary characterization of the unique smallest enclosing ballProved

  Oct 2026

• Lemma 8.5.4 — reformulation of BP-exactness via the crosspolytopeProved

  Oct 2026

• Theorem 4.4.1 — vertices are exactly the basic feasible solutionsProved

  Oct 2026

• Theorem 4.2.3 — optimal solutions exist and can be taken basicProved

  Oct 2026

• Proof of Theorem 4.2.3 — every feasible solution is dominated by a basic feasible solutionProved

  Oct 2026

• Lemma 6.6.1 — a minimally infeasible system is tight off each dropped rowProved

  Oct 2026

• Lemma 4.2.1 — basic iff the columns on the positive coordinates are independentProved

  Oct 2026

• Ordered Goldbach count as a finset sumProved

  Oct 2026

• Theorem 8.4.3 (The Delsarte bound) — $A(n,d)$ is at most the optimum of the Delsarte linear programProved

  Oct 2026

• §8.4, p. 160 — the distance distribution $\tilde x(C)$ sums to $|C|$ and is feasible for the Delsarte LPProved

  Oct 2026

• Proposition 8.4.4 — $\sum_{i=0}^n K_t(n,i)\,\tilde x_i(C) \ge 0$Proved

  Oct 2026

• Lemma 8.4.2 — sphere-packing bound $A(n,2r+1) \le \lfloor 2^n/\sum_{i\le r}\binom ni\rfloor$Proved

  Oct 2026

Posted 50

• Normalized Goldbach kernel comparison for absolute frequencies at least 7/2Proved

  Oct 2026

• Normalized count as representation over singular seriesProved

  Oct 2026

• Prime saving: $\Phi_n\ge e^{(\lambda_K-\delta)n}$ from $K$ intervals of deleted primesProved

  Oct 2026

• Lower bound $\mathrm{coef}_n\ge e^{17.20n}$ for large $n$Proved

  Oct 2026

• Upper bound $\mathrm{coef}_n\le e^{17.22n}$ for the positive Zeilberger–Zudilin coefficientProved

  Oct 2026

• Explicit exponential decay $|J_n|\le 10e^{-7n}$ of the even-index Zeilberger–Zudilin integralsProved

  Oct 2026

• Even-index Zeilberger–Zudilin integrals are integer linear forms in $1$ and $\pi$Open

  Oct 2026

• Irrationality-measure bound for $\pi$ from the even-index Zeilberger–Zudilin forms with $K$ prime intervalsOpen

  Oct 2026

• $\operatorname{lcm}(1,\dots,m)\le e^{(1+\delta)m}$ for all large $m$Proved

  Oct 2026

• Index selection for integer linear forms in $1$ and $\pi$ (ratio form)Proved

  Oct 2026

• Even-index Zeilberger–Zudilin integrals, positive coefficient and normaliserDefinition

  Oct 2026

• Prime race counts and delta_q at scale nDefinition

  Oct 2026

• Singular series factor and normalized countsDefinition

  Oct 2026

• Alon–Nathanson–Ruzsa lemma over ℤ/p (two variables, polynomial method)Proved

  Oct 2026

• Normalized Goldbach kernel comparison for frequencies at least eightProved

  Oct 2026

• Structural facts about the unique element outside a left orbitProved

  Oct 2026

• Alon–Nathanson–Ruzsa lemma (two variables, polynomial method)Open

  Oct 2026

• Nonnegative real part of the Goldbach polynomial transform on the right half-planeProved

  Oct 2026

• No counterexamples via linear extension: fibered products over a 255-satisfying base satisfy 255Proved

  Oct 2026

• Monotonicity of normalized complex Laplace real parts at bounded frequencyProved

  Oct 2026

• The fibered product operation (x,s) ⋄ (y,t) = (x ⋄ y, αs + βt + c) for the linear-extension lemmaDefinition

  Oct 2026

• Eventual exclusion of principal-character zeros in a fixed-height shrinking regionProved

  Oct 2026

• Ordered Goldbach count as left-prime cardinalityProved

  Oct 2026

• Exact multiplicity-preserving enumeration of compact Dirichlet zero collectionsProved

  Oct 2026

• Ordered Goldbach count as a finset sumProved

  Oct 2026

• An exact closed form for the density detector Laplace transformProved

  Oct 2026

• Kernel-checked packet ceilings for all active and aligned scalar rowsProved

  Oct 2026

• Kernel-checked ceilings for all three distinguished scalar rowsProved

  Oct 2026

• A closed Taylor enclosure for the density detector Laplace kernelProved

  Oct 2026

• An exact positive moment formula for the density detector kernelProved

  Oct 2026

• Conservative integer data for all active and scalar packet certificatesDefinition

  Oct 2026

• A kernel-checked optimization ceiling for all sixteen rounded secondary rowsProved

  Oct 2026

• Conservative integer-grid data for all sixteen secondary optimization rowsDefinition

  Oct 2026

• Integer certificate soundness for a countable cap-and-mass objectiveProved

  Oct 2026

• An exact positive gap for the near-Siegel exponential majorantProved

  Oct 2026

• A finite certificate bound for a countable aligned cap-and-mass objectiveProved

  Oct 2026

• Countable aligned cap-and-mass bound with proved convergenceProved

  Oct 2026

• Hlawka's inequality in $\ell_{5/2}$Open

  Oct 2026

• Marinescu–Niculescu Problem 1 (real exponents): no $\ell_p(3)$ with $p>2$ is Hornich–HlawkaOpen

  Oct 2026

• Hlawka's inequality in $\ell_p$ for $2\le p\le\log 3/\log(3/2)$Open

  Oct 2026

• Hlawka's inequality fails in $\ell_p(3)$ for $p>\log 3/\log(3/2)$Proved

  Oct 2026

• Erdős–Heilbronn conjecture, h = 2 (restricted two-fold sumset)Proved

  Oct 2026

• Erdős–Heilbronn restricted sumset theorem (two sets, prime modulus)Proved

  Oct 2026

• Finite aligned cap-and-mass bound with separate coordinate budgetsProved

  Oct 2026

• Extract a prime pair using Chebyshev bounds for squares and higher powersProved

  Oct 2026

• Sharp complex coordinate Hlawka constant for p ≥ 87Proved

  Oct 2026

• The real coordinate Hlawka bound for p ≥ 87Proved

  Oct 2026

• Extract a prime pair from the sharper weighted convolution thresholdProved

  Oct 2026

• Weighted prime-power contamination bound without the extra logarithmic factorProved

  Oct 2026

• A finite E677 magma with 496 elements that is not right-cancellativeProved

  Oct 2026