Certifying non-existence of integer points on curves arXiv:2610.18916 Generalized Pellet's theorem for analytic matrix-valued functions arXiv:2610.18941 Even and Odd Integer Values of the Secondary Zeta Function arXiv:2610.19175

A Multipatch Model for Evaluating Interdivisional Connectivity and V... arXiv:2610.18911 There are only finitely many irregular Diophantine quadruples arXiv:2610.18912 A finite coefficient theory for shape identification in tilted gener... arXiv:2610.18915

A Symbolic Differentiation_Summation Framework for Power Sums of Ari... arXiv:2610.18898 Adjoint Transfer and Order-Lifting Dichotomies for 2 x 2 Matrices ov... arXiv:2610.18900 Cyclic Kronecker Fourier Transforms, Weber Norms, and Rogers-Ramanuj... arXiv:2610.18910

An improved lower bound for the minimum-autocorrelation constant arXiv:2610.18888 Harmonic numbers and Lerch functions behind falling factorial genera... arXiv:2610.18893 On the nonnegative integer solutions to the equation F_n^2+F_m=2^{a} arXiv:2610.18894

The first type of power mean bounds for the Gaussian hypergeometric ... arXiv:2610.10581 A Local Proof of Langlands's First Main Lemma for Local Epsilon Fact... arXiv:2610.10583 On the Rank Condition for Perfect Cuboids arXiv:2610.10643

Octonionic Kittaneh Numerical Radius Inequalities arXiv:2610.10567 Partition-theoretic density formulas: radial Tauberian theory and no... arXiv:2610.10570 On a new class of q-fractional integral operators involving multivar... arXiv:2610.10574

Polynomial \mathcal{Z}-contraction: A unified approach with Application arXiv:2610.10546 The Mirror Theorem: Central Incidence Saturation in Keith Recurrences arXiv:2610.10557 Unilateral and Equitransitive Tilings by Squares of Sizes 1, 2, 3, a... arXiv:2610.10566

A Divisor-Weighted Golomb Sequence: Zeta Asymptotics and Arithmetic ... arXiv:2610.03811 The upper semi-Fredholm radius, extensions of restrictions, and subp... arXiv:2610.03835 Ascertaining Learning: Generative AI, the Proxy Problem, and Cogniti... arXiv:2610.03844

Tilings of Closed Surfaces by Congruent Most Curvilinear Polygons arXiv:2610.03786 Repunit Coordinates for the Erd\H{o}s Ternary-Digit Problem arXiv:2610.03789 Umbral Hermite representations of canonical catastrophe integrals arXiv:2610.03809

Fractional-order differential geometry of Gielis curves: chart regul... arXiv:2610.03754 Multi-Index Recovery for Total-Degree Multivariate Vandermonde Matrices arXiv:2610.03775 Neural Network Solvers for Nonlinear ODEs: Benchmarking MLPs and B-S... arXiv:2610.03783

Finiteness in Square Classes and Weighted Zero Density of Perfect Cu... arXiv:2609.38650

Vector balancing in convex order arXiv:2609.38228 Matrix roots of order n of a multivariate polynomial arXiv:2609.38238 Zero Harmonic Density implies Zero Density arXiv:2609.38240

A density deficit for sums of three cube-full numbers arXiv:2609.35772 A Hypotenuse-Angle Axiomatization of the Hilbert Plane arXiv:2609.35853

The Erd\H{o}s--S\'os Conjecture: A visual exposition of the proof di... arXiv:2609.32011 Almost-Boundedness of Collatz-Type Maps on Number Rings via Archimed... arXiv:2609.33018 Counting Reachable Positions in a Simplified Model of Connect Four arXiv:2609.33068

Formalization of Langlands's Second Main Lemma for Local Epsilon Fac... arXiv:2609.30301

Parallel Searching Method for Verifying Finiteness of Prime Numbers ... arXiv:2609.28805 Extension Theorems in Measure and Integration Theory as Completeness... arXiv:2609.29510 Conditional Aggregation in Context-Aware Fuzzy Systems: A Fibered Re... arXiv:2609.29535

Inequalities for ratios of Gamma functions arXiv:2609.28523 Asymptotic Balance and Structural Rigidity in the Riemann Zeta Function arXiv:2609.28529 Primitive norm extraction and a signed descent for the cubic Fermat ... arXiv:2609.28566

Finite Weil Jets, Identity Transfer, and the Exponential Geometry of... arXiv:2609.28505 A Measure-Theoretic Derivation of Zadeh Fuzzy Logic arXiv:2609.28510 Counterexamples to a conjecture of Kamenetsky on OEIS A173419 arXiv:2609.28512

The Missing Zigzag: Cycles of Semitone Trichords and a Conservation ... arXiv:2609.26114

A Kernel-Certified Verification of the Erd\H{o}s-Mollin-Walsh Conjec... arXiv:2609.25011 Algebraic Proof of Completeness of a Positional Numeral System in th... arXiv:2609.25091 A new proof of the irrationality of e arXiv:2609.25096