2211 papers
This paper presents a generalized framework for the SQIsign signature scheme by incorporating level structures into the isogeny challenge, which leads to a new explicit Deuring correspondence for supersingular elliptic curves and solutions to constrained norm equations.
This paper reinterprets Gödel's second incompleteness theorem through proof-theoretic semantics by demonstrating that while certain arithmetical theories cannot prove their own consistency, they nonetheless semantically support it via a compositional notion of consequence based on inferential roles, thereby reframing incompleteness as a divergence between derivability and internal semantic support rather than a gap between syntax and external truth.
This paper extends fundamental homotopical concepts to -categories and presentable enriched categories by introducing homotopy posets indexed by categorical disk boundaries, which assemble into a Postnikov tower converging for -categories and characterize Postnikov complete -categories as the limit of -categories under truncation.
This paper revisits Kippenhahn's conjecture regarding the unitary equivalence of Hermitian matrix pairs with repeated characteristic polynomial factors by employing local spectral analysis to establish necessary and sufficient conditions for the conjecture's validity.
This paper establishes a generalized version of Reshetnyak's theorem for quasiregular values mapping from generalized -manifolds with controlled geometry to Euclidean space , extending prior results by Kangasniemi and Onninen from the Euclidean setting.
This paper proposes an efficient offline-online subspace decomposition preconditioner that leverages localized defect structures to robustly solve elliptic diffusion problems with multiscale heterogeneous coefficients, significantly reducing the computational cost of uncertainty quantification in Monte-Carlo simulations.
This paper introduces a two-phase approximation method that resolves singularities in three-dimensional harmonic Dirichlet problems by decomposing the solution into a singular component handled via Green's formula with high-order quadrature and a regular component recovered through collocation with a harmonic basis.
This paper investigates the qualitative dynamics and wave-character transitions in radially symmetric isentropic Euler flows across outward supersonic, subsonic, and inward supersonic regimes, establishing structural restrictions, identifying novel asymmetric transition mechanisms, deriving conditions for finite-time singularity formation, and validating these theoretical findings through Semi-Discrete Lagrangian-Eulerian numerical simulations.
This paper introduces a model-agnostic framework that improves function extrapolation by projecting baseline approximations onto feasible sets defined by anchor functions, thereby providing rigorous, proven bounds that guarantee error reduction in extrapolation regions.
This paper resolves a conjecture from OEIS entry A005243 by proving that the greedy self-generating sequence defined by Hofstadter, where each term is the smallest integer greater than the previous one representable as a sum of at least two consecutive earlier terms, omits infinitely many positive integers.
This paper establishes a universal method for solving the Poincaré center problem by proving that every analytic center admits a Laurent inverse integrating factor, thereby enabling a theoretical procedure to characterize centers in polynomial vector fields, including nontrivial families that have resisted previous approaches.
This paper establishes the well-posedness of a cubic nonlinear Schrödinger equation with irregular coefficients in the regime by introducing and proving the existence, uniqueness, and classical compatibility of "very weak solutions," while also validating these findings through numerical experiments.
This paper proves that the local index of an isolated umbilic point on a -smooth convex surface in Euclidean 3-space is strictly less than two by employing a "totally real blow-up" technique to reduce the local problem to a global result regarding Lagrangian surfaces, thereby suggesting the potential existence of exotic umbilic points with index 3/2 that exceed the bounds known for real analytic surfaces.
This paper investigates analogues of exactness for locally compact groupoids, proving that six natural definitions of exactness are equivalent for the class of inner amenable étale groupoids and highlighting the crucial role of exactness in understanding the relationship between groupoid amenability and the coincidence of full and reduced C*-algebras.
This paper introduces a complexity-based measure called "intelligence" to evaluate the quality of approximations of real numbers within a specific model, demonstrating its consistency with classical rational Diophantine approximation while posing an open question regarding the universal existence of such intelligent approximations.
This paper claims to prove the twin prime conjecture by establishing a lower bound for the count of twin primes up to using a new general method for estimating correlations of arithmetic functions.
This paper establishes a sufficient condition for an isomorphism between finite-order real matrix spaces and bivariate polynomial subspaces by linking a proposed polynomial problem to Lagrange bivariate interpolation, thereby proving the existence and uniqueness of solutions and providing construction formulas for these polynomials on finite rectangular grids.
This paper establishes that the explorability of a finitely generated group's Cayley graph by finite automata systems depends on the group's periodicity: periodic groups confine automata to finite areas, groups with non-periodic elements are explorable by automata with three pebbles, and aperiodic groups cannot be explored by any finite automata system.
This paper introduces and develops the concept of ramification within a given modulus, exploring its properties and its potential connections to significant mathematical problems, particularly the Goldbach conjecture.
This paper investigates the distribution of boundary points of expansion to establish a lower bound on the mutual distances between runners on a circular track under specific equidistant spacing conditions, thereby providing a partial application toward the Lonely Runner Conjecture.