math-ph papers | Gist.Science

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🌀 nonlinear sciences

Learning Lax Pairs: Revisiting the Classical Paradigm

This paper challenges the conventional view of Lax pairs as strict structural certificates of integrability by demonstrating through five case studies and the Sparse Identification of Lax Operators (SILO) framework that compatibility conditions often underdetermine the representation, allowing "anomalous" or "fake" pairs to still generate full conservation hierarchies and thus revealing a more nuanced landscape than the binary distinction between true and fake Lax pairs.

Jimmie Adriazola, Gino Biondini, Wei Zhu, Panayotis G. Kevrekidis2026-07-03

🔢 mathematics

A Local Linking Theorem for Relativistic Action Functionals

This paper establishes a local linking theorem for relativistic action functionals by overcoming compactness challenges through a novel perturbative construction combining min-max geometry and Ekeland-Lasry regularization, thereby proving the existence of at least two non-constant solutions for the Lorentz force equation and the prescribed mean curvature operator in Minkowski space.

Manuel Garzón, Salvador López-Martínez2026-07-03

🔢 mathematics

Double-scaled SYK from boundary metrics of planar maps

This paper demonstrates that for a specific family of bipartite planar maps with q-deformed face weights arising from the double-scaled SYK model, the weighted enumeration of maps with a fixed boundary metric depends solely on the crossing number of the associated geodesic chord diagram, thereby establishing an exact correspondence between the induced law of these diagrams and the chord diagram representation of the DSSYK model.

Timothy Budd2026-07-03

🔢 mathematics

Foliations by constant spacetime mean curvature surfaces for asymptotically hyperboloidal initial data sets

This paper constructs an exhaustive foliation of constant spacetime mean curvature surfaces for asymptotically hyperboloidal initial data sets close to the anti-de Sitter-Schwarzschild hyperboloid as the long-time limit of a volume-preserving flow, and applies this result to define and study the center of mass in this setting.

Jacopo Tenan2026-07-03

🔢 mathematics

Flux solutions for stochastic chemical systems with sources and sinks

This paper rigorously defines and analyzes non-equilibrium stochastic chemical systems with sources and sinks as non-explosive Markov chains that converge to steady states, demonstrating their application in modeling molecular fluxes through membrane channels.

E. Franco, J. J. L. Velázquez2026-07-03

🔢 mathematics

On a Rosenzweig-Porter-type model

This paper establishes a comprehensive analysis of a general Rosenzweig-Porter model ( $H=H_0+\lambda W$ ) by proving uniform localization properties and ETH validity across all coupling strengths, thereby generalizing previous deformed Wigner matrix results and revealing the emergence of mobility edges and re-entrant localization.

Giorgio Cipolloni, László Erdős, Joscha Henheik2026-07-03

🔢 mathematics

Orthogonal Dualities of Dynamic Stochastic Higher Spin Vertex Models, using the Drinfeld Twister

This paper introduces a new algebraic method based on the universal Drinfeld twister of $U_q(\mathfrak{sl}_2)$ to construct duality functions for dynamic stochastic higher spin vertex models, proving that these functions are ${}_3 \varphi_2$ hypergeometric series that degenerate to dual $q$ -Krawtchouk polynomials.

Jeffrey Kuan, Zhengye Zhou2026-07-02

🔢 mathematics

Strong Hamel functions and symmetries

This paper characterizes strong Hamel functions on Finsler spaces through their relationship with strong dual and dynamical symmetries, demonstrating that projective deformations by these functions preserve $\chi$ -curvature and clarifying their connection to other curvature-preserving function classes.

Ioan Bucataru, Georgeta Cretu2026-07-02

🔢 mathematics

Generalized Kramers-Wannier Duality from Bilinear Phase Map

This paper introduces the bilinear phase map (BPM) as a generalized framework for Kramers-Wannier duality in qudit spin chains, enabling the exploration of nonunitary dualities, the derivation of noninvertible fusion rules, and the establishment of microscopic anomaly classifications for a broad class of lattice models.

Linhao Li, Masaki Oshikawa, Han Yan2026-07-02

🔢 mathematics

Knizhnik-Zamolodchikov equations in Deligne categories

This paper investigates the Knizhnik-Zamolodchikov equations within Deligne categories under $(\mathfrak{gl}_m,\mathfrak{gl}_{n})$ and $(\mathfrak{so}_m,\mathfrak{so}_{2n})$ dualities, deriving integral formulas for solutions in the former case and computing monodromy for both.

Pavel Etingof, Ivan Motorin, Alexander Varchenko, Isaac Zhu2026-07-02

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