Tootfinder

Type Theory with Single Substitutions
Ambrus Kaposi (E\"otv\"os Lor\'and University), Szumi Xie (E\"otv\"os Lor\'and University)
https://arxiv.org/abs/2510.12303

Type Theory with Single Substitutions
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient inductive-inductive type. Algebraic definitions of type theory include Ehrhard's definition of model, categories with families (CwFs), contextual categories, Awodey's natural models, C-systems, B-systems. With the exception of B-systems, these notions are based on a parallel substitution calculus where substitutions …

from my link log —
Arend: a theorem prover based on Homotopy Type Theory.
https://arend-lang.github.io/
saved 2019-08-07 https://dotat.at/:/AR6J2.html

Fascinating talk on
Type Theory in Type Theory using a Strictified Syntax
Presented by Ambrus Kaposi, joint work with Loïc Pujet.
#icfpsplash25

On the growth of Tate-Shafarevich groups of $p$-supersingular abelian varieties of ${\rm GL}_2$-type over $\mathbb{Z}_p$-extensions of number fields
Erman Isik, Antonio Lei
https://arxiv.org/abs/2510.11511

On the growth of Tate-Shafarevich groups of $p$-supersingular abelian varieties of ${\rm GL}_2$-type over $\mathbb{Z}_p$-extensions of number fields
We study the boundedness of the Mordell-Weil rank and the growth of the $v$-primary part of the Tate-Shafarevich group of $p$-supersingular abelian varieties of ${\rm GL}_2$-type with real multiplication over $\mathbb{Z}_p$-extensions of number fields, where $v$ is a prime lying above $p$. Building on the work of Iovita-Pollack in the case of elliptic curves, under precise ramification and splitting conditions on $p$, we construct explicit systems of local points using the theory of Lubin-Tate …

Some capacitary strong type inequalities and related function spaces
Keng Hao Ooi, Nguyen Cong Phuc
https://arxiv.org/abs/2510.08982 https://arxiv.org/pdf/…

Some capacitary strong type inequalities and related function spaces
We verify a conjecture of D. R. Adams on a capacitary strong type inequality that generalizes the classical capacitary strong type inequality of V. G. Maz'ya. As a result, we characterize related function spaces as Köthe duals to a class of Sobolev multiplier type spaces. Moreover, using tools from nonlinear potential theory, weighted norm inequalities, and Banach function space theory, we show that these spaces are also isomorphic to more concrete spaces that are easy to use and fit in well w…

Fixed Point Theory For Singh-Chatterjea Type Contractive Mappings
Zouaoui Bekri, Nicola Fabiano
https://arxiv.org/abs/2510.11975 https://arxiv.org/pdf/2510…

Fixed Point Theory For Singh-Chatterjea Type Contractive Mappings
In this paper, we introduce a new contraction condition that combines the framework of Singh's extension with the classical Chatterjea contraction. This generalized form, called the Singh-Chatterjea contraction, is defined on the p-th iterate of a mapping. We establish fixed point theorems for such mappings in complete metric spaces and show that our results extend and unify both Singh's and Chatterjea's classical fixed point theorems. Illustrative examples and a simple numerical implementation…

Humanoid Artificial Consciousness Designed with Large Language Model Based on Psychoanalysis and Personality Theory
Sang Hun Kim, Jongmin Lee, Dongkyu Park, So Young Lee, Yosep Chong
https://arxiv.org/abs/2510.09043

Humanoid Artificial Consciousness Designed with Large Language Model Based on Psychoanalysis and Personality Theory
Human consciousness is still a concept hard to define with current scientific understanding. Although Large Language Models (LLMs) have recently demonstrated significant advancements across various domains including translation and summarization, human consciousness is not something to imitate with current upfront technology owing to so-called hallucination. This study, therefore, proposes a novel approach to address these challenges by integrating psychoanalysis and the Myers-Briggs Type Indic…

A Graded Modal Type Theory for Pulse Schedules
Robin Adams
https://arxiv.org/abs/2510.03130 https://arxiv.org/pdf/2510.03130…

A Graded Modal Type Theory for Pulse Schedules
We propose a language for representing the pulse schedules that a superconducting quantum computer accepts as input. The language is a graded modal type theory named PSTT (Pulse Schedule Type Theory). Graded modals type theories are type systems where each variable is annotated with a parameter or grade. These can be used to represent, for example, resource usage, where the grade denotes how many times a given resource may be used; or privacy levels, whether a resource is private or public. In …

K-Points and Type IIB/Heterotic Duality with NS5-Branes
Jeroen Monnee, Timo Weigand, Max Wiesner
https://arxiv.org/abs/2510.02435 https://arxiv.org/pdf/251…

K-Points and Type IIB/Heterotic Duality with NS5-Branes
We revisit type II$_0$ limits in the vector multiplet moduli space of compactifications of Type IIB string theory on Calabi-Yau threefolds. These limits are special because they cannot be described using mirror symmetry. While we showed in previous work that the gravitational duality frame emerging in such limits corresponds to a weakly coupled heterotic string compactified on K3 times a string-sized torus, our focus here is on the additional field theory sectors that decouple from gravity in t…

Great expectations: Unifying Statistical Theory and Programming
Bradley Saul
https://arxiv.org/abs/2510.09853 https://arxiv.org/pdf/2510.09853

Great expectations: Unifying Statistical Theory and Programming
Beginning in the 1970s, statistician-cum-logician Per Martin-Löf wrote a series of papers developing what became Martin-Löf type theory, realizing a system where the distinction between mathematics and programming disappears. Inspired by this vision, this paper introduces dependent type theory (of which Martin-Löf type theory is an example) to a statistical audience. Examples from statistics and probability theory demonstrate how dependent type theory and an algebraic perspective can unify t…

Two-temperature fluid models for a polyatomic gas based on kinetic theory for nearly resonant collisions
Kazuo Aoki, Niclas Bernhoff
https://arxiv.org/abs/2510.12464 https://

Two-temperature fluid models for a polyatomic gas based on kinetic theory for nearly resonant collisions
A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a linear combination of inelastic and elastic (or resonant) collisions, and its basic properties are discussed. Then, in the case where the elastic collisions are dominant, fluid dynamic equations of Euler and Navier--Stokes type including two temperatures, i.…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Homotopy type theory as a language for diagrams of $\infty$-logoses
Taichi Uemura

The Theory of Strategic Evolution: Games with Endogenous Players and Strategic Replicators
Kevin Vallier
https://arxiv.org/abs/2512.07901 https://arxiv.org/pdf/2512.07901 https://arxiv.org/html/2512.07901
arXiv:2512.07901v1 Announce Type: new
Abstract: This paper develops the Theory of Strategic Evolution, a general model for systems in which the population of players, strategies, and institutional rules evolve together. The theory extends replicator dynamics to settings with endogenous players, multi level selection, innovation, constitutional change, and meta governance. The central mathematical object is a Poiesis stack: a hierarchy of strategic layers linked by cross level gain matrices. Under small gain conditions, the system admits a global Lyapunov function and satisfies selection, tracking, and stochastic stability results at every finite depth. We prove that the class is closed under block extension, innovation events, heterogeneous utilities, continuous strategy spaces, and constitutional evolution. The closure theorem shows that no new dynamics arise at higher levels and that unrestricted self modification cannot preserve Lyapunov structure. The theory unifies results from evolutionary game theory, institutional design, innovation dynamics, and constitutional political economy, providing a general mathematical model of long run strategic adaptation.
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Pedro Abreu aka #TypeTheoryForall had an epic conversation with me about all things programming languages, out now on the podcast.
https://www.typetheoryforall.com/…

Best Proximity Points for Geraghty-Type Non-Self Mappings with a Registration-Inspired Alignment Model
Fatemeh Fogh, Sara Behnamian
https://arxiv.org/abs/2510.02406 https://

Best Proximity Points for Geraghty-Type Non-Self Mappings with a Registration-Inspired Alignment Model
We study Geraghty-type non-self mappings within the framework of best proximity point theory. By introducing auxiliary functions with subsequential convergence, we establish general conditions ensuring the existence and uniqueness of best proximity points. Our results extend and unify earlier work on proximal and Kannan-type contractions under a Geraghty setting, and we provide counterexamples showing that the auxiliary assumptions are essential. To demonstrate applicability, we construct a reg…

Effective integration of Lie type algebras
Bruno Vallette
https://arxiv.org/abs/2510.10144 https://arxiv.org/pdf/2510.10144

Effective integration of Lie type algebras
This is a short survey on the recent developments made in the integration theory with effective formulas of algebraic structures stronger or higher than Lie algebras.

Radially weighted Backus- and Childress-type bounds for spherical dynamos
Ralf Kaiser, Andreas Tilgner
https://arxiv.org/abs/2510.05884 https://arxiv.org/p…

Radially weighted Backus- and Childress-type bounds for spherical dynamos
In MHD dynamo theory well-known necessary criteria for dynamo action are formulated in terms of lower bounds either on the maximum modulus of the velocity field (Childress-type) or the maximum strain of the velocity field (Backus-type). We generalize these criteria for spherical dynamos by introducing a radially varying weight $f(r)$. The corresponding {\em l}ower {\em b}ound Reynolds numbers $R_{lb}^C [f]$ (based on velocity) and $R_{lb}^B [f]$ (based on strain) are determined for two types of…

Crosslisted article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Semisimple module categories with fusion rules of the compact full flag manifold type
Mao Hoshino
…

Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra
Zhiyuan Chen
https://arxiv.org/abs/2510.10737 https://arxiv.org/pd…

Finite generation of higher rank quasi-monomial valuations via the extended Rees algebra
In the algebraic theory of K-stability, one of the most challenging problems is to show the graded algebra associated with certain higher rank quasi-monomial valuations are finitely generated. In the global case of Fano varieties and local case of klt singularities, the finite generation has been proved for quasi-monomial valuations on models of qdlt Fano type. In this paper, we generalize these results using a different argument, by studying the extended Rees algebra via a more algebraic appro…

Dimensionality reduction and width of deep neural networks based on topological degree theory
Xiao-Song Yang
https://arxiv.org/abs/2511.06821 https://arxiv.org/pdf/2511.06821 https://arxiv.org/html/2511.06821
arXiv:2511.06821v1 Announce Type: new
Abstract: In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the established theory, we provide some fascinating insights into classification and approximation problems in deep learning theory in the setting of deep neural networks.
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Formalizing the zigzag construction of path spaces of pushouts
Vojt\v{e}ch \v{S}t\v{e}pan\v{c}\'ik
https://arxiv.org/abs/2510.08452 https://arxiv.org/p…

Formalizing the zigzag construction of path spaces of pushouts
A recent pre-print of Wärn gives a novel pen-and-paper construction of a type family characterizing the path spaces of an arbitrary pushout, and a natural language argument for its correctness. We present the first formalization of the construction and a proof that it is fiberwise equivalent to the path spaces. The formalization is carried out in axiomatic homotopy type theory, using the Agda proof assistant and the agda-unimath library.

On Korovkin-type theorems including exponential test functions on infinite intervals through power series convergence
Dilek S\"oylemez, Mehmet \"Unver
https://arxiv.org/abs/2510.12568

On Korovkin-type theorems including exponential test functions on infinite intervals through power series convergence
Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which provide simple and elegant criteria for convergence by testing only on a small set of functions. Motivated by these classical results and their extensions, we focus on versions that preserve exponential functions and incorporate modern summability techniques…

A Continuum Beck-type Theorem for Hyperplanes
Paige Bright, Alexander Ortiz, Dmitrii Zakharov
https://arxiv.org/abs/2510.10907 https://arxiv.org/pdf/2510.1…

A Continuum Beck-type Theorem for Hyperplanes
We prove a sharp continuum Beck-type theorem for hyperplanes. Our work is inspired by foundational work of Beck on the discrete problem, as well as refinements due to Do and Lund. The inductive proof uses recent breakthrough results in projection theory by Orponen--Shmerkin--Wang and Ren, who proved continuum Beck-type theorems for lines in $\mathbb{R}^2$ and $\mathbb{R}^n$.

Noncommutative Regge-Wheeler potential: some nonperturbative results
Nikola Herceg, Tajron Juri\'c, A. Naveena Kumara, Andjelo Samsarov, Ivica Smoli\'c
https://arxiv.org/abs/2510.08125

Noncommutative Regge-Wheeler potential: some nonperturbative results
We study the gravitational perturbation theory of black holes in noncommutative spacetimes with noncommutativity of the type $[t\stackrel{\star}{,} r] = i a αA(r)$ and $[φ\stackrel{\star}{,} r] = i a βA(r)$ for arbitrary $A(r)$, which includes several Moyal-type spaces and also the $κ$-Minkowski space. The main result of this paper is an analytical expression for the effective potential of the axial perturbation modes, valid to all orders in the noncommutativity parameter. This is achieved …

Replaced article(s) found for math.SP. https://arxiv.org/list/math.SP/new
[1/1]:
- On the Hausdorff measure of sets of non-Lyapunov behaviour, and a Jarnik-type theorem for random ...
Sasha Sodin

A doubly composite Chernoff-Stein lemma and its applications
Ludovico Lami
https://arxiv.org/abs/2510.06342 https://arxiv.org/pdf/2510.06342

A doubly composite Chernoff-Stein lemma and its applications
Given a sequence of random variables $X^n=X_1,\ldots, X_n$, discriminating between two hypotheses on the underlying probability distribution is a key task in statistics and information theory. Of interest here is the Stein exponent, i.e. the largest rate of decay (in $n$) of the type II error probability for a vanishingly small type I error probability. When the hypotheses are simple and i.i.d., the Chernoff-Stein lemma states that this is given by the relative entropy between the single-copy p…

Topological Structure of Infrared QCD
J. Gamboa
https://arxiv.org/abs/2511.07455 https://arxiv.org/pdf/2511.07455 https://arxiv.org/html/2511.07455
arXiv:2511.07455v1 Announce Type: new
Abstract: We investigate the infrared structure of QCD within the adiabatic approximation, where soft gluon configurations evolve slowly compared to the fermionic modes. In this formulation, the functional space of gauge connections replaces spacetime as the natural arena for the theory, and the long-distance behavior is encoded in quantized Berry phases associated with the infrared clouds. Our results suggest that the infrared sector of QCD exhibits features reminiscent of a \emph{topological phase}, similar to those encountered in condensed-matter systems, where topological protection replaces dynamical confinement at low energies. In this geometric framework, color-neutral composites such as quark--gluon and gluon--gluon clouds arise as topological bound states described by functional holonomies. Illustrative applications to hadronic excitations are discussed within this approach, including mesonic and baryonic examples. This perspective provides a unified picture of infrared dressing and topological quantization, establishing a natural bridge between non-Abelian gauge theory, adiabatic Berry phases, and the topology of the space of gauge configurations.
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Hydrodynamic models of Reheating
Juan Pablo El\'ia, Lucas Cantarutti, Nahuel Mir\'on-Granese, Esteban Calzetta
https://arxiv.org/abs/2510.08685 https://

Hydrodynamic models of Reheating
We develop a causal hydrodynamic model that provides an effective macroscopic description of the field-theoretic dynamics during the early stages of reheating. The inflaton condensate is treated as a homogeneous background coupled to a relativistic fluid that represents its inhomogeneous fluctuations. Within the divergence-type theory framework derived from kinetic considerations, the model captures essential dissipative and non-equilibrium effects while remaining stable and causal. We find tha…

Majority relations for Condorcet domains of tiling type
Victor Reiner, Bridget Eileen Tenner
https://arxiv.org/abs/2509.19614 https://arxiv.org/pdf/2509.19…

Majority relations for Condorcet domains of tiling type
Condorcet domains are subsets of permutations arising in voting theory: regarding their permutations as preference orders on a list of candidates, one avoids Condorcet's paradox when aggregating the preferences via a simple majority relation. We use poset theory to show that, for the subclass of Condorcet domains of tiling type, the majority rule has stronger properties. We then develop techniques to predict the majority rule explicitly for the uniform vote tally on Condorcet domains of tiling …

Infinite-dimensional Lagrange-Dirac systems with boundary energy flow II: Field theories with bundle-valued forms
Fran\c{c}ois Gay-Balmaz, \'Alvaro Rodr\'iguez Abella, Hiroaki Yoshimura
https://arxiv.org/abs/2511.05687 https://arxiv.org/pdf/2511.05687 https://arxiv.org/html/2511.05687
arXiv:2511.05687v1 Announce Type: new
Abstract: Part I of this paper introduced the infinite dimensional Lagrange--Dirac theory for physical systems on the space of differential forms over a smooth manifold with boundary. This approach is particularly well-suited for systems involving energy exchange through the boundary, as it is built upon a restricted dual space -a vector subspace of the topological dual of the configuration space- that captures information about both the interior dynamics and boundary interactions. Consequently, the resulting dynamical equations naturally incorporate boundary energy flow. In this second part, the theory is extended to encompass vector-bundle-valued differential forms and non-Abelian gauge theories. To account for two commonly used forms of energy flux and boundary power densities, we introduce two distinct but equivalent formulations of the restricted dual. The results are derived from both geometric and variational viewpoints and are illustrated through applications to matter and gauge field theories. The interaction between gauge and matter fields is also addressed, along with the associated boundary conditions, applied to the case of the Yang-Mills-Higgs equations.
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Ground state magnetic structure of Mn3Sn
Jeppe Jon Cederholm, Zhian Xu, Yanfeng Guo, Martin Ovesen, Thomas Olsen, Kristine M. L. Krighaar, Chrystalla Knekna, Jian Rui Soh, Youngro Lee, Navid Qureshi, Jose Alberto Rodriguez Velamazan, Eric Ressouche, Andrew T. Boothroyd, Henrik Jacobsen
https://arxiv.org/abs/2510.06808

Ground state magnetic structure of Mn3Sn
We use spherical neutron polarimetry to determine the ground state magnetic structure of Mn3Sn. We find that Mn3Sn adopts an inverse triangular structure with spins parallel to <100> (Type III) rather than spins parallel to <110> (Type IV). Density functional theory calculations reveal no energy difference between these two structures, suggesting that the selection is caused by subtle effects such as sixth-order anisotropy. Partial control of the magnetic domain population through a moderate ma…

@… In your note on algebraic type theory you mention the "Lindenbaum-Tarski model generated by the raw syntax of pure MLTT without connectives". Just to be sure, this model is trivial, right? There are no types, so the only context is the terminal one.

Regularity Theory for the Space Homogeneous Polyatomic Boltzmann Flow
Ricardo Alonso, Milana \v{C}oli\'c
https://arxiv.org/abs/2510.10523 https://arxiv…

Regularity Theory for the Space Homogeneous Polyatomic Boltzmann Flow
In this paper, we study the polyatomic Boltzmann equation based on continuous internal energy, focusing on physically relevant collision kernels of the hard potentials type with integrable angular part. We establish three main results: smoothing effects of the gain collision operator, propagation of velocity and internal energy first-order derivatives of solutions, and exponential decay estimates for singularities of the initial data. These results ultimately lead to a decomposition theorem, sh…

Modular theory and symmetry resolution in hyperfinite von Neumann algebras
Giuseppe Di Giulio, Moritz Dorband, Johanna Erdmenger, Henri Scheppach
https://arxiv.org/abs/2510.02441

Modular theory and symmetry resolution in hyperfinite von Neumann algebras
We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of finite-dimensional algebras with fixed subregion charge values. An important ingredient is the combination of these algebras using direct integrals. This allows us to obtain the symmetry-resolved modular operator, modular flow, and modular correlation functi…

Hausdorff dimension of the Wedding cake type surfaces
Bal\'azs B\'ar\'any, Manuj Verma
https://arxiv.org/abs/2510.04613 https://arxiv.org/pdf/2…

Hausdorff dimension of the Wedding cake type surfaces
In this paper, we study the Hausdorff dimension of fractal interpolation surfaces (FISs) over a triangular domain. These FISs are known as `wedding cake surfaces'. These surfaces are the attractor of some deterministic self-affine iterated function systems (IFS) on $\mathbb{R}^3$ generated by a fractal interpolation algorithm. Due to the recent seminal result of Rapaport (Adv. Math. 449 (2024) 109734), the dimension theory of self-affine IFS on $\mathbb{R}^3$ is known whenever the IFS is strong…

Mean-Field Price Formation on Trees
Masaaki Fujii
https://arxiv.org/abs/2510.11261 https://arxiv.org/pdf/2510.11261…

Mean-Field Price Formation on Trees
In this work, we combine the mean-field game theory with the classical idea of binomial tree framework, pioneered by Sharpe and Cox, Ross & Rubinstein, to solve the equilibrium price formation problem for the stock. For agents with exponential utilities and recursive utilities of exponential type, we prove the existence of a unique mean-field equilibrium and derive an explicit formula for equilibrium transition probabilities of the stock price by restricting its trajectories onto a binomial tre…

Constraining GREA, an alternative theory accounting for the present cosmic acceleration
R. Calderon, J. Garcia-Bellido, B. Vos-Gines, V. Gonzalez-Perez, A. Shafieloo, J. Aguilar, S. Ahlen, D. Bianchi, D. Brooks, T. Claybaugh, A. de la Macorra, J. E. Forero-Romero, E. Gazta\~naga, S. Gontcho A Gontcho, G. Gutierrez, K. Honscheid, C. Howlett, M. Ishak, R. Joyce, R. Kehoe, T. Kisner, A. Kremin, O. Lahav, A. Lambert, M. Landriau, M. Manera, R. Miquel, F. Prada, I. Perez-Rafols, E. Sanchez,…

Constraining GREA, an alternative theory accounting for the present cosmic acceleration
The origin of the Universe's late-time accelerated expansion remains unknown. The General Relativistic Entropic Acceleration (GREA) theory offers a compelling alternative to $Λ$CDM, attributing cosmic acceleration to entropy growth associated with cosmic and black hole horizons, without invoking a cosmological constant. We test GREA against the latest DESI DR2 Baryon Acoustic Oscillations (BAO), multiple Type Ia supernova compilations (Union3, Pantheon$\texttt{+}$, DES-SN5YR), and cosmic micro…

One-sided Hom shifts
Marie-Pierre B\'eal, Alexi Block Gorman
https://arxiv.org/abs/2509.24754 https://arxiv.org/pdf/2509.24754

One-sided Hom shifts
We prove that it is decidable whether a one-sided shift of finite type is conjugate to a one-sided Hom-shift, and whether a tree-shift of finite type is conjugate to a Hom tree-shift. The proof uses Williams's theory for one-sided shifts

Crosslisted article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Reconstruction of tensor categories of type $G_2$
Lilit Martirosyan, Hans Wenzl

from my link log —
Homotopy type theory for dummies.
http://www.chriswarbo.net/blog/2015-09-11-hott_for_dummies.html
saved 2025-11-03 …

Duality theory of tautological systems
Paul G\"orlach, Christian Sevenheck
https://arxiv.org/abs/2510.01980 https://arxiv.org/pdf/2510.01980

Duality theory of tautological systems
We discuss the holonomic dual of tautological systems, with a view towards applications to linear free divisors and to homogeneous spaces. As a technical tool, we consider a Chevalley--Eilenberg type complex, generalizing Euler--Koszul technology from the GKZ theory, and show equivariance and holonomicity of it.

Poincar\'e-Einstein 4-manifolds with conformally K\"ahler geometry
Mingyang Li, Hongyi Liu
https://arxiv.org/abs/2510.04928 https://arxiv.org/pdf/…

Poincaré-Einstein 4-manifolds with conformally Kähler geometry
We study 4-dimensional Poincaré-Einstein manifolds whose conformal class contains a Kähler metric. Such Einstein metrics are non-Kähler and admit a Killing field extending to the conformal infinity, and the Einstein equation reduces to a Toda-type equation. When the Killing field integrates to an $\mathbb{S}^1$-action, we formulate a Dirichlet boundary value problem and establish existence and uniqueness theory. This construction provides a non-perturbative realization of infinite-dimensiona…

Replaced article(s) found for cs.PL. https://arxiv.org/list/cs.PL/new
[1/1]:
- A Two-Level Linear Dependent Type Theory
Qiancheng Fu, Hongwei Xi
https://

Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations
Zhen-Chen Guo, Xin Liang
https://arxiv.org/abs/2509.25942 https://

Flexible fixed-point iteration and its applications for nonsymmetric algebraic Riccati equations
In this paper, we reveal the intrinsic Toeplitz structure in the unique stabilizing solution for nonsymmetric algebraic Riccati equations by employing a shift-involved fixed-point iteration, and propose an RADI-type method for computing this solution for large-scale equations of this type with sparse and low-rank structure by incorporating flexible shifts into the fixed-point iteration. We present a shift-selection strategy, termed Leja shifts, based on rational approximation theory, which is i…

Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory
Stefano Boccelli, Giorgio Martal\`o, Romina Travaglini
https://arxiv.org/abs/2509.20268

Turing instability and 2-D pattern formation in reaction-diffusion systems derived from kinetic theory
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of Brusselator type, which, compared with the classical formulation, presents an additional parameter whose role in stability and pattern formation is discussed. In the second framework, the system exhibits standard nonlinear diffusion terms typical of predator-pr…

Category Theory for Supercomputing: The Tensor Product of Linear BSP Algorithms
Thomas Koopman, Rob H. Bisseling, Sven-Bodo Scholz
https://arxiv.org/abs/2510.00979 https://

Category Theory for Supercomputing: The Tensor Product of Linear BSP Algorithms
We show that a particular class of parallel algorithm for linear functions can be straightforwardly generalized to a parallel algorithm of their tensor product. The central idea is to take a model of parallel algorithms -- Bulk Synchronous Parallel (BSP) -- that decomposes parallel algorithms into so-called supersteps that are one of two types: a computation superstep that only does local computations, or a communication superstep that only communicates between processors. We connect each type …

Complexity of Activity Patterns in a Bio-Inspired Hopfield-Type Network in Different Topologies
Marco Cafiso, Paolo Paradisi
https://arxiv.org/abs/2509.18758 https://

Natural transformations between braiding functors in the Fukaya category
Yujin Tong
https://arxiv.org/abs/2511.10462 https://arxiv.org/pdf/2511.10462 https://arxiv.org/html/2511.10462
arXiv:2511.10462v1 Announce Type: new
Abstract: We study the space of $A_\infty$-natural transformations between braiding functors acting on the Fukaya category associated to the Coulomb branch $\mathcal{M}(\bullet,1)$ of the $\mathfrak{sl}_2$ quiver gauge theory. We compute all cohomologically distinct $A_\infty$-natural transformations $\mathrm{Nat}(\mathrm{id}, \mathrm{id})$ and $\mathrm{Nat}(\mathrm{id}, \beta_i^-)$, where $\beta_i^-$ denotes the negative braiding functor. Our computation is carried out in a diagrammatic framework compatible with the established embedding of the KLRW category into this Fukaya category. We then compute the Hochschild cohomology of the Fukaya category using an explicit projective resolution of the diagonal bimodule obtained via the Chouhy-Solotar reduction system, and use this to classify all cohomologically distinct natural transformations. These results determine the higher $A_\infty$-data encoded in the braiding functors and their natural transformations, and provide the first step toward a categorical formulation of braid cobordism actions on Fukaya categories.
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Global Convergence of Four-Layer Matrix Factorization under Random Initialization
Minrui Luo, Weihang Xu, Xiang Gao, Maryam Fazel, Simon Shaolei Du
https://arxiv.org/abs/2511.09925 https://arxiv.org/pdf/2511.09925 https://arxiv.org/html/2511.09925
arXiv:2511.09925v1 Announce Type: new
Abstract: Gradient descent dynamics on the deep matrix factorization problem is extensively studied as a simplified theoretical model for deep neural networks. Although the convergence theory for two-layer matrix factorization is well-established, no global convergence guarantee for general deep matrix factorization under random initialization has been established to date. To address this gap, we provide a polynomial-time global convergence guarantee for randomly initialized gradient descent on four-layer matrix factorization, given certain conditions on the target matrix and a standard balanced regularization term. Our analysis employs new techniques to show saddle-avoidance properties of gradient decent dynamics, and extends previous theories to characterize the change in eigenvalues of layer weights.
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The 2025 OpenAI Preparedness Framework does not guarantee any AI risk mitigation practices: a proof-of-concept for affordance analyses of AI safety policies
Sam Coggins, Alex Saeri, Katherine A. Daniell, Lorenn P. Ruster, Jessie Liu, Jenny L. Davis
https://arxiv.org/abs/2509.24394

The 2025 OpenAI Preparedness Framework does not guarantee any AI risk mitigation practices: a proof-of-concept for affordance analyses of AI safety policies
Prominent AI companies are producing 'safety frameworks' as a type of voluntary self-governance. These statements purport to establish risk thresholds and safety procedures for the development and deployment of highly capable AI. Understanding which AI risks are covered and what actions are allowed, refused, demanded, encouraged, or discouraged by these statements is vital for assessing how these frameworks actually govern AI development and deployment. We draw on affordance theory to analyse t…

Functional Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem
K. Mahesh Krishna
https://arxiv.org/abs/2510.09609 https://arxiv.org/pdf/2510.09609

Functional Donoho-Elad-Gribonval-Nielsen-Fuchs Sparsity Theorem
Celebrated breakthrough sparsity theorem obtained independently by Donoho and Elad \textit{[Proc. Natl. Acad. Sci. USA, 2003]} and Gribonval and Nielsen \textit{[IEEE Trans. Inform. Theory, 2003]} and Fuchs \textit{[IEEE Trans. Inform. Theory, 2004]} says that unique sparse solution to NP-Hard $\ell_0$-minimization problem can be obtained using unique solution to P-Type $\ell_1$-minimization problem. In this paper, we extend their result to abstract Banach spaces using 1-approximate Schauder fr…

The magnon spectra of g-type altermagnet bulk CrSb
Murat Tas
https://arxiv.org/abs/2510.03759 https://arxiv.org/pdf/2510.03759

The magnon spectra of g-type altermagnet bulk CrSb
We present a calculation of the magnon spectra and chiral lifetimes of altermagnons in bulk CrSb using the many-body perturbation theory. The spin-split band structure is evident in the magnon spectra. Altermagnons attain an energy of 275 meV at the K point of the Brillouin zone. Due to large spin splitting at a specific ${\bf q}$ point along the A - M direction, lifetime differences of chiral altermagnons reach approximately 20 fs.

On Bergman projections and sharp decomposition theorems in tubular and related domains in $C^n$
R. F. Shamoyan
https://arxiv.org/abs/2509.22024 https://arx…

On Bergman projections and sharp decomposition theorems in tubular and related domains in $C^n$
The theory of analytic function spaces in very general tubular domains over symmetric cones is a relatively new interesting research area. Tube domains are very general and very complicated domains. Recently several new results in this research area were provided in papers of B. Sehba and his coauthors concerning Bergman type operators in such type complicated unbounded domains. In this note we expand their results to certain spaces of analytic functions in products of tube domains. We define n…

Regularity theory for mixed local-nonlocal problem involving general stable operators
Pedro Fellype Pontes, Minbo Yang
https://arxiv.org/abs/2510.06569 https://

Regularity theory for mixed local-nonlocal problem involving general stable operators
In this paper, we study the regularity of solutions to a linear elliptic equation involving a mixed local-nonlocal operator of the form $$Lu - \operatorname{div}\big(a(x)\nabla u(x)\big)= f, \quad \text{in } Ω\subset \mathbb{R}^n,$$ where $L$ is a general stable Lévy type operator and $a(\cdot)$ is a positive Hölder continuous weight. By establishing a maximum principle and a Liouville-type result in the entire space, we are able to derive the interior regularity and the regularity up to the…

Isoenergetic description of induced fission pathways within energy-density functional theory
Alan A. Dzhioev, N. V. Antonenko
https://arxiv.org/abs/2509.22006 https://

Isoenergetic description of induced fission pathways within energy-density functional theory
A thermodynamically consistent description of induced fission pathways in the superheavy nucleus $^{296}$Lv is presented within the framework of nuclear energy-density functional theory. Using self-consistent finite-temperature Hartree-Fock-Bogoliubov calculations with the Skyrme-type energy-density functional SkM$^*$, we derive and compare effective potentials corresponding to different thermodynamic processes -- isothermal ($T=\text{const}$), isentropic ($S=\text{const}$), and isoenergetic ($…

Ab initio calculation of atomic solid hydrogen phases based on Gutzwiller many-body wave functions
Zhuo Ye, Jun Liu, Yong-Xin Yao, Feng Zhang, Kai-Ming Ho, Cai-Zhuang Wang
https://arxiv.org/abs/2510.02064

Ab initio calculation of atomic solid hydrogen phases based on Gutzwiller many-body wave functions
We apply two ab initio many-body methods based on Gutzwiller wave functions, i.e., correlation matrix renormalization theory (CMRT) and Gutzwiller conjugate gradient minimization (GCGM), to the study of crystalline phases of atomic hydrogen. Both methods avoid empirical Hubbard U parameters and are free from double-counting issues. CMRT employs a Gutzwiller-type approximation that enables efficient calculations, while GCGM goes beyond this approximation to achieve higher accuracy at higher comp…

Is the Wikipedia page on the calculus of constructions wrong? It seems to present a type theory with Prop : Type and where both are impredicative, while also claiming that this is consistent...
(ping @… since you seem to be on an editing roll)

$\chi$ -extending modular lattices
Jesus Adrian Celis-Gonz\'alez, Hugo Alberto Rinc\'on-Mej\'ia
https://arxiv.org/abs/2509.22903 https://arxiv.…

$χ$ -extending modular lattices
This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly extending counterparts. Modular and upper continuous lattices are analyzed, with lemmas establishing relationships between pseudo-complements, complements, and essential elements. Applications to module theory are highlighted.

Nonparametric hazard rate estimation with associated kernels and minimax bandwidth choice
Luce Breuil, Sarah Kaaka\"i
https://arxiv.org/abs/2509.24535 https://

Nonparametric hazard rate estimation with associated kernels and minimax bandwidth choice
In this paper, we consider the general theory of nonparametric hazard rate estimation with associated kernels, for which the shape of the kernel depends on the point of estimation. We prove MISE convergence results and a central limit theorem for such estimators. We then prove an oracle type inequality for both a local and global minimax bandwidth choice. The results are then illustrated by showing that they apply to the Gamma and providing numerical simulations and an application to biological…

S-D-RSM: Stochastic Distributed Regularized Splitting Method for Large-Scale Convex Optimization Problems
Maoran Wang, Xingju Cai, Yongxin Chen
https://arxiv.org/abs/2511.10133 https://arxiv.org/pdf/2511.10133 https://arxiv.org/html/2511.10133
arXiv:2511.10133v1 Announce Type: new
Abstract: This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks, compressed sensing, and so on. Stochastic gradient descent (SGD) and its variants are commonly employed to solve such problems. However, existing algorithms often rely on vanishing step sizes, strong convexity assumptions, or entail substantial computational overhead to ensure convergence or obtain favorable complexity. To bridge the gap between theory and practice, we integrate consensus optimization and operator splitting techniques (see Problem Reformulation) to develop a novel stochastic splitting algorithm, termed the \emph{stochastic distributed regularized splitting method} (S-D-RSM). In practice, S-D-RSM performs parallel updates of proximal mappings and gradient information for only a randomly selected subset of agents at each iteration. By introducing regularization terms, it effectively mitigates consensus discrepancies among distributed nodes. In contrast to conventional stochastic methods, our theoretical analysis establishes that S-D-RSM achieves global convergence without requiring diminishing step sizes or strong convexity assumptions. Furthermore, it achieves an iteration complexity of $\mathcal{O}(1/\epsilon)$ with respect to both the objective function value and the consensus error. Numerical experiments show that S-D-RSM achieves up to 2--3$\times$ speedup compared to state-of-the-art baselines, while maintaining comparable or better accuracy. These results not only validate the algorithm's theoretical guarantees but also demonstrate its effectiveness in practical tasks such as compressed sensing and empirical risk minimization.
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from my link log —
Identity types.
https://bartoszmilewski.com/2025/09/22/identity-types/
saved 2025-09-26 https://dotat.…

Identity Types
Previously: Models of (Dependent) Type Theory. There is a deep connection between mathematics and programming. Computer programs deal with such mathematical objects as numbers, vectors, monoids, fu…

On the finiteness of logarithmic Hamiltonians for Volterra-type lattices in terms of the spectral measures of Jacobi operators
Andrey Osipov
https://arxiv.org/abs/2509.26250 htt…

On the finiteness of logarithmic Hamiltonians for Volterra-type lattices in terms of the spectral measures of Jacobi operators
We establish a correspondence between the semi-infinite and infinite Volterra lattices having a finite logarithmic Hamiltonian and certain classes of even probability measures. In doing so, we apply the inverse spectral theory of Jacobi operators and the theory of orthogonal polynomials. A similar correspondence is established for semi-infinite modified Volterra lattices.

On Dynamic Programming Theory for Leader-Follower Stochastic Games
Jilles Steeve Dibangoye, Thibaut Le Marre, Ocan Sankur, Fran\c{c}ois Schwarzentruber
https://arxiv.org/abs/2512.05667 https://arxiv.org/pdf/2512.05667 https://arxiv.org/html/2512.05667
arXiv:2512.05667v1 Announce Type: new
Abstract: Leader-follower general-sum stochastic games (LF-GSSGs) model sequential decision-making under asymmetric commitment, where a leader commits to a policy and a follower best responds, yielding a strong Stackelberg equilibrium (SSE) with leader-favourable tie-breaking. This paper introduces a dynamic programming (DP) framework that applies Bellman recursion over credible sets-state abstractions formally representing all rational follower best responses under partial leader commitments-to compute SSEs. We first prove that any LF-GSSG admits a lossless reduction to a Markov decision process (MDP) over credible sets. We further establish that synthesising an optimal memoryless deterministic leader policy is NP-hard, motivating the development of {\epsilon}-optimal DP algorithms with provable guarantees on leader exploitability. Experiments on standard mixed-motive benchmarks-including security games, resource allocation, and adversarial planning-demonstrate empirical gains in leader value and runtime scalability over state-of-the-art methods.
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Crosslisted article(s) found for math.KT. https://arxiv.org/list/math.KT/new
[1/1]:
- On the representation type of a finite tensor category
Petter Andreas Bergh, Karin Erdmann, Julia Yael Plavnik, Sarah Witherspoon

Higher H\"older regularity for degenerate elliptic PDEs with data in Morrey spaces
Giuseppe Di Fazio, Rafayel Teymurazyan, Jos\'e Miguel Urbano
https://arxiv.org/abs/2510.10359

Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces
We establish sharp local $C^{1,α}$-regularity for weak solutions to degenerate elliptic equations of $p$-Laplacian type with data in Morrey spaces. The proof relies on the Fefferman-Phong inequality and standard tools from regularity theory for nonlinear PDEs.

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Tilting representations of finite groups of Lie type
Arnaud Eteve
https://

After a few intense weeks — first at #icfpsplash25 in Singapore, then four days of interviewing candidates for tenure-track positions as part of the faculty appointment committee (Lärarförslagsnämnd) at the University of Gothenburg — I’m now in Budapest for (mostly) vacation.
Tomorrow (2025-10-27) I’ll give a talk at the local Type Theory Seminar (invited by Ambrus Kaposi). Looking f…

Neural network approximation of Euclidean path integrals and its application for the $\phi^4$ theory in 1 1 dimensions
Gabor Balassa
https://arxiv.org/abs/2509.18785 https://

Ghost-free, gauge invariant SVT generalizations of Horndeski theory
S. Mironov, A. Shtennikova, M. Valencia-Villegas
https://arxiv.org/abs/2509.16850 https://

Ghost-free, gauge invariant SVT generalizations of Horndeski theory
We present a new type of Scalar-Vector-Tensor (SVT) theories with higher derivatives of all the fields in the action, but with second order equations of motion. The higher derivative vector field is invariant under a U(1) gauge transformation and the Scalar-Tensor sector corresponds to Horndeski theory. We also present a subclass of these SVT theories with 8 free functions of $π$ and $X$ where the speed of the tensor and vector modes is exactly the same. In particular, the Horndeski functions …

Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves
Soheyla Feyzbakhsh, Naoki Koseki, Zhiyu Liu, Nick Rekuski
https://arxiv.org/abs/2509.24990 https…

Stability conditions on Calabi-Yau threefolds via Brill-Noether theory of curves
Fix a polarised Calabi-Yau threefold $(X,H)$. We reduce a version of the Bayer-Macrì-Toda conjecture for $(X,H)$, which ensures the existence of Bridgeland stability conditions on $X$, to verifying a Brill-Noether-type inequality for curves on $X$. We then prove this inequality for a broad class of Calabi-Yau threefolds, including complete intersection Calabi-Yau threefolds in weighted projective spaces.

… zwischen zwei Saunagängen ne Idee gehabt wie man Martin-Löf dependent type theory im @… erklärt und mir jetzt was Schickes angezogen. Jetzt geht’s noch auf nen 80. Geburtstag (nicht meiner).
What a Life. 🤗
*so lange Star Wars Raumschiffe sagen bis einer keine neuen mehr weiß.
2/2

The orbital-driven topological phase transition and planar Hall responses in ternary tellurides Weyl semi-metals
Banasree Sadhukhan, Tanay Nag
https://arxiv.org/abs/2509.19818 h…

The orbital-driven topological phase transition and planar Hall responses in ternary tellurides Weyl semi-metals
Here we study electronic properties of the ternary tellurides TaXTe$_4$ (X=Rh, Ir) using density functional theory and investigate chiral anomaly mediated planar Hall response from ab initio calculations. We show that TaRhTe$_4$ is a hybrid Weyl semimetal (WSM), hosting Weyl points (WPs) of both type-I, type-II, while TaIrTe$_4$ is a type-II WSM as it hosts only type-II WPs with spin-orbit couplings (SOC). All WPs lie in the $k_z=0$ plane, and remain well-separated in both momentum and energy l…

From finding a spanning subgraph $H$ to an $H$-factor
Allan Lo
https://arxiv.org/abs/2509.18832 https://arxiv.org/pdf/2509.18832

from my link log —
Type theory and functional programming. (1999)
https://www.cs.cornell.edu/courses/cs6110/2015sp/textbook/Simon Thompson textbook.pdf
saved 2025-08-14

Hamiltonian flow between standard module Lagrangians
Yujin Tong
https://arxiv.org/abs/2511.06431 https://arxiv.org/pdf/2511.06431 https://arxiv.org/html/2511.06431
arXiv:2511.06431v1 Announce Type: new
Abstract: In Aganagic's Fukaya category of the Coulomb branch of quiver gauge theory, the $T_\theta$-brane algebra gives a symplectic realization of the Khovanov-Lauda-Rouquier-Webster (KLRW) algebra, where each standard module is known to admit two Lagrangian realizations: the 'U'-shaped $T$-brane and the step $I$-brane. We show that the latter arises as the infinite-time limit of the Hamiltonian evolution of the former, thus serving as a generalized thimble. This provides a geometric realization of the categorical isomorphism previously established through holomorphic disc counting.
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Holographic description of 4d Maxwell theories and their code-based ensembles
Ahmed Barbar, Anatoly Dymarsky, Alfred Shapere
https://arxiv.org/abs/2510.03392 https://

Holographic description of 4d Maxwell theories and their code-based ensembles
We formulate a precise holographic duality between an ensemble of 4d $U(1)^g$ Maxwell theories living on a spin four-manifold $M_4$ and an Abelian BF-type 2-form gauge theory of level $N$, summed over all five-manifolds with boundary $M_4$. The elements of the boundary ensemble are Abelian gauge theories specified by self-dual symplectic codes over $Z_N$, that parameterize topological boundary conditions in the 5d TQFT. Similarly, the equivalence classes of topologies distinguished by the 5d th…

Invariant Price of Anarchy: a Metric for Welfarist Traffic Control
Ilia Shilov, Mingjia He, Heinrich H. Nax, Emilio Frazzoli, Gioele Zardini, Saverio Bolognani
https://arxiv.org/abs/2512.05843 https://arxiv.org/pdf/2512.05843 https://arxiv.org/html/2512.05843
arXiv:2512.05843v1 Announce Type: new
Abstract: The Price of Anarchy (PoA) is a standard metric for quantifying inefficiency in socio-technical systems, widely used to guide policies like traffic tolling. Conventional PoA analysis relies on exact numerical costs. However, in many settings, costs represent agents' preferences and may be defined only up to possibly arbitrary scaling and shifting, representing informational and modeling ambiguities. We observe that while such transformations preserve equilibrium and optimal outcomes, they change the PoA value. To resolve this issue, we rely on results from Social Choice Theory and define the Invariant PoA. By connecting admissible transformations to degrees of comparability of agents' costs, we derive the specific social welfare functions which ensure that efficiency evaluations do not depend on arbitrary rescalings or translations of individual costs. Case studies on a toy example and the Zurich network demonstrate that identical tolling strategies can lead to substantially different efficiency estimates depending on the assumed comparability. Our framework thus demonstrates that explicit axiomatic foundations are necessary in order to define efficiency metrics and to appropriately guide policy in large-scale infrastructure design robustly and effectively.
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Continuum Fractons: Quantization and the Many Body Problem
Ylias Sadki, Abhishodh Prakash, S. L. Sondhi
https://arxiv.org/abs/2510.00110 https://arxiv.org/…

Continuum Fractons: Quantization and the Many Body Problem
We formulate a continuum quantum mechanics for non-relativistic, dipole-conserving fractons. Imposing symmetries and locality results in novel phenomena absent in ordinary quantum mechanical systems. A single fracton has a vanishing Hamiltonian, and thus its spectrum is entirely composed of zero modes. For the two-body problem, the Hamiltonian is perfectly described by Sturm--Liouville (SL) theory. The effective two-body Hamiltonian is an SL operator on $(-1,1)$ whose spectral type is set by th…

Finite-blocklength Fluid Antenna Systems
Zhentian Zhang, Kai-Kit Wong, David Morales-Jimenez, Hao Jiang, Hao Xu, Christos Masouros, Zaichen Zhang, Chan-Byoung Chae
https://arxiv.org/abs/2509.15643

Finite-blocklength Fluid Antenna Systems
This work introduces and investigates finite blocklength fluid antenna systems (FBL-FASs). To meet the stringent key performance indicators (KPIs) of 6G and beyond networks, including ultra-massive machine-type communications (mMTC), ultra-reliable low-latency communications (URLLC), and enhanced mobile broadband (eMBB), it is necessary to evaluate the performance of FAS under limited channel uses across time, frequency, and other domains. By exploiting random matrix theory and extreme value th…

Approximation by multivariate neural network operators in mixed norm space: theory and application
Priyanka Majethiya, Shivam Bajpeyi
https://arxiv.org/abs/2509.18740 https://…

Type-II Band Alignment in the ${\beta}$-Ga$_2$O$_3$/Rutile GeO$_2$ Heterojunction toward Solar-Blind Photodetection: A first-principles study
D. Q. Fang
https://arxiv.org/abs/2509.19948

Type-II Band Alignment in the $β$-Ga$_2$O$_3$/Rutile GeO$_2$ Heterojunction toward Solar-Blind Photodetection: A first-principles study
Semiconductor heterostructures capable of separating photogenerated electrons and holes have a wide range of optoelectronic applications, including photodetectors, solar cells, and photocatalysts. $β$-Ga$_2$O$_3$ and rutile GeO$_2$ are both ultrawide-bandgap semiconductors, with bandgaps of 4.85 eV and 4.68 eV, respectively. In this work, we employ first-principles calculations based on density functional theory to investigate the band alignment of the $β$-Ga$_2$O$_3$/rutile GeO$_2$ heterojun…

Frieze patterns in representation theory
Eleonore Faber
https://arxiv.org/abs/2509.16764 https://arxiv.org/pdf/2509.16764

Frieze patterns in representation theory
Friezes are infinite arrays of numbers, in which every four neighbouring vertices arranged in a diamond satisfy the same arithmetic rule. Introduced in the late 1960s by Coxeter, and further studied by Conway and Coxeter in their remarkable papers from 1973, this topic has been nearly forgotten for over thirty years. But since the discovery of connections to cluster algebras and categories of type $A$, interest in friezes has exploded, several generalizations have been studied, and links to geo…

Dynamical Triangulations for 2D Pure Gravity and Topological Recursion
Hiroyuki Fuji, Masahide Manabe, Yoshiyuki Watabiki
https://arxiv.org/abs/2509.18916 https://

Dynamical Triangulations for 2D Pure Gravity and Topological Recursion
We show that, in two-dimensional Euclidean quantum gravity without matter fields, the Schwinger-Dyson equations derived within the Hamiltonian framework of non-critical string field theory can be reformulated in terms of the Chekhov-Eynard-Orantin topological recursion, and we explicitly compute the associated low-order amplitudes. In particular, we establish this reformulation for two discrete models -- the basic type and the strip type -- as well as for the continuum limit of dynamical triang…

General Riemann Integration on Partially Ordered Net Convergence Structures
Alexandre Reggiolli Teixeira
https://arxiv.org/abs/2509.24430 https://arxiv.org…

General Riemann Integration on Partially Ordered Net Convergence Structures
In this article, we propose a general theory of integration of the Riemann type with respect to arbitrary measures and functions, connected by a continuous bilinear product, with values in abstract Riesz spaces endowed with a general convergence given by nets. This covers both the topological and order based convergences in the literature. We then show that this integral satisfies most of the common order based properties of the objects that comprises integration theory. By establishing a gener…

Preformed Cooper Pairing and the Uncondensed Normal-State Component in Phase-Fluctuating Cuprate Superconductivity
F. Yang, Y. Shi, L. Q. Chen
https://arxiv.org/abs/2509.21133 h…

Preformed Cooper Pairing and the Uncondensed Normal-State Component in Phase-Fluctuating Cuprate Superconductivity
We develop a self-consistent microscopic framework beyond mean-field theory for superconductivity in cuprates. It couples fermionic quasiparticles with collective phase dynamics to treat the superconducting gap and superfluid stiffness. The phase sector explicitly incorporates both smooth bosonic Nambu-Goldstone phase fluctuations, renormalized by long-range Coulomb interactions, and topological Berezinskii-Kosterlitz-Thouless-type vortex-antivortex fluctuations. The required input is the corre…

Supergroup Invariants and the Brane/Negative Brane Expansion
Kasia Budzik
https://arxiv.org/abs/2509.20451 https://arxiv.org/pdf/2509.20451

Supergroup Invariants and the Brane/Negative Brane Expansion
We propose a Molien--Weyl-type formula computing generating functions of invariants of supergroups $U(N|M)$, i.e. polynomials in supertraces, which arise as gauge groups of brane/negative brane systems in string theory. We either prove or numerically verify the formula in various examples. The formula further leads to a new expansion relating finite-$N$ and infinite-$N$ indices of $U(N)$ gauge theories. We comment on its relation to Murthy's Giant Graviton expansion, for which we suggest a…

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Exceptional sequences of type $B_n/C_n$ and those in the abelian tube
Kiyoshi Igusa, Emre Sen

Cu2XSiS4 (X = Ge, Sn, and Pb) materials for solar-cell applications: A DFT SCAPS-1D simulation
H. Laltlanmawii, L. Celestine, R. Zosiamliana, B. Chettri, S. Bhattarai, K. C. Bhamu, D. P. Rai
https://arxiv.org/abs/2509.20845

Cu2XSiS4 (X = Ge, Sn, and Pb) materials for solar-cell applications: A DFT+SCAPS-1D simulation
By means of the first-principles density functional theory (DFT), I2-II-IV-VI4 type Cu-based quaternary chalcogenides Cu 2 XSiS 4 (X = Ge, Sn, and Pb) have been thoroughly investigated. We report the study of Ge and Sn substitution in the divalent cation site for their potential applications in photovoltaics for the first time. The structural, electronic, optical, and mechanical properties have been calculated. The structural and thermal stability is verified by calculating the elastic constant…

On the Landis Conjecture for Positive Quasi-linear Operators on Graphs
Ujjal Das, Matthias Keller, Yehuda Pinchover
https://arxiv.org/abs/2509.20559 https://

On the Landis Conjecture for Positive Quasi-linear Operators on Graphs
We prove a Landis type unique continuation result for positive quasi-linear operators on graphs. Specifically, we give decay criteria that ensures when a harmonic function for a positive quasilinear Schrödinger operator with potential less than 1 is trivially zero. The assumption of positivity of the operator allows the application of criticality theory such as the Liouville comparison theorem. Furthermore, our results fundamentally build on the so called simplified energy. As an application w…

Correlation Effects on Magnetic Structure and Lattice Dynamics of LaMn$_7$O$_{12}$: A First-Principles Study
Haeyoon Jung, Indukuru Ramesh Reddy, Bongjae Kim, Jiyeon Kim, Sooran Kim
https://arxiv.org/abs/2509.15665

Correlation Effects on Magnetic Structure and Lattice Dynamics of LaMn$_7$O$_{12}$: A First-Principles Study
LaMn$_7$O$_{12}$, a quadruple perovskite oxide (AA'$_3$B$_4$O$_{12}$-type), has attracted attention for its notable bifunctional activity in oxygen evolution and reduction reactions. Here, we systematically investigate the magnetic phase diagram and lattice dynamics of LaMn$_7$O$_{12}$ using two density functional theory plus Hubbard U (DFT + U) approaches: the spin-density and the charge-only-density formalism. Phase diagram analysis as a function of U and J shows that both methods stabilize t…