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arXiv:2602.17845v2 Announce Type: replace Abstract: Coron established a homological obstruction to continuous feedback stabilization of nonlinear control systems $\dot{x}=f(x,u)$ with $f \in C(\Omega,\mathbb{R}^n)$ and $f(0,0)=0$, showing that local asymptotic stabilizability implies the induced homomorphism $f_*$ satisfies $f_*\big(H_{n-1}(\Sigma_\epsilon)\big)=H_{n-1}(S^{n-1})$, where $\Sigma_\epsilon:=\Big(\big(\mathbb{B}_\epsilon^{\mat..
arXiv:2602.21640v2 Announce Type: replace Abstract: We study the ground-state of a Fermi gas with short range attrative interactions in one or two dimensions. N fermions are placed in a confining potential, and interact with each other through a negative potential, whose range is larger than the typical distance between particles. We show the convergence of the ground state energy of the Hamiltonian to a Thomas-Fermi energy in the large N ..
arXiv:2602.22767v3 Announce Type: replace Abstract: We prove the persistence of boundary smoothness of vortex patches for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations generalize the Euler equations by including an additional parameter, the Rossby radius $\varepsilon^{-1}$, which modifies the relationship between the streamfunction and the (potential) vorticity. In addition, we prove that solutions of the QGSW eq..
arXiv:2602.23572v2 Announce Type: replace Abstract: SJT reducibility between sets $A,B \subseteq \mathbb N$ is defined by $A \le_{SJT} B$ if for each computable function $h$ that is unbounded and nondecreasing, there is an $h$-bounded uniformly $B$-c.e.\ trace $(T_n)_{n \in \mathbb N} $ such that for each $n$, the value $J^A(n)$ of the jump is in $T_n$, if defined. This reducibility is slightly weaker than Turing reducibility. We study SJT..
arXiv:2602.24219v2 Announce Type: replace Abstract: A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random membership. We prove some asymptotic properties and apply the framework to the stratified sampling context.
arXiv:2603.00752v4 Announce Type: replace Abstract: In this paper we give a construction for a linear quotient ordering of a class of products of two ideals which have linear quotients. We apply this construction to give a class of modified anticycle graphs whose square and cube have linear quotients.
arXiv:2603.02410v2 Announce Type: replace Abstract: We present a theoretical and numerical dynamical-systems analysis of tubular origami tessellations by identifying the inverse module number, $N^{-1}$, as a perturbation parameter within the framework of Kolmogorov--Arnold--Moser (KAM) theory. In the large-module limit ($N \to \infty$), we show that the conservative dynamics formally converges to an integrable map with a variational struct....
arXiv:2603.05455v3 Announce Type: replace Abstract: This is the third paper in a series, following [FPVa] and [FPVb]. We classify all modular compactifications of the universal Jacobian over $\overline{\mathcal{M}}_{g,n}$, both as stacks and as their relative good moduli spaces. Our main result gives a combinatorial parametrization of compactified universal Jacobian stacks by $V$-functions on a stability domain $\mathbb{D}_{g,n}$ of half-....
arXiv:2603.06033v2 Announce Type: replace Abstract: We prove Oort's conjecture that generically on the supersingular locus of the moduli space of principally polarized abelian varieties of genus g and in characteristic p, the automorphism group of the universal principally polarized abelian variety consists only of $\pm 1$, unless g=2 or 3 and p=2. On the way, we provide an explicit description of the a=1-locus in the Rapoport-Zink space o..
arXiv:2603.06678v2 Announce Type: replace Abstract: Partial Information Decomposition (PID) has become one of the most prominent information-theoretic frameworks for describing the structure and quality of information in complex systems. Despite its widespread utility, there exists no unique solution constraining precisely how a PID should be constructed, leading to a multiverse of different formalisms with different mathematical commitmen....
arXiv:2603.06886v2 Announce Type: replace Abstract: We consider a general round-robin tournament model with equally strong players, where $X_{ij}$ denotes the score of player $i$ against player $j$. We assume that $X_{ij}$ takes values in a countable subset of $[0,1]$ and satisfies $X_{ij}+X_{ji}=1$. We prove that if $k(n)\to\infty$ as $n\to\infty$ and $ \frac{k(n)^2\log\!\bigl(n/k(n)\bigr)}{\sqrt n}\to 0, $ then, with probability tending ..
arXiv:2603.07439v3 Announce Type: replace Abstract: Given any two forests (pseudoforests) with the same degree sequence, we show that one can be transformed into the other by a sequence of 2-switches in such a way that all the intermediate graphs of the transformation are forests (pseudoforests). We also prove that the 2-switch operation perturbs minimally some well-known integer parameters in families of graphs with the same degree sequen..
arXiv:2603.08994v3 Announce Type: replace Abstract: According to the classical Wagstaff heuristic, the probability that a Mersenne number \(M_p=2^p-1\) is prime depends primarily on the size of the exponent \(p\). We investigate whether the divisor structure of \(p-1\) produces detectable secondary variations within this asymptotic framework. We introduce the normalized divisor parameter S(p)=\frac{\log\tau(p-1)}{\log\log p}, which measure....
arXiv:2603.10312v3 Announce Type: replace Abstract: In this paper, we establish the Kobayashi-Hitchin correspondence for nef and big cohomology classes by introducing the notions of adapted closed positive $(1,1)$-currents and adapted Hermitian-Yang-Mills metrics. As applications, we investigate the equality cases of both the Bogomolov-Gieseker inequality for semistable reflexive sheaves with respect to big classes admitting a bimeromorphi..
arXiv:2603.11022v2 Announce Type: replace Abstract: We show that for generic smooth compact initial surfaces the mean curvature flow in $\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial sur..
arXiv:2603.16111v2 Announce Type: replace Abstract: We study the perturbed Hofstadter $Q$-recursion \[ Q(1)=Q(2)=1,\qquad Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2))+(-1)^n \quad (n\ge3). \] We investigate its value frequencies and dyadic fluctuation structure. Our first main result is an explicit dyadic frequency law: if $F(s)$ denotes the number of occurrences of the value $2s-1$, then for every $k\ge0$, \[ \{F(s):2^k\le s<2^{k+1}\} = \{3+\nu_2(j):1\le....
arXiv:2603.16698v4 Announce Type: replace Abstract: Recently Watanabe has given an algorithm to compute a bijection, that he calls (quantum) Littlewood-Richardson (LR) map (or quantum LR rule of type AII), between semi-standard Young tableaux of shape a partition with at most $2n$ parts and pairs of tableaux consisting of a symplectic tableau with shape a partition with at most $n$ parts, and a recording tableau of skew-shape given by the ....
arXiv:2603.17805v2 Announce Type: replace Abstract: We prove that if \(B\) is a finite skew brace with \((B,\cdot)\cong S\times T\), where \(S\) and \(T\) are non-abelian simple groups, then \((B,+)\) is not supersolvable.
arXiv:2603.20438v2 Announce Type: replace Abstract: We study the relationship between disturbance decoupling (DD) and H2 optimal control for linear time-invariant (LTI) systems, revealing a fundamental gap between DD subspace constraints and semi-definite program (SDP)-based H2 minimization. We show that DD is equivalent to the existence of zero H2 gain without requiring internal stability, whereas SDP-based H2 minimization strictly optimi....
arXiv:2603.21001v2 Announce Type: replace Abstract: Let G be a primitive permutation group on a finite set Omega. Let p^2 divide |G|, for a prime p. We show that when G is solvable, there exists a subset of Omega whose stabilizer S has the property that 1<|S|_p<|G|_p. We offer a counting argument which should be helpful when G is not solvable.
arXiv:2603.24340v3 Announce Type: replace Abstract: We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to projective space. Let $A/F$ be a simple abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism which is finite onto its image, and $\Gamma \subseteq A(F)$ be a finite-rank subgroup. We show that for any affine chart $\mathbb{A}^n \subseteq \mathbb..
Invertibility, Often - arxiv.org - 1 month ago - eng
arXiv:2603.26376v2 Announce Type: replace Abstract: By using a similar pattern of arguments, we show that in three categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at measure preserving maps on Polish measure spaces. Finally, we examine continuous, measure preserving maps on Cantor spaces equipped with so-called good..
arXiv:2603.27712v2 Announce Type: replace Abstract: We study a semimartingale optimal transport problem interpolating between the Schr\"odinger bridge and the stretched Brownian motion associated with the Bass solution of the Skorokhod embedding problem. The cost combines an entropy term on the drift with a quadratic penalization of the diffusion coefficient, leading to a stochastic control problem over drift and volatility. We establish a....
arXiv:2603.29923v3 Announce Type: replace Abstract: This paper investigates the scaling limit of the one-dimensional lattice Ising--Kac--Kawasaki dynamics near the critical temperature. Starting from a martingale formulation for the Kac coarse-grained field, we decompose the microscopic dynamics into a discrete conservative drift and a pure-jump Dynkin martingale. Under a critical scaling regime, the nonlinear drift is identified via a con....
arXiv:2603.29998v5 Announce Type: replace Abstract: We provide representations of Euler's constant $\gamma=0.577...$ as series which converge geometrically fast (but use a certain sequence whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are determined to all orders. A result of independent interest, about sufficient conditions for the validity, in the case of unbounded parameters, for the Tric..
arXiv:2604.00539v2 Announce Type: replace Abstract: Alexander polynomial was born one century ago, but explicit formulas have been found for only a few families of links. In this paper, we present an efficient method of computing Alexander polynomial for arborescent links. Applying this method, we express the Alexander polynomials of Montesinos links in terms of certain polynomials associated to rational tangles which can be computed recur..
arXiv:2604.03399v2 Announce Type: replace Abstract: Impulse-to-peak response (I2P) analysis for state-space ordinary differential equation (ODE) systems is a well-studied classical problem. However, the techniques employed for I2P optimal control of ODEs have not been extended to partial differential equation (PDE) systems due to the lack of a universal transfer function and state-space representation. Recently, however, partial integral e....
arXiv:2604.03567v2 Announce Type: replace Abstract: For a graph $H$ and an integer $k\ge 1$, the \emph{Token Sliding reconfiguration graph} $\mathsf{TS}_k(H)$ and the \emph{Token Jumping reconfiguration graph} $\mathsf{TJ}_k(H)$ have as vertices the $k$-cliques of $H$, with two vertices adjacent when one clique is obtained from the other by replacing one vertex with an adjacent non-member, and respectively by an arbitrary non-member. For a..
arXiv:2604.03989v3 Announce Type: replace Abstract: This paper develops a Finsler-based LMI for robust $\mathcal{H}_\infty$ observer design with integral quadratic constraints (IQCs) and block-structured uncertainty. By introducing a slack variable that relaxes the coupling between the Lyapunov matrix, the observer gain, and the IQC multiplier, the formulation addresses two limitations of the standard block-diagonal approach: the LMI requi..
arXiv:2604.06557v2 Announce Type: replace Abstract: Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial algebras, and provide several easily checkable combinatorial invariants for derived equivalences between them. In particular, we show that these algebras..
arXiv:2604.07186v2 Announce Type: replace Abstract: For a wide range of functions $W\colon\mathbb{N}\to\mathbb{N}$, we establish a general result for estimating weighted averages of the form\[\mathbb{E}^{W}_{n \le N} f(\vartheta(n))= \frac{1}{W(N)}\sum_{n=1}^N (W(n)-W(n-1))f(\vartheta(n)),\]where $f\colon \{1,\ldots,N\}\to\mathbb{C}$ is an arbitrary function, and $\vartheta(n)$ is any arithmetic function that adheres to a certain Gaussian ....
arXiv:2604.08684v2 Announce Type: replace Abstract: We construct a family of solutions $(u,B)$ of the incompressible magnetohydrodynamic (MHD) system, the $L^\infty$ norm of which blows up instantaneously at the critical rate. The solutions remain smooth except at the blowup time. An inverse energy cascade mechanism and a convex integration scheme along a time sequence are the main ingredients of the construction, inspired by our recent wo....
arXiv:2604.09116v2 Announce Type: replace Abstract: We investigate infinite-level Shimura varieties within the framework of analytic stacks of Clausen-Scholze, developing their smooth, completed, locally analytic, and de Rham realizations. We formulate a Grothendieck-Messing-Hodge-Tate period map, and establish a Grothendieck-Messing theory for locally analytic infinite-level Shimura varieties. This theory, combined with a reformulation of....
arXiv:2604.09808v2 Announce Type: replace Abstract: We present a complete formalization, in the Lean interactive theorem prover with the Mathlib library, of the Ramanujan--Nagell theorem: the only integer solutions to the Diophantine equation $x^2 + 7 = 2^n$ are $(n,x) \in \{(3,\pm1),(4,\pm3),(5,\pm5),(7,\pm11),(15,\pm181)\}$. The formalization includes all dependencies, notably the computation of the ring of integers of the quadratic fiel..
arXiv:2604.11063v2 Announce Type: replace Abstract: The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. Capturing both the non-polynomial singularities at the origin and the state-dependent asymptotic decay on semi-infinite domains presents a significant computational challenge. In this wor....
arXiv:2604.11569v2 Announce Type: replace Abstract: We study the semiring $\mathbb{N}_0[\alpha]$ as an additive monoid where $\alpha$ is a positive real algebraic number. In the atomic case, the atoms of $\mathbb{N}_0[\alpha]$ are precisely the powers $\alpha^n$ up to a certain nonnegative integer $n$, and finite generation is governed by divisibility of the minimal polynomial by a negative-tail polynomial. Our first main result gives a co..
arXiv:2604.11769v2 Announce Type: replace Abstract: We construct a family of solutions $(u,b)$ of the incompressible flow with a passive tracer for which both $\|u(t)\|_{L^\infty}$ and $\|b(t)\|_{L^\infty}$ blow up at time $T_*$. Away from $T_*$, the solutions remain smooth in both space and time. The argument adapts the inverse cascade mechanism from [CDP25] to the presence of an advected scalar, but the passive component creates a new co....
arXiv:2604.14850v2 Announce Type: replace Abstract: We show that the very general Verra fourfold is irrational, using the Hodge atom framework of Katzarkov--Kontsevich--Pantev--Yu. Two novel points are: a refined analysis of Hodge atoms, based on the involution on the cohomology of $X$, and a derivation of the quantum multiplication matrix from the quantum differential operator. This gives the first successful application of the method of ..
arXiv:2604.16126v3 Announce Type: replace Abstract: The two pillars of Algebraic topology - homology and homotopy theory rely on the availability of basic building blocks called cells. Cells take the form of simplexes, and have properties such as faces, sub-cells, convexity and contractibility. The first two cells, namely the line and point lead to the concept of homotopy. The collection of maps from the cells and the redundancies among th..
arXiv:2604.16805v2 Announce Type: replace Abstract: Let \(\Lambda\) be a finite-dimensional Koszul algebra with Koszul dual \(\Lambda^!\). We establish derived Koszul dualities at the level of bounded derived categories, both in the graded setting \(\mathsf{D}^{b}(\Lambda\textup{-gmod})\) and in the ungraded setting \(\mathsf{D}^{b}(\Lambda\textup{-mod})\), without imposing finiteness conditions on \(\Lambda^!\). We first prove a graded de....
arXiv:2604.17924v2 Announce Type: replace Abstract: In this paper we provide conditions for a Wasserstein barycenter to be absolutely continuous with respect to its Hausdorff measure away from the vertices of the graph. One assumption removed in v2, the result is now optimal.
arXiv:2604.21240v2 Announce Type: replace Abstract: In this paper, we define real link Floer homology for strongly invertible and doubly periodic links in closed real $3$-manifolds with connected fixed sets, which generalizes real Heegaard Floer homology and real sutured Heegaard Floer homology. We give a combinatorial description of the theory in $S^3$ via real grid diagrams and use it to investigate structural properties of the theory as..
arXiv:2604.21946v2 Announce Type: replace Abstract: The Chebyshev bounds for the prime-counting function, i.e., $\pi(x) \asymp x/\ln x$, is established in a new way. This new approach follows the outline $\pi(x) \asymp \bigl(\sum_{p \le x} \sqrt{\ln p / p}\bigr)^{2} \asymp x/\ln x$. Here, the second $\asymp$ is derived from the classical estimate by Mertens, i.e., $\sum_{p \le x} (\ln p)/p = \ln x + O(1)$; while the first $\asymp$ is prove..
arXiv:2604.22991v2 Announce Type: replace Abstract: We study a sequential coin-flipping game: a player starts with $n$~coins, each heads with probability~$p$, and in each round flips all remaining coins and must set aside at least one head, losing if none shows. The player wins once all coins have been set aside. The optimal winning probability~$w_{n,p}$ obeys a Bellman equation with a nonlinear suffix-maximum operator. For $p=\tfrac12$ ev....
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