Papers

We study the distribution of closed geodesics in homology classes on random hyperbolic surfaces of large genus. Viewing the surface as a random point in moduli space equipped with the Weil–Petersson probability measure, we investigate the fluctuations of the weighted counting function of closed geodesics in homology classes modulo $q$. We show that, in the large genus limit, the variance is asymptotic to $X\log X$ for every modulus $q>2$, with an exceptional factor of two when $q=2$. We relate our findings to a conjecture of Hooley, and to work of Friedlander and Goldston, on primes in arithmetic progressions. We also introduce a statistical model based on the random allocation of weighted balls which exhibits analogous behavior.

Domain decomposition methods have been established as efficient and parallel scalable iterative solvers and preconditioners for the solution of large-scale systems arising from the discretization of partial differential equations. In particular, overlapping Schwarz methods have been successfully applied to a wide range of linear and nonlinear problems. However, for problems with highly heterogeneous coefficients, standard domain decomposition methods typically suffer from deteriorating convergence rates. Robustness with respect to the coefficient contrast can be achieved by enriching the coarse space with adaptively selected constraints obtained from local generalized eigenvalue problems. The construction of these adaptive coarse spaces, however, can account for a significant part of the overall computing time. In the present work, machine learning techniques are employed to reduce this part of the computing time in the context of the adaptive Generalized Dryja-Smith-Widlund (AGDSW) coarse space. A two-stage approach is proposed in which regression neural networks are used to predict the adaptive coarse basis functions, while a classification neural network is employed to predict the number of basis functions required to ensure robustness. As a consequence, adaptive coarse spaces can be set up in the online phase without solving any eigenvalue problem. Particular attention is paid to problem-specific aspects, including sign-invariant loss functions and post-processing strategies to significantly improve the predicted constraints. The proposed approach is first investigated for scalar diffusion problems with high coefficient contrasts and is subsequently transferred, without retraining, to problems of linear elasticity and to nonlinear $p$-Laplace problems, also within a nonlinear Schwarz framework.

Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations. These challenges limit the applicability of classical probabilistic inference methods such as Markov chain Monte Carlo, especially in high-dimensional Bayesian inverse problems. As data from scientific experiments become increasingly available, machine learning methods offer a flexible alternative to explicit parametric modelling. We study neural likelihood approximation, where the goal is to learn the likelihood function directly from data without explicit knowledge of the underlying data-generating process. A common approach trains likelihood surrogates by minimizing the Kullback-Leibler divergence between the true posterior and an approximate posterior, which is equivalent to minimizing the expected negative log-likelihood. This work improves the theoretical foundations of neural likelihood approximation by alleviating limitations of restrictive model classes: we show that, by working with un-normalized potentials and folding normalization into the training objective, the resulting learning problem is strictly convex. We show that empirical minimizers of the resulting data-driven objective converge to the true likelihood as the sample size grows. Numerical experiments for the neural likelihood approximation are conducted for a deblurring and a non-linear PDE based imaging problem.

This paper is devoted to a general study of $f$-polyharmonic maps of order $k$ (or $f$-$k$-harmonic maps), defined as critical points of the weighted $k$-energy functional \[ E_{f,k}(\phi)=\frac{1}{2}\int_\Omega f |\overline{\Delta}^{k/2}\phi|^2 dv_g. \] This framework provides a unifying perspective that extends previous theories including $f$-harmonic maps ($k=1$), biharmonic and $f$-biharmonic maps ($k=2$), and polyharmonic maps ($k\ge 3$ with constant $f$), with the classical harmonic maps recovered as the special case $k=1$ by setting $f\equiv \mathrm{const}$. We derive the Euler–Lagrange equation for general $f$-polyharmonic maps. As concrete applications, we classify $f$-$k$-harmonic curves with positive constant geodesic curvature in a space form $N^2(C)$ for $k=3,4$. Several explicit constructions of proper $f$-polyharmonic functions and maps are also provided, and a Liouville-type theorem is proved: every $f$-polyharmonic function on a closed Riemannian manifold is constant.

Let $\mathbb F\in\{\mathbb R,\mathbb C\}$ and $d_{\mathbb F}=\dim_{\mathbb R}\mathbb F$. If $A_m\in\mathbb F^{N_m\times m}$ has independent standard Gaussian entries and $N_m/m\to\gamma>1$, then \[ \min_{\substack{T\subset[N_m]\\ |T|=m}} \sigma_{\min}(A_{m,T}) = \left(\frac{\gamma^\gamma}{(\gamma-1)^{\gamma-1}}\right)^{-m/d_{\mathbb F}+o_P(m)} . \] If $N_m=\gamma m+O(1)$, the convergence of $m^{-1}\log M_m^{\mathbb F}$ has probability error $O(m^{-1})$. In particular, at the real phase-retrieval threshold $N=2m-1$, \[ \omega(A_m)=4^{-m+o_P(m)}, \] so the Gaussian Balan–Wang critical exponential base is $1/4$.

We define an involution $h$ on Catalan structures through an abstract framework, prove an equidistribution theorem for four canonical statistics and present a generating function carrying these. This framework encompasses all combinatorial structures with a decomposition mirroring the first-return decomposition of Dyck paths. The fixed points of~$h$ are counted by Catalan numbers. Canonical bijections transport the equidistribution to eight well known concrete families, identifying the canonical statistics with native ones on each. In addition to its primary structure, each Catalan structure has a derived secondary structure, and $h$~interchanges primary and secondary structure. The involution factors as $h = \rev \circ \corev \circ \rev$, where $\rev$ and $\corev$ are two simpler involutions, and the composition $M = h \circ \rev$ coincides with Donaghey's automorphism on plane trees. This yields $M^{-1} = \rev \circ M \circ \rev$ and a period theorem: Iterating the secondary structure construction produces a sequence that repeats with period equal to the order of~$M$. It is an open problem to describe $h$ and the canonical statistics explicitly on most of the more than two hundred known families of Catalan structures.

We provide a resolution to the non-Abelian Rainich problem. By canonically identifying traceless symmetric $(0,2)$-tensors with Hermitian forms on the vector bundle of chiral 2-forms, we define the internal square roots of a stress-energy tensor. We then prove that the existence of a local $\operatorname{SU}(2)$ Yang-Mills field with prescribed stress-energy tensor $T$ is equivalent to a single differential condition on internal square roots of $T$.

This paper studies the long time statistics and small noise asymptotics of Markov cocycles associated with Markov processes in random environments modeled by measure preserving dynamical systems on a standard Borel probability space. Our first result provides an abstract criterion for exponential mixing of stationary measures for such cocycles, formulated toward SPDE applications with assumptions that can be verified directly from a priori estimates. To overcome the nonuniformity from the environment, we combine generalized coupling arguments with ergodic theoretic methods. This allows us to convert nonuniform estimates along the environment into contraction on a positive density set of times, and then upgrade this to all time contraction by introducing a block gap-counting argument. Our second result establishes a Freidlin–Wentzell large deviation principle(LDP) for the unique stationary measure in the small noise limit with a good rate function. For the upper bound, the noise is allowed to be degenerate, while the deterministic pullback attractor may have nontrivial dynamics. The abstract theory applies to nonautonomous SPDEs. We illustrate it with two examples: the two-dimensional Navier–Stokes equations on bounded domains and damped Sine–Gordon equations, where both the deterministic forcing and the degenerate additive noise depend on the random environment.

A drawing of a graph is {\em $x$-monotone} if every vertical line intersects each edge of the graph at most once. We present an $O(n^5)$ time algorithm for deciding whether a simple drawing of the complete graph $K_n$ is weakly isomorphic to an $x$-monotone drawing. We note that this algorithm can also decide whether a drawing of $K_n$ is strongly isomorphic to an $x$-monotone drawing.

Inverse problems governed by partial differential equations are difficult when observations are sparse and the unknown coefficient field contains both large- and small-scale structures. We introduce a residual-based, physics-aware multilevel discrete neural field framework, ResiPhy-MDNF, for such problems. The method couples a coarse-to-fine discrete neural field (DNF) optimizer with a residual-based graph neural network (GNN) transfer operator, called ResiPhy-GNN. At each level, the DNF directly optimizes trainable grid- or mesh-based state and coefficient arrays using the prescribed numerical model. Between levels, ResiPhy-GNN maps the coarse representation to the fine representation through a learned prolongation based on graph connectivity, spatial features, and residual information. The method requires neither surrogate models nor offline pretraining. We evaluate the framework on coefficient inversion in Darcy flow for subsurface modeling and on electrical impedance tomography (EIT). In the controlled Darcy test case, the \(64^2\!\to128^2\) multilevel path uses \(1.25\times\) the cumulative grid-work proxy of the direct single-level \(128^2\) solve, while achieving \(6.76\times\) lower permeability error and \(10.4\times\) lower state error. On measured Kuopio Tomography Challenge 2023 EIT data, the framework improves the mean intersection-over-union after Otsu thresholding by roughly \(3.4\%\) over the official linearized complete electrode model reconstruction and by \(16.9\%\) over direct single-level discrete-field optimization. These results indicate that the same multilevel construction can be used across different coefficient structures, discretizations, and observation geometries.

Twistor theory forms the basis for many surprising advances in areas ranging from dynamical systems to quantum field theory. Yet for almost fifty years, one of the main drawbacks of twistor theory has been its inability to give non-perturbative descriptions of non-chiral (or non-self-dual) field configurations. This difficulty is known as `the googly problem.' In this paper, we provide a resolution of the googly problem for a particular solution of the vacuum Einstein equations: the Schwarzschild metric. We start with the twistor space of the self-dual Taub-NUT Euclidean gravitational instanton, expressed in Kerr-Schild form. Within this twistor space, we then consider a quadric which corresponds to the anti-self-dual Taub-NUT metric. While the full quadric is not holomorphic with respect to the complex structure of the self-dual Taub-NUT twistor space, its holomorphic locus still has complex dimension two. This `coincidence locus' – points in twistor space on the holomorphic portion of the quadric – inherits a complex structure from the twistor space and a symplectic form from the quadric itself. Remarkably, these structures are compatible, giving rise to a non-self-dual, four-dimensional Kähler metric which is conformal to Schwarzschild (in Lorentzian or Euclidean signature). This is the first instance of a non-self-dual Einstein metric constructed entirely from holomorphic data in a twistor space.

The study of matroid products has become an active area of research, owing to their connections with tropical ideals and linear representability. In this paper, we study matroidal abstractions of the multilinearity of symmetric powers of vector spaces, using a duality between symmetric powers of matroids and abstract rigidity. These observations allow us to solve Mason's conjecture concerning the equivalence of two definitions of a symmetric power of a matroid. We show that Mason's conjecture holds for second symmetric powers of matroids whereas it fails for third symmetric powers.

Originally, an exotic Diophantine triple is a set $\{a,b,c\}$ of distinct nonzero rational numbers for which \[ a+1,\quad b+1,\quad c+1,\quad ab+1,\quad ac+1,\quad bc+1,\quad abc+1 \] are all perfect squares. We prove that there is no such triple in $\mathbb{R}[X]$, with at least one nonconstant element, if none of $a,b,c$ is equal to $1$. Equivalently, under the distinct nonzero convention, every exotic Diophantine triple in $\mathbb{R}[X]$ with a nonconstant element must contain the element $1$.

We present a succinct encoding of planar graphs that supports executing a breadth-first search directly on the encoding. The succinct encoding can be constructed in expected $O(n)$ time using $O(n)$ bits during construction; a compact variant can be constructed in deterministic $O(n)$ time using $O(n)$ bits. Once the encoding is constructed, a BFS from any start vertex can be computed in $O(n)$ time using $o(n)$ additional bits, including the space needed to represent the BFS tree. The resulting BFS tree $T$ remains available for standard tree operations, such as traversal, parent and child queries, layer queries, and lowest common ancestor queries, in constant time per query or output element. The encoding also supports standard graph queries. For plane graphs $G=(V, E)$, we provide traversal of the interdigitating tree $\hat T$, i.e., the spanning tree of the dual graph whose edges correspond to $E \setminus E(T)$. As our main application, we implement the well-known planar separator theorem in a space-efficient way. For biconnected plane graphs, our encoding allows us to compute a balanced separator of size $O(\sqrt n)$ in $O(n)$ time using $o(n)$ additional bits. Along the way, we show that biconnected plane graphs encoded by our representation can be triangulated in expected $O(n)$ time and $o(n)$ bits in the succinct variant, or in deterministic $O(n)$ time using $O(n)$ bits in the compact variant. Further applications include computation of a tree decomposition of width $O(d)$ where $d$ is the diameter of the plane graph at hand and testing for bipartiteness. Finally, all results that do not rely on a plane embedding generalize to separable graph classes.

The relations between many-one degrees and one-one degrees have been studied since the beginning of recursion theory; early results from the 1960s include that many-one degrees always have a largest one-one degree and either that one-one degree is the only one-one degree inside the many-one degree or every countable linear order is noneffectively embeddable into the structure of one-one degrees inside the given many-one degree. Furthermore, the greatest recursive many-one degree is a special case, as it allows to embed ascending infinite chains but not descending infinite chains, all other many-one degrees fall into the two cases mentioned above. It remained open whether infinite antichains can always be embedded when the many-one degree is nonrecursive and nonirreducible; Odifreddi stated in a survey 1981 and in his book Classical Recursion Theory in the year 1989 this question explicitly as an open problem. Dëgtev had already in 1976 constructed antichains of one-one degrees inside all nonrecursive and nonirreducible recursively enumerable many-one degrees and Batyrshin generalised the result to all nonrecursive and nonirreducible limit-recursive many-one degrees. In 2026, Cintioli showed that there is a measure $1$ class of sets whose many-one degrees contain infinite antichains of one-one degrees. This class contains all rigid many-one degrees. The present work generalises Batyrshin's result to all nonrecursive and nonirreducible many-one degrees and solves therefore Odifreddi's open problem. The present work also proposes to deepen the study of reducibilities between one-one and many-one in recursion theory in order to get a more complete and detailed picture for the structures inside many-one degrees. In particular it studies finite-one and bounded finite-one reducibilities where the first was introduced by Maslova in the 1970ies.

Computational modeling and simulation have emerged as powerful tools for assessing medical device performance and safety, particularly in silico clinical trials (ISCTs) for automated medical systems. In ventilation, where gas exchange, respiratory mechanics, and patient-ventilator interaction must be managed under evolving pathophysiology, clinical translation of automated control strategies remains slow and resource-intensive. These challenges are particularly relevant for AI-based therapy-control systems, whose data-driven decision-making must be evaluated across heterogeneous and safety-critical patient states that may be sparsely represented in clinical datasets. Mechanistic, physiology-based models provide a complementary and interpretable environment for testing such scenarios. This paper applies a standards-aligned framework for credibility assessment of a computational respiratory model, demonstrated using an automated weaning case study. The framework operationalizes ASME V&V 40 and FDA principles within a structured validation workflow. The model integrates respiratory mechanics, gas exchange, respiratory control, and a ventilator representation, with validation under a defined context of use and explicit questions of interest. Model credibility is assessed through calibration, physiological plausibility, population-based evaluation, and reproduction of emergent behavior. All model requirements derived from the intended context of use are addressed, and gaps are transparently reported. The resulting credibility argument supports applicability of the model for medium-low-risk preclinical ISCTs of automated weaning strategies. Residual limitations relate to the extent of in vivo evidence, population representativeness, and external validation. The validation procedure provides a blueprint for validation of this and similar models in mechanical ventilation and related use cases.

A real sequence $(a_k)_{k=0}^\infty$ is called totally positive if all minors of the infinite Toeplitz matrix $ \left\| a_{j-i} \right\|_{i, j =0}^\infty$ are nonnegative (where $a_k=0$ for $k<0$). In this paper, we investigate the following question: for which real polynomials $P$ the sequence $(P(k))_{k=0}^\infty$ is totally positive? We establish a few new necessary conditions, sufficient conditions, present a number of important examples and formulate several open problems.

In this work, a description of the automorphism group schemes is given for the Kantor pairs (and for some Kantor triple systems related to them) associated to associative central simple structurable algebras in the three “split” cases, where the base field is algebraically closed of characteristic different from $2$. For two of the three cases (the ones with orthogonal and symplectic involutions), we relate the decomposition (as a central product) of the automorphism group scheme to a decomposition (as a tensor product) of the corresponding Kantor pair regarded as a metric generalized Jordan pair.

We investigate the independence of the axioms in the Banaś–Goebel approach to the theory of measures of non-compactness. We present a complete answer for four of the five axioms. For the remaining axiom, we provide a full solution in finite-dimensional spaces and a partial one in the infinite-dimensional case.

We show that several apparently different aspects of a permutation are all tied to a single quantity, the cyclomatic number of its inversion graph. Every reduced word for the permutation orders the edges of the inversion graph one at a time, with the edges from first-occurrence letters forming a spanning forest and the edges from repeated letters accounting for the rest; the number of repeated letters is therefore the cyclomatic number. The excess of permutation cycles over sum components is also at most this quantity, and it follows that the gap between the Coxeter and reflection lengths is at least the cyclomatic number and at most twice it. When the inversion graph is a forest, these results unify classical characterizations of the boolean permutations due to Edelman, to Tenner, and to Petersen and Tenner. We also give a new proof that every connected acyclic inversion graph is a caterpillar.

We prove a wall-crossing formula for the Euler characteristics, considered as virtual mixed Hodge structures, of moduli spaces of $\varepsilon$-stable quasimaps to the Grassmannian $\mathbb{G}(r, N)$. For each $\varepsilon > 0$, we define a $\mathbb{Q}$-algebra automorphism of the ring of symmetric functions which takes the generating function for the $\mathbb{S}_n$-equivariant Euler characteristics of the moduli spaces of stable maps $\overline{\mathcal{M}}_{g, n}(\mathbb{G}(r, N), d)$ to the corresponding generating function for Toda's moduli spaces of $\varepsilon$-stable quasimaps $\overline{\mathcal{Q}}_{g, n}^{\varepsilon}(\mathbb{G}(r, N), d)$. The automorphism is given by explicit $q$-deformations of the power sum symmetric functions. The $\varepsilon \to 0$ limit of our formula exchanges the spaces of stable maps and the Marian–Oprea–Pandharipande moduli spaces of stable quotients. Our proof uses the geometry of relative Quot schemes to relate the quasimap spaces to moduli spaces of weighted stable maps, for which we obtain wall-crossing formulas via symmetric function theory.

The deep operator network (DeepONet) is one of the basic architectures for learning nonlinear operators with neural networks. However, for operators that describe the dynamic response of physical systems, DeepONet does not naturally respect fundamental time properties, including time causality and time invariance. We propose time-invariant neural operator (TINO) to overcome these limitations, by creating the connection between time-delay neural network (TDNN) and DeepONet. We then extend the proposal to solving time-dependent PDEs with initial values, which can be treated as truncated time-invariant systems, with spatial proper orthogonal decomposition (POD) implementation in the output function space. Various numerical tests comparing TINO, neural operators with time causality, and those without time properties justify the enhanced precision of the proposed neural operator frameworks.

Levenshtein's sequence reconstruction model plays an essential role in information retrieval of advanced memory systems, such as the DNA-based storage systems. In the model, a word $\mathbf{x}\in\mathbb{Z}_q^n$ is transmitted through $N$ noisy channels, and the goal is to recover it. Errors occurring in the channels usually involve substitutions, insertions and deletions. Our focus is on insertions. One of the main questions in this context is determining the minimum number of channels $N$ required to recover the transmitted word $\mathbf{x}$. The original formulation of the reconstruction problem requires that all the output words from the channels are distinct. However, different insertion errors may lead to the same output words. In this paper, we investigate two reconstruction models where the channels are allowed to produce identical output words even though different insertion errors occur in the channels. These two models, called the multiset model and non-multiset model, generalize the Levenshtein's model. We denote the minimum number of channels required to unambiguously recover the transmitted word $\mathbf{x}\in\mathbb{Z}_q^n$ by $N_q^m(n,t)+1$ in the multiset model and $N_q^{nm}(n,t)+1$ in the non-multiset model, where $t$ is the exact number of insertions occurring in a channel. We determine $N_q^m(n,1)$ and $N_q^{nm}(n,1)$ for all $n$ and $q$, and show the somewhat surprising fact that $N_q^m(n,1)=N_q^{nm}(n,1)$. We also provide a full characterization of the words attaining this value and give a general lower bound on $N_q^m(n,t)$ for $t\ge1$ and a recursive upper bound. For $t=1$, we construct codes $C'\subseteq\mathbb{Z}_q^{n+2}$ from codes $C\subseteq\mathbb{Z}_q^n$ such that the number of channels required to determine the transmitted word $\mathbf{x}\in C'$ is small. This construction is shown to be optimal for certain parameters.

We show that every Lindelöf scattered $W$-space is $\sigma$-compact. This result generalizes a theorem proved recently by Avilés and the author in [Topology Appl. 363 (2025), Paper No. 109234] and answers a question posed by Tkachuk.

In this paper, we study discrete quasi-copulas and discrete imprecise copulas of minimal range, which naturally correspond to alternating sign matrices. We identify dense alternating sign matrices as a particularly well-behaved subclass. We prove that the associated discrete imprecise copulas are always coherent and hence avoid sure loss. We further show that a particular extension of the corresponding discrete quasi-copulas to the full domain preserves this structure and yields self-dual imprecise copulas. To the best of our knowledge, this provides the first general result in the literature showing how properties established for discrete imprecise copulas can be preserved when extending them to their full-domain counterpart. We conclude the paper by showing that, for general alternating sign matrices, the associated discrete imprecise copulas need not avoid sure loss, further emphasizing the special role of the subclass of dense alternating sign matrices. We establish, however, that the class of discrete quasi-copulas of minimal range is invariant under all defect transformations

Holmsen proved in 2016 a generalization of the classical colorful Caratheodory theorem in which a matroid imposes additional constraints on the desired colorful transversal. His approach also works in the more general setting of oriented matroids, rather than relying directly on convex hulls. In this paper, we extend these ideas in several directions. First, we study which colorful Caratheodory-type results remain valid when convex cones replace convex hulls, as well as analogous modifications in the oriented matroid setting. Second, we consider variants in which the additional constraint on the transversal is not encoded by a matroid. This leads to new extensions of the classical Tverberg theorem. Our approach is topological, following the methods of Holmsen, and Kalai and Meshulam, on which it builds. The key idea is to analyze homology groups of simplicial complexes that encode colorful Caratheodory-type phenomena, such as the support complex of an oriented matroid. In particular, one shows that these complexes are (near-)d-Leray. We extend this analysis by carrying out more detailed homology computations for these complexes, with the aim of enabling further and more refined applications of the method.

Let $H$ be an inclusion-free hypergraph on $n$ vertices. A weight assignment $w:[n]\to[d]$ is isolating if there is a unique edge $e$ whose weight $w(e) = \sum_{i \in e} w(i)$ is minimum. We show that the number of isolating weight assignments is at least $$ n\sum_{j=0}^{d-1} j^{n-1}, $$ a bound which is attained with equality by the hypergraph consisting of the $n$ singleton edges. This proves the conjecture stated in Faber & Harris (2018). We also prove the bound for a more general class of edge-weight objectives, including arbitrary edge offsets.

Meeting the growing demand for quality-of-service (QoS) guarantees in 5G networks requires an accurate characterization of delay performance, commonly captured by the delay violation probability (DVP) at a specified delay target. Although hybrid automatic repeat request (HARQ) is a fundamental reliability mechanism in wireless systems and is central to supporting QoS, many existing approaches to DVP prediction for HARQ remain overly simplified. In particular, they omit important delay components and adopt assumptions that do not reflect the operation of HARQ in slot-based systems such as 5G. Consequently, these models can substantially underestimate the DVP, especially under stringent latency requirements, where the contribution of the neglected components becomes critical. To address this gap, we develop a tractable DVP characterization for 5G HARQ that accounts for queueing, transmission, decoding, and feedback delay, as well as the contribution of Control Signaling (CS) transmissions to the overall delay, under practical timing assumptions consistent with 3GPP operation. Moreover, we incorporate parallel packet transmissions that proceed without waiting for earlier packets to succeed, an essential HARQ behavior frequently overlooked in prior work. Using tools from queueing theory and Markov analysis, we then derive upper bounds on the DVP and validate them against ns-3 5G-LENA simulations.

Let $R_m$ be the least positive integer $r$ such that there exists a set $A\subseteq \mathbb{Z}_{m}$ with $A+A=\mathbb{Z}_m$ for which the number of ordered solutions of $n=x+y$ with $x,y\in A$ is at most $r$ for every $n\in \mathbb{Z}_m$. In this note we prove that $R_m\leqslant 128$ for every positive integer $m$, improving the previous bound $R_m\leqslant 192$.

We show that the Brauer group of any resolution of singularities of the moduli space of semistable quiver representations is trivial. We do this by extending the quiver-curve dictionary, translating a proof of the analogous result by Biswas-Hogadi-Holla for moduli of vector bundles on a curve to the setting of moduli of quiver representations, giving an algebro-geometric proof. This gives a new proof of this triviality, first proved by Le Bruyn-Schofield, building on algebraic (resp. cohomological) vanishing results due to Saltman (resp. Colliot-Thélène-Sansuc). Reversing the logic, our approach gives a new algebro-geometric proof of these vanishing results.