We use height arguments to prove two results about the dynamical Mordell-Lang problem. (i) For an endomorphism of a projective variety, the return set of a dense orbit into a curve is finite if any cohomological Lyapunov multiplier of any iteration is not an integer. (ii) Let $f\times g:X\times C\rightarrow X\times C$ be an endomorphism, where $f$ and $g$ are surjective endomorphisms of a projective variety $X$ and a projective curve $C$, respectively. If the degree of $g$ is greater than the first dynamical degree of $f$, then the return sets of the system $(X\times C,f\times g)$ have the same form as the return sets of the system $(X,f)$. Using the second result, we deal with the case of split self-maps of products of curves, for which the degrees of the factors are pairwise distinct. In the cases that the height argument cannot be applied, we find examples which show that the return set can be very complicated -- more complicated than experts once imagined -- even for endomorphisms of tori with zero entropy. One may compare them with the conjectures and results stated in [CGSZ21] and [XY25].

Broadband measurements of glycidaldehyde in the frequency ranges 75-170 and 500-750 GHz were recorded to extend previous analyses of its pure rotational spectrum in the microwave region. The rotational parameters of the ground vibrational states for the main isotopologue and the three singly 13C-substituted isotopologues were considerably improved, and additional higher-order parameters were determined. To identify new vibrationally excited states in the dense and convoluted spectrum, an updated version of the double-modulation double-resonance spectroscopy technique was used. Connecting transitions with a shared energy level into series and expanding these via Loomis-Wood plots proved to be a powerful method, which allowed the identification of 11 new vibrationally excited states in addition to the already known aldehyde torsions, v21 = 1 to v21 = 6. Interactions between several vibrational states were observed, and three interacting systems were treated successfully. Rotational transitions of glycidaldehyde were searched for in the imaging spectral line survey ReMoCA obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the high-mass star-forming region Sgr B2(N). The observed spectra were modeled under the assumption of local thermodynamic equilibrium (LTE). Glycidaldehyde, an oxirane derivative, was not detected toward Sgr B2(N2b). The upper limit on its column density implies that it is at least six times less abundant than oxirane in this source.

We study online scheduling to minimize total completion time with explorable uncertainty on single and multiple machines. Each job comes with an upper limit of its processing time, which could be potentially reduced by testing the job, which also takes time. The objective is to schedule all jobs with minimum total completion time. The challenge lies in deciding which jobs to test, the order of testing/processing jobs, and in multiple machine case which machine a job is allocated to. In multiple machine case, testing and processing of a job are allowed to be scheduled on different machines. Different settings have been studied before. In this work, we first consider the variable testing times setting. We enhance the analysis framework in Albers and Eckl (2020) and improve the analysis of the competitive ratio of their deterministic single machine algorithm from $4$ to $1+\sqrt{2} \approx 2.4143$. Using the new analysis framework, we propose a new deterministic algorithm that further improves the competitive ratio to $2.316513$. The new framework also enables us to develop a randomized algorithm improving the expected competitive ratio from $3.3794$ to $2.152271$. We further show that with $m$~machines, by extending the framework of Gong et al. (2024), there exists a deterministic $2.77629-(0.45977/m)$-competitive algorithm and a randomized $2.51098-(0.3587/m)$-competitive algorithm. The performance of the algorithms on multiple machines when $m = 1$ matches the current best algorithms on a single machine for variable testing times shown in this paper.

Computerized adaptive tests (CATs) play a crucial role in educational assessment and diagnostic screening in behavioral health. Unlike traditional linear tests that administer a fixed set of pre-assembled items, CATs adaptively tailor the test to an examinee's latent trait level by selecting a smaller subset of items based on their previous responses. Existing CAT frameworks predominantly rely on item response theory (IRT) models with a single latent variable, a choice driven by both conceptual simplicity and computational feasibility. However, many real-world item response datasets exhibit complex, multi-factor structures, limiting the applicability of CATs in broader settings. In this work, we develop a novel CAT system that incorporates multivariate latent traits, building on recent advances in Bayesian sparse multivariate IRT. Our approach leverages direct sampling from the latent factor posterior distributions, significantly accelerating existing information-theoretic item selection criteria by eliminating the need for computationally intensive Markov Chain Monte Carlo (MCMC) simulations. Recognizing the potential sub-optimality of existing item selection rules, which are often based on myopic one-step-lookahead optimization of some information-theoretic criterion, we propose a double deep Q-learning algorithm to learn an optimal item selection policy. Through simulation and real-data studies, we demonstrate that our approach not only accelerates existing item selection methods but also highlights the potential of reinforcement learning in CATs.

Rapid development of quantum computing technology has led to a wide variety of sophisticated quantum devices. Benchmarking these systems becomes crucial for understanding their capabilities and paving the way for future advancements. The Quantum Volume (QV) test is one of the most widely used benchmarks for evaluating quantum computer performance due to its architecture independence. However, as the number of qubits in a quantum device grows, the test faces a significant limitation. It requires determining the subspace of the most probable outcomes, a task that is typically performed via classical simulation of the quantum circuit and therefore incurs an exponential computational cost. In this work, we propose modifications to the QV test, by adopting a carefully restricted circuit ensemble generated from a gate set that remains universal for quantum computation, that allows for the direct determination of the heavy-output subspace. Crucially, the modified circuits remain capable of general quantum computation. This approach overcomes the scalability barrier of the Quantum Volume test beyond classical computational limits, while still probing the key features of universal quantum computing.

This paper presents a simplified geometric proof of the Molino-Alexandrino-Radeschi (MAR) Theorem, which states that the closure of a singular Riemannian foliation on a complete Riemannian manifold is itself a smooth singular Riemannian foliation. Our approach circumvents several technical and analytical tools employed in the previous proof of the Theorem, resulting in a more direct geometric demonstration. We first establish conditions for a projectable foliation to be Riemannian, focusing on compatible connections. We then apply these results to linear foliations on vector bundles and their lifts to frame bundles. Finally, we use these findings to the linearization of singular Riemannian foliations around leaf closures. This method allows us to prove the smoothness of the closure directly for the linear semi-local model, bypassing the need for intermediate results on orbit-like foliations.

Depending on the lattice geometry, the nearest-neighbor (NN) tight-binding model for free fermions gives rise to particle-hole symmetric emergent Dirac liquid, Fermi liquid, and flat bands near the half-filling or zero-energy on bipartite Euclidean and hyperbolic lattices, respectively embedded on the flat and negatively curved spaces. Such noninteracting electronic fluids are characterized by a vanishing, a finite, and a diverging density of states near half-filling, respectively. A non-Hermitian generalization of this scenario resulting from an imbalance of the hopping amplitudes in the opposite directions between any pair of NN sites continues to accommodate a real eigenvalue spectrum over an extended non-Hermitian parameter regime. Most importantly, it reduces the band width without altering the characteristic scaling of the density of states close to the zero-energy. Here, we show that on two-dimensional bipartite Euclidean and hyperbolic lattices such a non-Hermiticity catalyzes the formation of both charge-density-wave and spin-density-wave orders at weaker (in comparison to the counterparts in conventional or Hermitian systems) NN Coulomb and on-site Hubbard repulsions, respectively. These two ordered states correspond to staggered patterns of average electronic density and spin between the NN sites, respectively, and both cause insulation in half-filled systems. We arrive at these conclusions by combining biorthogonal quantum mechanics and lattice-based self-consistent numerical mean-field analysis in the Hartree channel. We discuss the scaling of the associated mass gaps near the zero-energy with the non-Hermitian parameter, and also address the finite size scaling of the order parameters specifically on hyperbolic lattices with open boundary conditions. A robust general mathematical criterion for the proposed non-Hermitian catalysis mechanism for ordered phases is showcased.

The discovery of nontrivial topology in quantum critical states has introduced a new paradigm for classifying quantum phase transitions and challenges the conventional belief that topological phases are typically associated with a bulk energy gap. However, realizing and characterizing such topologically nontrivial quantum critical states with large particle numbers remains an outstanding experimental challenge in statistical and condensed matter physics. Programmable quantum processors can directly prepare and manipulate exotic quantum many-body states, offering a powerful path for exploring the physics behind these states. Here, we present an experimental exploration of the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to $100$ qubits. We develop an efficient method to probe the boundary $g$-function based on prepared low-energy states, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, by adapting the entanglement Hamiltonian tomography technique, we recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary condition, experimentally verifying the universal bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.

A timelike splitting theorem for Finsler spacetimes was previously established by the third author, in collaboration with Lu and Minguzzi, under relatively strong hypotheses, including the Berwald condition. This contrasts with the more general results known for positive definite Finsler manifolds. In this article, we employ a recently developed strategy for proving timelike splitting theorems using the elliptic $p$-d'Alembertian. This approach, pioneered by Braun, Gigli, McCann, Sämann, and the second author, allows us to remove the restrictive assumptions of the earlier splitting theorem. For timelike geodesically complete Finsler spacetimes, we establish a diffeomorphic splitting. In the specific case of Berwald spacetimes, we show that the Busemann function generates a group of isometries via translations. Furthermore, for Berwald spacetimes, we extend these splitting theorems by replacing the assumption of timelike geodesic completeness with global hyperbolicity. Our results encompass and generalize the timelike splitting theorems for weighted Lorentzian manifolds previously obtained by Case and Woolgar-Wylie.

This paper presents a fast inverse design framework for complex multilayered, multiport pixelated surfaces - a class of structures largely unexplored in current research. Leveraging a method-of-moments (MoM) electromagnetic (EM) solver, the framework enables the rapid synthesis of pixelated device designs. A novel matrix reconstruction technique, based on pre-labeling matrix entries as "inter-pixel" or "inner-pixel," accelerates simulations for each variation of the pixelated structure. To mitigate the cubic increase in computation time associated with additional layers, GPU acceleration is employed. Further enhancing convergence speed, a stochastic multi-pixel flipping search algorithm is integrated into the framework. The effectiveness of this approach is demonstrated through the design of a diplexer achieving a -3-dB bandwidth for one channel spanning 5.23-5.94 GHz and another covering 6.17-7.15 GHz, validated by a full-wave solver.

Given a partition $μ$ of $-2$, the stratum $\mathcal{H}(μ)$ parametrizes meromorphic differential one-forms on the Riemann sphere $\mathbb{CP}^{1}$ with~$n$ zeros and $p$ poles of orders prescribed by $μ$. The isoresidual fibration is defined by assigning to each differential in $\mathcal{H}(μ)$ its configuration of residues at the poles. In the case of differentials with $n=2$ zeros, generic isoresidual fibers are complex curves endowed with a canonical translation structure, which we describe extensively in this paper. Quantitative characteristics of the translation structure on isoresidual fiber curves, including the orders of the singularities and a period central charge encapsulating the linear dependence of periods on the underlying configuration of residues, provide rich discrete invariants for these fibers. We also determine the Euler characteristic of generic isoresidual fiber curves from intersection-theoretic computations, relying on the multi-scale compactification of strata of differentials. In particular, we describe a wall and chamber structure for the Euler characteristic of generic isoresidual fiber curves in terms of the partition $μ$. Additionally, we classify the connected components of generic isoresidual fibers for strata in genus zero with an arbitrary number of zeros.

Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive codes can always be attained with equality if the minimum distance is sufficiently large. This solves the problem for the optimal parameters of additive codes when the minimum distance is large and yields many infinite series of additive codes that outperform linear codes.

An exact result for the reduced density matrix on a finite interval for a $1+1$ dimensional free real scalar field in the ground state is presented. In the massless case, the Williamson decomposition of the appearing kernels is explicitly performed, which allows to reproduce the known result for the entanglement (modular) Hamiltonian and, for a small mass $M$ of the field, find the leading $\sim1/\ln M$ non-local corrections. In the opposite $M\to\infty$ case, it is argued that, up to terms $O(M^{-1/2})$, the entanglement Hamiltonian is local with the density being the Hamiltonian density spatially modulated by a triangular-shape function.

This paper addresses dynamic task allocation in resource-constrained multi-agent systems (MASs) with sequentially updated assignments. We develop a submodular maximization framework integrated with $q$-independence systems, demonstrating greater flexibility than conventional matroid-based constraints for modeling heterogeneous resource limitations. The proposed distributed greedy bundles algorithm (DGBA) addresses communication limitations in MASs while providing rigorous approximation guarantees for submodular maximization under a $q$-independence system constraint, ensuring low computational complexity. DGBA achieves feasible task allocation in polynomial time with reduced space complexity compared to existing methods. Extensive Monte Carlo simulations in a micro-satellite observation scenario demonstrate that DGBA consistently outperforms benchmark algorithms in total utility, resource efficiency, and assignment stability, while maintaining real-time computational feasibility.

This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs) explored in \cite{Ca2018} for $Π_{2}$-statements to statements of arbitrary quantifier complexity in prenex normal form and use this to compare various fundamental set-theoretical principles, including the power set axiom, the separation scheme, the collection scheme and the replacement scheme and various principles related to the notion of cardinality, with respect to effective reducibility. This notion of reducibility is both different from (i.e., strictly weaker than) classical truth and from the OTM-realizability of the corresponding implications. Along the way, we obtain a computational characterization of HOD as the class of sets that are OTM-computable relative to every effectivizer of $Σ_{2}$-separation. We also consider an associated variant or Weihrauch reducibility.

Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the classical method used to decode the syndrome measurements. These classical algorithms traditionally only interpret binary data, ignoring valuable information contained in the complete analog measurement data. In this work, we leverage this richer "soft information" to decode repetition code experiments implemented on superconducting hardware. We find that "soft decoding" can raise the threshold by 25%, yielding up to 30 times lower error rates. Analyzing the trade-off between information volume and decoding performance we show that a single byte of information per measurement suffices to reach optimal decoding. This underscores the effectiveness and practicality of soft decoding on hardware, including in time-sensitive contexts such as real-time decoding.

The beyond-the-standard-model scenario in this work is motivated from the observations of neutrino masses, anomalous magnetic moments of electron and muon, and dark matter in the Universe. We explain these observations by extending the standard model with two generations of vector-like fermions and an inert scalar doublet, all odd under a $Z_2$ symmetry. The light neutrino masses and mixings are generated radiatively while maintaining consistency with bounds on lepton flavor violation. Loop diagrams with the very same fields also serve to explain the anomalous magnetic moments. Similarly, the correct dark matter relic abundance is reproduced without coming into conflict with direct detection constraints, or those from big bang nucleosynthesis or the cosmic microwave observations. Finally, prospective signatures at the LHC are discussed.

A quantum analogue of the Central Limit Theorem (CLT) for bosonic system, first introduced by Cushen and Hudson (1971), states that the $n$-fold convolution $ρ^{\boxplus n}$ of an $m$-mode quantum state $ρ$, with zero first moments and finite second moments, converges weakly, as $n$ increases, to a Gaussian state $ρ_G$ with the same first and second moments as those of $ρ$, called its Gaussification. Recently, this result has been extended with estimates of the convergence rate in various distance measures. In this paper, we establish optimal rates of convergence in both the trace distance and quantum relative entropy. Specifically, we show that for a centered $m$-mode quantum state with finite third-order moments, the trace distance between $ρ^{\boxplus n}$ and $ρ_G$ decays at the optimal rate of $\mathcal{O}(n^{-1/2})$. Furthermore, for states with finite fourth-order moments (order $4+δ$ for an arbitrary small $δ>0$ if $m>1$), we prove that the relative entropy between $ρ^{\boxplus n}$ and $ρ_G$ decays at the optimal rate of $\mathcal{O}(n^{-1})$. Both of these rates are proven to be optimal, even when assuming the finiteness of all moments of $ρ$. These results relax previous assumptions on higher-order moments, yielding convergence rates that match the best known results in the classical setting. By giving explicit examples we also show that our moment assumptions are essentially minimal. Our proofs draw on techniques from the classical literature, including Edgeworth-type expansions of quantum characteristic functions, adapted to the quantum context. A key technical step in the proof of our entropic CLT is establishing an upper bound on the relative entropy distance between a general quantum state and its Gaussification, which is of independent interest.

We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this class is necessarily equi-affine. We use techniques, adapted to symplectic billiards, inspired to the paper by J. De Simoi, V. Kaloshin and Q. Wei (2017).

We formulate a polynomial GCD certificate for exact flat bands in finite-range periodic tight-binding Hamiltonians. Writing the characteristic polynomial of the Bloch Hamiltonian as a Laurent polynomial \( P_L(\mathbf{z},λ)=\det(λI-H_B(\mathbf{z}))=\sum_{\mathbf{t}}c_{\mathbf{t}}(λ)\mathbf{z}^{\mathbf{t}}, \) we show that the monic greatest common divisor \(G_L(λ)=\gcd_{\mathbf{t}}c_{\mathbf{t}}(λ)\) is precisely the maximum factor of \(P_L\) that depends only on the energy variable. Its roots are exactly the exact flat-band energies, and their multiplicities give common algebraic multiplicities of these flat bands throughout the Brillouin zone. The coefficient-vanishing criterion underlying this statement is known in the flat-band and periodic-graph literature; the contribution emphasized here is the compact GCD formulation, its unit cell and Bloch-gauge invariance, and its use as a symbolic computation tool for hopping parameter engineering. The method is illustrated on kagome, dice and octahedron-chain examples, including weighted kagome and dice lattices. The certificate detects exact dispersionless eigenvalues; compact localized states, band touching and topological character must be analyzed in a subsequent eigenvector or projector calculation.

After the optimal parameters of additive quaternary codes of dimension $k\le 3$ have been determined there is some recent activity to settle the next case of dimension $k=3.5$. Here we complete dimension $k=3.5$ and $k=4$. We also solve the problem of the optimal parameters of additive quaternary codes of arbitrary dimension when assuming a sufficiently large minimum distance.

We give a method for effectively generating generalised loxodromics in subgroups of graph products, using positive words. This has several consequences for the growth of subsets of these groups. In particular, we show that graph products of groups with strong product set growth properties also share those properties. We additionally show that the set of growth rates of a class of subgroups of any graph product of equationally noetherian groups is well-ordered.

As an IT-enabled multi-passenger mobility service, microtransit can improve accessibility, reduce congestion, and promote sustainability. However, realizing its business potential requires a deeper understanding of traveler preferences, highlighting the need for more effective tools for demand forecasting and revenue management, especially when actual usage data are limited. We propose an innovative modeling approach that integrates travel behavioral insights into microtransit policymaking. The approach operates by (1) leveraging citywide synthetic data to achieve greater spatiotemporal granularity, (2) estimating a nonparametric nested model for joint travel mode and ride-pass subscription choices, and (3) employing a simulation-based method to calculate revenue and traveler benefits under various policy scenarios. We demonstrate the applicability of our approach through a case study in Arlington, TX, one of the largest deployments of microtransit (Via) in the U.S. Using the simulation-based workflow, we evaluate alternative policy scenarios, including ride-pass discounts, event-based subsidies, and place-based subsidies, to assess their impacts on microtransit ridership, system revenue, and traveler welfare. The results indicate that reducing the weekly pass price from $25 to $18.9 and the monthly pass price from $80 to $71.5 would increase total revenue by approximately $127 per day. A 100% trip fare discount could reduce 61 car trips to AT&T Stadium during a game event while generating an additional 82 microtransit trips per day to Medical City Arlington. However, achieving these mode shifts would require subsidies of approximately $533 per event and $483 per day, respectively.

We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the grammar, this gives rise to a (single) exponential running time. Previously only a double-exponential algorithm was known. As an application, we provide a conversion from context-free session types to simple grammars whose valuation is linear in the size of the type. In this way, we provide the first polynomial-time algorithm for deciding context-free session type equivalence.

Quantifying uncertainty in detected changepoints is an important problem. However it is challenging as the naive approach would use the data twice, first to detect the changes, and then to test them. This will bias the test, and can lead to anti-conservative p-values. One approach to avoid this is to use ideas from post-selection inference, which conditions on the information in the data used to choose which changes to test. As a result this produces valid p-values; that is, p-values that have a uniform distribution if there is no change. Currently such methods have been developed for detecting changes in mean only. This paper presents two approaches for constructing post-selection p-values for detecting changes in variance. These vary depending on the method use to detect the changes, but are general in terms of being applicable for a range of change-detection methods and a range of hypotheses that we may wish to test.

Quantum machine learning (QML) leverages quantum computing for classical inference, furnishes the processing of quantum data with machine-learning methods, and provides quantum algorithms adapted to noisy devices. Typically, QML proposals are framed in terms of the circuit model of quantum computation. The alternative measurement-based quantum computing (MBQC) paradigm can exhibit lower circuit depths, is naturally compatible with classical co-processing of mid-circuit measurements, and offers a promising avenue towards error correction. Despite significant progress on MBQC devices, QML in terms of MBQC has been hardly explored. We propose the multiple-triangle ansatz (MuTA), a universal quantum neural network assembled from MBQC neurons featuring bias engineering, monotonic expressivity, tunable entanglement, and scalable training. We numerically demonstrate that MuTA can learn a universal set of gates in the presence of noise, a quantum-state classifier, as well as a quantum instrument, and classify classical data using a quantum kernel tailored to MuTA. Finally, we incorporate hardware constraints imposed by photonic Gottesman-Kitaev-Preskill qubits. Our framework lays the foundation for versatile quantum neural networks native to MBQC, allowing to explore MBQC-specific algorithmic advantages and QML on MBQC devices.

In this paper, we first propose a unified framework for analyzing the stability of the phaseless operators for both amplitude and intensity measurement on an arbitrary geometric set, thereby characterizing the robust performance of phase retrieval via the empirical minimization method. We introduce the random embedding of concave lifting operators to characterize the unified analysis of any geometric set. Similarly, we investigate the robust performance of structured matrix restoration problem through the robust injectivity of a linear rank one measurement operator on an arbitrary matrix set. The core of our analysis is to establish unified empirical chaos processes characterization for various matrix sets. Talagrand's $γ_α$-functionals are employed to characterize the connection between the geometric constraints and the number of measurements required for stability or robust injectivity. We also construct adversarial noise to demonstrate the sharpness of the recovery bounds derived through the empirical minimization method in the both scenarios.

Bibliographic data is a rich source of information that goes beyond the use cases of location and citation -- it also encodes both cultural and technological context. For most of its existence, the scholarly record has changed slowly and hence provides an opportunity to gain insight through its reflection of the cultural norms of the research community over the last four centuries. While it is often difficult to distinguish the originating driver of change, it is still valuable to consider the motivating influences that have led to changes in the structure of the scholarly record. An "initial era" is identified during which initials were used in preference to full names by authors on scholarly communications. Causes of the emergence and demise of this era are considered as well as the implications of this era on research culture and practice.

Description of electrons in a dielectric as solitons of the polarization field requires that the interaction between the solitons (prior to their coupling to electromagnetism) is short-range. We present an analytical study of the mechanism by which this is achieved. The mechanism is unusual in that it enables screening of electrically neutral soliton cores by polarization charges. We also argue that the structure of the solitons allows them to be quantized as either fermions or bosons. At the quantum level, the theory has, in addition to the solitonic electric, elementary magnetic excitations, which give rise to a topological contribution to the magnetic susceptibility.

We present the first detection in space of thionylimide (HNSO) toward the Galactic Center molecular cloud G+0.693-0.027, thanks to the superb sensitivity of an ultradeep molecular line survey carried out with the Yebes 40$\,$m and IRAM 30$\,$m telescopes. This molecule is the first species detected in the interstellar medium containing, simultaneously, N, S and O. We have identified numerous $K$$_a$ = 0, 1 and 2 transitions belonging to HNSO covering from $J$$_{\rm up}$ = 2 to $J$$_{\rm up}$ = 10, including several completely unblended features. We derive a molecular column density of $N$ = (8 $\pm$ 1)$\times$10$^{13}$ cm$^{-2}$, yielding a fractional abundance relative to H$_2$ of $\sim$6$\times$10$^{-10}$, which is about $\sim$37 and $\sim$4.8 times less abundant than SO and SO2, respectively. Although there are still many unknowns in the interstellar chemistry of NSO-bearing molecules, we propose that HNSO is likely formed through the reaction of the NSO radical and atomic H on the surface of icy grains, with alternative routes also deserving exploration. Finally, HNSO appears as a promising link between N- , S- and O- interstellar chemistry and its discovery paves the route to the detection of a new family of molecules in space.