In this paper, we investigate the split Grothendieck group $K^{\rm sp}_{0}(\mathcal{M})$ of a $d$-rigid subcategory $\mathcal{M}$ in an extriangulated category $\mathscr{C}$. As applications, we prove the following results: (1) If $\mathcal{M}$ is a silting subcategory, then the Grothendieck group $K_{0}(\mathscr{C})$ is isomorphic to $K_{0}^{\rm sp}(\mathcal{M})$; (2) If $\mathcal{M}$ is a $d$-cluster tilting subcategory, then $K_{0}(\mathscr{C})$ is isomorphic to the index Grothendieck group $K_{0}^{\rm in}(\mathcal{M})$; (3) Let $\mathcal{C}_{A_{n}}^{d}$ be the $d$-cluster category of type $A_n$. If $d$ is even, then $K_0(\mathcal{C}_{A_{n}}^{d})\cong \mathbb{Z}/(n+1)\mathbb{Z}$. If $d$ is odd, then $K_0(\mathcal{C}_{A_{n}}^{d})\cong \mathbb{Z}$ if $n$ is odd; $K_0(\mathcal{C}_{A_{n}}^{d})\cong 0$ if $n$ is even.

A novel vegetation model involving seasonal succession to distinguish the dryperiod, growth period and grazing period is proposed. The main aim is to explore the effects of duration and intensity of grazing season on the dynamic behaviors of a single vegetation population and the competitive outcomes between two competing vegetation species. The critical duration of drought period and grazing period that enable the persistence of a single vegetation population is obtained. Further, we found that both the duration andi ntensity of grazing significantly impact the competitive outcomes between two vegetation populations. Numerical examples are performed to validate our theoretical results and in particular to obtain the bifurcation diagram for the duration of dry season and grazing period.

Rouché's Theorem is among the most useful results in complex analysis for counting zeros of analytic functions. Rouché's Theorem also admits a harmonic analogue for counting zeros of complex harmonic functions. Previously, this analogue has been applied primarily to closed curves of simple geometry, such as circles, to count zeros. We demonstrate that non-circular critical curves can serve as effective contours by applying a harmonic Rouché-type argument to determine the total number of zeros of the complex harmonic family given by $f(z) = z^n + az^k + b\overline{z}^k - 1 $, where $n>k\geq1$ and $a,b > 0$. Under explicit inequalities relating $a$ and $b$, we determine the total number of zeros is either $n$ or $n+2k$ (counted with multiplicity). We also prove the zeros of $f$ are confined to the union of two explicit annuli in the plane: an inner annulus containing $k$ zeros and an outer annulus containing the remainder.

The ability to prepare states for quantum chemistry is a promising feature of quantum computers, and efficient techniques for chemical state preparation is an active area of research. In this paper, we implement and investigate two methods of quantum circuit preparation for multiconfigurational states for quantum chemical applications. It has previously been shown that controlled Givens rotations are universal for quantum chemistry. To prepare a selected linear combination of Slater determinants (represented as occupation number configurations) using Givens rotations, the gates that rotate between the reference and excited determinants need to be controlled on qubits outside the excitation (external controls), in general. We implement a method to automatically find the external controls required for utilizing Givens rotations to prepare multiconfigurational states on a quantum circuit. We compare this approach to an alternative technique that exploits the sparsity of the chemical state vector and find that the latter can outperform the method of externally controlled Givens rotations; highly reduced circuits can be obtained by taking advantage of the sparse nature (where the number of basis states is significantly less than 2$^{n_q}$ for $n_q$ qubits) of chemical wavefunctions. We demonstrate the benefits of these techniques in a range of applications, including the ground states of a strongly correlated molecule, matrix elements of the Q-SCEOM algorithm for excited states, as well as correlated initial states for a quantum subspace method based on quantum computed moments and quantum phase estimation.

Coorbit spaces provide a rigorous framework for the assessment of the approximation theoretic properties of generalized wavelet systems. It is therefore useful to understand when two different wavelet systems give rise to the same scales of coorbit spaces. This paper provides an exhaustive answer to this question for the case of continuous wavelet transforms associated with matrix groups in dimension two.

In the 1950s Morse defined the analogue of Morse functions for topological manifolds. In many instances, when mathematicians are using techniques on topological manifolds that appear to be Morse-theoretic in nature, there is a topological Morse function implicit in the argument. Topological Morse functions are known to inherit most of the familiar properties of the usual (smooth) Morse functions, with two crucial exceptions: existence and deformability. This paper gives a simple construction of continuous families of topological Morse functions.

We analyse a coupled 3D-2D model with a free fluid governed by Stokes flow in the bulk and a poroelastic plate described by the Biot-Kirchhoff equations on the surface. Assuming the form of a double perturbed saddle-point problem, the unique solvability of the continuous formulation is proved using Fredholm's theory for compact operators and the Babuska--Brezzi approach for saddle-point problems with penalty. We propose a stable virtual element method, establishing a discrete inf-sup condition under a small mesh assumption through a Fortin interpolant that requires only $H^1$-regularity for the Stokes problem. We show the well-posedness of the monolithic discrete formulation and introduce an equivalent fixed-point approach employed at the implementation level. The optimal convergence of the method in the energy norm is proved theoretically and is also confirmed numerically via computational experiments. We demonstrate an application of the model and the proposed scheme in the simulation of immune isolation using encapsulation with silicon nanopore membranes.

Change detection encompasses a variety of task types, and the goal of building change detection (BCD) tasks is to accurately locate buildings and distinguish changed building areas. In recent years, various deep learning-based BCD methods have achieved significant success in detecting difference regions by using different change information enhancement techniques, effectively improving the precision of BCD tasks. To address the issue of BCD with special colors, we propose the change-guided cross correlation enhancement network (CGCCE-Net). We design the change-guided residual refinement (CGRR) Branch, which focuses on extending shallow texture features to multiple scale features obtained from PVT, enabling early attention and acquisition of special colors. Then, channel spatial attention is used in the deep features to achieve independent information enhancement. Additionally, we construct the global cross correlation module (GCCM) to facilitate semantic information interaction between bi-temporal images, establishing building and target recognition relationships between different images. Further semantic feature enhancement is achieved through the semantic cognitive enhancement module (SCEM), and finally, the cross fusion decoder (CFD) is used for change information fusion and image reconstruction. Extensive experiments on three public datasets demonstrate that our CGCCE-Net outperforms mainstream BCD methods with outstanding performance.

In this paper we construct the non-trivial, renormalized Hamiltonian for a class of spin-boson models with supercritical form factors, including the one describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed through both a self-energy and mass renormalization, in the so-called Hamiltonian formalism of constructive quantum field theory, implemented by a non-unitary dressing transformation. This solves the problem of triviality for unitarily-renormalized supercritical spin-boson models.

Quantum steering enables one party to influence another remote quantum state by local measurement. While steering is fundamental to many quantum information tasks, the existing detection methods in the literature are mainly constrained to either specific measurement scenario or low-dimensional systems. In this work, we propose a majorization lattice framework for steering detection, which is capable of exploring the steering in arbitrary dimension and measurement setting. Steering inequalities for two-qubit states, high-dimensional Werner states and isotropic states are obtained, which set even stringent bars than what has been reached yet. Notably, the known high-dimensional results turn out to be some kind of approximate limits of the new approach.

We derive the expression for the local Hall conductivity for systems that lack translation symmetry and use it to study the local fluctuations of the Hall signal around disordered patches in magnetic insulators. We find that the regime in parameter space over which the system is a Chern insulating state increases upon inclusion of non-magnetic potential disorder. In addition, the phase space over which the topological Anderson insulator exists can be enhanced by breaking up a single disordered patch into multiple smaller patches with the same total amount of disorder. We expect our results will motivate the next generation of local scanning and local impedance spectroscopy experiments to visualize Hall currents around patches in the bulk of a disordered topological insulator.

Python software development heavily relies on third-party packages. Direct and transitive dependencies create a labyrinth of software supply chains. While it is convenient to reuse code, vulnerabilities within these dependency chains can propagate through dependencies, potentially affecting down-stream packages and applications. PyPI, the official Python package repository, hosts many packages and lacks a comprehensive analysis of the prevalence of vulnerable dependencies. This paper introduces PyPitfall, a quantitative analysis of vulnerable dependencies across the PyPI ecosystem. We analyzed the dependency structures of 378,573 PyPI packages and identified 4,655 packages that explicitly require at least one known-vulnerable version and 141,044 packages that permit vulnerable versions within specified ranges. By characterizing the ecosystem-wide dependency landscape and the security impact of transitive dependencies, we aim to raise awareness of Python software supply chain security.

Quantum networks (QNs) have been predominantly driven by discrete-variable (DV) architectures. Yet, optical platforms naturally generate Gaussian states--the common states of continuous-variable (CV) systems, making CV-based QNs an attractive route toward scalable, chip-integrated quantum computation and communication. To bridge the gap between well-studied DV entanglement percolation theories and their CV counterpart, we introduce a Gaussian-to-Gaussian entanglement distribution scheme that deterministically transports two-mode squeezed vacuum states across large CV networks. Analysis of the scheme's collective behavior using statistical-physics methods reveals a new form of entanglement percolation--negativity percolation theory (NegPT)--characterized by a bounded entanglement measure called the ratio negativity. We discover that NegPT exhibits a mixed-order phase transition, marked simultaneously by both an abrupt change in global entanglement and a long-range correlation between nodes. This distinctive behavior places CV-based QNs in a new universality class, fundamentally distinct from DV systems. Additionally, the abruptness of this transition introduces a critical vulnerability of CV-based QNs: conventional feedback mechanism becomes inherently unstable near the threshold, highlighting practical implications for stabilizing large-scale CV-based QNs. Our results unify statistical models for CV-based entanglement distribution and uncover previously unexplored critical phenomena unique to CV systems, providing valuable insights and guidelines essential for developing robust, feedback-stabilized QNs.

Diversification is usually viewed as a reliable way to reduce risk, yet it can dramatically fail for heavy-tailed losses with infinite mean: pooling independent losses of this type may increase tail risk at every threshold. We study this reversal by comparing a diversified portfolio (a weighted average) of risks to a "one-basket" benchmark that concentrates the full exposure on a single component chosen at random according to the same weights. In the iid case, the benchmark reduces to a single risk, recovering the classical comparison between a single risk and a diversified portfolio. Our main result -- the one-basket theorem -- provides new sufficient conditions under which the diversified portfolio has larger tail probabilities for all thresholds (first-order stochastic dominance) than this benchmark. The theorem enables weight-specific verification of the stochastic dominance relation and yields new applications, notably to averages of infinite-mean discrete Pareto risks. We further show that these failures of diversification are boundary cases of a general phenomenon: diversification always increases the likelihood of exceeding thresholds near zero, and under specific conditions this local effect extends to all thresholds, yielding first-order stochastic dominance.

We consider the construction of quantum-integrable spin chains with q-deformed long-range interactions by `freezing' integrable quantum many-body systems with spins. The input is a (quantum) spin-Ruijsenaars system along with an equilibrium configuration of the underlying spinless classical Ruijsenaars-Schneider system. For a distinguished choice of equilibrium, the resulting long-range spin chain has a real spectrum and admits a short-range limit, providing an integrable interpolation from nearest-neighbour to long-range interacting spins. We focus on the elliptic case. We first define an action of the modular group on the spinless elliptic Ruijsenaars-Schneider system to show that, for a fixed elliptic parameter, it has a whole modular family of classical equilibrium configurations. These typically have constant but nonzero momenta. Then we use the setting of deformation quantisation to provide a uniform framework for freezing elliptic spin-Ruijsenaars systems at any classical equilibrium whilst preserving quantum integrability. As we showed in previous work, the results include the Heisenberg, Inozemtsev and Haldane-Shastry chains along with their xxz-like q-deformations (face-type), or the antiperiodic Haldane-Shastry chain of Fukui-Kawakami, its elliptic generalisation of Sechin-Zotov, and their completely anisotropic q-deformations due to Matushko-Zotov (vertex type). Finally, we show how freezing fits in the setting of 'hybrid' integrable systems.

The expansion of wind and solar power is driving the European energy system transformation, thereby also driving our reliance on this weather-dependent resources. Integrating renewable scarcity events into long-term planning has therefore become essential. This study demonstrates how worst-case regional renewable scarcity events - such as the Dunkelflaute, prolonged periods of low wind and solar availability - can be incorporated endogenously into the planning of a weather-robust, interconnected energy system. We develop a capacity expansion model for a fully decarbonized European electricity system using an adaptive robust optimization framework which incorporates multiple extreme weather realizations within a single optimization run. Results show that system costs rise nonlinearly with the geographic extent of these events: a single worst-case regional disruption increases costs by 9%, but broader disruptions across multiple regions lead to much sharper increases, up to 51%. As Dunkelflaute conditions extend across most of Europe, additional cost impacts level off, with a maximum increase of 71%. The optimal technology mix evolves with the severity of weather stress: while renewables, batteries, and interregional transmission are sufficient to manage localized events, large-scale disruptions require long-term hydrogen storage and load shedding to maintain system resilience. Central European regions, especially Germany and France, emerge as systemic bottlenecks, while peripheral regions bear the cost of compensatory overbuilding. These findings underscore the need for a coordinated European policy strategy that goes beyond national planning to support cross-border infrastructure investment, scale up flexible technologies such as long-duration storage, and promote a geographically balanced deployment of renewables to mitigate systemic risks associated with Dunkelflaute events.

We present a hardware-based validation of angular droop control for grid-forming DC/AC converters, a control strategy that establishes active power-to-angle droop. Angular droop control enables exact frequency regulation at steady state, thereby combining primary and secondary control into a single layer. We provide traceable analysis and suggest solutions to the main implementation challenges with angular droop control, specifically addressing the challenges concerning discretization and clock drift in hardware experiments. This is illustrated in two different scenarios. Experimental results from the single converter to load scenario demonstrate black start capability and power-to-angle droop behavior for two different implementation schemes. A multi-converter setup validates frequency synchronization and power-sharing properties, proving the ancillary services that angular droop control provides in the real-world experimental setup.

Exciton plays an important role in optics and optics-related behaviors and leads to novel correlated phases like charge order, exciton insulator, and exciton-polariton condensation. Dark exciton shows distinct properties from bright one. However, it cannot be directly detected by conventional optic measurements. The electronic modulation effect of dark excitons in quasi-equilibrium distribution, critical for electronic devices in working status, is still elusive. Here, using angle-resolved photoemission spectroscopy, we report creating, detecting, and controlling dark excitons in the quasi-equilibrium distribution in a doped semiconductor SnSe2. Surprisingly, we observe an excitonic gap phase, with a conduction band opening an anisotropic gap. Our results broaden the scope of dark excitons, extending their studies from the picosecond timescale in the ultrafast photoemission process to conditions occurring under quasi-equilibrium. We reveal the light-matter interaction in the engineering of electronic structures and provide a new way to realize the excitonic gap phase in semiconductors with large band gaps.

We investigate the topological consequences of coupling chiral fermions to local, dispersionless phonons. This interaction induces a splitting of the phonon spectrum into three bands: a flat band and two bands with linear dispersion, all of which are degenerate at a nodal point located at zero wavevector. The flat band exhibits vanishing Berry curvature, while the linearly dispersing bands carry nontrivial topological features. Their Berry curvature fields assume a hedgehog-like structure in momentum space, analogous to monopole configurations, and reflect the chirality of the underlying fermionic system. Moreover, the effective phonon response reveals a phonon parity anomaly, observable as a discontinuity in the phonon current. This anomaly originates from the singularities of the fermion Green's function and signals the transfer of topological information from fermions to phonons. Our results demonstrate that phonon currents provide a direct probe of electronic chirality and topological structures.

One of the manifestations of the quantum Mpemba effect (QME) is that a tilted ferromagnet exhibits faster restoration of the spin-rotational symmetry after a quantum quench when starting from a larger tilt angle. This phenomenon has recently been observed experimentally in an ion trap that simulates a long-range spin chain. However, the underlying mechanism of the QME in the presence of long-range interactions remains unclear. Using the time-dependent spin-wave theory, we investigate the dynamical restoration of the spin-rotational symmetry and the QME in generic long-range spin systems. We show that quantum fluctuations of the magnetization drive the restoration of symmetry by melting the initial ferromagnetic order and are responsible for the QME. We find that this effect occurs across a wide parameter range in long-range systems, in contrast to its absence in some short-range counterparts.

GRB 221009A is the brightest gamma-ray burst (GRB) observed to date. Extensive observations of its afterglow emission across the electromagnetic spectrum were performed, providing the first strong evidence of a jet with a nontrivial angular structure in a long GRB. We carried out an extensive observation campaign in very-high-energy (VHE) gamma rays with the first Large-Sized Telescope of the future Cherenkov Telescope Array Observatory, starting on 2022 October 10, about 1 day after the burst. A dedicated analysis of the GRB 221009A data is performed to account for the different moonlight conditions under which data were recorded. We find an excess of gamma-like events with a statistical significance of 4.1$σ$ during the observations taken 1.33 days after the burst, followed by background-compatible results for the later days. The results are compared with various models of afterglows from structured jets that are consistent with the published multiwavelength data but entail significant quantitative and qualitative differences in the VHE emission after 1 day. We disfavor models that imply VHE flux at 1 day considerably above $10^{-11}$ erg cm$^{-2}$ s$^{-1}$. Our late-time VHE observations can help disentangle the degeneracy among the models and provide valuable new insight into the structure of GRB jets.

Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von Neumann algebras.

Programmable optical neural networks (ONNs) can offer high-throughput and energy-efficient solutions for accelerating artificial intelligence (AI) computing. However, existing ONN architectures, typically based on cascaded unitary transformations such as Mach-Zehnder interferometer meshes, face inherent scalability limitations due to spatial encoding, which causes optical components and system complexity to scale quadratically with network size. A promising solution to this challenge is the use of synthetic dimensions to enhance scalability, though experimental demonstration has remained scarce. Here, we present the first experimental demonstration of an all-optical, highly scalable, programmable ONN operating in a time-synthetic dimension. By implementing a time-cycle computation paradigm analogous to gate cycling in conventional spatial photonic circuits, our approach achieves a gate count surpassing that of state-of-the-art programmable photonic processors. Unlike conventional ONN architectures that rely on real-space wave interferences, our framework exploits time-reflection and time-refraction to perform computations, fundamentally eliminating backscattering errors through causality constraints. To bridge the gap between simulation and reality, we introduce an in-situ training framework that dynamically adapts to experimental errors, achieving performance exceeding traditional in silico learning paradigms. Our synthetic-dimension-based approach provides a compact, scalable, backscattering-free, and programmable neuromorphic computing architecture, advancing the potential for next-generation photonic AI systems.

Interparticle cohesion is prevalent in stored powders, geological formations, and infrastructure engineering, yet a comprehensive understanding of the effects of its micro-mechanics on bulk properties has not been established experimentally. One challenge has been that while photoelasticy has been widely and successfully used to measure the vector contact forces within dry granular systems, where the particle-particle interactions are solely frictional and compressive in nature, it has seen little development in systems where tensile forces are present. The key difficulty has been the inability to distinguish between compressive and tensile forces, which appear identically within the photoelastic response. Here, we present a novel approach which solves this problem, by an extension to the open-source PeGS (Photoelastic Grain Solver) software available at https://github.com/photoelasticity. Our new implementation divides the procedure of finding vector contact forces into two steps: first evaluating the vector contact forces on the non-cohesive particles present in the ensemble, followed by using an equilibrium constraint to solve for the forces in the bonded particles. We find that in the dilute limit, for up to 25% bonded dimers, we can solve for all forces since each particle has only one force bearing contact that can potentially transmit tensile forces. While the case of dimers is an idealised version of cohesive granular ensemble, it provides an important first step towards experimentally studying the micro-mechanics of cohesive granular materials.

In this paper, we present a residual-driven multiscale method for simulating Darcy flow in perforated domains, where complex geometries and highly heterogeneous permeability make direct simulations computationally expensive. To address this, we introduce a velocity elimination technique that reformulates the mixed velocity-pressure system into a pressure-only formulation, significantly reducing complexity by focusing on the dominant pressure variable. Our method is developed within the Generalized Multiscale Finite Element Method (GMsFEM) framework. For each coarse block, we construct offline basis functions from local spectral problems that capture key geometric and physical features. Online basis functions are then adaptively enriched using residuals, allowing the method to incorporate global effects such as source terms and boundary conditions, thereby improving accuracy. We provide detailed error analysis demonstrating how the offline and online spaces contribute to the accuracy and efficiency of the solution. Numerical experiments confirm the method's effectiveness, showing substantial reductions in computational cost while maintaining high accuracy, particularly through adaptive online enrichment. These results highlight the method's potential for efficient and accurate simulation of Darcy flow in complex, heterogeneous perforated domains.

Bureau proposed a classification of systems of quadratic differential equations in two variables which are free of movable critical points, which was recently revised by Guillot. We revisit the quadratic Bureau-Guillot systems with the first and second Painlevé transcendent in the coefficients. We explain their birational equivalence by using the geometric approach of Okamoto's spaces of initial conditions and the method of iterative polynomial regularisation, solving the Painlevé equivalence problem for the Bureau-Guillot systems with non-rational meromorphic coefficients. We also find that one of the systems related to the second Painlevé equation can be transformed into a Hamiltonian system (which we call the cubic Bureau Hamiltonian system) via the iterative polynomial regularisation.

We present a large-scale, longitudinal dataset capturing user activity on the online platform of DerStandard, a major Austrian newspaper. The dataset spans ten years (2013-2022) and includes over 75 million user comments, more than 400 million votes, and detailed metadata on articles and user interactions. It provides structured conversation threads, explicit up- and downvotes of user comments and editorial topic labels, enabling rich analyses of online discourse while preserving user privacy. To ensure this privacy, all persistent identifiers are anonymized using salted hash functions, and the raw comment texts are not publicly shared. Instead, we release pre-computed vector representations derived from a state-of-the-art embedding model. The dataset supports research on discussion dynamics, network structures, and semantic analyses in the mid-resourced language German, offering a reusable resource across computational social science and related fields.

Bose-Einstein condensation of spin-polarized triplet excitons can give rise to an intriguing spin supercurrent, enabling experimental detection of exciton condensation. In this work, we predict that Ta3X8 (X=I, Br) ferromagnetic monolayers are spin-polarized triplet excitonic insulators (EIs), based on the systematic first-principles GW calculations coupled with the Bethe-Salpeter equation (GW+BSE). The single-particle calculations of spin-polarized band structures reveal that these monolayers are bipolar magnetic semiconductors, where the highest valence band and the lowest conduction band possess opposite spin polarization. The two low-energy bands, primarily originating from Ta $d_{z^2}$ orbitals, are almost flat. The same-orbital parity and opposite-spin natures of the band-edge states effectively suppress dielectric screening, promoting the emergence of the EI state. The GW+BSE calculations reveal that the binding energy of the lowest-energy exciton is 1.499 eV for Ta3I8 monolayer and 1.986 eV for Ta3Br8 monolayer. Since both values exceed the respective GW band gaps, these results indicate a strong excitonic instability in these monolayers. A wavefunction analysis confirms that the lowest-energy exciton is a tightly bound Frenkel-like state, exhibiting a spin-polarized triplet nature with $S_z=1$. Our findings establish a valuable material platform for investigating spin-polarized triplet EIs, offering promising potential for spintronic applications.

Planning and extension of water distribution systems (WDSs) plays a key role in the development of smart cities, driven by challenges such as urbanization and climate change. In this context, the correct estimation of physically correct hydraulic states, i.e., pressure heads, water demands and water flows, is of high interest. Hydraulic simulators such as EPANET or more recently, physic-informed surrogate models are used to solve this task. They require a subset of observed states, such as heads at reservoirs and water demands, as inputs to estimate the whole hydraulic state. In order to obtain reliable results of such simulators, but also to be able to give theoretical guarantees of their estimations, an important question is whether theoretically, the subset of observed states that the simulator requires as an input suffices to derive the whole state, purely based on the physical properties, also called hydraulic principles, it obeys. This questions translates to solving linear and non-linear systems of equations. Previous articles mainly investigate on the existence question under the term observability analysis, however, they rely on the approximation of the non-linear principles using Taylor approximation and on network-dependent numerical or algebraic algorithms. In this work, we provide purely theoretical guarantees on the existence and uniqueness of solutions to the non-linear hydraulic principles, and by this, the existence and uniqueness of physically correct states, given a variety of common subsets of them -- a result that seems to be common-sense in the water community but has never been rigorously proven. We show that previous existence results are special cases of our more general findings, and therefore lay the foundation for further analysis and theoretical guarantees of the before-mentioned hydraulic simulators.

While bursty star formation in low-mass galaxies has been observed in local populations and reproduced in simulations, the dormant phase of the burst cycle has not been well studied beyond the local Universe due to observational limitations. We present a unique sample of 43 JWST PRISM spectra of low-mass galaxies ($M_\star < 10^{9.5}\,M_\odot$) at cosmic noon ($1<z<3$), uniformly selected on F200W magnitude and precise photometric redshifts enabled by 20-band JWST photometry from the UNCOVER and MegaScience surveys. The spectra reveal numerous strong Balmer breaks, which are negatively correlated with the galaxies' H$α$ equivalent width. By comparing these observations to synthetic samples of spectra generated using a simple parametrization of bursty star formation histories, we show that star formation in low-mass galaxies at cosmic noon is likely dominated by burst cycles with long timescales ($\gtrsim 100$ Myr) and large deviations below the star-forming main sequence ($\gtrsim 0.8$ dex). Our results suggest that galaxies in this population--at least those within our detection limits--should not be classified solely by their current star formation rates, but instead viewed as a unified population undergoing dynamic movement above and below the star-forming main sequence. The derived constraints demonstrate that long-timescale fluctuations are important for this class of galaxies, indicating that galaxy-scale gas cycles--rather than molecular-cloud-scale stochasticity--are the primary regulators of star formation variability in low-mass galaxies at cosmic noon.