The OpenClaw platform provides a practical foundation for automation through its skill-oriented architecture, organizing external capabilities into lightweight, reusable components that can be invoked efficiently through a command-line interface (CLI). However, a significant bottleneck remains: many real-world tasks are confined to graphical user interfaces (GUIs) with no stable API available. While LLM-based GUI agents offer generality, their reliance on repeated live model inference makes them too slow, costly, and inconsistent to serve as efficient OpenClaw skills. In this paper, we present AppAgent-Claw, a demonstration-driven system that converts GUI workflows into reliable, reusable skills without runtime inference. By following a ``record-once, replay-many'' paradigm, the system captures rich contextual metadata to facilitate robust execution. It employs a layered localization strategy to handle visual shifts and a validation-coupled execution model to ensure intended on-screen effects. AppAgent-Claw provides a practical, efficient, and diagnosable solution for integrating GUI-bound tasks into the OpenClaw ecosystem.

Parametrically driven cavity solitons (PDCS), unlike single-pumped cavity solitons, are localized optical pulses arising from parametric processes. These cavity solitons, recently discovered in pure-Kerr media, offer great promise for nonlinear dynamics studies and metrology. Here, we present the first multimode quantum description of pure-Kerr PDCS. In the below threshold regime, we verify single- and two-mode squeezing, while above threshold we uncover novel "quantum" dispersive waves - the quantum analog of soliton Cherenkov radiation. Besides revealing these unexplored quantum properties, we show that PDCS generates up to 20 dB of squeezing, only limited by overcoupling and intrinsic losses for experimentally routine parameters. We therefore provide a pathway to observe strong multimode quantum noise reduction in these systems.

Spatially embedded networks are central to many physical and biological systems, where geometry and connectivity jointly shape structure and function. Examples abound across the scales of biological organization, from network-like membrane-bound organelles in the cell to mesoscale tissue organization of multiple distinct flow networks in organs and beyond. In each of these cases, the complexity of the architectures has heretofore frustrated our ability to link mechanism or regulation of these structures to reduced modeling or even relevant characterization, putting structure-function relationships largely out of reach. Complex, functional spatial networks can be decomposed into tree-like and cyclic substructures, but we still lack both an understanding of how these elements intertwine to give rise to function, and the tools to holistically quantify both the topological and geometric aspects of these features in their full network context. To close this gap, we here introduce GEMINI, a topology and geometry aware operator that directly characterizes incomplete linking and more general spatial associations between edges in spatially embedded network architectures. GEMINI contains information on edge-edge association through an incomplete version of the Gauss linking integral which simultaneously endows it with topological sensitivity when collections of edges form linked assemblages. Validation on both synthetic lattices and on mouse brain vasculature data demonstrates that GEMINI systematically captures and classifies the complexity of structural organizations. Our results provide a general approach for analyzing spatial networks in realistic data, where topology and geometry together determine function, thus opening the door to a more complete understanding of structure-function relationships across a broad set of biological examples where complex network organization is key.

Sensitivity analysis asks how strong unmeasured confounding needs to be to explain away an observational study's conclusion. The conventional approach in matched studies conducts inference conditional upon the potential outcomes as well as both observed and unobserved confounders, and then finds the worst-case distribution for the conditional treatment assignments across all possible realizations of the unobserved confounder. The resulting worst-case allocation imagines strong, near perfect, correlations between the potential outcomes and hidden bias. We propose a stochastic sensitivity analysis that instead targets inference conditional upon potential outcomes and observed confounders while treating the hidden confounders as random with unknown conditional laws. Rather than finding the worst-case realizations for the hidden confounders, we instead determine the worst-case conditional law over a broad class of distributions. This preserves the adversarial spirit of sensitivity analysis while allowing for imperfect alignment between hidden bias and potential outcomes to a degree controlled by a scalar sensitivity parameter. We consider restrictions to both an interpretable class with no parametric assumptions and a Bernoulli class of conditional laws. Design sensitivity calculations and real-data demonstrations illustrate that allowing for even a small degree of stochasticity can materially increase reported robustness to hidden bias relative to the conventional approach.

We prove that there is a universal constant $c > 0$ such that, along an infinite sequence of dimensions $N$, there are lattice sphere packings in $\mathbb{R}^N$ of density at least $c N^2 \log\log N \, 2^{-N}$, improving the previous best bound due to Klartag by a $\log\log N$ factor. The proof follows Klartag's stochastic ellipsoid evolution process, subject to the cyclotomic symmetries introduced by Venkatesh.

We investigate fermionic Kaluza-Klein (KK) mode mixing in thick braneworld models subjected to generic background perturbations. Conventionally, isolated static backgrounds are completely described by a Schroedinger-like formulation, which yields an unperturbed orthogonal basis of KK eigenstates. However, generic perturbations possess a non-trivial spatial profile along the extra dimension. When the full interacting Dirac operator is expanded in this original basis, the spatial variation inevitably yields non-vanishing overlap integrals between distinct KK levels, thereby inducing off-diagonal couplings in the 4D effective mass matrix. Consequently, the original eigenstates are no longer exact physical eigenmodes of the perturbed system. To rigorously preserve the underlying 5D chiral structure and resolve the true physical states, we employ an exact Singular Value Decomposition (SVD) of the full, off-diagonal Dirac mass matrix. Our exact analysis reveals that this mode mixing introduces small but highly structured corrections to the mass eigenvalues. Specifically, parity-odd perturbation operators strictly induce same-parity mixing that preserves the macroscopic Z2 spatial symmetry, whereas parity-even operators trigger cross-parity mixing that shatters the Z2 symmetry, resulting in severe spatial polarization of the KK probability densities. Phenomenologically, such polarization shifts the wave functions toward the brane, turning probability zeros into non-zero values, which directly illuminates previously "dark" KK modes.

The rise of decentralized social media platforms like Mastodon and Bluesky highlights the challenge of scaling self-governance and moderation. As communities grow, they face new issues that demand increasingly complex governance structures. However, as moderation is mainly volunteer-driven, there is limited formal guidance on how community rules and moderation practices should evolve with growth. This study investigates how moderation scale with Mastodon instances by analyzing community rules across servers of varying sizes. We categorize these rules to identify key governance priorities and find that these priorities are remarkably consistent across instance sizes: rules addressing problematic content, such as harassment, hate speech, and illegal content, dominate regardless of scale. While smaller communities focus on narrower sets of topics, larger servers maintain a more balanced coverage of a broad range of topics. Our analysis of rule formalization reveals that community size strongly predicts rule development. As instances grow, their rules become more extensive and topically diverse, but also exhibit lower readability and linguistic diversity. In contrast, external federation interactions have a limited role, mainly associated with a broader scope of rules without substantially affecting their diversity or form. These findings highlight the relative influence of internal versus external factors, suggesting that local scaling pressures outweigh network-level dynamics in decentralized social media governance. The scaling pattern observed on Mastodon resemble those previously identified on centralized platforms such as Reddit, suggesting that community size imposes fundamental constraints on self-governance that transcend platform architectures

We present new solutions in type II supergravities describing AdS$_9$ geometries warped over an interval. In type IIB, we construct an analytic family of backgrounds supported by a non-trivial axio-dilaton profile. Despite the presence of strong-coupling singularities at both ends of the interval, these solutions exhibit both a finite Euclidean on-shell action and a finite holographic central charge. Moreover, they possess a $\mathbb Z_2$ symmetry under which the axion transforms as $C_0\rightarrow -C_0$. We also investigate AdS$_9$ backgrounds in massive IIA supergravity supported by the Romans mass and the dilaton. Numerical integration reveals solutions with a strong-coupling singularity whose asymptotic behavior is consistent with the characteristic D8/O8 profile. In contrast to the type IIB case, our analysis indicates that the Euclidean on-shell action diverges. Finally, we identify a family of perturbative dS$_9$ solutions in massive IIA supergravity.

We study non-supersymmetric $\mathrm{AdS}_D\times I$ solutions in the context of $(D+1)$ dimensional gravity coupled to an axio-dilaton with arbitrary runaway potential for the dilaton and arbitrary exponential coupling of the dilaton to the axion kinetic energy. We analyze the equations of motion, reformulate them in terms of a first order autonomous dynamical system, and discuss the set of fixed points, their physical interpretation and their stability conditions. We find a few special classes of analytic solutions for arbitrary $D$, including $\mathrm{AdS}_9\times I$ backgrounds in type IIB supergravity. We conclude by discussing the properties of numerical flows including the massive IIA supergravity case.

Low-Earth Orbit (LEO) mega-constellations such as Starlink by SpaceX and Kuiper by Amazon rely on optical Inter-Satellite Links (ISLs) for autonomous mesh routing to provide low-latency telecommunication, Internet of Things (IoT), and security services globally. As commercial operators and governments deploy increasingly dense constellations and form multi-operator peering coalitions, ISL integrity becomes critical to both commercial availability and national security. However, there is a lack of real-world data for LEO constellations and existing real-time security approaches focus strictly on physical layer security, leaving blind spots in the coverage of network-layer and composite attacks. In this paper, we present a cross-layer, lightweight behavioral fingerprinting framework that fuses onboard physical-layer measurements with network-layer data to detect anomalies at low computational overhead. We construct an orbital simulation covering the first shells of Starlink (1,584 satellites), Kuiper (1,156 satellites), and a joint multi-operator peering scenario (2,740 satellites), injecting ten attack types that span spoofing, traffic manipulation, and routing subversion at varying severity. We evaluate three unsupervised, per-satellite detectors among which our Mahalanobis-distance-based detector achieves 99.5% recall on Starlink, 99.4% on Kuiper, and 94.8\% on the multi-operator constellation, while maintaining False Positive Rates (FPR) below 0.7%. Our results demonstrate that cross-layer feature fusion is not only necessary for comprehensive security of LEO constellations but highly cost-effective for large-scale networks while fitting into the strict onboard energy budgets of resource-constrained satellites.

Trusted Execution Environments (TEEs)-aided federated learning protocols emerge as promising solutions to counter server-side adversaries and ensure the trustworthiness of the server. In this paper, we dissect existing protocols and demonstrate that server-side adversaries can still manipulate client selection and replay aggregation to compromise system robustness and privacy, by exploiting TEE limitations, i.e., state rollback and I/O manipulation. To this end, we present DIST-FL, a distributed system of servers guarded by multiple TEEs forming an append-only ledger for privacy-preserved, robust FL aggregation. Specifically, DIST-FL ensures operation linearizability to thwart state rollback attacks and incorporates inputs from reliable servers to mitigate I/O manipulation threats. We implement DIST-FL and conduct evaluations in WAN settings. Experimental results demonstrate that DIST-FL can effectively counter the proposed attacks and match the single-TEE's performance while offering a 6x throughput boost over its counterparts, leveraging TEE's computational advantages.

Finite Difference Schemes are widely used in the approximation of different hyperbolic (wave-like) differential equations, and are particularly important for seismic wave modelling and its applications. Classical methods based on Taylor Series are dominant in the literature; however, it is known that these methods can suffer from excessive numerical dispersion. In this paper, we review and extend existing high-order in space finite difference schemes for acoustic wave propagation, featuring different stencil geometries ranging from classical cross stencils to stencils with rhombus or square-like shapes, and propose a general mathematical framework for their derivation. The numerical implementation is performed in a symbolic, high-level framework (Devito), which compiles and runs highly optimized, stencil-based computations, allowing for a low-level interpretation of the methods efficiency. We demonstrate that non-cross stencil shapes, such as rhombus and square-based stencils, do not necessarily provide added accuracy or dispersion reduction in general, despite their increased computational cost. However, results on both idealized and realistic velocity models confirm the benefits of using dispersion-optimized cross-stencils, indicating adequate accuracy with reduced computational cost on more compact stencils compared to classic approaches. Finally, our implementation of the methods provides ease of use for full-scale acoustic seismic inversion problems using Devito.

The subcategory of gamma Cas analogs gathers Be stars with bright and hard X-ray emission. Long-term variations are expected in such objects for two reasons: their Be disk builds and dissipates, and such stars are suspected long-period binaries. Seven targets are analysed in this paper: five of them benefit from a spectroscopic monitoring in the visible (ESO, TIGRE, and amateur data) and three of them have been repeatedly observed at X-ray wavelengths (using XMM-Newton, Chandra, and Swift). Broad-band photometric data are also examined. We confirm the binary status of five targets (HD44458, HD110432, HD119682, HD161103, and HD162718) and propose first orbital solutions for all of them (they remain preliminary for two cases). Their long periods (59-322 d) and small velocity amplitudes (K~5km/s) imply low-mass (~1 M_sol) companions, as in other Be binaries and in agreement with expectations from binary interaction models. In parallel, variations of the X-ray flux are detected in all three targets with a large dataset of X-ray observations. For NGC 6649 9 and HD162718, these changes are modest (a factor of three) and uncorrelated to simultaneous optical broad-band photometry (which remains rather stable). In contrast, SS397 varies by nearly one dex and the largest and best monitored X-ray changes correlate well with optical variations. At minimum flux, SS397 keeps a hard X-ray spectrum despite a nearly normal L_X/L_BOL ratio, which has not been seen yet among gamma Cas analogs. Finally, the photometric behaviours on short timescales of HD161103, SS397, and NGC 6649 9 appear linked to broad frequency groups, as typically found for Be stars. The frequency spectrum of HD162718 displays a complex mix of (isolated) periodicities with the main one at 6.658/d. This target is thus one of the rare gamma Cas analogs to display a strong high-frequency signal typical of beta Cep activity. [summarized]

Let $A$ be a finite universal algebra. Then the orders of the $n$-generated free algebras $F_n$ in the variety (equational class) generated by $A$ satisfy G. Birkhoff's inequality: $|F_n|\le |A|^{|A|^n}$ for $n=1,2,\dots$ It follows that $\limsup_{n\to\infty}\sqrt[n]{\log |F_n|}\le |A|$. When $A$ is a finite group or a finite nonassociative algebra, we obtain a criterion for equality in this estimate; equivalently, a criterion for maximal growth of the sequence $\{|F_n|\}_{n=1}^{\infty}$.

This study addresses the boat river-crossing problem under non-uniform flow velocities by constructing three models: constant flow (Model 1), linear distribution (Model 2), and even-power function distribution (Model 3, adjustable via parameter n ). By using the vector addition, combined with the solutions of calculus and differential equations, the analytical expression of the ship's spatial trajectory under a fixed heading angle relative to the water flow is derived. For the shortest-time control problem, the Lagrange multiplier method is introduced to construct a constrained optimization model, and the analytical solution of the optimal heading angle that satisfies the boundary condition of reaching the direct opposite bank is solved. The research results provide theoretical support for the path planning of inland ship intelligent navigation systems, and the proposed multi-model analysis framework can effectively simulate the complex flow velocity distribution scenarios of real rivers.

Myroshnychenko, Tatarko, and Yaskin constructed a body $K$ in $\mathbb{R}^n$, $n \geq 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K\cap H$ coincides with $c(K)$. This construction provided answers to questions of Grünbaum and Loewner for $n\geq 5$, which are still open in dimensions $3$ and $4$. We study analogues of these questions in the settings of hyperbolic space $\mathbb H^n$ and $s$-concave functions on $\mathbb R^n$.

For given graphs $G_{1}, G_{2}, \dots, G_{t}$ and $G$, let $G\rightarrow (G_{1}, G_{2}, \dots, G_{t})$ denote that each $t$-coloring of $E(G)$ yields a monochromatic copy of $G_{i}$ in color $i$ for some $i\in [t]$. The {\it size Ramsey number} $\hat{r}(G_{1}, G_{2}, \dots, G_{t})$ is the minimum size of $G$ such that $G\rightarrow (G_{1}, G_{2}, \dots, G_{t})$. A graph $G$ is a {\it size Ramsey minimal graph} for $(G_{1}, G_{2}, \dots, G_{t})$ if $G\rightarrow (G_{1}, G_{2}, \dots, G_{t})$ and $e(G)= \hat{r}(G_{1}, G_{2}, \dots, G_{t})$. A {\it star forest} is a vertex-disjoint union of stars, and a {\it uniform star forest} is a star forest with the same size of each component. In 1978, Burr, Erdős, Faudree, Rousseau and Schelp, and in 2025, Davoodi, Javadi, Kamranian and Raeisi completely characterized the size minimal graphs for uniform star forests. In this paper, we completely characterize the size Ramsey minimal graphs for uniform star forests in multicolors.

Electron spin polarization in radiative plasmas with ultrarelativistic kinetic turbulence under highly magnetized conditions is investigated using particle-in-cell simulations. We observe that a significant spin polarization can be sustained when the leptons undergo energetic photon emission accompanied by spin flips during the nonequilibrium turbulent evolution. By analyzing the time evolution of spatially dependent spin polarization, we identify an electromagnetic (EM) regime of kinetic turbulence, distinct from the well-known density-dominated regime characterized by vortex currents and magnetic islands. While in the latter regime the spin polarization exists only transiently, in the EM regime significant anisotropic net polarization emerges and persists in non-dissipative scenarios. The correlation between spin signals and turbulence features is leveraged to introduce the characteristic parameter delimiting the EM regime via the ratio of electric and magnetic energy densities and to gain insight into complex plasma turbulence. This study demonstrates the versatility of a spin-resolved study of the plasma turbulence in extreme environments, such as black holes and magnetar magnetospheres.

We rederive the Cosmological Supersymmetry Breaking Relation $m_{3/2} = \frac{C}{\sqrt{R_{dS} L_P}}$ from a deformation of the Awada-Gibbons-Shaw local supersymmetry algebra.

This contribution presents an experimental integrated real-time 8 x 8 distributed MIMO (D-MIMO) testbed for wideband backscatter communication (BSC) and wireless power transfer (WPT). The testbed operates in the 2.45 GHz band with coherent sampling at 200 MS/s, employs a backscatter link frequency of 40 kHz, and uses wideband 5G NR reference signals for excitation. We evaluate the testbed by exploiting the estimated channel state information (CSI) in two target applications: wireless power transfer towards the backscatter device (BD) and real-time positioning of a BD in an indoor environment. In conjunction with the baseband processing chain introduced, the testbed requires less than 2 ms of total airtime to excite the system and acquire the signals for subsequent synchronization and CSI estimation on uplink BSC signals. With the CSI, we demonstrate effective energy harvesting gains of up to 12 dB.

Let $A$ be either a classical generalized Weyl algebra (also known as a noncommutative deformation of type A Kleinian singularity) or the enveloping algebra $U(\mathfrak{sl}_{2})$ over $\mathbb{Z}/p^n\mathbb{Z}.$ In this paper we compute the center and derivations of $A.$ More specifically, we show that the center of $U(\mathfrak{sl}_2)$ is generated by the Casimir element over the ring of the Witt vectors (of length $n$) of its $p$-center. Our description of derivations of $A$ implies that if the ground ring is a field $k$ of characteristic $p>2,$ then the restriction homomorphism $HH^1_{k}(A)\to Der_{k}(Z(A), Z(A))$ from the first Hochschild cohomology of $A$ to $k$-derivations of the center is an isomorphism.

The ASCCR (Attitude-Structure-Content-Communication-Relationship) framework was recently developed to teach collaboration skills to statisticians and data scientists. However, its effectiveness in real-world settings has not yet been systematically evaluated. To assess this, we evaluated novice undergraduate and graduate students' performances in initial collaboration meetings with real domain experts and compared them to an expert collaborator. Using video recordings, rubric scores, and domain expert feedback surveys, we found that novices performed surprisingly well compared to the expert. Specifically, novices scored nearly as well as the expert on the Attitude, Structure, and Relationship components of the ASCCR framework. Although novices did not initially perform as well on the Content or Communication aspects, they were able to close the gap. By the end of the collaboration projects, the novices had higher overall domain expert feedback scores than the expert. The primary implication of our study is that novices can become effective collaborators in a very short time. We discuss our findings' practical implications and provide recommendations for integrating the ASCCR framework into statistics and data science collaboration, consulting, and capstone courses.

Complex software systems such as autonomous vehicles, robotics increasingly interact with dynamic physical, cyber, and social environments. Reasoning about their behavior, maintaining them under continuous change, and evolving them safely require trustworthy knowledge about the system, its assumptions, and its operating context. Knowledge models (KMs) provide a practical basis for such reasoning, but they may themselves become incomplete, inconsistent, or outdated as systems evolve. This paper presents TrustModel, a vision for the agentic generation and evolution of living KMs. TrustModel comprises three agentic subsystems: Modeling, for constructing and updating KMs; Conformance, for assessing their alignment with the system and its environment; and Evolution, for generating guidance to keep KMs synchronized with emerging changes. We demonstrate how TrustModel can be instantiated for model-based testing and discuss its potential for supporting other MDE activities, such as requirements and assumption monitoring, architectural drift tracking, and change impact assessment. Overall, TrustModel positions living KMs as a foundation for dependable engineering of continuously evolving software systems.

The rapid advancement of Generative AI has introduced remarkable opportunities while simultaneously raising critical concerns regarding content authenticity. While recent work has increasingly focused on improving the generalization of deepfake detectors across unseen generative models, their robustness against adversarial attacks remains limited. In particular, Abdullah et al. (IEEE SP 2024) evaluated eight detectors and demonstrated that most of them exhibit significant performance degradation under adversarial attacks. We also observed the same phenomenon by testing seven most recent state-of-the-art detectors. To address this problem, we propose a unified framework that integrates three complementary design principles without relying on adversarial training data: (i) higher-order statistical modeling in the frequency domain via Discrete Cosine Transform (DCT)-based moment pooling up to fourth order, (ii) content-agnostic feature representations derived from noise residuals, and (iii) cross-scene generalization enforced through patch-level semantic disruption. A key insight underpinning our approach is that adversarial attacks primarily operate on low-order statistics and visual semantics, leaving higher-order residual-frequency characteristics, particularly kurtosis, largely unconstrained. Extensive experiments demonstrate that our method consistently improves robustness across six architecturally diverse detectors. Notably, we achieve up to 88.9% reduction in recall degradation on current adversarial benchmarks, and improve the best-performing recent detector (Yang et al., IEEE CVPR 2025) from 81.9% to 97.15% accuracy under attack. Overall, our method provides a principled, architecture-agnostic approach for improving deepfake detection robustness against current attacks.

We prove that the Poisson semigroup on free group von Neumann algebras satisfies hypercontractivity with optimal time.

An analytic Gentzen-style proof system of first-order Łukasiewicz logic, hypersequent calculus $\text{GŁ}\forall$, and its approximate completeness have been extensively studied. In this paper, we prove the approximate strong completeness of $\text{GŁ}\forall$ by a labelled tableau method. As applications, we prove a variant of Gentzen's midsequent theorem in $\text{GŁ}\forall$ and an approximate Herbrand's theorem. We also introduce a new cut rule $(\text{s-Cut})$ of $\text{GŁ}\forall$ and show the approximate strong completeness of $\text{GŁ}\forall+(\text{s-Cut})$.

The quantum-computing speedup theory considers the symmetric structures and properties of quantum systems as the fundamental Quantum-Computing-Speedup (QCS) resources which are responsible for exponentially speeding up quantum computing and simulating. At present a large and important problem is how to make use of the fundamental QCS resources to speed up essentially quantum computing and simulating. Here the author makes a great effort toward solving this important problem. The theoretical research work in this paper is mainly divided into the two Parts I and II. The Part I investigates mainly the multiple-quantum operator algebra spaces. And the relationships are analyzed among the multiple-quantum operator algebra spaces, quantum simulating for the unitary time-evolutional processes, and the fundamental QCS resources which exist in the different kinds of basic quantum spaces: the multiple-quantum operator algebra spaces, the density operator spaces, and the Hilbert spaces. It concludes that the multiple-quantum operator algebra space must be positioned as the central place where the fundamental QCS resources are exploited to speed up quantum computing and simulating. The Part II investigates mainly the subspace-selective unitary manipulation based on the Hilbert-space symmetric structures. Recognize that the multiple-quantum operator algebra space is the central place. Then those fundamental QCS resources original from the Hilbert space (a quantum-state space) must be explicitly taken into account in the multiple-quantum operator algebra space (a linear operator space). This is an important problem. The subspace-selective unitary manipulation is able to solve this problem. It aims to harness the fundamental QCS resources original from the Hilbert space to speed up quantum computing and simulating in the multiple-quantum operator algebra space.

The Wigner-Araki-Yanase (WAY) theorem is a well-known theorem regarding limitations of quantum measurement in the presence of additive conservation laws. Under the assumptions of the von Neumann measurement model, for which the system conserved quantity $L_{S}$ is bounded, given a conserved total additive system plus apparatus quantity $L_{SA}$, the measurement operator $E_{S}$ must commute with $L_{S}$. Prior proofs have exploited the properties of unitary evolution constrained by momentum conserving operations that tend to obscure the physical nature of the WAY theorem and as well lead to bounds on performance. As it is generally agreed that momentum is always exactly conserved in measurement, we instead develop a general angular momentum conserving model of measurement. This model is shown to lead to a simple explanation of the major implications of the WAY theorem and provides exact results of the effects of measurement based on the apparatus model. This is shown by both tracing the apparatus from the density matrix and also via a system-only channel model based on Kraus operators.

Multiferroic oxides, which combine coupled ferroelectric and magnetic orders, are central to understanding correlated quantum phenomena. Yet, as thickness approaches the two-dimensional (2D) limit, both ferroelectricity and magnetism are conventionally expected to vanish due to depolarization fields and finite-size effects, respectively. Here, we demonstrate that hexagonal LuFeO3 (h-LuFeO3) retains coupled ferroelectricity and magnetism at the 2D limit, with a thickness of just one and a half unit cells. Remarkably, the ferroelectric polarization remains comparable to bulk values at room temperature, while long-range magnetism and magnetoelectric coupling persist at low temperatures. We further show that the K3 phonon mode, which mediates the polarization-magnetism coupling, is stable down to the 2D limit. Our results establish h-LuFeO3 as the first oxide system to exhibit genuine 2D-limit multiferroicity, providing a fundamental breakthrough in the long-standing quest to understand and control coupled ferroic orders at the atomic scale.

Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.