We study two-photon entangled states for quantum radar cross section (QRCS), which is an extension of a single-photon QRCS formula. Since signal-idler entanglement does not provide any enhancement of the QRCS [Brandsema's PhD Thesis (2017)], we focus on signal-signal entanglement and derive the corresponding biphoton QRCS. We show that it can provide an enhancement over the single-photon QRCS and two-photon separable QRCS, where the performance is evaluated for various two-dimensional target geometries in monostatic/bistatic configurations. Furthermore, using the double-Gaussian approximation, we derive QRCS formula for biphoton states with arbitrary degree of entanglement and compute the resulting scattering patterns.

Renewed interest in cislunar space has created opportunities for sustained operations in extremely low-lunar orbits (eLLOs), where altitudes below 50~km enable close surface proximity. However, these orbits are strongly perturbed by the irregular lunar gravity field, leading to rapid eccentricity growth, high station-keeping costs or even surface impact. Recent advances in our understanding of the lunar `translation theorem' have revealed predictable behavior in the eccentricity vector, offering new opportunities for efficient control. This paper introduces a two-stage framework for solar sail station-keeping in eLLOs. First, a mixed-integer second-order cone programming (MISOCP) approach leverages the translational behavior of the eccentricity vector to identify orbit and sail configurations favorable for station-keeping. Second, a lightweight sequential convex programming (SCP) formulation refines these into high-fidelity trajectories, enabled by a recently developed lossless convexification of solar sail dynamics. A case study inspired by the Lunar Reconnaissance Orbiter (LRO) mission demonstrates that a realistic solar sail spacecraft can be maintained within the eLLO regime for at least 1~year without propellant expenditure, suggesting that longer-duration, or even indefinite station-keeping, may be feasible. The approach remains effective at reduced control update frequencies (down to monthly) and exhibits low sensitivity to uncertainties.

This paper investigates a rotatable antenna (RA)-enabled uplink non-orthogonal multiple access (NOMA) system, where a base station equipped with multiple independently RAs serves both ground and aerial users. Specifically, we formulate an energy efficiency (EE) maximization problem by jointly optimizing receive beamforming, user power allocation, and RA rotation. To make the problem tractable, a new block coordinate descent-based algorithm is developed, in which the receive beamforming is updated via the minimum mean square error criterion, while the power allocation and RA rotation are handled by fractional programming and successive convex approximation. Numerical results demonstrate the EE superiority of the proposed RA-NOMA scheme over several benchmarks.

We report on experimental and theoretical investigation of mode-splitting dynamics in a ring cavity under the perturbation of fractional Bragg reflection from a periodically-poled nonlinear crystal. Counterintuitively, pronounced mode splitting in the spectral domain could been observed even with a tiny intensity reflection of 0.0003. The breaking of running-wave operation in the ring-cavity configuration resulted in comparable circulating fields in forward- and counter-propagation directions, which thus dramatically reduced the enhancing factor for the resonating field. In contrast, a linear cavity with intrinsically bidirectional operation was immune to the small intra-cavity reflection. Therefore, the linear-cavity layout could provide an expedient solution for a given internal reflection to obtain more stable and higher enhancement, which was confirmed by comparative studies of mid-infrared generation based on pump-enhanced difference frequency conversion. The underlying mechanism was further modeled by numerical simulations, which agreed well with experimental results. These findings could not only shed light on the understanding of the exotic feature of concatenated optical cavities, but also provide a useful guide to practical design of enhancement cavities for cavity-based frequency conversion with periodically-poled nonlinear crystals.

In this paper, we study multi-objective submodular maximization (MOSM) subject to a cardinality constraint under differential privacy (DP). Specifically, we aim to select a set of at most $k \in \mathbb{Z}_{+}$ elements to maximize the minimum of $d > 1$ monotone submodular functions while satisfying $\varepsilon$-DP. Although extensive studies have been conducted on both differentially private single-objective submodular maximization on sensitive data and non-private MOSM, to the best of our knowledge, there has not yet been any prior work on MOSM with DP. We propose two novel algorithms: the first extends the classic greedy algorithm and the second employs a truncation technique, both of which are integrated with DP mechanisms for privacy protection and achieve approximation guarantees for MOSM. Finally, we conduct numerical experiments on two submodular maximization applications, namely maximum coverage and facility location, in multi-objective settings to validate the efficacy and efficiency of our proposed algorithms.

We have proposed and implemented a novel scheme for passive all-optical synchronization between erbium and ytterbium mode-locked fiber lasers. The passive locking of repetition rates for the dual-color pulses was realized by cross-phase modulation within phase-biased nonlinear amplifying loop mirrors. In contrast to previous demonstrations, the synchronization system was configured in an all-polarization-maintaining structure, thus gaining substantially improved stability and robustness. Consequently, the maximum tolerance of cavity-length mismatch of 16.2 mm was achieved unprecedentedly, which was at least one order of magnitude longer than previously reported results for comparable temporal durations of involved pulses. The corresponding relative timing jitter was measured to be 31 fs within 1-MHz bandwidth. Such tight and robust synchronization fiber laser system offers a great potential for various applications, such as pump-probe microscopy, Raman scattering spectroscopy and nonlinear frequency generation.

We solve interface problems on the line between various constant coefficient linear evolution partial differential equations. Our prototypical examples are the heat, linear Schrödinger, Airy, linearized Korteweg de Vries, and biharmonic Schrödinger equations. In each problem, one of the listed equations is posed on one spatial half line, and another on the other half line, with appropriate interface conditions. These problems are solved by means of novel extensions of Fokas's unified transform method and the explicit solution formulae are evaluated using Filon quadrature.

We study a class of nonlinear nonlocal elliptic equations in $\mathbb{R}^N$ involving superpositions of Hartree-type nonlinearities. Motivated by the Schrödinger-Poisson-Slater system, these equations arise as natural generalizations of problems with a single nonlocal interaction term. More precisely, we consider equations driven by a family of Riesz potentials weighted by a positive Borel measure, which gives rise to a superposed nonlocal operator. To treat this problem variationally, we introduce suitable functional settings, namely the superposed Coulomb space and the associated superposed Coulomb-Sobolev space, and study their main properties. Combining variational methods with a recently developed scaling-based critical point theory, we prove existence and multiplicity results for radial solutions. We also investigate a Brezis-Nirenberg-type problem and obtain multiplicity results near eigenvalues of an associated nonlinear eigenvalue problem. Our results extend previous works on single Hartree-type equations and provide a unified framework for treating superpositions of nonlocal interactions of Hartree type.

Indirect reciprocity explains how cooperation evolves through social reputations. People observe others, assign reputations, and condition their future actions on these assignments. This process is cognitively demanding, and stereotyping offers a simpler alternative by replacing individual-level reputation with group-level information. Theoretical models commonly implement stereotyping through exogenously given group labels. In real societies, however, group-level impressions may be associated with observable patterns of behavior. Here we propose a framework of stereotyping by strategy standing, in which mutants may condition their actions on the overall reputation level associated with a resident strategy rather than on the recipient's reputation. We show that this form of stereotyping can diversify stable cooperation in indirect reciprocity. As the strength of stereotyping increases, additional cooperative evolutionarily stable norm-strategy (ESS) pairs emerge in substantial numbers. In particular, we identify eight highly cooperative ESS pairs that become stable under very weak stereotyping. These pairs, which we call the counterparts of the leading eight, share the same social norms as the classical leading eight and differ only in how they prescribe behavior between bad individuals. They are unstable without stereotyping because they can be invaded by their corresponding leading strategies, but they become stable once stereotyping exceeds a critical threshold. Our results suggest that group-level impressions based on strategy standing can provide a coarse-grained informational route to stable cooperation and offer a more behaviorally grounded perspective on how stereotyping affects indirect reciprocity.

Despite significant advancements in parameterizations of boundary layer processes, forecasting, and nowcasting low-level clouds using numerical models remain challenging. The purpose of this study is to test a prototype of a high-resolution stochastic-deterministic model designed to simulate the life cycle of fog cover based on the Ising model from statistical mechanics. The case of advection fog around St. John's Airport in Newfoundland (Canada) has been considered. The model demonstrates promising capabilities in forecasting mean fog cover and replicating the horizontal structure observed in satellite imagery, including bands, rolls, and closed or open cells. We evaluate the model's predictive skill by analyzing its effectiveness in reproducing the evolution of fog cover across three representative cases. A contingency table and associated performance metrics are used to assess its accuracy.

As sixth-generation (6G) wireless systems evolve toward higher frequency bands, large-scale antenna arrays, and intelligent interaction with the wireless environment, conventional fixed-position antennas (FPAs) are increasingly constrained by limited spatial degrees of freedom and insufficient hardware-level adaptability. Fluid antenna systems (FAS) provide new physical-layer flexibility by dynamically reconfiguring antenna ports, geometries, and radiation characteristics. However, existing studies have mainly focused on one- or two-dimensional apertures, leaving the spatial reconfigurability required for complex three-dimensional (3D) propagation environments insufficiently exploited. In this article, we present a 3D spherical fluid antenna system (3D SFAS) architecture for flexible spatially reconfigurable communications. By activating radiating elements in different spherical regions, 3D SFAS realizes array-level spatial reconfiguration through flexible region switching. Within the selected regions, element-level reconfiguration further adjusts the effective aperture size, array topology, and radiation characteristics. This joint framework enables flexible beamforming, concurrent multi-region transmission, blockage-adaptive aperture switching, effective-aperture reconfiguration, and high-resolution 3D aperture control. We also discuss its potential applications in space-air-ground integrated networks, high-mobility communications, integrated sensing and communication systems, and emergency communications. Numerical results demonstrate the potential of 3D SFAS to improve wireless communication performance through flexible spatial reconfiguration. Overall, 3D SFAS extends FAS design beyond 2D position switching toward comprehensive 3D spatial reconfigurability.

High tides are a threat to damage the coast and onshore structures. To investigate mitigation strategies, we simulate waves and a flood-like situation from two-dimensional (2D) dam-break flow with a ramp section at the end of the channel using smoothed particle hydrodynamics (SPH). We analyse the effects of ramps with various topographies to reduce the pressure on structures exerted by the wave. Structures of ramp surfaces influence flow behaviour significantly, absorbing kinetic energy of the wave. Increasing the ramp angle reduces the impact on the structure. A wave with a large velocity intensifies the flow impact, rendering the effects on all topography of the ramp almost insignificant. The ramp experiences the highest force exerted by the fluid on the bottom section. These insights enhance the understanding of ramp-induced energy dissipation and provide valuable implications for hydraulic engineering and structural resilience.

The weighted center of imputations (CIS) value allocates the surplus of the grand coalition equally after granting each player a fixed proportion of his individual worth. This paper provides three axiomatic characterizations of this value by generalizing the individual rationality and subgame order preservation axioms. The first characterization employs individual rationality with respect to the weights together with the equal surplus increment property. The second relies on efficiency, additivity, symmetry adjusted by the weights, and a dummifying player property adapted to the weights. The third builds on efficiency and a weak subgame order preservation axiom that incorporates the weights. These results unify and extend recent findings, covering both the equal division and the standard CIS values as special cases.

We studied dam-break flow in the smoothed particle hydrodynamics framework using periodic boundary condition (PBC) instead of usually employed rigid wall boundary condition (WBC) and assessed the effects of impact of the flow on the downstream structure due to the presence of an obstacle in front of it. The results show that higher dam heights lead to larger pressure on the wall. The WBC yields higher peak pressures compared PBC. A larger hydraulic diameter of the pillar is found to be more efficient in reducing the flow's impact. A pillar located closer to the wall reduces the effect of dam-break flow and minimises structural damage. The square-shaped pillars are found to be the most effective in reducing pressure on the wall among the considered pillar shapes. These findings will help to mitigate the damage of a structure due to dam-break flow/high-tide and improve the safety of the structures downstream. These findings have direct implications for the design and management of structures in areas prone to dam-break flows.

We introduce Transition states (T states), denoted by $\ket{T_k^n}$, as a class of multipartite entangled states characterized by a fixed number of state transitions between adjacent qubits. These states form equal-amplitude superpositions over all states with a specified transition count. Unlike Bell states based on two-qubit correlations, GHZ states characterized by global correlations among all qubits, and W and Dicke states based on fixed numbers of qubit excitations, T states are defined by transition counts along an ordered sequence of qubits. We prove that T states are unitarily equivalent to Dicke states through a chain of CX (controlled-X) operations, thereby establishing a direct correspondence between transition-based and excitation-based representations of multipartite entanglement.

We show that two families of operator algebras, the CSL algebras of multiplicity free CSLs and the semicrossed products of commutative C$^*$-algebras, demonstrate a strong form of rigidity with respect to isometric isomorphisms. Specifically, the isomorphism class of any such algebra remains unchanged within its family, even if we allow for isomorphism after tensoring with operator algebras containing the compact operators. For semicrossed products of commutative C$^*$-algebras, the same conclusion holds even when tensoring with operator algebras whose diagonals are irreducibly acting. Collectively, these results imply rigidity with respect to stable isomorphisms: two algebras are isometrically isomorphic if and only if they are stably isomorphic.

We introduce a new topological method to naturally extend a partial function $h \colon X \rightharpoonup [-\infty, \infty]$ on a ``generalization'' of a metric space $X$ equipped with a dynamical system $f \colon X \rightharpoonup X$, to a function $h_f^{\varepsilon\text{-}\ell^p} \colon X \to [-\infty,\infty]$ with parameters $\varepsilon,p$, which allows us to apply existing topological data analysis techniques to functions defined on the whole space. Moreover, given a function $h$ that evaluates the ``quality'' of points within $\mathop{\mathrm{dom}}h$, using this extended function, one can construct a sufficient condition for the existence of an optimal $\varepsilon$-perturbation path from any point into $\mathop{\mathrm{dom}}h$ that minimizes the value of $h$ under the condition $X = \mathop{\mathrm{dom}} f \sqcup \mathop{\mathrm{dom}}h = \bigsqcup_{n = 0}^\infty f^{-n}(\mathop{\mathrm{dom}}h)$. In addition, if the domain $X$ is finite, then the function $h_f^{\varepsilon\text{-}\ell^p} \colon X \to [-\infty,\infty]$ can be computed recursively. As an application, for a given partial evaluation function on a space equipped with a dynamical system, one can construct a three-parameter filtration associated with its extension, which naturally identifies minimal paths. This clarifies the relationship among three factors: the evaluation of the cost norm, the strength of control, and the resulting value.

Code Agents have achieved remarkable advances in recent years, exhibiting strong capabilities across a wide range of software engineering tasks. However, their misuse often produces bloated and disorganized code that impairing readability, extensibility, and robustness. Despite this risk, existing benchmarks largely evaluate functional correctness rather than long-term maintainability of code agents. In this paper, we propose SmellBench, an extensible code refactoring benchmark that proactively injects code smells into clean code snippets from real-world repositories. This design enables the generation of controlled, high-quality, and diverse refactoring cases with human-written ground truth. Specifically, it contains 294 cases spanning 7 popular smell types, 3 difficulty levels, 2 instruction settings across 7 real-world repositories. We further design 3 evaluation aspects covering functional correctness, localization ability, and refactoring quality assessment. Experiments with 2 popular agents and 6 large langauge models (LLMs) show that the best combination - Qwen Code + Claude Sonnet 4.5 - achieved only a 50.34 score of smell elimination. Further analysis reveals that this gap arises from a focus on local code smells and a lack of cross-file understanding, which hinders comprehensive smell elimination.

We study the problem of robust repair of a single erasure in Reed--Solomon codes under low communication bandwidth. Focusing on the Guruswami--Wootters trace repair framework, we investigate whether a failed node can be correctly repaired in the presence of erroneous responses from helper nodes. Equivalently, we view the collection of downloaded traces as a code, which we call the repair-trace code. By characterizing the zero coefficients of the associated polynomial in terms of cyclotomic cosets, we derive upper bounds on the dimension $k$ that allow correction of a given number of erroneous traces $e$, as well as lower bounds on the minimum distance as a function of $k$. For the case $q=2$, we exploit explicit formulas for cyclotomic coset representatives to obtain the exact optimal dimension bound for single-error correction. We also propose two efficient robust repair schemes. Our first scheme achieves the error-correction capability guaranteed by the BCH bound. To approach a stronger bound based on character sums, we develop a second scheme that tolerates more errors at the cost of an additional factor $n$ in computational complexity.

LLM-driven automated penetration testing agents are typically evaluated against static targets that neither detect nor respond to attacks, so their behavior under intelligent defense remains untested. The causal consistency of multi-step attack chains likewise hinges on unstable LLM reasoning, and agent decisions remain opaque to human analysts. These three shortcomings, in realism, consistency, and auditability, are usually patched in isolation. We present ZERO-APT, a turn-based attacker-defender-judge framework that addresses them within a single architecture. For realism, ZERO-APT embeds a configurable LLM Defender that consumes Sysmon telemetry and detects attacks in real time, exposing the attacker to a live opponent rather than a passive target. For consistency, three architectural mechanisms move causal consistency from unstable LLM reasoning into enforced system architecture: separation of planning from execution, multi-dimensional ReAct feedback, and a hard-constraint-filtered action library. For auditability, a dedicated Judge agent adjudicates each round, maintains global state, and emits structured post-hoc CTI reports that make every decision traceable. We evaluate a Windows Server 2022 post-exploitation prototype across five scenarios with three Defender configurations. ZERO-APT reaches 79\% attack success rate (Aurora 22\%, PentestGPT 39\%), a Causal Consistency Score of 0.860 (Aurora 0.930, Claude Code 0.520), and end-to-end decision auditability through structured CTI reports. We release the benchmark to support evaluation of penetration agents under intelligent defense.

Lévy's Dragon Curve is a well-known self-similar fractal, notable for its ability to tile the complex plane. We review a representation of the curve as a set of points given by complex power series satisfying a revolving condition, and study how this representation changes under linear transformations, while preserving its characteristic geometric properties. We introduce a labeled directed graph that encodes these series representations and show that this directed graph remains invariant under linear transformations, with only the labeling subject to change. Furthermore, we provide a geometric characterization of the resulting variations in graph labeling.

We explore Yang-Mills-Chern-Simons theories coupled to a Higgs-like field in the fundamental representation of $SU(2)$ quantized in linear covariant gauges in three Euclidean dimensions. We analyze the modifications in the analytic structure of the gluon propagator due to the elimination of infinitesimal Gribov copies. The interplay between the Higgs, the Chern-Simons and Gribov mass parameters is investigated. Two different phases are identified: a confining one, where all poles are complex, and a deconfined one, where would-be physical gluon excitation can appear. Unlike previous works, the Gribov parameter is consistently fixed by its gap equation as a function of the other mass parameters and the gauge coupling. This imposes a constraint in the parameter space and makes transparent how the competition of the mass parameters affects the relevance of the Gribov parameter for the characterization of the spectrum of the theory.

Exponential smoothing (ES) often outperforms other techniques in time series forecasting across a wide range of data-generating processes. While ES has traditionally been applied to time series in $\mathbb{R}$, this paper extends the methodology to distributional time series, where each observation is a probability distribution on $\mathbb{R}$. The primary contribution of this work is twofold. First, we propose a principled and intuitive generalization of ES within the Wasserstein space, which retains the exceptional parsimony of classical ES. Second, we theoretically and empirically demonstrate that the smoothing parameter can be consistently estimated by minimizing a Wasserstein distance. Applications to distributional time series of high-frequency financial returns and household electricity demands confirm the practical effectiveness of our Wasserstein ES model.

We provide a theorem on the role of risk and risk attitudes in macroeconomic models that clarifies and extends the Tallarini (2000) separation result. Under (1) separation of intertemporal and risk preferences, (2) separation of drivers of first and higher moments in the model primitives, and (3) approximate linearity of constraints, risk aversion and time-varying risk are irrelevant for the elasticity of any endogenous variable with respect to state variables that don't drive variation in higher moments. We discuss how models generate a more prominent role for risk by ``breaking'' or ``adapting'' to the assumptions in the theorem.

Many physical systems with or without nonholonomic constraints have a Lagrangian description. In the first case, the Lagrangian model can be represented by second-order ODEs that are constrained to a submanifold of velocities; in the latter case the ODEs are unconstrained. In this paper, using geometric techniques, we address the more general inverse problem: ``When can a given constrained or unconstrained system of second order ODEs on a manifold be the representation of a Lagrangian model?''. We show that the constrained case has many more ambiguities and complexities than its well-understood, unconstrained counterpart.

Using degenerate Whittaker functions and explicit computations of Eisenstein series, we obtain explicit formulas for the Fourier expansions of theta lifts to the special orthogonal group $G={\rm SO}(3,n+1)$ over $\mathbb{Q}$, where $n\ge 3$ and $G$ splits at all finite places. The theta lifts in question are Hecke eigen, non-cuspidal, square-integrable automorphic forms of weight $l$ ($l\ge n+2$, even), arising from elliptic newforms for $\SL_2(\Z)$ of weight $l-\frac{n-2}{2}$ when $n$ is even and $2l-n+1$ when $n$ is odd.

We prove an arithmetic analogue of Kashiwara regularity for filtered strongly equivariant Berthelot arithmetic $\mathscr D^\dagger$-modules on formal flag varieties. Let $\mathcal G$ be a split connected reductive group scheme over a complete discrete valuation ring of mixed characteristic, let $\mathfrak X=\widehat{\mathcal G/\mathcal B}$ be the formal flag variety, and let $\mathcal K\subseteq\mathcal G$ be a smooth closed subgroup whose special fiber acts on $X_s$ with finitely many separable orbits. We introduce a filtered strong equivariance condition requiring infinitesimal equivariance to be realized on good finite-level models. This condition allows the principal symbols of the fundamental vector fields to be controlled at the level where Berthelot characteristic varieties are defined. We prove that the characteristic variety of every filtered strongly equivariant coherent $\mathscr D^\dagger_{\mathfrak X,\mathbb Q}$-module is contained in the union of conormal bundles to the $\mathcal K_s$-orbits; hence such modules are holonomic. In the Frobenius range, Caro's stability theorem for $F$-holonomicity over smooth projective formal schemes upgrades this to geometric overholonomicity. As a consequence, simple Frobenius filtered strongly equivariant coherent arithmetic $\mathscr D^\dagger$-modules are classified by pairs $(O,E)$, where $O$ is a $\mathcal K_s$-orbit and $E$ is an irreducible $\mathcal K$-equivariant overconvergent $F$-isocrystal on $(O,\overline O)$ whose intermediate extension satisfies the filtered strong condition. The result is a regularity theorem under a finite-level equivariance hypothesis, rather than an existence theorem for that hypothesis.

In the classic online min-cost matching problem, the goal is to match a sequence of requests that arrive dynamically over time to a set of static servers, aiming to minimize the total cost of the matching. This assumes that there are two distinct "sides" and that only one of these sides arrives online, but many of the motivating applications violate these assumptions. We study online min-cost perfect-matching when \emph{all} participants arrive online and, upon arrival, they need to either be matched to someone from a waiting pool or to join the waiting pool. We evaluate the competitive ratios achievable in different input models and show that for both the adversarial and the random-order input models the competitive ratio of any algorithm is unbounded. In contrast, for i.i.d. arrivals we give a $O( \log^2{n})$-competitive algorithm, even if the distribution that generates these arrivals is unknown to the algorithm. This result implies a rare example of separation in the achievable competitive ratio between the random-order and the unknown-i.i.d. input models.

We study $(-2)$-form symmetries of a $d$-dimensional quantum field theory, via a $(-1)$-form symmetry of its $(d+1)$-dimensional Symmetry Topological Field Theory (SymTFT), realized by a non-genuine codimension-one defect in the SymTFT bulk attached to a spacetime-filling topological operator. Unlike a $(-1)$-form symmetry of a $d$-dimensional theory, which merely shifts a parameter of the absolute theory, a $(-2)$-form symmetry modifies the SymTFT action, and thereby relates theories whose ordinary global symmetries differ by anomaly data or by the associator data of a non-invertible symmetry. We illustrate the construction in two-dimensional toy models, three-dimensional ABJM-type theories, four-dimensional generalized Yang--Mills theory, and in a fusion-categorical example relating the non-invertible symmetries $\operatorname{Rep}(D_4)$ and $\operatorname{Rep}(Q_8)$. We then develop a club-sandwich realization, in which a quarter-gauging operation interfaces between IR phases of distinct RG flows of a common UV theory, and an alternative realization via nested discrete gauging. Finally, we present a holographic, top-down realization in which the type IIA Romans mass plays the role of a $(-2)$-form background for a three-dimensional Chern--Simons-matter theory, with shifts of the Romans mass realizing shifts of the boundary anomaly coefficients. We also discuss related constructions for coupled bulk--boundary systems.

We study the long-time dynamics of many-body bosonic lattice systems under translation-invariant Gaussian quantum cellular automata. We formulate two sets of conditions on GQCAs which separately guarantee thermalization of any state on the local Weyl algebra to the infinite temperature state, whenever the state is locally normal and has uniformly bounded particle density. Our main intermediate result is a quantum many-body generalization of the classic Riemann-Lebesgue lemma which is a bound on expectation values of local Weyl operators involving their support and the state's particle density.