In this paper, we establish local decay estimates for the bi-Laplacian Schrödinger equation with time-dependent (in particular, quasi-periodic) potentials in spatial dimension $n\ge14$. Moreover, under stronger spectral regularity hypotheses, the same result can be extended to dimension $n\ge9$. Our approach, based on asymptotic completeness and the existence of the channel wave operator, departs from standard resolvent-based methods. In addition, global-in-time Strichartz estimates are derived from the local decay estimates.

Quantum gravity may modify the fundamental symmetries that govern identical particles. In particular, noncommutative spacetime frameworks predict deformations of Bose and Fermi statistics. Here we develop a relativistic quantum field theory based on the most general oscillator algebra compatible with $θ$-deformed Poincaré symmetry. This construction generalizes twisted statistics to a class of quon-like deformations allowing non-involutive particle exchange. We show that the resulting theory is consistent at both the free and interacting levels and derive its implications for atomic systems. Purely twisted statistics predicts Pauli-forbidden atomic transitions at rates incompatible with experiments. By contrast, a class of quon deformations suppresses such processes by powers of the noncommutativity scale, but only if superselection rules between permutation-symmetry sectors are violated. This implies an effective breakdown of particle indistinguishability and provides theoretical motivation for high-precision experimental tests of the Pauli exclusion principle.

This paper investigates an uplink multi-user covert communication system with spatially distributed users. Unlike prior works that approximate channel statistics using averaged parameters and homogeneous assumptions, this study explicitly models each user's geometric position and corresponding user-to-Willie and user-to-Bob channel variances. This approach enables an accurate characterization of spatially heterogeneous covert environments. We mathematically prove that a generalized on-off power control scheme, which jointly accounts for both Bob's and Willie's channels, constitutes the optimal transmission strategy in heterogeneous user configurations. Leveraging the optimal strategy, we derive closed-form expressions for the minimum detection error probability and the minimum number of cooperative users required to satisfy a covert constraint. With the closed-form expressions, comprehensive theoretical analyses are conducted, which are validated by Monte-Carlo simulations. One important insight obtained from the analysis is that user spatial heterogeneity can enhance covert communication performance. Building on these findings, a piecewise search algorithm is proposed to achieve exact optimality with significantly reduced computational complexity. We demonstrate that optimization considering user's spatial heterogeneity achieves substantially improved covert communication performance than that based on the assumption of spatial homogeneity.

The twist-3 transverse spin--dependent nucleon structure function $g_2$ arises in high-energy processes involving a transversely polarized nucleon. Its connection to quark--gluon correlations allows for an interpretation in terms of the average transverse color Lorentz force acting on unpolarized quarks inside a transversely polarized nucleon. In this work, we investigate this force using light-front wave functions obtained by diagonalizing the light-front Hamiltonian with quantum chromodynamics inputs within the Basis Light-front Quantization approach. We evolve our results to a common scale of $5~\mathrm{GeV}^2$ and present the corresponding form factors in momentum space as well as the transverse force components in impact-parameter space. These distributions provide a complementary perspective on the Sivers asymmetry in transversely polarized deep-inelastic scattering. In the forward limit, we extract the twist-3 reduced matrix element $d_2$, and our results are found to be comparable with those from other theoretical calculations and experimental determinations.

This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are asymptotically stable. Conditions are also given which characterise when the solution and its derivative tend to zero. Finally, we give sharp sufficient conditions under which the solution of the forced equation has the same asymptotic behaviour as the unforced equation, to leading order.

This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded, but not convergent, or is unbounded. We see thereby that forcing terms can exhibit unbounded and high--frequency oscillation, and yet the solution may still tend to zero, even though the first and second derivative may become unbounded.

Missing channels in radio-interferometric visibility data can introduce systematic artifacts into the estimated 21-cm power spectrum. A common workaround is to first estimate the two-frequency correlation $C(Δν)$ and then Fourier-transform it to obtain the power spectrum $P(k_\parallel)$. This procedure yields an unbiased estimate when the signal is statistically homogeneous (ergodic) along the line-of-sight, but it fails in the presence of non-ergodic foregrounds. Smooth Component Filtering (SCF) has recently been proposed as a solution to this problem, in which the dominant non-ergodic (spectrally smooth) component is removed prior to estimating $C(Δν)$. In existing implementations, the smooth component is estimated by convolving the visibilities with a Hann window along the frequency axis. We demonstrate that this Hann-based SCF performs adequately only when foregrounds are extremely spectrally smooth, i.e., when they possess a long frequency-correlation length. In contrast, it breaks down when foregrounds exhibit short correlation lengths, as is frequently encountered in real observations. We introduce a Bayesian extension, Bayes-SCF, based on Gaussian Process (GP) regression, which overcomes this limitation. Bayes-SCF models the smooth component via a covariance function with a fixed correlation length, enabling a controlled and data-driven filtering. Using simulated data, we show that Bayes-SCF robustly recovers the input model 21-cm power spectrum even in the presence of spectrally unsmooth foregrounds. Bayes-SCF is also effective in a delay-spectrum approach. The primary trade-off introduced by the Bayesian framework is increased computational cost; future work will focus on optimizing the algorithm and applying it to real MWA data.

Florida has experienced significant population increase in recent years, driven in part by domestic migration from other states. This study analyzes the migration patterns of voters in Florida between 2017 and 2022 using voter registration data. By examining demographic characteristics such as race/ethnicity, gender, age, and party affiliation, I identify trends in voter migration and their implications for Florida's political landscape. The findings reveal that minorities, younger individuals, Republicans, and those possibly with non-conforming gender are more likely to migrate into Florida. These insights contribute to understanding the dynamics of Florida's migration patterns and the effect of migration on recent elections.

We study simplicial complexes with a given number of vertices whose Stanley-Reisner ring has the minimal possible Betti numbers. We find that these simplicial complexes have very special combinatorial and topological structures. For example, the Betti numbers of their Stanley-Reisner rings are given by the binomial coefficients, and their full subcomplexes are homotopy equivalent either to a point or to a sphere. These properties make it possible for us to either classify them or construct them inductively from instances with fewer vertices.

We use supersymmetric localization and integration by parts to derive variational and convex correlation inequalities in statistical physics. As a primary application, we give an alternative proof of the monotonicity theorem for the $H^{2|2}$ supersymmetric hyperbolic sigma model. This recovers a result of Poudevigne without relying on probabilistic couplings.

Traditional plastics demand a choice between durability (thermosets) and reprocessability (thermoplastics). Vitrimers are a recent class of polymer network combining both these qualities. Their increased cost of production can be offset by mixing them with a traditional thermoplastic; however, phase separation in such blends can lead to inhomogenous materials. In this paper, we adapt an existing model for the free energy of dissociative polymer networks to their associative, vitrimeric counterpart. We test the accuracy of the model's predictions by comparing them with the results of novel molecular-dynamics simulations. We demonstrate that such melts can undergo phase separation even in the absence of energetic interactions between the components. We find furthermore that the phase diagram of the melts is qualitatively similar to that of dissociative systems, and that the critical degree of conversion for the onset of phase separation depends reciprocally on the number of function sites per vitrimer chain.

Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker decomposition (FTD) that embeds mode-wise continuity constraints directly into the decomposition. The FTD employs reproducing kernel Hilbert spaces (RKHS) to model continuous modes without requiring an a-priori basis, while preserving the multi-linear subspace structure of the Tucker model. Through RKHS-driven representation, the model yields adaptive and expressive factor descriptions that enable targeted modeling of subspaces. The value of this approach is demonstrated in domain-variant tensor classification. In particular, we illustrate its effectiveness with classification tasks in hyperspectral imaging and multivariate time series analysis, highlighting the benefits of combining structural decomposition with functional adaptability.

Large Language Models (LLMs) possess a theoretical capability to model information density far beyond the limits of classical statistical methods (e.g., Lempel-Ziv). However, utilizing this capability for lossless compression involves navigating severe system constraints, including non-deterministic hardware and prohibitive computational costs. In this work, we present an exploratory study into the feasibility of LLM-based archival systems. We introduce \textbf{Hybrid-LLM}, a proof-of-concept architecture designed to investigate the "entropic capacity" of foundation models in a storage context. \textbf{We identify a critical barrier to deployment:} the "GPU Butterfly Effect," where microscopic hardware non-determinism precludes data recovery. We resolve this via a novel logit quantization protocol, enabling the rigorous measurement of neural compression rates on real-world data. Our experiments reveal a distinct divergence between "retrieval-based" density (0.39 BPC on memorized literature) and "predictive" density (0.75 BPC on unseen news). While current inference latency ($\approx 2600\times$ slower than Zstd) limits immediate deployment to ultra-cold storage, our findings demonstrate that LLMs successfully capture semantic redundancy inaccessible to classical algorithms, establishing a baseline for future research into semantic file systems.

Structured reinforcement learning and stochastic optimization often involve parameters evolving on matrix Lie groups such as rotations and rigid-body transformations. We establish a representation-optimization dichotomy for Lie-algebra-parameterized Gaussian policy objectives in the Lie Group MDP class: the gradient Lipschitz constant L(R), governing step size, convergence, and sample complexity of first-order methods, depends only on the algebraic type of g, uniformly over all objectives, independent of reward or transition structure. Specifically, L = O(1) for compact g (e.g., so(n), su(n)), and L = Theta(exp(2R)) for g = gl(n), with O(exp(2R)) for all algebras with a hyperbolic element. A key lower bound shows this exponential growth cannot be canceled by interaction between the exponential map and the objective, making the dichotomy intrinsic to the algebra.This yields an algorithmic consequence: for compact algebras, radius-independent smoothness enables O(1/sqrt(T)) convergence using an O(n^2 J) Lie-algebraic projection step instead of O(d_g^3) Fisher inversion. A Kantorovich alignment bound alpha >= 2 kappa / (kappa + 1) provides a computable condition under which this projection approximates natural gradient updates. Experiments on SO(3)^J and SE(3) confirm the theory: constant smoothness for compact algebras, polynomial growth for SE(3), and alignment across condition regimes. The projection step achieves 1.1-1.7x speedup over Cholesky-based Fisher inversion, with increasing gains at larger scales.

Accurate non-invasive estimation of trans-stenotic pressure gradients remains a challenge. In clinical practice, pressure gradients are often estimated from velocity measurements using Bernoulli-based formulas, but these simplified relations do not explicitly account for how pressure losses change with the flow regime. Here, we introduce a modified Bernoulli (MB) formulation that incorporates regime-dependent pressure losses through a Reynolds-number-dependent loss coefficient. Steady in-vitro experiments were performed in an idealized stenosis model over physiologically relevant flow rates (0.65-3.9 L/min), combining direct pressure measurements with ultrasound imaging velocimetry and phase-contrast magnetic resonance imaging (PC-MRI) to measure velocities. The MB model was calibrated from the measured pressure drops and then evaluated against the simplified Bernoulli (SB) and extended Bernoulli (EB) formulations. Over the tested flow regime, MB agreed best with the measurements. SB and EB showed larger biases, with errors of roughly 10-55% (SB) and -15 to 25% (EB), and overestimated the pressure drop in the clinically relevant range. We additionally quantified the effect of PC-MRI in-plane pixel size on MRI-based pressure estimates. Coarse sampling of the stenosis throat led to systematic underestimation of flow rate and bulk velocity and, consequently, of the MB-predicted pressure drop. In contrast, the peak throat velocity was substantially less sensitive to pixel size, resulting in smaller estimation errors when used as input for the MB. Overall, the results demonstrate that accounting for flow-regime-dependent loss mechanisms enhances pressure drop estimation, and that sufficient sampling of the stenotic throat is crucial for MRI-based flow rate and pressure drop estimation. In addition, peak-velocity-based MB pressure drop estimations are less sensitive to pixel size.

We study the stability and Hölder continuity of solutions to degenerate complex Monge--Ampère equations associated with a (non-closed) big form on compact Hermitian manifolds. We also show that the solution is globally continuous when the reference form is the pullback of a Hermitian metric. As a consequence, we establish a uniform diameter bound for the twisted Chern--Ricci flow.

Robust oscillations play crucial roles in a wide variety of biological processes and are often generated by deterministic mechanisms. However, stochastic fluctuations often generate complex perturbations of these deterministic oscillations, potentially strengthening or weakening their robustness. In this paper, we study bistable phosphorylation as a mechanism for robust oscillation. We present a simple nucleocytoplasmic transport and cell growth model where cargo proteins undergo bistable phosphorylation prior to nuclear import. We perform a detailed bifurcation analysis to examine the system's dynamical behavior. We then introduce additive noise into the model and study the stochastic resonance behavior and robustness of oscillations under noise. Our results show that, depending on the phosphorylation threshold, time-scale parameters, and nucleocytoplasmic transport rate, bistable phosphorylation may generate oscillations via Hopf bifurcations; moreover, stochastic resonance and Bautin bifurcations enhance the robustness of the oscillations.

We propose a method to accurately calculate the momentum distributions and the phase distributions of the probability amplitude for both boson and fermion pair production in a spatially homogeneous and time-dependent electric field. Applying this method to multiphoton pair production in a circularly polarized electric field rotating around the $z$-axis, we clarify that the topological charge appearing in the phase distribution of the probability amplitude for pair production reflects the orbital angular momentum (OAM) of the produced pairs rather than that of individual particles. On this basis, we demonstrate that, within the semiclassical framework, the $z$-component of the total angular momentum of the field and the particles is conserved, whereas the conservation of total angular momentum cannot be verified. The results also reveal that the pair production is also constrained by $C$-parity conservation, and that pairs with smaller OAM are produced more favorably. These findings provide deeper insight into angular momentum transfer in pair production.

Interfacial charge transfer (ICT) provides a powerful route to engineer electronic phases in correlated oxide heterostructures, yet predictive design principles remain elusive. Here, we systematically investigate superlattices composed of the 5d spin-orbit coupled semimetal SrIrO3 and a series of correlated 3d perovskites (LaMnO3, LaFeO3, LaCoO3, and NdNiO3), thereby establishing a quantitative framework for ICT across 3d/5d interfaces. Combining element-specific x-ray absorption spectroscopy with spatially resolved electron energy loss spectroscopy, a homogeneous electron transfer from the 5d to the 3d layers is directly quantified, reaching up to 0.35 e per unit cell in the cobaltate superlattice. We show that the magnitude of ICT scales linearly with the difference in electronegativity between the transition-metal oxide layers, identifying electronegativity-driven band alignment as the dominant mechanism for ICT. Beyond interfacial doping, we find that strong 3d-5d hybridization induces a complete low-spin to high-spin conversion in the cobaltate layers, demonstrating interface-controlled spin-state engineering without chemical substitution. These results establish electronegativity mismatch as a predictive design parameter for correlated oxide interfaces and provide a materials platform for tailoring band filling, orbital hierarchy, and spin configurations in quantum oxide heterostructures, paving the way towards advanced oxide electronics and next-generation information technologies.

Time-local generators of open quantum systems are generically divergent at long times, even though the reduced dynamics remains regular. We construct, by analytic continuation, nonperturbative dynamical maps consistent with these generators. For the weak-coupling unbiased spin--boson model, this construction yields an explicit dynamical map that nonperturbatively resums the TCL generator and exposes how the divergences signal the approach to a singular time at which the reduced dynamics becomes noninvertible. The reconstructed map is validated against TEMPO simulations at short times and the exactly solvable rotating-wave model at all times. In the full spin--boson model, the same continuum mechanism produces both an early-time anisotropy, with a measurable phase shift that provides a signature of the environmental correlation and the pointer direction, and a late-time singularity at which the reduced dynamics becomes noninvertible. By contrast, in the rotating-wave model the map approaches this point without reaching it and remains invertible at all times. These results establish a nonperturbative framework for reconstructing reduced dynamics from divergent time-local generators, diagnosing the onset of noninvertibility, and identifying experimentally accessible early-time signatures of environment-induced anisotropy.

We study wavepackets of exotic excitations after two-dimensional fermions are scattered by the boundary condition constructed by Maldacena and Ludwig, which turns elementary excitations into exotic fractionally-charged objects. They are of interest in the s-wave approximation of the fermion-monopole scattering in four-dimensional QED and of the multi-channel Kondo effect. We in particular give an explicit expression of the outgoing state of a pair of such particles; we then examine its properties, such as the charge density $\langle J(x)\rangle$ and the expectation value $\langle N\rangle$ of the number of fermions and anti-fermions in the state. The charge density $\langle J(x)\rangle$ is found to be localized with its integral finite and fractional, while the expectation value $\langle N\rangle$ diverges when the wavepacket is localized to a point.

The rheological behavior of ring-linear polymer blends under uniaxial elongational flow has remained a subject of intense debate, particularly regarding the emergence of stress overshoot. Herein, we employ coarse-grained molecular dynamics simulations to investigate the chain-length dependence of elongational viscosity in 1:1 ring-linear blends of flexible chains with the equal molecular weight. Our results reveal a distinct threshold in the degree of threading, quantified by the number of entanglements Z = N /Ne (where N is the number of beads per chain and Ne is the entanglement chain length), for the appearance of stress overshoot: while blends with shorter chains (Z $\le$ 2) exhibit monotonic stress growth, a clear stress overshoot emerges when the chain length reaches a threshold value (Z $\approx$ 4). Consistent with previous reports, this overshoot originates from a thread-to-unthread transition. At the threshold chain length, multiple linear chains penetrate a single ring, providing sufficient topological constraints to significantly stretch the ring under elongational flow. We predict that this transition can be experimentally validated via 2D small-angle neutron scattering patterns in the plane of the stretching and perpendicular directions, offering a direct structural signature of the ring recoil process for future experimental verification.

We explore different implementations of the quantum Bell causality (QBC) condition in the quantum sequential growth (QSG) dynamics of causal set quantum gravity, for non-commuting transition operators. Assuming a non-singular dynamics we show that for the two most natural choices of operator orderings for the QBC, the transition operator algebra reduces to a commutative one. As a third choice, we take the operator ordering to depend on the size of the precursor set. We find several new commutation relations which further constrain the algebra but do not imply commutativity. On the other hand, if any of the generators of the ``antichain subalgebra'' belongs to its center, then this implies commutativity of the full algebra. The complexity of the algebra prevents us from obtaining a general form for the transition operators, which hinders computability. In an attempt to construct the simplest non-trivial d=2 representation, we find that a Pauli matrix representation of the generators of the antichain subalgebra leads to inconsistencies, implying that if a non-trivial representation exists, it must be higher dimensional. Our work can be viewed as a first step towards finding a non-commutative realisation of QSG.

The emergence of Large Language Model-enhanced Search Engines (LLMSEs) has revolutionized information retrieval by integrating web-scale search capabilities with AI-powered summarization. While these systems demonstrate improved efficiency over traditional search engines, their security implications against well-established black-hat Search Engine Optimization (SEO) attacks remain unexplored. In this paper, we present the first systematic study of SEO attacks targeting LLMSEs. Specifically, we examine ten representative LLMSE products (e.g., ChatGPT, Gemini) and construct SEO-Bench, a benchmark comprising 1,000 real-world black-hat SEO websites, to evaluate both open- and closed-source LLMSEs. Our measurements show that LLMSEs mitigate over 99.78% of traditional SEO attacks, with the phase of retrieval serving as the primary filter, intercepting the vast majority of malicious queries. We further propose and evaluate seven LLMSEO attack strategies, demonstrating that off-the-shelf LLMSEs are vulnerable to LLMSEO attacks, i.e., rewritten-query stuffing and segmented texts double the manipulation rate compared to the baseline. This work offers the first in-depth security analysis of the LLMSE ecosystem, providing practical insights for building more resilient AI-driven search systems. We have responsibly reported the identified issues to major vendors.

We present an in-depth study of end states in honeycomb nanoribbons, focusing on the interplay between nanoribbon termination, chiral symmetry, and complex next-nearest-neighbor hopping in the framework of the Haldane model. Although previous work has identified zero-dimensional end states in such systems, this analysis is incomplete. Here, we systematically investigate zigzag and armchair nanoribbons of various widths, using the multiband Zak phase to characterize the topological properties of the occupied bands. We show that the Zak phase is quantized only for certain ribbon terminations, and we elucidate how this termination dependence governs the existence and robustness of end states. Furthermore, we explore the effect of varying the complex next-nearest-neighbor hopping phase, demonstrating the breakdown of chiral symmetry, the evolution of the bulk gap, and the resulting depinning of end-state energies. Finally, we place our findings in the context of previous studies and discuss connections to the Kane-Mele model, including the role of Rashba spin-orbit coupling. Our work provides a more detailed analysis of topological end states in nanoribbons described by the Haldane and Kane-Mele models and offers a framework for their characterization in related systems.

Landau analysis in momentum twistor space can be formulated as the study of varieties of lines in three-dimensional projective space, together with their projections and discriminants. Within this framework, we define enumerative invariants (LS degrees) that count leading singularities. Leading Landau singularities (LS discriminants) arise as discriminants detecting the collision of leading singularities. We uncover a recursive mechanism underlying Landau singularities, governed by substitution maps between Grassmannians. Applying this framework, we prove positivity and factorization into cluster variables for the LS discriminant of a large class of Landau diagrams at arbitrary loop order. This provides a first-principles explanation for the emergence of positivity and cluster algebra structures in the singularities of planar N=4 super Yang-Mills theory.

The tensor-network renormalization group (TNRG) is an accurate numerical real-space renormalization group method for studying phase transitions in both quantum and classical systems. Continuous phase transitions, as an important class of phase transitions, are usually accompanied by spontaneous breaking of various symmetries. However, the understanding of symmetries in the TNRG is well-established mainly for global on-site symmetries like U(1) and SU(2). In this paper, we demonstrate how to incorporate lattice symmetries (including reflection and rotation) and the PT symmetry in the TNRG in two dimensions (2D) through a case study of the hard-square lattice gas with nearest-neighbor exclusion. This model is chosen because it is well-understood and has two continuous phase transitions whose spontaneously-broken symmetries are lattice and PT symmetries. Specifically, we write down proper definitions of these symmetries in a coarse-grained tensor network and propose a TNRG scheme that incorporates these symmetries. We demonstrate the validity of the proposed method by estimating the critical parameters and the scaling dimensions of the two phase transitions of the model. The technical development in this paper has made the 2D TNRG a more well-rounded numerical method.

The magnetospheres of magnetars, a class of highly magnetized neutron stars, host magnetic fields exceeding the Schwinger limit, where Quantum Electrodynamics (QED) becomes nonlinear. In such environments, QED scattering processes are strongly modified, which may affect plasma dynamics. In this work, we apply a formalism originally developed for the study of magnetic-field effects in hot quark-gluon plasma to strong-field QED. The method resums interactions between virtual electrons and the external magnetic field, consistently incorporating the finite decay widths of excited Landau levels derived from the fermion self-energy. Using this framework, we perform the first systematic analysis of tree-level QED scattering processes in strong magnetic fields, concentrating on the processes of highest relevance for the plasma dynamics of magnetars. All resulting cross sections are provided in an open-source Python package.

The presence of integer variables in the European day-ahead electricity market renders the social welfare maximization problem non-convex and non-differentiable, making classical marginal pricing theoretically inconsistent. Existing pricing mechanisms often struggle to balance revenue adequacy with incentive compatibility, typically relying on discriminatory uplift payments or suffering from weak duality. Leveraging the Augmented Lagrangian Duality (ALD) framework, which establishes strong duality for Mixed-Integer Linear Programming (MILP), this paper proposes a novel ALD pricing mechanism. We analytically prove that this mechanism is inherently incentive-compatible, aligning centralized dispatch with individual incentives without requiring side payments. Notably, we demonstrate that the ALD price signals intrinsically eliminate Paradoxically Rejected Orders (PROs) and Paradoxically Accepted Orders (PAOs) for supply orders. For the demand side, a sufficient condition is introduced to further guarantee revenue adequacy, resulting in a transparent and financially consistent settlement system. To ensure computational tractability, we modify the Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) method to efficiently compute the exact penalty coefficients and optimal Lagrangian multipliers. Numerical experiments on illustrative examples and the Nordic 12-area electricity market model confirm the superior economic properties of the ALD pricing mechanism and the tractability of the modified SAVLR algorithm.

We study the hydrodynamic limit of the nonisothermal BGK model toward smooth Euler Maxwellians. For a prescribed smooth Euler solution, we derive a relative entropy stability estimate between a BGK solution and the associated Maxwellian. The main new ingredient is the control of an additional velocity-cubic term in the relative entropy identity. Under a uniform sixth velocity-moment bound and suitable bounds on the BGK macroscopic quantities, we obtain a uniform-in-time relative entropy estimate. For well-prepared initial data, this yields strong $L^1$ convergence of the BGK solution and the local Maxwellians to the target Euler Maxwellian, together with convergence of the associated macroscopic quantities.