Papers

Dyer conjectured that the join of two biclosed sets of positive roots can be described by increasing Bruhat paths whose reflection labels belong to their union. We give a type-uniform proof of this conjecture for all finite Coxeter groups. More generally, for a $2$-coclosed set $C$ of positive roots contained in an inversion set, we show that its $2$-closure is an inversion set $I(w)$ and that the elements reachable from the identity using reflections labeled by roots in $C$ form exactly the set $[e,w]_B w^{-1}$. The proof combines Dyer's closure criteria with a root-selection argument.

The Platonic Representation Hypothesis suggests that increasingly capable models converge toward shared representations. Recent work narrows this claim to shared local neighborhood relationships, finding that capacity-dependent trends in several global similarity measures largely disappear after calibration. We challenge this interpretation by showing that prior local-global comparisons confound structural scale (local versus global) with what is compared: relational structure, defined by which samples are related, versus metric geometry, characterized by quantitative relations such as distances, similarities, or correlations. To disentangle these factors, we construct a controlled $2\times2$ framework that evaluates both relational structure and metric geometry at local and global scales. We introduce $H_0$ skeleton overlap as a global counterpart to mutual $k$-nearest neighbors, together with matched distance-aware variants. Across vision-language models, relational structure exhibits robust representational convergence at both scales after calibration, whereas increasingly stringent distance agreement substantially weakens alignment and progressively flattens the capacity-dependent trend. We further extend the analysis beyond ambient Euclidean geometry by evaluating distance agreement under a Riemannian metric approximation and recover the same structure-geometry pattern. The pattern is also reproduced in video-text representations. Together, these results show that relational convergence extends beyond local neighborhoods to global spanning structure, whereas metric geometry exhibits substantially weaker convergence.

The Schrödinger bridge owes its computational power to a single structural fact: by Girsanov's theorem the controlled problem is a Kullback–Leibler (KL) projection onto a fixed reference measure, solvable by alternating projections. This letter shows that the fact does not survive risk sensitivity. When the expected path cost is replaced by the entropic risk measure and both endpoint marginals are kept as hard constraints, the resulting fixed-point bridge value $J_\theta$ (the soft-problem value at the multiplier that enforces the terminal constraint) admits no representation as a constrained KL minimum against any fixed path-space reference with a regular endpoint law (a class strictly larger than the uniformly elliptic diffusion references: no Markov property is required), even allowing an additive normalisation depending on the initial marginal. Moreover, no single reference generates the one-parameter family in the risk parameter. The obstruction is computed in closed form: the Gaussian bridge value violates, by exactly $\theta/2$, a heat equation that any Gaussian smoothing of a fixed endpoint density must obey. In place of the projection, the theory rests on a terminal-multiplier fixed point and an asymmetric factorisation penalising the score energy of the backward factor.

Variational data assimilation computes a Bayesian update through optimization on a fixed posterior geometry, whose conditioning is determined by the prior covariance and the observation operator. In strongly anisotropic, weakly observed, or highly informative regimes, this geometry can become severely ill conditioned, leading to substantial sensitivity to solver design and preconditioning. This work investigates an alternative computational route based on flow-based transport, using the ensemble score filter as a training-free realization. Rather than repeatedly optimizing over the full posterior geometry, the flow-based update transports the predictive distribution through a sequence of intermediate distributions whose covariance and curvature are progressively regularized before reaching the target posterior. In the linear-Gaussian setting, we characterize this mechanism through the evolution of the diffused posterior covariance and the associated time-dependent curvature, revealing a continuation from a near-isotropic reference geometry to the ill-conditioned posterior geometry targeted by variational assimilation. Numerical stress tests show that this geometric regularization makes the flow-based method substantially less sensitive to severe ill-conditioning than the variational method, while a heterogeneous $10^4$-dimensional Lorenz-96 benchmark demonstrates improved robustness and lower delivered computational cost. These results identify posterior-geometry regularization as a key mechanism distinguishing transport-based from optimization-based data assimilation.

This work revisits a fundamental question in active learning: how powerful is the ability to synthesize arbitrary queries? Compared to pool-based active learning, where the learner only selects queries from a given unlabeled pool, it has been observed that this seemingly mild change in query ability may dramatically alter the difficulty of statistical learning. In particular some hypothesis classes, such as two dimensional halfspaces, permit only polynomial error decay in the number of samples when the learner must draw its labels from the pool, yet become exponentially learnable once synthesized queries are allowed. This striking gap suggests that membership query synthesis induces a fundamentally different mode of learning, one that is not adequately captured by existing active learning theory and calls for new analytical tools to characterize its sample complexity for general hypothesis classes. Motivated by this phenomenon, we develop several sufficient conditions, present intriguing examples, and propose a conjectural perspective toward understanding which hypothesis classes admit efficient learning through synthesized queries.

A high dimensional bi-directionally coupled $N$-loop thermosyphon system in a tandem is modeled by $3N$ Lorenz type of differential equations. The fluid flow in each loop is driven by the heat source (Rayleigh numbers) as well as the moment and heat exchanges between the adjacent loops. The flow becomes chaotic when the Rayleigh numbers are large. A decentralized controller design via proportional local state feedback is employed to stabilize the chaotic flows in each loop. As a result of the stability analysis, we show that there exist lower bounds on the controller gains that guarantee global stability of the system. Under the scenario of unknown parameters, we augment the original system with additional dynamic equations of the feedback gains to adaptively determine the feasible gains that stabilize the system. The analysis also sheds insight on the role of thermal coupling in the stability of the control system, which allows us to extend the results to negative $z$-state coupling coefficient as well as a class of nonlinear $z$-state coupling functions. Numerical simulations further demonstrate the effectiveness of the proposed controller design

Reliable power grid control requires sequential decisions under transmission constraints, time-varying demand, renewable variability, and imperfect load information. We investigate how load information quality affects control in a customized transmission network simulator inspired by Grid2Op and based on a DC power flow model. The environment includes stochastic spatial loads, temporally correlated renewable-like generation, energy storage, line protection, generator dispatch, and line reconnection. An Ensemble Score Filter (EnSF) corrects noisy load information before it is passed to the controller. A heuristic study first isolates the effect of this correction under a fixed feedback rule. Proximal policy optimization (PPO) agents are then trained for sequential generator and reconnection control, frozen, and evaluated with Forward, EnSF-corrected, and Truth load information on paired stochastic scenarios. EnSF consistently lowers load estimation error. Under heuristic control, the correction extends survival and reduces warning and overload exposure. With frozen PPO policies, it increases cumulative return and keeps performance closer to the Truth benchmark, with a larger advantage when load uncertainty is amplified beyond the nominal training distribution. In both experiments, EnSF reduces load-estimation error and improves the resulting control performance in the simplified transmission network.

Topology optimization (TO) remains computationally intensive due to repeated finite element analysis (FEA) evaluations required at each iteration. While neural network-based surrogates offer potential acceleration, existing approaches often suffer from gradient inconsistency between predicted objectives and sensitivities, leading to optimization instability. This work presents KATOsuper, an objective-agnostic framework that couples neural-reparameterized topology optimization with a Sensitivity-Consistent Fourier Neural Operator (SC-FNO). The framework employs the forward_split architecture, which derives deployed sensitivities via automatic differentiation through the predicted objective field and thereby preserves consistency between the predicted objective and the gradient used for optimization. The case studies include three 2D benchmark problems and three 3D structures considering compliance or stress minimization. A physics-informed multi-channel input encoding with Fourier position embedding enables resolution-invariant learning, supporting zero-shot extrapolation beyond the training resolution, with useful performance at moderate scaling factors and topology-preserving exploration at up to 64x without retraining. The framework extends to 3D through KATO3D, featuring novel KANConv3D blocks with learnable B-spline activations. KATOsuper demonstrates 15–110x deployment-time speedup over MATLAB baselines while maintaining competitive optimality, with the clearest gains observed in complex 3D and stress-optimization cases. The insight that sensitivity direction matters more than magnitude enables robust optimization even with approximate physics evaluation, extensible to other differentiable physics-driven design objectives.

In this paper, we consider the strong operator topology (SOT) on the space $\mathcal{L} (X)$ of continuous linear operators on an infinite-dimensional Fréchet space $X$. The existence of SOT-dense subspaces as well as of SOT-closed infinite-dimensional subspaces inside the family of all non-cyclic operators is established. Other classes of operators, such as non-dense range or non-injective operators, are also studied in this regard. Moreover, we prove for the sequence space $\ell_p$ $(0 < p < \infty)$ that the family of all non-cyclic members of $\mathcal{L}(\ell_p)$ contains an isometric copy of $\ell_p$.

In this paper, we prove that $\mathbb{Z}$ is first-order definable in the ring of integers $\mathbb{Z}^{\text{ab}}$ of the maximal abelian extension $\mathbb{Q}^{\text{ab}}$ of $\mathbb{Q}$, which implies that the first-order theory of $\mathbb{Z}^{\text{ab}}$ is undecidable. More generally, writing $i = \sqrt{-1}$ and $\mathbb{Q}^{\text{tr}}$ for the field of all totally real numbers, we prove new definability and undecidability results for rings of integers of subfields of $\mathbb{Q}^{\text{tr}}(i)$, focusing especially on fields which contain infinitely many roots of unity. The key ingredient for these results is that there is a parameter-free positive-existential formula which defines the roots of unity $\mu(\mathcal{O}_L)$ inside $\mathcal{O}_L$ for every field $L\subseteq \mathbb{Q}^{\text{tr}}(i)$.

Let H be a linear group. We show that if there is an invertible matrix x such that all the elements of xH share the same characteristic polynomial then H is virtually solvable. There are plenty of applications that will be presented in future paper. Here, we discuss some applications to the generalized Weigold conjecture and present an alternative straightforward proof of the Formanek–Procesi nonlinearity theorem for Aut(F_n), n>2, over every field. When n>4 our non-linearity proof gives a stronger result than the original Formanek–Procesi theorem.

We study identity testing for high-dimensional covariance matrices against dense alternatives of unknown direction, with $p/n \to \gamma$. Along a globally positive quadratic precision path, mixing Gaussian alternatives over a Gaussian Orthogonal Ensemble direction yields a contiguous experiment whose log likelihood reduces to the corrected Frobenius statistic; its upper-tail test attains the limiting weighted-power envelope at every fixed strength. Fixing the prior's Frobenius radius perturbs the mixture by only $O(p^{-1/2})$ in total variation, and exact whitening carries the experiment, the statistic, and its null law to any known null covariance. Separately, under a product-coordinate null, feasibility needs only $4+\eta$ moments, plus identical distributions over time when means are estimated; studentization and an exact degrees-of-freedom correction preserve the local power. A stability inequality turns near-envelope attainment into null agreement with the Frobenius rule, so uniform noninferiority on the typical dense bulk precludes gains at any contiguous alternative. For trace-matched rank-one alternatives, the corrected statistic is the first likelihood direction when $\vartheta_n \to 0$ and $n\vartheta_n \to \infty$; at fixed strength, the log likelihood ratio in the Onatski-Moreira-Hallin fixed-spike benchmark is governed by a richer linear spectral statistic below the Baik-Ben Arous-Peche threshold, while eigenvalue separation permits cost-free largest-eigenvalue enhancement above it. Simulations illustrate the theory.

Sparse communication in decentralized zeroth-order learning requires compatible peer-state coordinates. We characterize this one-hop condition and develop ZO-COSMO, coupling two-query estimation with average-preserving masked consensus using $q$ values per active link. Global supports serve all-neighbor mixing; matching updates require agreement only within each pair. We derive a sharp contraction-per-scalar bound within the matching class and convergence guarantees for the core and sparse-momentum updates. At fixed matching, exact moment identities characterize how shared directions preserve gradient-heterogeneity cancellation and redistribute estimation error and disagreement. Mechanism experiments cover unequal curvatures, noise, and sparse momentum. Further tests span $64$ synthetic agents and eight logical Qwen LoRA workers. At matched payload budgets, Qwen2-7B QNLI gains $3.65$ accuracy points over explicit-index Rand-$k$; edge-local updates gain $3.42$ and $2.53$ points over all-neighbor mixing on eight-worker complete and ring graphs. A matched-first-step ablation gives a $3.92$-point momentum benefit. Seed-aware and same-matching controls distinguish encoding, scheduling, and query correlation.

Let $N_g$ be the number of Ekedahl-Oort strata intersecting the supersingular locus in the Siegel modular variety. We prove that $N_g\sim 2^{g-1}$ as $g\to\infty$.

Let $n\ge 3$ and let $K\subset\mathbb R^n$ be a convex body. For a two-dimensional linear subspace $P\subset\mathbb R^n$, let $K|P$ be the orthogonal projection of $K$ onto $P$. We prove that if for every two-dimensional subspace $P$, the planar convex body $K|P$ has $q$-fold rotational symmetry up to translation, then for $q\ge4$, this forces $K$ to be an Euclidean ball. The case $q=3$ is exceptional: non-spherical examples exist.

We construct infinitely many pairwise non-derived-Morita-equivalent phantom categories $\mathcal{P}_{m}, m\in\mathbb{Z}$ from concrete directed DG quivers with 3 vertices. Moreover, there exists a fixed finite-dimensional DG algebra $C$ such that for each $m\in\mathbb{Z}$, there is a way to reassign cohomological gradings on $C$ (without changing the differential) to obtain a new DG algebra $C_{m}$ with $\mathrm{Perf}(C_{m})\cong \mathcal{P}_{m}$.

For the infinite Fermi-Pasta-Ulam (FPU) system, general solutions can be approximated by counter-propagating waves associated with solutions to the Korteweg-de Vries (KdV) equation as the lattice mesh size goes to zero. We show that, by exploiting the conservation of the FPU Hamiltonian, the continuum limit from the FPU system to the KdV equation with $L^2$-level initial data holds in appropriate norms on an arbitrary time interval, thereby answering an open question posed by Hong, Kwak, and Yang (2021). Moreover, for the local-in-time continuum limit of the FPU system to the KdV equation, we lower the required Sobolev regularity to $H^s$ with $s > - \frac 34$. Our continuum limit results also apply to the case of the Toda lattice in Flaschka's form, thereby lowering the regularity requirement in our previous work (2026). To establish this low-regularity continuum limit, we prove key trilinear estimates that are sharp up to the endpoint by combining linear estimates, the transversality of characteristic curves, and multilinear dispersive smoothing properties of the linear FPU flow.

We develop a general framework for model specification testing in stationary functional time series. The approach is based on an autoregressive approximation that represents a broad class of stationary functional processes through coefficient kernels whose dimension and autoregressive order may increase with the sample size. Different model assumptions induce different structural restrictions on these kernels, and our tests are constructed by measuring deviations from the corresponding restrictions. We illustrate this principle for three problems: testing a prescribed order of a functional autoregressive model, testing a functional autoregressive moving-average specification, and testing separability of autoregressive coefficient kernels. The resulting statistics are based on weighted $\mathcal{L}^2$-distances, and the critical values are obtained by a multiplier bootstrap. We establish a quantitative bootstrap approximation that is uniform over a class of weight functions and prove asymptotic validity and consistency of the proposed tests. The methodology allows for data-adaptive weighting and is illustrated by simulations and a data example.

Learning an interacting many-body Hamiltonian at the Heisenberg limit generally requires control that preserves local information for evolution times of order $1/\varepsilon$ to attain $\varepsilon$ precision. To achieve this, existing protocols often rely on trusted many-qubit operations or increasingly rapid control pulses, creating a precision barrier when gates involve unknown multi-qubit interaction or have finite duration. We show that neither resource is necessary for geometrically local Hamiltonians. Our protocol applies only static single-qubit fields, whose strength is independent of system size and grows polylogarithmically with $1/\varepsilon$. These fields generate emergent prethermal symmetries that suppress thermalization for the entire learning experiment while retaining informative symmetry-preserving dynamics. On a $d$-dimensional lattice of $n$ qubits, this enables learning every coefficient to accuracy $\varepsilon$, with failure probability at most $\delta$, using total evolution time $\mathcal{O}(\log^d(1/\varepsilon)\log^2(n/\delta)/\varepsilon).$ Thus, our learning protocol attains the information-theoretically optimal \(1/\varepsilon\) dependence up to polylogarithmic factors using product-state preparation, single-qubit measurements, and non-adaptive experiments. More broadly, our results establish emergent prethermal symmetries as a resource for quantum learning, opening a route to Heisenberg-limited characterization of many-body systems where fast or trusted many-qubit control is unavailable.

We study distribution-free sequential changepoint detection for independent observations with unknown and unrestricted pre- and post-change laws. We build on the conformal test martingales and associated e-detectors of Vovk(2021), which control the probability of false alarm (PFA) and the average run length (ARL) respectively. The majority of these works focus on validity, with statistical efficiency usually left for simulations. We develop a comprehensive theory of how conformal p-values behave under non-exchangeable data with a changepoint at an unknown time $T$. We use this to analyze the post-change growth and resulting detection delay of conformal martingale methods, and prove that the standard existing methods are suboptimal for PFA and ARL control, and can lead to delays that are $\Omega(T)$ and $\Omega(\sqrt{\text{ARL}})$ respectively. We propose different conformal e-processes and e-detectors that are provably minimax optimal, with delays $\Theta(\log T)$ and $\Theta(\log \text{ARL})$ respectively, and have much shorter delays in simulations.

We study the fluctuation spectrum and renormalized one-loop quantum mass of the Christ–Lee kink over the full positive range of its deformation parameter. The fluctuation equation is reduced exactly to general-Heun form, yielding parity-resolved continuum solutions and implicit quantization conditions for the discrete spectrum. At the first nontrivial continuum crossing, the odd Heun solution truncates to a polynomial, giving the exact threshold \(\epsilon_1=\sqrt{\sqrt{3}-1}\). For small deformation, the kink separates into two widely spaced \(\phi^6\)-like interfaces and the fluctuation operator develops a long central cavity. This geometry explains the logarithmic growth of the bound-state count, the asymptotically geometric hierarchy of continuum-threshold crossings, and the emergence of a soft relative-translation mode. In the opposite limit, the spectrum approaches the \(\phi^4\) Pöschl–Teller problem, while its even threshold resonance becomes a shallow bound state at finite deformation. The one-loop correction is evaluated in a fixed vacuum-normal-ordering prescription using a common-regulator spectral trace and independently through an imaginary-frequency functional determinant. The two calculations agree throughout representative finite deformations and reproduce the exact \(\phi^4\) limit. In the small-deformation regime, the extended central region produces a logarithmically enhanced negative quantum correction. These results provide a unified analytic and numerical description of how the spectral reorganization of the Christ–Lee kink controls its semiclassical quantum mass.

Guo, Fang, and Lu recently proved the Komlós conjecture: for vectors $v_1,\ldots,v_n\in\mathbb R^d$ of Euclidean norm at most one, there are signs $\varepsilon_j\in\{-1,1\}$ with $\|\sum_j\varepsilon_jv_j\|_\infty\le3\sqrt{2\pi}$. We give a short proof of the bound $3\pi$ that keeps the geometric lifting framework of (Guo, Fang, and Lu 2026a) while replacing the analytic core by a quadratic Dirichlet energy. Moreover, using a more fine-grained analysis of the stability of the product-cosine function of (Smirnov and Vershynin 2026) under translations, we further sharpen the bound to below $6.9013$. On the algorithmic side, based on the polynomial-time construction of (Guo, Fang, and Lu 2026b) we give a deterministic algorithm that finds a coloring of discrepancy at most $37.54$ using at most $\widetilde O(mn+n^4)$ arithmetic operations.

We compute the smallest non-abelian quotients of spherical and affine Artin groups. Usually, these are isomorphic to the smallest non-abelian quotients of the corresponding Coxeter groups. As applications, we deduce that two affine Artin groups are isomorphic if and only if their Coxeter diagrams are isomorphic and that irreducible spherical Artin groups are distinguished from each other by their finite quotient groups.

A graph is 1-planar if it has a drawing in which every edge is crossed at most once. We show that the smallest cubic non-1-planar graphs have $30$ vertices. Two such graphs are the Tutte-Coxeter graph of girth eight and a graph of girth seven that we call the Byte graph. Every subcubic graph with fewer than $30$ vertices is 1-planar. Our proof is computer-assisted, but directly testing all relevant graphs is impractical. To establish non-1-planarity of the two graphs, we extend a SAT-based solver with a custom clause propagator based on separating cycles and a case split based on graph automorphisms, allowing independent cases to be solved in parallel. To show that all smaller subcubic graphs are 1-planar, we introduce the concept of $k$-flexibility: every set of at most $k$ prescribed edges can remain uncrossed in some 1-planar drawing. We use this property to reconstruct 1-planar drawings of larger graphs from drawings of smaller $k$-flexible graphs. This replaces exhaustive testing of more than forty billion cubic graphs with computations on far fewer graphs of smaller order.

We prove that the three-element additively idempotent semiring $S_7$ is strongly nonfinitely based: every finite additively idempotent semiring whose generated variety contains $S_7$ has no finite equational basis. This answers Problem~1.2 in Yue, Ren and Gao's paper Explicit equational bases for the power semirings of $S_7$ affirmatively. The proof combines a rigidity property of set systems with private points and a probabilistic construction derived from semilinear sets of letter counts in finite semigroups. The argument allows arbitrary polynomial substitutions and does not assume commutative multiplication. As consequences, both power semirings of the multiplicative reduct of $S_7$, and both power semirings of every finite group of order at least three, are strongly nonfinitely based. All algebras are considered in the signature $(+,\cdot)$ without nullary operations.

This paper reports an improved numerical lower bound for packing 203 equal spheres in a unit cube. Let r denote the maximum common radius of equal non-overlapping spheres that can be packed in a unit cube. For N = 203, the configuration currently listed in Packomania has a feasible radius of approximately r = 0.088145402159. Starting from this public configuration, we perform further numerical optimization and obtain a new feasible configuration with r > 0.088145634693. The final configuration is checked by an independent verification program using 100-digit arithmetic. All 20503 sphere-pair constrains and all 1218 sphere-wall constraints are satisfied. The coordinates of the new configuration and the related programs are provided as supplementary material.

We study generating sets for the kernels of the Frobenius polarization operators associated with elements of finite groups. By applying the discrete Fourier transform on each coset, we describe these kernels in terms of additive semigroups defined by zero-sum relations among roots of unity. We show that the monomials corresponding to the minimal nonzero elements of these semigroups form generating sets of minimum cardinality. We further describe the minimal nonzero elements in the general case in terms of those in the cyclic case and obtain a formula for the minimum number of generators. For the operator associated with a generator of a cyclic group, we also show, as a consequence of known results on integer zero-sum relations and circulant determinant representations, that its kernel and the subalgebra generated by these circulant determinants have the same field of fractions.

We show that the six-element additively idempotent semiring $B_2^1$ is inherently nonfinitely based. More precisely, for every positive integer $n$, we construct an infinite additively idempotent semiring, generated by at most $(6n+8)^2$ elements, that satisfies every $n$-variable identity of $B_2^1$.

Let $X$ be an algebraic K3 surface defined over a global field $K$ of characteristic $0$ or $p \geq 3$, assumed ordinary in the case where $K$ is a global function field. We provide an exact formula for the density of primes $p$ of $K$ at which the geometric Neron-Severi group of the reduction $X_p$ has a given rank in terms of the Galois representation attached to $X$. As an extension, we prove that there are infinitely many reductions of $X$ with an element of the geometric Neron-Severi group representing a fixed square class under the intersection pairing and prove results about the density of such places. In particular, we show that if $X$ corresponds to a sufficiently generic moduli point, a density zero set of places of $K$ satisfy this condition.

Distributed mixture-of-experts (MoE) inference is a promising architecture for deploying large language models (LLMs) at wireless edge networks because sparse experts can be placed across coordinated base stations (BSs), while the anchor node and user equipment (UE) can offload LLM inference tasks to BSs. The communication bottleneck is the MoE aggregation, where the anchor BS must recover a weighted sum of selected expert outputs before each decoding step. Over-the-air computation (AirComp) is well matched to this operation because the wireless multiple-access channel naturally superposes simultaneous transmissions. However, conventional AirComp minimizes communication distortion, whereas MoE aggregation errors have unequal impact on LLM outputs. We propose a logit-aware MIMO AirComp framework that estimates local logit sensitivity as block-level weights and jointly optimizes receive combiners and BS precoders under per-BS power constraints. We also develop an alternating algorithm that protects decoding decisions from aggregation perturbations. Using OpenCompass, we evaluate Qwen3-30B-A3B-Instruct-2507-FP8 on GSM8K and ARC-Challenge. At 30 dB aggregation SNR, perturbed Qwen3 retains 99.3% of clean GSM8K accuracy and 94.8% of clean ARC-Challenge accuracy. In a direct ARC-Challenge closed-loop audit over 295 examples, SW-AirComp achieves 43.73% accuracy at 30 dB and 26.78% at 20 dB, outperforming unweighted, matched-filter, and zero-forcing AirComp. In the wireless simulator, SW-AirComp reduces decision-relevant aggregation distortion; at 20 dB, its final weighted-sum mean-squared error is 53.5% lower than unweighted AirComp under the same channels, samples, and sensitivity weights. Logit-RMSE and logit-gap diagnostics further show that the gain comes from reducing output-logit perturbation and lowering the risk of top-token changes.