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arXiv2026

Global Integrated Null Energy Contribution : Classification of Traversable Wormholes

We argue that the local violation of null energy condition at the throat of a traversable wormhole does not necessarily indicate that the total volume integrated null energy contribution is negative. It is already known that it can be arbitrarily close to zero. We show that it can even be positive and use this argument to reconstruct a family of wormhole geometries. We also propose a novel classification of traversable wormholes based on the global volume integrated measure of null energy condition.

gr-qc↗

arXiv2026

Mesh-Free Numerical Approximation of the Biharmonic Equation via Optimized Kolmogorov--Arnold Neural Networks

A mesh-free numerical framework based on \textit{Kolmogorov--Arnold Physics-Informed Neural Networks} (KAN-PINNs) is developed for the approximation of fourth-order elliptic boundary value problems, with specific application to the biharmonic equation governing thin plate deflection. Unlike conventional Multi-Layer Perceptrons relying on fixed nodal activations, learnable univariate functions parameterized via radial basis functions are deployed on network edges, while high-order differentiability is preserved through hyperbolic tangent activation mappings. The severe numerical stiffness inherent to fourth-order differential operators and fully clamped boundary conditions is addressed through a direct normalized residual formulation coupled with a hybrid, multi-stage AdamW-to-L-BFGS optimization pipeline. An automated \textit{24/7 hill-climbing search protocol} is implemented to systematically calibrate boundary penalty weights and optimization schedules. When evaluated on a smooth manufactured benchmark on the unit square, an error reduction factor exceeding $150\times$ is attained over successive iterations, culminating in a final relative $L_2$ error of $1.593 \times 10^{-5}$ ($0.00159\%$) and a training loss of $3.065 \times 10^{-6}$ utilizing only $7,801$ trainable parameters. These results demonstrate that high-order PDE problems can be accurately resolved using compact, mesh-free KAN-PINNs architecture without requiring auxiliary variable transformations or discrete mesh generation.

math.NA↗

arXiv2026

Dispersion relation, propagation features and canonical gauge structure of GNLED

We investigate the propagation properties and canonical gauge structure of Generalised Non-Linear Electrodynamics (GNLED) in the presence of a non-dynamical background field. Starting from the quadratic photon sector of the theory, we perform a field redefinition that converts the background-induced derivative coupling into a mass-like contribution characterized by the vector $V_μ=\partial_μα/α$ where $α= \sqrt{\left.\frac{\partial\mathcal{L}}{\partial \mathcal{F}}\right|_B}$. For a constant background, we derive the corresponding dispersion relation and show that, for a purely space-like $V_μ$, the propagating mode obeys $ω^2=\|\vec k\|^2+\|\vec V\|^2$, defining an effective mass scale $m_{\rm eff}=|\vec{V}|$ and a finite rest frequency. The resulting phase and group velocities exhibit the characteristic dispersive behaviour of a gapped mode, with subluminal group velocity and superluminal phase velocity. We then construct the propagator and show that the massive pole resides in the transverse sector, while the longitudinal singularity is associated with gauge fixing. A complete Hamiltonian analysis yields two first-class constraints and only two physical degrees of freedom, demonstrating that the effective mass does not introduce an additional polarisation. The associated gauge transformation is a deformed Abelian $U(1)$ symmetry. Finally, we show that the Hamiltonian is positive definite for purely space-like backgrounds.

hep-th↗

arXiv2026

Soliton resolution conjecture for the Calogero--Moser derivative nonlinear Schrödinger equation in the scaling-critical space

We prove the soliton resolution conjecture for the Calogero--Moser derivative nonlinear Schrödinger equation in the scaling-critical space $L^2_+(\mathbb R)$. For a natural class of initial data including a broad spectral Dini---moment class, global flow--Lax admissible solutions decompose into finitely many explicit modulated solitons plus a dispersive radiation, while finite-time blow-up solutions resolve into quantized zero-carrier $R$-bubbles and a strongly convergent endpoint remainder. This work extends soliton resolution to the optimal critical regularity. Previous results had required weighted $H^{1,1}$ initial data, and in the global case the solution was additionally required to remain in $H^{1,1}$ for all time, which amounts to an extra spatial decay assumption. One key ingredient in our argument is a new modular operator-theoretic framework that separates the discrete and continuous spectral channels and identifies the radiation profile through the distorted Fourier transform. A second ingredient is the development of several independent rigidity criteria for the discrete soliton profiles, which avoids inverse scattering and handles embedded eigenvalues. Our framework also yields a unified description of both global and finite-time asymptotics, with exact mass partition and mass-defect quantization.

math.AP↗

arXiv2026

Aligning feature-mapping designs to given density fields, first and second order

Feature-mapping methods represent structural designs by explicit geometric primitives on fixed analysis grids, an interpretable and parametric alternative to the density fields of density-based topology optimization (SIMP). In contrast to SIMP, however, feature-mapping optimization is sensitive to the initial design. We present a gradient-based approach to align a feature-mapping configuration to a given (pseudo) density field, e.g., to initialize a subsequent feature-mapping optimization. The staged approach is based on a least-squares tracking formulation, preceded by a variant that only rewards alignment and does not penalize mismatch. Without an underlying finite element simulation, iterations are cheap, but isolated features receive little sensitivity information. As a remedy, we propose an asymmetric transition function based on automatically parametrized Bézier curves. We demonstrate the approach for a 2D cantilever and the five-bar design; for the latter, we show optional feature minimization based on the feature scaling variable of the geometry projection method. The approach works well with first-order optimizers. The absence of a state problem and the small number of variables, however, also make a second-order formulation attractive. To the best of the authors' knowledge, we present the first Hessian formulation for feature mapping and report the behavior of first- and second-order optimizers on our benchmark problems. For completeness, we also give the exact Hessian of the state-based compliance, which requires one additional solution of the FEM system per feature variable.

math.OC↗

arXiv2026

Beyond the Shadows of Plato's Cave: Evaluating False Memory in Autonomous Agents via Counterfactual Reasoning

Autonomous agents increasingly rely on memory to generalize beyond their training environments. However, agents are bounded by what they have seen and believed, and leveraging such memories in unseen environments can introduce biases into their internal beliefs. We formalize this phenomenon as \textit{false memory}, which can arise from spurious correlations, environment shifts, and knowledge conflicts. Despite its importance, false memory is difficult to evaluate because it stems from agent internal beliefs and is easily confounded with ordinary generalization failures. Therefore, we propose FAME, a training-free framework that evaluates false memory through the evolution of agent beliefs under counterfactual reasoning. Specifically, counterfactual scenarios reveal how beliefs change as the latent concept of memory shifts under hypothetical interventions; thus, measuring the resulting concept drift provides a signal for distinguishing faithful versus false memory. Such concepts can be estimated from agent hidden states before answer generation, avoiding the need for reward design or answer sampling. Empirical experiments reveal that simply monitoring answers often fails to detect false memory, while FAME achieves AUROCs of 76.2% - 96.7% across false-memory settings, and outperforms the best baseline by 3.4% - 23.3% across realistic benchmarks, spanning math reasoning (GSM-Symbolic), code generation (GitChameleon), and complex reasoning (BigBench-Hard). We further release corresponding counterfactual templates and facilitate future research on false memory.

cs.AI↗

arXiv2026

A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows

Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis $Λ=1/4$, $ω^+=ω^-=1$ makes one collision eliminate all non-hydrodynamic perturbations; $η(ν)=|6ν-1|/(6ν+1)$ vanishes at $ν=1/6$, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at $N=256$, $\mathrm{Re}=1$ under matched-accuracy and $1\%$ gates. The matched speedup rises monotonically to 122.02 at $N=1024$, with gains persisting across $\mathrm{Re}=10^{-4}$--$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at $N=128$, $\mathrm{Re}=1$. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at $\mathrm{Re}=10$ and 3.84 at $\mathrm{Re}=100$ for $N=128$. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.

physics.flu-dyn↗

arXiv2026

Excitation gap of a blockade structure with $\mathbb{Z}_2$ topological order

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

quant-ph↗

arXiv2026

Conserved currents associated with conformal symmetry in linearized gravity

Extending a previous work on the energy-momentum tensor of the linearized gravitational field in Minkowski background, conserved currents in linearized gravity associated with Lorentz transformations, dilatations and special conformal transformations are explored in the framework of Lagrangian field theory. Both outstanding special cases and general parametric families of currents are considered. Regarding the former, the distinguished energy-momentum tensor $T_{\mathrm{lg}}^{ab}$ we found earlier, guided by similarities between linearized gravity and electrodynamics, is supplemented with an angular momentum tensor $M_{\mathrm{lg}}^{abc}$ and a dilatation current $D_{\mathrm{lg}}^a$, associated with Lorentz and dilatation symmetries. Concerning special conformal transformations, a generalization of Noether's theorem that is useful if additional conditions (such as gauge fixing conditions) are imposed is formulated, it is shown that special conformal transformations are Noether symmetries of linearized gravity in the generalized harmonic gauges, and a special conformal tensor $C_{\mathrm{lg}}^{ab}$, accompanying $T_{\mathrm{lg}}^{ab}$, is obtained using the generalized Noether's theorem. The angular momentum tensor, dilatation current and special conformal tensor accompanying two other notable energy-momentum tensors are discussed as well. General multi-parameter families of $M^{abc}$, $D^a$ and $C^{ab}$ tensors accompanying a general family of energy-momentum tensors, which was found earlier and includes canonical energy-momentum tensors, are also determined, and local balance equations that are relevant if matter is present are derived for them. Their members do not depend on higher than first derivatives of the linearized metric.

gr-qc↗

arXiv2026

Resource-Efficient Semantic Communication for Heterogeneous Agentic Teams

Teams of autonomous agents, including large language model (LLM) agents, must coordinate over scarce and unreliable wireless links. We propose goal-oriented semantic communication (GOSC), a closed-loop co-design that jointly decides what each agent sends, when it sends it, and how reliably it is transmitted, based on each message's value to the team task. An edge broadcast of the team's common knowledge closes the loop by updating these values. We prove that a message is sent only if its value exceeds the cost of delivering it and that more valuable messages receive more robust transmission rates, and we show that the scheduler solves each scheduling step exactly whenever the radio budget is not saturated, which held in 95% of scheduling decisions. In search-and-rescue missions validated on unseen scenarios, GOSC meets the same mission targets as carefully tuned periodic semantic schemes with 1.2--8.5 times fewer uplink channel uses. In most settings, this advantage persists with realistic packet overheads, reaching 16.6 times fewer uplink channel uses and 13.8 times lower cost when downlink costs are included; in the rescue task, it also persists when all agents share one uplink. Rough value estimates suffice, whereas values that ignore message content can fail. With three different LLMs, GOSC uses 3.2--3.5 times fewer channel uses, while completion-time gains depend on the model.

cs.NI↗

arXiv2026

Also Small Models Can Reasonably Self-Evaluate Their Confidence

This study systematically evaluates self-evaluation-based uncertainty quantification across different language models of varying sizes on question-answering tasks spanning general to specialized knowledge domains. Using various self-evaluation methods where models judge their own predictions, we examine how model scale and domain specificity affect the quality of self-assessed confidence signals. Our results reveal that while accuracy predictably declines with smaller models and more specialized domains, the reliability of self-evaluated confidence remains largely stable across both dimensions. This independence means the most capable model is not necessarily the best at self-assessing prediction reliability. These findings suggest that smaller models can achieve reasonable self-assessed confidence despite lower accuracy, making them viable for resource-constrained deployments.

cs.LG↗

arXiv2026

Version Age-of-Information-based Semantic Secrecy Region Analysis

This paper investigates semantic secrecy in wireless status-update systems using Version Age of Information (VAoI). We model the fundamental tradeoff between informative updates and confidentiality (semantic asymmetry between the legitimate destination and the eavesdropper) using a three-node wiretap channel. To evaluate secrecy performance, we introduce the concept of a semantic secrecy region (SSR) and analyze it from a geometrical perspective. By developing a two-dimensional Markov chain, we derive closed-form expressions for the destination's average VAoI and the probability of semantic asymmetry at the eavesdropper. These results enable the joint optimization of transmission probability and power control. For Rayleigh fading channels, we characterize the optimal SSR boundary and power allocation. Numerical results validate our analysis, showing that optimized power allocation significantly enlarges the secrecy region compared with fixed-power benchmarks.

cs.IT↗

arXiv2026

Analysis and Approximation of Spatially Wideband Array Factor of Thinned Antenna Arrays

This work investigates the spatially wideband (SWB) array factor (AF) of linear thinned antenna arrays. The SWB AF is formulated as a matched filter and expressed as a spatially variant convolution of a spatially narrowband (SNB) AF and a SWB kernel. Originally derived for uniform arrays, the SWB AF approximation is revisited and extended to thinned arrays. The approximation is shown to remain accurate across a wide range of parameters. Representing the SWB AF as a convolution offers an intuitive interpretation of how the bandwidth-aperture product modifies the SNB AF. Specifically, the SWB kernel acts as an averaging window for the SNB AF, suppressing the sidelobe levels (SL) of the SNB AF. In thinned arrays, the sidelobes away from the mainlobe can be treated as random, noise-like, making averaging and suppression particularly effective. Next, the analytical formulas for the expected SL and peak-to-sidelobe level (PSL) in SNB thinned arrays are first introduced and subsequently extended to the SWB regime. Finally, simple closed-form expressions for the expected SL and PSL levels of the uniformly thinned arrays with a uniform spectrum are provided. The expected SWB SL and PSL are formulated as functions of the bandwidth-aperture product and are shown to steadily decrease with distance from the mainlobe.

eess.SP↗

arXiv2026

Generation of large-amplitude squeezed cat states with near-unity efficiency

The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.

quant-ph↗

arXiv2026

Who Owns That? Evaluating Ownership Intuitions in Large Language Models

Ownership establishes rights over the use, control, and transfer of objects. Understanding these relations is essential for AI systems to interact appropriately with people and their resources. Yet how large language models (LLMs) attribute ownership under competing claims remains unclear. We introduce the Competing Ownership Attribution Task (COAT), comprising 42 scenarios, and compare ownership allocations from 24 LLM configurations with those of 108 human participants. Overall, human-model similarity is close to human-human similarity, but models show greater homogeneity in their ownership judgments. Within individual answers, models also divide ownership more evenly among claimants than humans do. Pooling responses across model configurations reveals more scenarios with a shared judgment and fewer with distinct viewpoint groups than in humans. When humans form distinct groups, models may converge on one viewpoint or between competing viewpoints. Further comparisons reveal different contextual sensitivities. As material value increases across scenarios, allocations to creators decline less sharply in models than in humans. Across scenarios differing in public recognition of later holders as owners, allocations to these holders increase in models but decrease slightly in humans. Together, these findings suggest that the evaluated LLM responses do not fully capture the diversity of participants' ownership judgments or how those judgments vary across situations. Developing socially capable AI therefore requires moving beyond overall similarity to capture the diversity and context dependence of human judgments.

cs.AI↗

arXiv2026

CAMOS: Coupled Oscillatory State-Space Model for Multimodal Clinical Time-Series

Longitudinal clinical cohorts are multimodal, irregularly sampled and pervasively incomplete: in ADNI, positron emission tomography and cerebrospinal fluid assays are absent from roughly half of all visits. Linear state-space models handle irregular sampling gracefully but treat a missing modality by masking the input, leaving the transition operator untouched. We prove that this is a representational limitation: the latent state of any linear state-space layer whose transition operator does not depend on the availability pattern is an additive function of the availability indicators, so no such layer can represent an interaction between two modalities being jointly present or jointly absent. We propose CAMOS, which gives each modality a bank of second-order oscillators coupled through a matrix that sits inside the differential equation and is gated by availability, so the transition operator itself becomes a function of which measurements were taken. Coupling invalidates the analysis of uncoupled oscillatory models, and we restore it: a per-channel Gershgorin budget makes the effective stiffness positive definite uniformly over all $2^M$ availability patterns and all gaps, an energy argument charges amplification to availability transitions rather than sequence length, and a channel factorization preserves exact associative parallel scans. On ADNI, CAMOS outperforms uncoupled oscillatory state-space models and clinical fusion models on same-visit staging, landmark prediction and longitudinal forecasting, and under zero-shot transfer to OASIS-3 it is the only model that avoids collapse to the majority class.

stat.ML↗

arXiv2026

Fair Variable Selection

Algorithms are increasingly being used to help automate and improve data-driven decisions, but care must be taken to prevent such algorithms from learning discriminatory patterns from historical data and perpetuating their biases. Statistical notions of fairness aim to mitigate either a model's disparate impact on disadvantaged groups (thus ensuring group fairness) or the resulting disparate treatment of individuals with similar features (thus ensuring individual fairness). Simultaneously mitigating disparate impact and disparate treatment is generally impossible for non-trivial models, necessitating a compromise. In this paper, we introduce the Fair Lasso and Fair Posterior as methods for selecting fair covariates in generalised linear models. By targeting variables that are simultaneously strong predictors of the response and weakly dependent on the sensitive group memberships, we aim to achieve favourable trade-offs between disparate treatment and disparate impact. Additionally, our selected set of fair features can be used as the conditioning set of legitimate features in the paradigm of Conditional Demographic parity (CDP) when no prescriptive legal framework exists.

stat.ME↗

arXiv2026

From Wrecks to Wisdom: Recovering Crash Mechanics from Real-World Multi-View Photos

Estimating accident mechanics from real-world crashes is important for vehicle-safety analysis, injury modeling, crash-severity prediction, and operational workflows such as insurance claim triage. In standard crash records, key metadata such as impact configuration, principal direction of force, and change in velocity ($ΔV$) may be missing, delayed, or corrupted, while post-crash photographs are widely available and contain rich visual evidence of deformation. We study how much crash-mechanics information can be recovered directly from vehicle photos when structured signals are absent. We formulate crash understanding as supervised prediction from per-case multi-view photo sets. Targets include six Collision Deformation Classification (CDC) descriptors and the longitudinal and lateral components of reconstructed $ΔV$. Each photo is encoded by a shared visual backbone, and the resulting view-level features are fused into a case-level representation from which target-specific heads predict crash descriptors. Using 15.2k training cases from the Crash Investigation Sampling System, drawn from about 1.5M photos before filtering, together with 1.15k validation and 1.15k test cases, we define an evaluation protocol for vision-based crash descriptor estimation from incomplete multi-view evidence. Post-crash imagery alone provides usable signal for several non-trivial crash-mechanics descriptors, while weakly observable and long-tailed targets remain challenging. Within the compared training regimes, the selected joint-training recipe reduces mean absolute angular error for principal direction of force from 20.1 to 14.05 degrees and longitudinal $ΔV$ MAE from 8.04 to 7.45 km/h. Our work provides a reference point for future multimodal fusion with structured crash metadata.

cs.CV↗