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arXiv2026

AI Risk Ontologies for the EU AI Act Compliance: AIRO, VAIR, and their Integration with DPV

As the use of AI, and consequently its harms, becomes more prevalent, the global discourse around AI has become increasingly risk-aware. With new risks emerging more frequently than ever, a key challenge is how to represent, document, and catalogue AI risks in an effective, interoperable, and queryable manner. Additionally, the European Union (EU) AI Act's requirements for "high-risk" AI systems to manage and document the risks creates the need for open and interoperable tools, methods, and standards that facilitate AI risk management in an ever-changing environment. In this paper, we present ontologies and taxonomies developed to assist with risk management and documentation, in line with the requirements of the EU the AI Act. We developed the AI Risk Ontology (AIRO) to specify AI use cases and their associated risks, complemented by the Vocabulary of AI Risks (VAIR), which populates AIRO with taxonomies of concepts. Key international standards on AI and risk, namely ISO/IEC 23894 on AI risk management and ISO/IEC 22989 on AI terminology informed the development of the ontologies. To promote reuse and enable multi-regulatory compliance, AIRO and VAIR have been integrated in the Data Privacy Vocabulary (DPV) through a consensus-building process, expanding DPV's scope from data to AI.

cs.CY↗
arXiv2026

An elliptic generalization of the $D^{(2)}_{2}$ Spin chain

An integrable elliptic generalization of the closed $D^{(2)}_2$ quantum spin chain is constructed. Taking the trigonometric limit, we have shown that the corresponding R-matrix reduces to that of the $D^{(2)}_2$ one, up to a similarity transformation. Basing on the very fact of the factorization for the R-matrix and the corresponding transfer matrix which indeed ensures the integrability of the model, we give the exact solution of the model which can be expressed in terms of a homogeneous T-Q relation.

math-ph↗
arXiv2026

Bounded symbols and one-component geometry

We prove that every bounded truncated Toeplitz operator on a Hardy model space admits a bounded symbol if and only if its defining inner function is one-component, meaning that it has a connected sublevel set at some level in $(0,1)$. This resolves the bounded symbol conjecture of Baranov, Chalendar, Fricain, Mashreghi and Timotin and, through known equivalences, the embedding and weak factorization conjecture of Baranov, Bessonov and Kapustin. A uniform bound $R$ for the ratio of least bounded symbol norm to operator norm on the rank-one family associated with point evaluation in the disk already forces this geometry. The corresponding bound for all bounded truncated Toeplitz operators is at most $CR\log(e+R)$, where $C$ is absolute, and the logarithmic factor is optimal. In a nonzero de Branges space, the same geometric condition characterizes when every sufficiently small equivalent change of norm preserving the de Branges structure is represented exactly by reweighting the original integral with a positive density bounded above and away from zero. This characterization remains valid when the norm changes are restricted to discrete sampling norms. Outside the one-component class, every model space admits self-adjoint trace class truncated Toeplitz operators without bounded symbols, with arbitrarily small norm and singular values satisfying any prescribed positive upper bounds.

math.FA↗
arXiv2026

Pipelining vs. Combining in Aggregation Tasks

We study the aggregation task (convergecast) in networks in the case that the values to be aggregated do not fit in a single message. We assume that every node starts with an input value, and there is an aggregation operator that is commutative, associative, and length-preserving, i.e., the result of aggregating two values has the same length as each of the input values. Since values do not fit in a message, they are transferred in a ``train'' of pipelined messages, which must be terminated whenever we want to aggregate values. The goal is to minimize the makespan time of aggregating all values. We present general lower bounds on the problem and optimal algorithms for several prevalent parallel computing architectures, including the hypercube and complete bipartite graphs, under both the splittable and unsplittable flows models. We also present an $O(\log n)$ approximation for general graphs in the unsplittable flows model.

cs.DC↗
arXiv2026

CoHelix: Event-Based Multi-Propeller Rotation-Rate Tracking with Shared Projective Geometry

Estimating propeller rates from a moving event camera requires separating blade rotation from the changing image geometry. Background activity mixes with blade events, while repeated blade appearances admit half- and double-rate ambiguities. We propose CoHelix, a recursive filter that estimates one shared homography and separate rotation states for four rigidly mounted, coplanar propellers. Each admitted event updates its assigned rotation state, and its accepted geometry measurements correct the shared homography used to interpret later events from every propeller. We report lock, the fraction of evaluated time for which an estimate remains within 2% of synchronized ground truth, because mean error alone does not show how long a tracker follows the true rate. With fixed-rate initialization, leave-one-recording-out evaluation on moving-camera data gives CoHelix 62.9% lock, compared with 39.8% for HelixTrack and 22.2% for EventPro. With other settings fixed, allowing four geometry contributors instead of one raises lock from 3.4% to 62.9%. On a private target-follower dataset with a different target quadcopter, CoHelix retains the measurement settings selected on moving-camera data and uses a fixed initial rate. It reaches 95.9% lock, compared with 56.2% for HelixTrack and 61.1% for EventPro.

cs.RO↗
arXiv2026

A Task-Centric Survey of Long-Document Visual Question Answering: Taxonomy, Evolution, and Future Directions

Visual document understanding is essential for acquiring knowledge from visually rich documents and is attracting growing research interest. Existing surveys emphasize architectures or technical approaches, with limited attention to how task bottlenecks shape technical choices and research priorities. We present a task-centric survey that decomposes long-document visual question answering (VQA) into four components: document parsing, evidence organization and retrieval, generator organization and learning, and evaluation. For each, we develop a fine-grained taxonomy and trace motivations, technical responses, and cross-component connections. We focus on explicit retrieval while covering direct reading. Our temporal analysis traces expanding priorities from multimodal content understanding to sufficient, high-fidelity evidence acquisition and sustained evidence management. We outline future directions in evidence sufficiency, verifiable and correctable understanding, and budget-aware coordination, with an outlook on continual document understanding.

cs.CV↗
arXiv2026

Convex Equilibrium Potentials for Monge--Ampère: Curvature Bounds and A Posteriori Evaluation

Equilibrium neural networks define their hidden state as the fixed point of a contraction, so their effective depth is set at evaluation time rather than by the architecture. Using them for fully nonlinear PDEs raises two issues that explicit networks avoid: second derivatives may grow with the effective depth, and the potential is only ever evaluated approximately. We study nonnegative softplus equilibrium networks with contraction factor $q<1$, a convex class suited to the Monge--Ampère equation. A positivity cancellation in the resolvent shows that the Hessian grows at most like $(1-q)^{-2}$, rather than the $(1-q)^{-3}$ of a direct estimate, and an explicit one-neuron family shows that this exponent is sharp; third derivatives satisfy a sharp $(1-q)^{-3}$ bound. Residual-based a posteriori estimates then control the state, its input derivatives and, in two dimensions, the Hessian determinant at an approximate equilibrium. Combined with interval arithmetic on complete covers of the domain, they yield rigorous uniform bounds on the Monge--Ampère residual and, through a comparison argument, on the solution error of a fixed trained network. On two manufactured Dirichlet problems on the unit disk, all six trained models are certified with residual below $0.25$ and boundary error below $0.01$. Adaptive stopping halves float64 evaluation time at best, whereas certified adaptive evaluation remains costlier than fixed depth.

math.NA↗
arXiv2026

Lower bounds on Steklov eigenfunctions for a class of curvilinear polygons

Steklov eigenfunctions, $\{ϕ_{σ_j}\}_{j=0}^\infty$, are the eigenfunctions of the Dirichlet to Neumann map on a bounded domain with eigenvalue $σ_j$. This paper considers Steklov eigenfunctions and eigenvalues on a family of curvilinear polygons, $Ω_α$ whose boundaries are smooth away from a single corner of angle $α$. We (i) prove optimal lower bounds on the decay of the harmonic extension, $u_{σ_j}$, of $ϕ_{σ_j}$ away from the boundary of $Ω_α$ and (ii) give optimal lower bounds on the degree to which the high energy Steklov spectrum of $Ω_α\setminus H_1$ may differ from that of $Ω_α\setminus H_0$ when $H_1$ and $H_0$ are isometric. This shows that the corresponding estimates in recent work by the authors together with Malagutti are optimal. The proof in this paper was obtained through an interaction with ChatGPT 6 Astra: While writing the work with Malagutti, the authors became curious about optimal error bounds for the difference between the Steklov spectra on a curvilinear polygon, $P$, and the spectrum of any operator which knows only local information about $\partial P$. The authors suggested to ChatGPT to remove two isometric, smooth domains from a curvilinear polygon. ChatGPT suggested the ideas for a proof based on a regularized trace and the singularity in the kernel of the DtN map near a corner. The authors then suggested a simpler, conformal approach, the method for handling small angles, and the idea to obtain lower bounds on Steklov eigenfunctions. The paper is entirely written by the authors and the argument has been significantly modified, clarified, and simplified from the ChatGPT ideas.

math.SP↗
arXiv2026

Auditing the Hand-Written Inputs of Learned Access Control

Learned access control is typically deployed behind two hand-built artefacts: a hard-deny set enforced by a small trusted shield, and a region map that decides which requests mined rules answer and which the learner answers. Verifying the shield or measuring the learner validates neither. We audit both on the five public ABAC Lab policies. First, we formalise hard-deny soundness and check it exhaustively over relations of up to 794,250 tuples. Clauses that faithfully transcribe an explicit restriction are unsound at rates of 0.50-0.70 across four elicitors - an author and three blind language-model elicitors - because prose scopes restrictions to a section while the grant relation is a disjunction over all rules: 97% of counterexamples are granted by other rules. Shipped unchecked, these deny sets would withhold 16-78% of everything the policies grant; certified, they withhold nothing. Vacuity, a second silent failure, also occurs. Second, hybrid routing needs a two-class, abstaining rule set that ABAC miners do not emit, and ranking a mixed-effect candidate pool under a cap is one-class in all 24 cells for the two commonest ranking keys. Third, for additive losses the hybrid-versus-learner effect factorises into covered mass times a rule-learner risk contrast that must be reported on both false-non-grant and false-permit loss: on two real policies, most selection rules give opposite verdicts on the two losses, and the one favourable on both holds for one policy, one learner configuration and a band of noise levels. A released artefact regenerates and checks every reported number.

cs.CR↗
arXiv2026

Stability of Fourier Restriction for a Class of Finite Type Surfaces in $\mathbb R^3$

We establish the stability of the optimal non-endpoint Fourier restriction range under smooth flat perturbations of curved-root surfaces in $\mathbb R^3$. Specifically, we consider graphs of $$ϕ(x_1,x_2)=(x_2-x_1^m)^n+R(x_1,x_2),$$ where $m,n\ge2$ are integers and $R$ is smooth and flat at the origin. On a sufficiently small neighborhood depending on the perturbation, we prove the local $L^p(\mathbb R^3)\to L^2(S,dσ)$ restriction estimate for $1\le p p_c$. Thus arbitrary smooth flat perturbations preserve the optimal restriction range away from the critical endpoint. For $n\ge3$, the main local estimate combines planar curve decoupling with a one-dimensional finite-type extension estimate, whose principal scale factors cancel exactly. For $n=2$, we prove a uniform $C^4$ perturbation estimate using a weighted convolution bound and an anisotropic Whitney decomposition. Anisotropic rescaling and summation complete the proof.

math.CA↗
arXiv2026

Orbital-coherence memory in electrical transport and its self-consistent Maxwell response

An internal electronic coherence changes electrical transport only when it feeds back on the physical current. We develop a reduced description of this feedback and distinguish its exact consequences from the assumptions required for a microscopic realization. An opposite-parity two-orbital Hamiltonian identifies a current-coupled orbital force. Under an explicitly stated moment closure and collision ansatz, it yields a passive three-state response with an exponentially damped oscillatory memory. The resulting conductivity redistributes a fixed optical weight and predicts a nonmonotonic dependence of dc conduction on coherence damping at fixed remaining parameters. The orbital reduction constrains the coupling and internal frequency through a shared bare splitting, providing a test beyond unconstrained spectral fitting. A charge-conserving spatial extension couples to Maxwell equations through a positive energy balance and separates the constitutive response from longitudinal collective and transverse electromagnetic modes. We formulate complex-conductivity and transmission tests, including the limits of parameter identification over a finite bandwidth. The model supplies a conditional connection between orbital dynamics, transport memory, and electromagnetic observables; conductivity alone does not establish a uniquely quantum mechanism, and a material-specific collision calculation and closure-error assessment remain necessary.

physics.app-ph↗
arXiv2026

Bridging persistence of discrete and continuous 1D maps: Total variation, permutation equivalence, and diagonal affine transformations

Fundamental to the field of topological signal processing (TSP) is the \textit{persistence diagram} (PD), or barcode, of a signal, which gives noise-resistant measures of topologically significant features as distinct from noise. Existing literature proves that the total persistence computed from these diagrams is equal to the total variation, for certain continuous signals on compact domains. We provide a closed formula for this shared quantity, and generalize to all continuous and discrete functions on bounded domains, and to certain functions on non-compact 1D manifolds. Extending the identification of continuous and discrete persistence, we investigate the similarities of functions with the same PDs, and prove that, for any $n$, the persistence diagram can be calculated as a function of the sequence of critical values; we compute these formulas for $n \leq 6$. Finally, we examine which function transformations cause predictable changes in the PD of the transformed function, characterizing affine and linear transformations.

math.AT↗
arXiv2026

Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions

For every pair of integers $d,n\geq1$, we construct a commutative noetherian local-Cohen-Macaulay DG-ring $A$ such that $\dim H^0(A)=d$, $\mathrm{amp}(A)=n$, $\mathrm{fpd}(A)=d-n$, and $\mathrm{FPD}(A)=d$. This gives a negative answer to the implication from local-Cohen-Macaulayness to equality of the two finitistic projective dimensions in a question of Bird, Shaul, Sridhar, and Williamson.

math.AC↗
arXiv2026

Qubits Are Not Enough: Deflation and Measurement Limits in Variational Quantum Modal Analysis

Amplitude encoding stores an N-degree-of-freedom structural mode using ceiling(log2 N) qubits. This article develops an evaluation framework for variational quantum eigensolvers in finite-element structural dynamics. A Cholesky transformation maps the generalized eigenproblem to a symmetric mass-orthonormal Hamiltonian, ensuring Euclidean quantum-state orthogonality equals structural mass orthogonality. For higher modes, the deflation penalty condition is sharpened to a necessary-and-sufficient threshold, with a Davis-Kahan bound quantifying effects of approximate projectors. Numerical studies separate mapping correctness, ansatz expressibility, preprocessing, Pauli growth, finite-shot uncertainty, and damage localization. For 128-DOF chains, consistent-mass whitening increases transformed-operator density from 0.023 to 0.308 and Pauli terms from 576 to 2950. Exact state-vector experiments show qubit count and circuit expressibility are distinct. At 10^5 shots per Pauli term, first-mode frequency RMS error is 2.45%. In an oracle-state study, 10% stiffness loss is localized in 84.5% of trials. Results sharpen the deflation condition, quantify resource bottlenecks, and claim no speedup.

quant-ph↗
arXiv2026

Krylov Complexity and Entropy of Composite Quantum Systems

We investigate the behaviour of Krylov complexity as the number of degrees of freedom of a quantum system increases. Specifically, we show that for tensor products of commuting subsystems, the leading excess complexity is controlled by a weighted variance of the subsystem Lanczos coefficients. This provides a quantitative measure of dynamical heterogeneity and a precise characterization of synchronous evolution. We also show that Krylov entropy is able to disambiguate the information associated with subsystems composition from that generated by dynamical mismatch, and that the same Lanczos variance controls the leading mismatch contribution to both complexity and the entropy. Our results establish excess complexity and Krylov entropy as complementary probes of the emergence of collective dynamics in large quantum systems.

hep-th↗
arXiv2026

$N \to Δ$ Transition Form Factors in the Thermal AdS/QCD Soft-Wall Model with Modified Propagators

We investigate electromagnetic (EM) and axial vector (AV) form factors of the nucleon-Delta baryon transition within the thermal AdS/QCD soft-wall model. While the vector bulk-to-boundary propagator admits a well-behaved analytical solution, the transverse axial vector equation of motion involves the vacuum expectation value of the bifundamental scalar (generating chiral symmetry breaking). Due to this, the axial propagator diverges asymptotically, rendering it unsuitable for computing observables in the soft-wall model. To address this problem, we implement a regularization for the axial propagator in the form of a momentum-dependent cut-off, that identifies its correct physical regime. This is achieved via an interior constraint approach to the boundary-value problem, that determines the cut-off point. The consistency of this procedure is verified near the UV limit. As a proof of concept, we test this modified propagator (and also a parametrically deformed version of it) to estimate axial vector form factors of the $N \to Δ$ transition, and find results moderately comparable with form factor profiles from experimental observations, lattice QCD, and other theoretical models. Equipped with this regularization, the thermal soft-wall model becomes a useful tool to probe thermal characteristics of QCD form factors. We demonstrate this for both, the EM and AV sectors of the $N \to Δ$ transition.

hep-ph↗
arXiv2026

Predictive electronic feedback control for narrow-linewidth lasers

Narrow-linewidth lasers are essential for various key atom-laser interaction processes and optical setups in quantum coherent control, quantum precision measurement, and quantum information science. The Pound-Drever-Hall (PDH) technique is the standard method for the frequency-stabilization of narrow-linewidth lasers, but the inherent time delay in its feedback loop inevitably induces excessive phase noise, commonly known as servo bumps. Previous solutions primarily rely on additional optical components outside the electronic feedback control loop. Here, we propose and implement a generic method based on the Smith predictor to address the time-delay issue entirely within the electronic part of the PDH feedback control loop. We systematically demonstrate its capability to suppress phase noise and reduce servo bumps by adding only a single Field-Programmable Gate Array (FPGA) controller to the loop. This class of methods is demonstrated to be conceptually concise with minimal hardware overhead, effective in practice, and holds potential for a wide variety of future applications.

physics.optics↗
arXiv2026

Parameter-Efficient Adaptation of Large Language Models to a Low-Resource Agglutinative Language: A Corpus, Datasets, and a Reproducible Benchmark for the Bashkir Language

Bashkir is a low-resource agglutinative language written in Cyrillic and remains poorly represented in modern LLMs. We present an open resource suite and a systematic benchmark of adaptation methods: the Bashkir Web Corpus (71,567 documents, 46.9M tokens, 16 sources) and three labelled datasets for binary, multiclass and multilabel text classification; the benchmark covers the first two. Experiments use eight architectures (82M-8B: DistilGPT2, GPT-2 base/medium, Phi-3-mini, Mistral-7B, YandexGPT-5-Lite-8B, mBERT, XLM-R) and three adaptation groups (full fine-tuning, QLoRA, in-context learning), plus continual pretraining (CPT). (1) QLoRA on 3.8-8B models outperforms encoder-only fine-tuning on binary classification: YandexGPT-5-Lite-8B with CPT reaches macro-F1 0.748 vs 0.653 (XLM-R) and 0.650 (mBERT); pairwise differences are significant after Holm correction (p<0.001). (2) YandexGPT-5-Lite-8B significantly outperforms Mistral-7B and Phi-3-mini on multiclass classification, BPB and native-speaker ratings (mean 3.28 vs 2.52 and 2.22; n=100; alpha=0.69-0.77; p<0.05); on binary classification its QLoRA advantage is not significant (p>=0.084). (3) CPT effects depend on model and task: perplexity improves for Phi-3-mini (+0.58) and YandexGPT-5-Lite-8B (+0.33) but worsens for Mistral-7B (-1.15, p<0.001); on binary classification CPT helps Mistral-7B most (+4.0 macro-F1). (4) Tokeniser fertility on Bashkir varies 2.67x (2.92-7.80) and tracks adaptation quality, while perplexity across tokenisers is not comparable. Cyrillic tokenisers with Russian pretraining are preferable; LLM judges reproduce native ratings for grammar and coherence (rho=0.33-0.46) but not language correctness (rho=0.16, p=0.11); native evaluation remains necessary. All artefacts are open-licensed.

cs.CL↗