Papers

Quasi-periodic oscillations are characterized by fitting Lorentzian functions to a nonparametric estimate of the power spectral density, a two-step procedure that separates estimation from modeling and does not accommodate measurement error. We develop a parametric alternative based on autoregressive moving-average (ARMA) processes observed with measurement error. We derive an exact decomposition of the ARMA spectral density into real-valued components, one for each class of autoregressive roots under complex conjugation, plus a polynomial term when the moving-average order is at least the autoregressive order. Each component is a Wrapped Cauchy kernel, and for complex roots it is accompanied by a conjugate-Poisson term that makes the peak asymmetric and displaces its maximum from the frequency given by the argument of the root. We obtain closed-form expressions for the location, height, width, and asymmetry of each peak, and a matching variance decomposition. Parameters are estimated by maximum likelihood through the Kalman filter, and all descriptors follow by plug-in. Simulations show that the closed-form peak location is recovered without appreciable bias. An X-ray binary light curve illustrates the methodology.

In this paper, we establish the stability of general entropy wave solutions of the compressible Euler equations (that is, profiles with constant velocity and pressure) in the class of vanishing dissipation limits from the Navier–Stokes–Fourier system. If the initial data of our sequence of solutions to the Navier–Stokes–Fourier system converges to the initial data of the entropy wave solution, we further have convergence of the solutions to the entropy wave. This gives uniqueness and stability of the entropy wave in this class. The proof is based on the $a$-contraction theory.

Agentic AI systems operating over geospatial data require more than autonomous reasoning and tool use; they must also support explicit orchestration, spatial validation, governance, provenance, failure handling, and human decision authority. Prior work introduced ANASSA, an agentic AI orchestration framework for spatial intelligence that established high-level components and responsibility boundaries for governed agentic execution (arXiv:2609.14824). However, the framework did not specify how those high-level responsibilities should be systematically decomposed into an implementation-facing low-level architecture. This paper addresses that gap by applying Design Science Research (DSR) to refine the ANASSA framework from high-level architectural (HLA) responsibilities into a low-level architecture (LLA). The resulting design preserves the responsibility boundaries of the foundational framework while translating them into executable architectural structures, including 47 logical roles, versioned task graphs, capability-based agent selection, typed contracts, explicit runtime states, spatial validation mechanisms, governance controls, failure and recovery paths, and provenance records. The architecture is demonstrated through an end-to-end execution trace and analytically evaluated for requirements traceability, internal consistency, responsibility preservation, and technology independence. The resulting high-level-to-low-level design provides an implementation-facing bridge between the ANASSA framework and future system implementations, defining how governed spatial agentic workflows can be made inspectable, reconstructable, and testable without binding the architecture to a specific AI model, geospatial platform, communication protocol, or deployment environment.

Large language models are increasingly used as scientific assistants, yet we still lack reliable ways to evaluate whether they can investigate a system rather than merely answer a prompt. A useful evaluation must let agents choose experiments, interpret finite evidence, and make causal decisions, while keeping the environment coherent across repeated observations and interventions and preserving objective ground truth. We introduce ACED-BENCH (Active Causal Evidence and Decision Benchmark), a neuro-symbolic benchmark built around this requirement. The key idea is to separate the readable scientific surface from the formal causal world: LLMs generate natural-language scenarios and task text, while hidden probabilistic graphical models define the causal graph, data-generating process, intervention semantics, validation checks, and oracle answers. This yields scientific worlds that are natural for agents to investigate but exact enough for scalable, programmatic evaluation. The main leaderboard ACED-CORE contains 180 tasks: 60 set-valued causal ancestry/descendancy questions and 120 constrained causal-decision tasks. We also report ACED-QUAL, a 150-question yes/no qualification check using the same hidden-PGM interface. We evaluate seven contemporary LLMs and two earlier-generation models across three active agent designs. ACED-QUAL checks whether agents can use the interface to draw conclusions from evidence, while ACED-CORE tests whether they can decide what evidence to collect and when to commit to an answer. Evidence-ledger analysis localizes failures within the investigation: agents test the wrong intervention, lose relevant evidence, or continue after sufficient evidence has appeared. These results suggest that reliable AI co-scientists need explicit support for experiment design, evidence retention, answer commitment, and stopping.

Let $\kappa_p(n)$ denote the maximum kissing number of a lattice $\mathcal{L} \subset \mathbb{R}^n$. We prove that $\kappa_p(n) \geq 2^{\Omega(\sqrt{n})}$ for all $p\ge 1$ and that $\kappa_p(n) \geq \Omega(\alpha_p^n)$ for all $p > 2$, where $\alpha_p > 1$ is a constant depending only on $p$. In particular, our former result improves on the previously best known lower bound of $\kappa_2(n) \geq 2^{\Theta(\log^2 n)}$ for the $\ell_2$ kissing number, which has stood for over $60$ years. (In concurrent and independent work, Laarhoven and Kominers [arXiv, 2026] showed a similar lower bound on $\kappa_2(n)$ using similar techniques.) In fact, our lower bounds follow from efficient (randomized) constructions of lattices with large kissing number. Our results use a general construction of lattices with large kissing number. Specifically, we show a simple equivalence between such lattices and a new object that we call an exact locally dense lattice. Closely related objects appear throughout the literature on computational lattice problems. Our constructions of lattices with large kissing number then follow as corollaries by showing that constructions due to Bennett and Peikert [RANDOM, 2023] (using Craig lattices) and Aggarwal and Stephens-Davidowitz [STOC, 2018] (using sparsification of $\mathbb{Z}^n$) in fact give exact locally dense lattices, as well as a new construction of exact locally dense lattices built from rotations of the $m$-dimensional checkerboard lattice $D_m$.

Retargeting human demonstrations into dynamically feasible dexterous hand trajectories requires resolving complex contact physics, yet current methods either omit physical constraints or rely on computationally expensive sampling-based optimization in simulation. Reinforcement learning has previously been used to achieve planning and control through contact dynamics; however, standard policies require object-specific training and fail to generalize across arbitrary geometries. This work reframes physics-based retargeting as a residual learning problem, where we demonstrate that zero-shot generalization across objects relies on structured state representations. Specifically, formulating the observation space to include a localized contact-error signal guiding each robot link to its target coordinate on the object surface enables a single, unified residual policy to successfully grasp novel, unseen object geometries. Rolling out this policy in simulation on a kinematic reference trajectory yields a physics-based retargeter, OATH. Operating at 0.4 seconds of compute per second of reference, OATH achieves 2.4x faster-than-real-time performance and a 60-350x reduction in computational cost compared to sampling-based methods. The system recovers 58% of held-out and 54% of unseen-object DexYCB trajectories while maintaining a sub-2 cm tracking error.

We introduce Tokenization-Invariant Watermarking (TI-WM), a method that embeds a watermark during token generation but keys and scores it on canonicalized UTF-8 bytes. The detector does not invoke the tokenizer. Canonicalizer-preserving edits leave its score unchanged; other localized canonical-byte edits affect a bounded number of scoring windows. Across three fixed keys and 128 prompts per key and model, a deterministic white-box attack at a 5% word-edit budget leaves mean attacked-AUC 0.530 on Qwen3-8B and 0.664 on Gemma 4 E4B, compared with 0.410 and 0.489 for Unigram with detection-side deletion. These operating points are not jointly matched on quality and clean detectability. Bias sweeps show model-dependent distortion costs, and shared-rule controls support a locality interpretation without establishing a unique advantage of bytes. Visible insertion outside the canonicalizer's deletion set defeats the default design. Alphabetic filtering closes that channel but does not resolve source shift or calibrated detection power. TI-WM thus provides a concrete construction with local scoring guarantees and measured attack-ranking gains, not a general robustness or low-false-positive-rate deployment guarantee.

The new framework of semi-tautological extensions has allowed for explicit understanding of low-degree odd cohomology groups of moduli spaces of stable curves. Let $S^*_\omega(\overline{\mathcal M}_{g,n}) \subset H^*(\overline{\mathcal M}_{g,n})$ denote the semi-tautological extension generated by $H^{11}(\overline{\mathcal M}_{1,11})$, that is, the smallest system of subrings of $H^*(\overline{\mathcal M}_{g,n})$ containing $H^{11}(\overline{\mathcal M}_{1,11})$ and the tautological subrings, which is also closed under pullbacks along forgetful maps and pushforwards along gluing maps. Recently, it has been shown that $H^{11}(\overline{\mathcal M}_{g,n}) = S^{11}_\omega(\overline{\mathcal M}_{g,n})$ and $H^{13}(\overline{\mathcal M}_{g,n}) = S^{13}_\omega(\overline{\mathcal M}_{g,n})$ for all $g$ and $n$. Meanwhile, $H^{15}(\overline{\mathcal M}_{1,n}) \neq S_\omega^{15}(\overline{\mathcal M}_{1,n})$ for all $n \geq 15$. Nevertheless, we prove that $H^{15}(\overline{\mathcal M}_{2,n}) = S^{15}_\omega(\overline{\mathcal M}_{2,n})$ for all $n$. Moreover, we determine all relations in $S_\omega^{15}(\overline{\mathcal M}_{g,n})$ for all $g \geq 2$ and give explicit bases for this vector space in terms of decorated graphs. Conditional upon the conjectured dimension of $H^{15}(\overline{\mathcal M}_{3,14})$, we also prove that $H^{15}(\overline{\mathcal M}_{3,n}) = S^{15}_\omega(\overline{\mathcal M}_{3,n})$ for all $n$. As an application, we prove $H^*(\overline{\mathcal M}_{g,n}) = RH^*(\overline{\mathcal M}_{g,n})$ for several new small pairs $(g,n)$.

Test-time adaptation (TTA) enables time series forecasters to update after deployment as new observations become available. However, adaptation objectives that focus primarily on prediction errors at individual time steps do not fully address the needs of financial time series forecasting. In addition to pointwise return fitting, return direction and the price trajectories reconstructed from sequences of returns are also important. To better account for these properties, we introduce Direction- and Price-Aware Adaptation Loss (DPAL), which combines pointwise return fitting with directional and price-calibration terms. We apply DPAL within existing TSF-TTA frameworks without modifying the source forecaster or the adapter architecture. Across a diverse collection of financial datasets, DPAL reduces reconstructed-price mean squared error in most evaluated settings.

The interplay between a weighted volume measure and its naturally associated weighted Laplace operator is fundamental to the geometric analysis of weighted structures governed by gradient vector fields. Beyond the gradient setting, however, the theory has remained considerably less developed, largely because this natural correspondence is lost. In this paper, we identify invariant measures as the appropriate framework for extending the theory to general drifted Laplace operators. This approach yields a systematic treatment of parabolicity in the non-gradient setting, reveals its connection with volume growth, and leads to new volume finiteness results for non-gradient geometric structures.

Brooks' Theorem is a foundational result in graph coloring: if a graph is connected, not a clique, and has maximum degree $\Delta \geq 3$, then it admits a proper $\Delta$-coloring. In this paper, we give a new proof of a much stronger result: every such graph admits exponentially many proper $\Delta$-colorings. Exponential lower bounds have been obtained previously by applying the Combinatorial Nullstellensatz. In contrast, our proof is via a surprisingly simple and constructive analysis of a textbook greedy coloring algorithm. The entire argument is accessible to non-specialists. We extend our techniques to provide quantitative lower bounds on the number of colorings in several more general settings, namely $\Delta$-length list coloring, degree-length list coloring (degree-choosability), and degenerate partitioning. In the latter setting, one is asked to partition the vertices such that each partite set induces a subgraph of bounded degeneracy. In contrast to the other coloring variants considered, no clean Brooks-type characterization is possible, since it is known that for some combinations of parameters determining the existence of even one valid partition is NP-hard. We give a new reduction which significantly extends the parameter regime for which determining the existence of a valid partition is NP-hard. Finally, we give a new proof of the classic degree-choosability theorem, generalizing the techniques behind a recent proof of Brooks' Theorem.

Let $G$ be a finite simple graph on the vertex set $[n]$, and let $\Gamma(G)$ be the Cayley graph of the symmetric group $S_n$ generated by the transpositions corresponding to the edges of $G$. We study the inverse spectral problem for the assignment $G\mapsto \Gamma(G)$ through the group-algebra operator $A_G=\sum_{\{i,j\}\in E(G)}(ij)$ and its regular spectral moments $M_k(G)=\operatorname{tr}(A_G^k)$. The moments admit two all-order forms: a universal support expansion in non-induced subgraph counts of $G$, and a representation-theoretic expansion over the irreducible representations of $S_n$. We compute the first nontrivial moments through order six. In particular, the fourth moment already contains the Coxeter triangle relation and determines the signed local invariant $6N_{K_3}(G)-N_{P_3}(G)$, rather than $N_{P_3}(G)$ alone. Consequently, for triangle-free graphs the spectrum determines the second moment of the degree sequence. We also give a simplified sixth-moment formula for triangle-free graphs, showing that in this class the spectrum determines $5N_{K_{1,3}}(G)+2N_{P_4}(G)+12N_{C_4}(G)$. Further structural consequences include bipartiteness and spectral symmetry of $\Gamma(G)$, a precise connectedness test, and the identification of the standard irreducible component with the shifted graph Laplacian $mI-L_G$.

Dexterous robot hands can receive useful motion intent from teleoperation or learned policies, but successful execution also depends on contact decisions that these commands rarely specify. We introduce DexFLEX, a contact-aware foundation controller that turns upstream fingertip-motion drafts into contact-consistent joint commands. Instead of treating a draft as a trajectory to copy, DexFLEX treats it as evidence about intent: from the current tactile-proprioceptive state, it proposes feasible short-horizon motion chunks, predicts their contact consequences, and selects the candidate that best follows the command while preserving future contact stability. At inference time, a simple Draft-Dream-Select procedure combines pure-prior proposals for recovery with draft-seeded proposals for responsiveness, then decodes the selected motion into executable joint-space targets. Across degraded-command simulation, real-world shared control, and visuomotor policy learning, the same trained controller improves robustness without retraining, increasing real-world teleoperation success from 29.2% to 78.3% and reaching 46.7% policy-learning success, 3.5 times direct joint-action prediction, and 1.56 times prior-only correction. Videos are available at dex-flex.github.io.

HD~158485 is an A-type $\delta$~Scuti star in the CALSPEC network and the JWST absolute-flux calibration program. Gaia DR3 assigns it a binary classification probability close to unity but provides no orbital solution. Using TESS observations from Sectors 14–26, 40–41, 47–60, and 73–86, we measure the pulsation phases of six $\delta$~Scuti modes. The frequencies form two groups with opposite light-travel-time delays, revealing two pulsating components. A direct light-curve forward model yields an orbital period of $P_{\rm orb}=382.80^{+0.80}_{-0.76}$~d, eccentricity $e=0.242^{+0.045}_{-0.046}$, projected light-time amplitudes of $195.8^{+9.2}_{-8.9}$ and $239.7^{+6.8}_{-6.8}$~s, and a dynamical mass ratio of $q=M_B/M_A=0.818^{+0.046}_{-0.045}$. A blind prediction based only on the first two long TESS campaigns reproduces the third campaign without updating the orbital parameters, with a Pearson correlation coefficient of $r=0.983$. Its held-out rms is 83.8~s, compared with 289.9~s when the period is fixed at 365.25~d. A 5.15-$\sigma$ Hipparcos–Gaia EDR3 proper-motion anomaly independently indicates unresolved astrometric motion. The unresolved companion can also affect spectrophotometric predictions: a conditional PB2-constrained two-atmosphere model differs from the corresponding single-star atmosphere prediction by 1.6% over 1–5~$\mu$m and 2.5% over 5–28~$\mu$m. HD~158485 therefore shows that a calibration-relevant binary can lack a catalogued orbital solution while two independent pulsation clocks reveal and measure its orbit.

Let $M$ be a binary matroid of rank $r$ with no $F_7$-minor, and let $B_M^\star$ denote the maximum of its basis-generating polynomial over nonnegative weights of total mass $r$. We prove the sharp inequality $B_M^\star\leq 2^r/(r+1)$, with equality holding if and only if the nonloop simplification of $M$ is $M(K_{r+1})$. Binary matroids with no $F_7$-minor also form the largest minor-closed class of matroids on which this inequality holds.

Dynamic Tensor Rematerialization (DTR) trains neural networks under a memory budget by evicting tensors and recomputing them on demand. A natural expectation is that a budget large enough to complete training stays sufficient when it is increased. Using DTR's reference simulator, simrd, to replay the public DTR training traces, we show that this expectation fails. We call the exceptions feasibility holes: memory budgets at which an eviction policy runs out of memory although both a smaller and a larger budget complete, a form of non-monotone feasibility. Under a written sweep protocol with dated amendments, a 0.01-step budget grid shows no such hole for DTR on any of six confirmatory traces, although unresolved timeouts prevent it from establishing monotonicity. Finer sampling finds holes on InceptionV4 (three regions) and U-Net (two regions), in addition to one on the ResNet-32 development trace. Every hole is reproduced by three repeats and by unmodified simrd. For one InceptionV4 pair (0.2343 versus 0.235 of peak memory) we trace the failure to individual allocations. The larger budget avoids one eviction at an operator where the smaller budget was 173,479 bytes short. The extra data it carries forward forces a later eviction of a tensor needed three operators afterwards, and rebuilding that tensor triggers a recomputation cascade that cannot fit. Keeping that one tensor resident under the same budget prevents the failure. The two simple score changes we tested do not remove holes across traces; both add failing budgets on some traces. All results are from simulation, with no allocator model; behaviour on GPU hardware is untested.

We study learned one-step predictive control of a synthetic population of 64 leaky integrate-and-fire neurons whose light sensitivity is scaled by a hidden factor s, using two prospective confirmations on plants simulated only after the analysis was frozen. In the first (50 plants, 11 conditions), removing the 200-ms input-output history substantially worsened a parameter-count-matched neural predictor at low and moderate gain (s = 0.6, 0.8; RMSE rose by 2.47 Hz at s = 0.6, 97.5% CI 2.43-2.51). In secondary comparisons, recursively adapted ARX had the lowest mean error of the deployable controllers in 10 of 11 conditions, tuned PI with anti-windup matched or beat the network for s >= 0.7, and training for 10,000 rather than 900 epochs lowered prediction error but worsened control. Development work suggested the network's learned action sensitivity did not track the hidden gain. A second protocol (50 new plants, 9 sensitivities, 2 noise levels) confirmed three pre-specified predictions at the primary noise level. Re-estimating a single multiplicative input gain recovered 87% (95% CI 86-88%) of the benefit of full adaptive ARX. Supplying that online estimate to the network as an extra input reduced high-gain tracking error by 1.84 Hz [1.81, 1.88]. Longer training worsened the plain network by 1.09 Hz but improved the gain-input network by 1.07 Hz, a differential of 2.16 Hz [2.13, 2.20]. Under high process noise (sigma = 2.0) the effects shrank to about 0.04 Hz or less and gain-only adaptation recovered only 24% of the adaptive-ARX benefit. In this synthetic plant, at the primary noise level, one-parameter online gain estimation accounts for most of the gap between a history-based network and full adaptive ARX, and for its prediction-control mismatch.

Quantum geometric quantities, such as Berry curvature (BC) and quantum metric, are known to govern the physical and topological properties of materials, making access to these quantities critically important for the comprehensive understanding of the materials. Chiral crystals offer a natural platform in which structural handedness can control quantum geometry and nonlinear transport, but direct experimental access to the quantum geometric quantities has remained elusive. Here, we show that trigonal tellurium (Te) hosts an enantiomer-dependent Berry curvature dipole (BCD) that can be accessed through the measurement of cross-axial nonlinear Hall effect (NHE), unlike previously studied in-plane configurations where the BCD contribution vanishes. Angle-resolved measurements on left- and right-handed Te devices reveal a second-order transverse response whose sign reverses with crystal chirality. The extracted cross-axial nonlinear susceptibility, $\chi_{yxz}$, exceeds the in-plane susceptibility, $\chi_{xxx}$, by more than two-folds, indicating a strong BCD-driven contribution. First-principles calculations attribute this behavior to a topologically nontrivial hedgehog-like BC texture near the H points and predict a BCD that reverses sign between opposite enantiomers, consistent with experiment. These results establish cross-axial nonlinear Hall transport as a symmetry-selective probe of chirality-controlled quantum geometry in tellurium and related chiral materials.

In most theories of electrolyte and polyelectrolyte solutions, the solvent is treated implicitly as a dielectric continuum. While this approximation has enabled major advances, it neglects coupling between ionic and dipolar degrees of freedom. Using molecular dynamics simulations and the mean-spherical approximation, we show that this coupling qualitatively alters electrostatically driven phase behaviour. At finite ion concentrations, many-body ion-dipole correlations reverse the temperature dependence of effective electrostatic interactions, leading to upper-critical solution temperature (UCST) behaviour in direct contrast to the lower-critical solution temperature (LCST) behaviour predicted by implicit-solvent electrostatic theories. This phase reversal arises from ion-induced suppression of local dipolar screening, a collective effect inaccessible to pairwise implicit-solvent descriptions.

Language model classifiers are increasingly deployed for high-stakes decisions such as phishing screening, content moderation, and fraud triage, yet validation-set thresholds provide no finite-sample control of deployment-time false positives. We present ConformalGuard, a model-agnostic calibration layer that wraps a fixed scoring function with finite-sample control over the rate at which legitimate inputs trigger an intervention tier. Our contribution is empirical and operational, not a new conformal theorem: zero-shot LM API scores can be coarse enough (10–11 unique values here) to make temperature scaling and isotonic regression operationally identical to raw thresholding for low-FPR action gating. We compare these methods with conformal calibration for fine-tuned BERT, Claude Sonnet 4, and GPT-4o on public email corpora. For Claude, conformal calibration reduces FPR from 0.040 to 0.008 while recall falls from 0.938 to 0.875. For deterministic GPT-4o scores, the 1% operating point is too conservative to deploy (recall 0.564); three-run stochastic averaging raises recall to 0.732 at FPR 0.005. At 2% prevalence with BERT, conformal calibration removes 25 false-positive reviews per 10,000 emails (95% CI [10, 43]). The guarantee is legitimate-event-rate control under exchangeability; discrimination, workload effects, and robustness to shift remain empirical.

Motivated by a recent paper where a convex portfolio optimization problem formulated by means of the entropic value-at-risk is solved via a primal-dual interior-point method, we propose an alternative way of dealing with such problems by means of splitting proximal point methods and making use of Lagrange duality. Numerical experiments where the new method is implemented for solving some portfolio optimization problems are presented as well. As byproducts, we also provide formulae for the projection on the epigraph of the weighted Shannon entropy, and the conjugate function and subdifferential of entropic value-at-risk.

A predictor is multicalibrated with respect to a class of subpopulations (formally, of functions on the inputs, called auditors) if, for every subpopulation in the class and every value the predictor outputs, the average outcome among the members of that subpopulation who receive that value is close to the value itself. For finite classes, about $\varepsilon^{-3}$ samples are necessary and sufficient to learn a predictor with multicalibration error $\varepsilon$, but the algorithms that attain this rate enumerate the class, which is impossible for the large classes of interest. We ask how many samples suffice when the learner accesses the class only through an empirical risk minimization (ERM) oracle. We give an algorithm that uses $\tilde{O}(d/\varepsilon^{3})$ samples and polynomially many ERM calls, where $d$ is the VC dimension of the class. Its dependence on $\varepsilon$ is optimal for all learners. When $d$ is at least about $1/\varepsilon$, every learner that can only access the class through polynomially many ERM calls needs $\tilde{\Omega}(d/\varepsilon^{3})$ samples. Learners with unlimited computation need only $\tilde{O}(\varepsilon^{-3}+d\varepsilon^{-2})$ samples, so the extra factor $1/\varepsilon$ on the dimension term is the price of oracle efficiency. For swap multicalibration, which allows a different function from the class for each predicted value, $\tilde{\Theta}(d/\varepsilon^{3})$ samples are necessary and sufficient. For estimating the error of a given predictor, the ordinary notion is the harder one: the swap error can be estimated with an ERM oracle, whereas the ordinary error is NP-hard to approximate even for classes with linear-time ERM. Consequently, there are classes for which it is computationally easier to learn a multicalibrated predictor than to compute the multicalibration error of a given predictor.

We consider the future of mathematics as a profession in a world where artificial intelligence may surpass human mathematicians in essentially every technical task. Through an informal dialogue, we explore why human mathematical expertise might nevertheless remain valuable, what kinds of expertise universities should cultivate, and how graduate education might adapt. We also discuss the institutional and economic uncertainties that threaten the continued existence of a thriving mathematical profession, even if the value of human mathematical understanding endures.

The low autocorrelation binary sequences (LABS) problem, often formulated as a spin-lattice energy-minimization problem, is a combinatorial optimization problem with a very rugged energy landscape. We demonstrate that iterative optimization of very small subsystems of n spins that are decoupled from the rest of the system achieves global optimization of LABS with a time-to-solution scaling that is competitive with heuristics that optimize the global system of N spins directly. Our isolated-subsystem heuristic with n = 4 achieves a time scaling of O(1.333^N ) on the interval N = [27, 60], while the current state-of-the-art classical and quantum scalings are respectively O(1.34^N ) and O(1.21^N ). Our results suggest that specialized optimization hardware with only small numbers of logical spins may be of practical relevance.

Large language model (LLM) alignment often assumes that the user interacting with a model is also the primary beneficiary of its behavior. Yet in many consequential settings, one person directs the system while another bears the consequences. We study this problem in caregiver-mediated healthcare, where parents, pet owners, and caregivers make decisions for children, animals, and older adults. We introduce an evidence-grounded benchmark spanning veterinary, pediatric, and older-adult care, and test whether AI advisors maintain appropriate care when users express clinically inferior preferences. Holding patient facts fixed, we vary stated care preferences and communication styles and evaluate both initial recommendations and multi-turn follow-up. Across frontier and open-weight models, inferior preferences substantially increase switching from appropriate to inappropriate care beyond neutral conversational drift and increase agreement with the requested action, while communication style alone has a smaller effect. These failures accumulate across turns, including on cases models initially answer correctly, and often carry moderate or severe potential harm. In matched eldercare cases, the effect of an inferior preference is similar whether it is expressed by the patient or by a caregiver. Together with models' limited tendency to elicit patient preferences in caregiver conversations, this suggests that current models are highly sensitive to expressed user preferences but less sensitive to whose preferences are represented and who bears the consequences. Our results expose a broader limitation of user-centric alignment in settings with multiple stakeholders.

We prove sharp improved Sobolev inequalities on $\mathbb S^n$, $n\ge3$, for antipodally even functions and for axially symmetric functions whose critical density $|u|^{2n/(n-2)}$ has zero barycenter. In both cases, the Dirichlet coefficient improves by the optimal factor $2^{-2/n}$, while the coefficient of the $L^2$ term remains one. Equality holds precisely for constant functions. The even case resolves a conjecture of Dolbeault (2021).

We investigate how femtoscopic correlations modify the relation between the spin entanglement of emitted particle pairs and that of pairs selected at a given relative momentum. For two spin-$\frac{1}{2}$ particles, we show that the momentum-selected spin state can be entangled even when the corresponding state at emission is separable. We derive a momentum-dependent separability criterion that determines whether the observed spin correlations require entanglement at emission. As an application, we consider a pair of identical $\Lambda$ hyperons, for which quantum statistics and final-state interactions affect the singlet and triplet spin channels differently at low relative momentum. Our results provide a framework for using experimentally accessible spin correlations to investigate entanglement at emission.

We investigate non-stationary wormhole geometries in General Relativity embedded in evolving cosmological backgrounds. We employ a Simpson-Visser-like regularization of the temporal coordinate of the $(n+1)$-dimensional FLRW metric, together with a homogeneous Cuscuton field, to construct cosmological backgrounds in which the scale factor remains finite and non-zero at the would-be initial singularity. We then consider two specific dynamical wormhole geometries: the four-dimensional defect wormhole and the topologically charged Perry-Mann type wormhole. We show that the former can be supported by a canonical scalar field with vanishing potential, while the latter requires a mimetic matter sector to support its spatial structure, with the Cuscuton governing the cosmological evolution in both cases. We subsequently generalize the analysis to a separable non-stationary spacetime and derive a scaling condition that strongly constrains the admissible matter sources. In particular, for minimally coupled scalar and nonlinear electrodynamics fields, this condition removes the functional freedom available in static reconstruction schemes. We show that, within this framework, regular, asymptotically flat wormhole geometries cannot be obtained while simultaneously satisfying the required smoothness and reflection symmetry conditions. Our results illustrate both the possibility of constructing specific non-stationary wormholes in regular cosmological backgrounds and the restrictions that arise when attempting to generalize such constructions to arbitrary spatial geometries.

AI-enabled systems must remain dependable when the conditions under which they operate change (e.g., due to input perturbations, distribution shifts, or changes in external dependencies). This makes robustness auditing of such systems important for judging whether the available evidence is sufficient to support a defined robustness conclusion. However, designing an AI robustness auditing framework is challenging. A key unresolved issue is determining the requirements such a framework should support; these requirements have not yet been consolidated. We address this gap through meta-requirements: higher-order requirements specifying what a class of auditing frameworks should support. In design science research, literature and domain experts are common sources of meta-requirements; accordingly, we derive the initial set from literature and validate and refine it with practitioners. Our systematic literature review retained 74 of 2,890 records and derived 43 meta-requirements across 16 categories. We evaluated them with 128 practitioners, obtaining 5,504 ratings and 586 substantive comments. Overall, 81.20% of ratings indicated agreement or strong agreement. In particular, 41 of the 43 literature-derived meta-requirements were classified as strongly supported. Practitioner feedback refined the requirements and identified an additional requirement concerning external components and supply chain dependencies. The final set comprises 44 meta-requirements across 16 categories, of which 43 received quantitative validation. These meta-requirements can help organizations implement AI robustness auditing frameworks, assess existing frameworks for completeness, and refine them.

Despite widespread enthusiasm, applying artificial intelligence and machine learning (AI/ML) to turbulence modeling has yielded only modest progress, primarily due to a lack of situation-aware deployment. Data-driven Reynolds-averaged Navier–Stokes (ML-RANS) closures frequently fail to generalize across diverse flow regimes, while scale-resolving simulations (SRS) remain computationally prohibitive. As a result, ML-RANS is often misapplied outside its domain of validity, and ML-SRS is unnecessarily deployed on flows fully amenable to RANS. To guide optimal AI/ML deployment, we propose a turbulence taxonomy map parameterized by degrees of freedom ($Re$) and the degree of non-equilibrium ($SK/\epsilon$). By applying Weaver's well-recognized complexity framework, we classify turbulence into distinct physical regimes. This categorization identifies where local ML-RANS surrogates can generalize, clarifies where explicit scale resolution is physically mandatory, and highlights where physics-informed neural networks (PINNs) are most effective. Ultimately, this perspective establishes a physics-grounded framework for the flow-aware, successful deployment of AI/ML in turbulence.