Papers

The Markov kernel based metric $D_1$ was introduced in 2011 in order to construct the scale-invariant dependence measure $\zeta_1$, which assign each bivariate copula $C$ a dependence value in $[0,1]$, with $0$ exclusively for the case of independence, and $1$ exclusively for complete/functional dependence. In the original paper it has been shown that the resulting metric space $(\mathcal{C},D_1)$ is separable and complete, however, no further topological properties were studied. Considering that $D_1$ has proved useful in a variety of contexts, using tools from infinite-dimensional topology, we here close this gap, show that $(\mathcal{C},D_1)$ is homeomorphic to the Hilbert space $(\ell_2,\Vert \cdot \Vert_2)$, and prove that several subfamilies are either homeomorphic to $(\ell_2,\Vert \cdot \Vert_2)$ or to the Hilbert cube $(\mathcal{H},\rho)$. Moreover, allowing for a better assessment of relative sizes, we show that various subfamilies are so-called $Z$-sets in $(\mathcal{C},D_1)$, implying that they are topologically negligible in the full space.

We introduce a class of generalised Killing spinors, termed affine Killing spinors (AKS), for which the associated endomorphism is a constant linear combination of the Ricci endomorphism and the identity map. We classify Riemannian spin manifolds admitting an AKS under two additional curvature hypotheses: harmonic curvature and local conformal flatness. Furthermore, we characterise Riemannian spin manifolds that admit a non-zero parallel one-form and an AKS. Additionally, we prove that in dimension three every curvature-homogeneous manifold carrying an AKS is locally homogeneous. Finally, we provide a complete classification of three-dimensional Lie groups equipped with a Bianchi metric admitting an invariant AKS.

We study units in group rings of the Hantzsche-Wendt group. We construct a compatible system of non-trivial unitary units over $\mathbb Z/2^n\mathbb Z$ for every $n\ge1$, and “almost-group” units over $\mathbb Z/2\mathbb Z$, meaning non-trivial units $u$ with the property that $u-g=u^{-1}-g^{-1}$ for some group element $g$.

A developed method, based on the stationary second-order Rayleigh-Schrödinger many-body perturbation theory in an irreducible tensorial form, allows us to determine the most important core-valence, core, core-core, and valence-valence correlations for any atom or ion with an arbitrary number of valence and core electrons. This paper presents the Feynman diagrams that describe these correlations. Additionally, it provides the rules for obtaining algebraic expressions in an irreducible tensorial form for any Feynman diagram coming from second-order many-body perturbation theory. Whereas some types of the valence-valence and core-valence correlations are described by the three-particle Feynman diagrams, additional developments to calculate the spin-angular parts of these diagrams have been made to the program library librang of the Grasp2018. As an example of the application of the developed method, the atomic calculations of the energy level structure and transition data for Ar II are presented.

The dynamical GW self-energy approximation is a key computational tool to provide the fundamental spectrum of electronic systems. We reformulate this approximation, representing the particle and hole parts of the GW self-energy through a highly compact set of Cayley-transformed moment constraints. The Cayley transformation maps real frequencies to the unit circle, keeping the moments bounded as their order increases, ensuring numerical stability and allowing resolution to be focused on an energy range of interest. We calculate these Cayley-transformed moments via an efficient O[N$^4$] scaling contour integration, and from them, construct a Hermitian upfolded Hamiltonian with a linearly scaling dimensionality with system size. A single-shot diagonalization of this effective Hamiltonian gives an explicit full-frequency G0W0 Green's function with manifestly real poles and non-negative spectral weights. This enables quasiparticle energies, satellite features, and their spectral weights to be obtained across the full G0W0 spectrum. Comparisons with exact G0W0 calculations and convergence across the GW100 test set and the larger Chlorophyll A molecule demonstrate substantially faster and more reliable convergence with moment order than an earlier monomial-moment approach. These Cayley moment representations therefore provide a stable, compact, and systematically improvable route to the complete spectral information of zero-temperature GW, without explicit frequency grids, plasmon-pole models and other common approximations, or analytic continuation.

Time-series explainability remains challenging because discriminative information is often encoded in latent frequency or time-frequency features rather than in the raw signal itself. Existing attribution methods typically operate either in the time domain or in a fixed transform domain, limiting their ability to capture salient information across different representations. We propose XACT, a general framework that learns sparse attribution masks over coefficients from arbitrary invertible time-frequency transforms. We evaluate the framework on the STFT, the continuous wavelet transform, and the discrete wavelet transform. In addition, we extend the virtual inspection layer approach from the STFT to both wavelet transforms, enabling LRP to generate explanations in these representations. On a synthetic dataset, XACT produces precise explanations and is less prone to highlighting spurious features than the tested baselines. Across two real-world datasets, XACT produces sparse and structured explanations, although no method performs best across all quantitative evaluation criteria. These results demonstrate that learning explanations directly in time-frequency representations offers a flexible approach to interpreting deep-learning models for time series data.

Knowledge editing changes what a model knows by modifying parameters so that a requested fact updates while unrelated behavior is preserved. This is usually treated as a write problem, but editing also involves an address problem: deciding which hidden states should receive the new residual. An update that activates too narrowly memorizes one prompt, while one that activates too broadly disrupts neighboring knowledge. Parametric editors encode this scope implicitly, whereas memory-based editors make the selection explicit but keep it outside the edited model. We propose ALOE (Addressed Low-rank Operator for Editing), which learns semantic addresses from paraphrases and hard same-subject negatives, aligns them with autoregressive hidden states through rollout refinement and gate calibration, and embeds the resulting gated low-rank operator within one MLP layer, so that the deployed model runs in a single forward pass with no external retriever or auxiliary router. Evaluated on CounterFact, ZSRE, and KnowEdit across three 7–8B model families, ALOE achieves efficacy between 0.955 and 0.999 and locality between 0.981 and 1.000; mechanistic analyses confirm that the learned geometry separates competing edits and that calibration suppresses out-of-scope activation. The remaining errors concentrate in paraphrase coverage and write fitting.

Temporal knowledge graph forecasting aims to infer future relational facts from the temporal structure of observed events. Existing forecasters mainly summarize history through entity states, relation states, paths, or exact recurrence. These views often miss pair-specific transition evidence, that is, the way prior relations between the query actor and a candidate change the odds of the target relation. We introduce BridgeMem, which estimates this quantity as a residual added to the log scores of a frozen full-vocabulary forecaster. For each candidate, BridgeMem retrieves the pair's events that strictly precede t, encodes their relations, directions, and lags, and converts them into a likelihood-ratio correction. A support-adaptive empirical-Bayes reader trusts exact transition counts where they are abundant and backs off to a learned attention estimator where they are sparse. The backbone's own uncertainty gates the correction, so confident queries and candidates without dyadic history are left unchanged. On five benchmarks, BridgeMem improves on the strongest of nine baselines from 2021–2026 in all 20 filtered MRR and Hits@{1,3,10} comparisons, with MRR gains of 0.0213, 0.0164, 0.0216, 0.0112, and 0.0028 over the best prior result. These results show the value of explicit dyadic transition modeling.

Magic-state cultivation offers a promising alternative for lowering the cost of non-Clifford operations in fault-tolerant quantum computing (FTQC). However, realizing cultivation in practice exposes two challenges: (i) the lack of an open-source classical runtime layer between logical software and physical control, and (ii) the latency constraints on protocol-specific decisions that determine magic-state readiness. To address these challenges, we adopt an algorithm–hardware co-design approach. At the algorithm level, we develop a two-stage early-escape scheme that identifies an informative subset of detectors offline, constructs a compact decoding problem, and performs partial decoding in parallel with complete decoding at runtime, allowing high-confidence attempts to advance before full decoding completes. At the hardware level, we present MagiCFirm, a configurable runtime that combines offline-compiled microprograms with dedicated datapaths for detector construction, event processing, and protocol control, enabling end-to-end execution of magic-state cultivation. Across evaluated configurations, MagiCFirm reduces wall-clock magic-state preparation time by up to 39.3% at matched logical error rate. For a representative magic-state-bound workload, this translates to an estimated 11% reduction in overall application runtime.

We develop a multi-label Polish content-safety classifier by fine-tuning allegro/herbert-base-cased (124M) across five categories (hate, vulgarity, sexual content, crime, self-harm) using a Focal + R-Drop objective, and evaluate the resulting model against Bielik Guard (Sójka) on the shared out-of-distribution Gadzi Język benchmark. Both systems are given per-category threshold tuning on the same calibration split. Under that matched protocol our model holds a small but statistically significant lead in micro F1, while an apparent macro-F1 lead does not survive: it was an artifact of comparing a tuned model against an untuned one. We also report what that micro figure is worth. Because Gadzi Język is 97% crime-positive, a classifier that flags crime on every input and nothing else already scores 0.910 micro F1 on the same test split, so micro separates neither system from a degenerate strategy and macro is the column that does. Per-category and per-protocol figures are reported in Section 4. The residual out-of-distribution gap is one of calibration rather than discrimination. Ranking quality stays high while positive probabilities collapse, and per-category temperature scaling recovers the loss where Platt scaling and isotonic regression do not. That recovery turns out to be conditional on the calibration set containing safe text. Gadzi Język contains almost none, so thresholds fitted on it flag crime on every safe input, and a balanced refit buys a deployable operating point at the cost of adversarial recall. We report both operating points rather than only the flattering one. Two changes that are standard practice, per-class cost-sensitive weighting and mean pooling, each raise in-distribution macro F1 while lowering the out-of-distribution figure, which indicates that robustness has to be selected for directly rather than inherited from in-distribution accuracy.

We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such problems, we derive a dual, a primal, and a primal-dual formulation, compatible with stochastic optimization. We show convergence of stochastic first-order methods to the optimal value under generic conditions. In addition, we introduce a computable metric that upper-bounds the performance of suboptimal controllers produced during optimization, under additional regularity assumptions. Preliminary results show that the method can efficiently solve a simple control problem. Finally, we discuss conditions for the boundedness of the optimal occupation measure, a key assumption for the primal and primal-dual approaches.

Artificial intelligence (AI) models are increasingly deployed through remote services, making model misappropriation a growing concern. Existing approaches, including watermarking, fingerprinting, and model similarity analysis, primarily rely on predefined evidence or direct behavioral comparison and do not explicitly evaluate whether the claimant currently possesses and can utilize model-dependent information relevant to the claimed model identity. In this paper, we propose Third-Party Challenge-Response Identity Verification (TP-CRIV) for AI models. TP-CRIV targets a third-party verification setting in which the verifier has neither white-box nor API access to the claimant's model, can interact with the suspicious deployed service only through its ordinary black-box inference interface, and does not require protocol-specific cooperation from the service provider. Under these constraints, the framework enables the verifier to obtain empirical evidence as to whether the claimant locally possesses a model satisfying a predeclared identity relative to the deployed model. Verification is conducted under fresh, previously undisclosed requirements and network isolation, so that the demonstrated capability cannot rely on online external assistance after challenge disclosure. The resulting evidence is interpreted relative to independently specified and calibrated matching and non-matching operating situations and is statistical rather than cryptographic. We instantiate TP-CRIV for CNN image classifiers using probability-control-based witness generation. Experiments on ten ImageNet-pretrained TorchVision models demonstrate clear same/cross-model separation and finite-challenge verification using independently calibrated thresholds.

The recent discovery of high-$T_c$ superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ (La-327) under applied pressure and compressive strain opened a new avenue to elucidate the interplay between multiorbital intralayer and interlayer electronically driven Cooper-pairing in bilayer systems. Depending on the details of the electronic structure in the normal state, the superconducting gap in bilayer nickelates is predicted to have either bonding-antibonding $s_{\pm}$-wave symmetry, driven by dominant interlayer Cooper-pairing, or $d$-wave symmetry with substantial intralayer Cooper-pairing. Despite this general picture, the orbital structure of the superconducting gap in these multiorbital systems has been less explored. Here, we analyze the consequences of an orbital-anti-phase structure of the superconducting gap and discuss its possible experimental signatures. We demonstrate that additional pairs of nodes may appear on the $\alpha$ and/or $\beta$ Fermi surface sheets due to the sign change of the superconducting gap between the involved orbitals. Apart from this additional nodal structure, which is not enforced by the symmetries of the gap function and can be probed in ARPES experiments, the orbital-anti-phase gap modifies the temperature dependence of the superfluid stiffness at low temperatures, providing a concrete experimental prediction to test its realization in bilayer nickelates and related multiorbital systems.

We prove the Marcus-Minc conjecture: let n be any integer at least 2, and let A be a nonnegative n by n matrix whose row and column sums are all one. Form a new matrix by subtracting A from the n by n matrix of ones and dividing by n minus one. Then the permanent of A is at least the permanent of the new matrix. We also determine all equality cases.

Obstacle-aided locomotion is a fundamental capability for snake robots to traverse complex environments. However, conventional rigid-link snake robots often suffer from stagnation or jamming caused by their low joint density (i.e., the number of joints per unit length). This results in discontinuous contact with obstacles, unlike the continuous adaptation of biological snakes. To investigate the effect of joint density on obstacle-aided locomotion performance, we utilized a joint-repositionable snake robot mechanism that decouples actuators from joints, enabling a high-density architecture. We developed two experimental models with identical total lengths but different joint densities (high-density and low-density) and conducted comparative propulsion experiments in obstacle environments with varying obstacle diameters. The experimental results demonstrate that the high-density model substantially suppresses the abrupt shifts in reaction forces that cause stagnation in the low-density model. By maintaining smooth contact points, the high-density configuration reduces power consumption and achieves stable, continuous propulsion. These results highlight high joint density as a key factor in improving the environmental adaptability of snake robots in complex terrains.

A regular observed statistical model may converge to a limit in which a previously identifiable signed parameter becomes identifiable only modulo a reflection. We study the local information geometry of this transition. For a twice differentiable Hellinger embedding with an exact limiting reflection, the observed displacement is forced into the two-jet form \(\varepsilon\lambda J_-+\lambda^2J_+/2\), up to higher-order terms. The mixed jet restores the sign away from the symmetric face, whereas the even jet is the first tangent inherited by the quotient. After nuisance elimination, a positive Gram determinant yields a nondegenerate cross-cap two-jet. The associated local asymptotic theory has three regimes governed by \(\tau_n=\sqrt n\,\varepsilon_n^2\): regular signed LAN, a critical curved Gaussian subexperiment, and a quotient regime with the \(n^{-1/4}\) signed scale. We prove that the same parabolic critical experiment persists for predictive likelihoods along a single stationary dependent trajectory. The limiting quotient has a regular Fisher metric in the invariant coordinate, while its pullback degenerates in the signed coordinate. For a solvable CIR–OU benchmark motivated by coherent sea-clutter observations, we derive the quotient Fisher metric and curvature explicitly and show that the curvature is strictly negative. We also determine the restricted holonomy of the full Amari family: \(\operatorname{Hol}_0(\nabla^{(a)})=SO(2)\) for \(a=0\), whereas \(\operatorname{Hol}_0(\nabla^{(a)})=GL^+(2,\mathbb R)\) for \(a\neq0\). The results separate the intrinsic geometry of the limiting quotient from the transverse geometry of its weak unfolding.

In this paper, the parameterized complexity of the multiplicative $\alpha$-spanner problem with independent weights and lengths on undirected graphs is considered for the first time. All prior FPT results (except one on DAGs) assume basic instances (i.e., with unit weights and lengths) and are parameterized in the stretch factor $\alpha$ and the (in practice typically non-constant) number of removed edges. We show that several parameterizations do not allow FPT algorithms. However, our exclusion approach generalizes an existing algorithm for basic instances to arbitrary weights and lengths. It is parameterized by the total removed weight and a new tightness parameter. The latter is more precise than $\alpha$ and allows us to also improve the best known result for basic instances. Our second algorithm, called inclusion approach, uses the natural parameterization in the spanner's total weight. We prove that this sole parameter leaves a W[2]-hard problem, but also show FPT algorithms exist when augmented with secondary parameters.

We establish a pointwise lower bound for the heat kernel of the elliptic operator $ \Lambda=(1+|x|^\alpha)\Delta +b|x|^{\alpha-2}x\cdot\nabla-|x|^\beta$, where $d\geq3$, $\alpha>2$, $\beta>\alpha-2$, and $b\in\mathbb R$. For every $\tau>0$, we prove that $$ \begin{aligned} p(t,x,y) &\geq C_\tau e^{\lambda_0t} \left(\frac{1+|y|^\alpha}{1+|x|^\alpha}\right)^{\frac{b}{2\alpha}} \frac{(|x||y|)^{-\frac{d-1}{2}-\frac{\beta-\alpha}{4}}}{1+|y|^\alpha}\\ &\quad\times\exp \left[ -\int_1^{|x|}\sqrt{\frac{s^\beta}{1+s^\alpha}}\,\mathrm ds -\int_1^{|y|}\sqrt{\frac{s^\beta}{1+s^\alpha}}\,\mathrm ds \right] \end{aligned} $$ for all $t\geq\tau$ and $|x|,|y|\geq1$, where $\lambda_0<0$ is the largest eigenvalue of $\Lambda$ and $C_\tau>0$ is independent of $t,x,y$. The proof applies the classical Davies - Simon argument in a weighted symmetric setting.

We develop and implement the quadratic density response function of non-interacting fermions at arbitrary temperature, frequencies, and wave vectors. Starting from a Green's function formulation, we derive the quadratic response and demonstrate its equivalence to the result obtained from the Wigner equation. We further derive the classical limit through a perturbative expansion of the Vlasov equation and demonstrate that the quantum and classical formulations agree in the high-temperature limit. We analyse the limiting behaviour with respect to wavenumber and derive the zeroth harmonic response. Two independent implementations are provided and extensively benchmarked against density-functional theory, canonical path integral Monte Carlo (PIMC), and grand canonical PIMC simulations. As the density response of the interacting electron gas is commonly modelled through the ideal response functions and approximate models for the local field correction, the presented formulation will also allow for more complete explorations of interacting systems. Especially, our efficient implementation, which evaluates the ideal static and dynamic quadratic response functions in less than 0.5 ms on a 1.3 GHz processor, will enable evaluation of quadratic corrections to integrated quantities such as interaction potentials and stopping powers in warm dense matter.

Glaucoma is the leading cause of irreversible blindness, and timely identification of fast progressors is essential to prevent disability. Current practice estimates progression by ordinary least-squares regression of mean deviation (MD) on time, requiring 6–10 visual field (VF) tests over several years to obtain a reliable slope. We present GLAM (Glaucoma Longitudinal Analysis Model), a deep learning framework that ingests longitudinal Humphrey 24-2 total deviation sequences with five clinical features and predicts MD and visual field index progression rates using attention-based fusion and aleatoric uncertainty. On the open-access University of Washington Humphrey Visual Field dataset (4,276 patient-eyes), GLAM achieved an MD-rate mean absolute error of 0.139 dB yr$^{-1}$ ($R^2 = 0.927$; 73.5% reduction over a ridge baseline) and an AUC of 0.990 for fast-progressor detection. VF-only deep learning can match multimodal pipelines for progression prognostication using routinely collected perimetry alone.

Hybrid interfaces formed by push-pull organic molecules physisorbed on two-dimensional (2D) semiconductors provide a structurally tunable platform for engineering second-harmonic generation (SHG). However, predicting and optimizing their macroscopic response remains a formidable challenge due to the phase-sensitive interference between the nonlinear responses of the adlayer and substrate. Here, we develop a physics-informed computational screening framework that decomposes the effective second-order susceptibility into its constituent substrate, molecular, and electric-field-induced SHG channels. Validated by fully atomistic first-principles calculations across representative interface structures, this model maps the complete orientation-resolved tensor landscape of chemically modulated carbon-conjugated polar molecules on 2D substrates with distinct symmetry. Crucially, our findings dismantle the conventional reliance on static polar descriptors, demonstrating that the ground-state permanent dipole magnitude is a fundamentally unreliable proxy for macroscopic nonlinear response. Instead, we show that the ultimate criterion for SHG maximization is encoded in the phase-resolved projection of the full anisotropic molecular hyperpolarizability tensor. On non-centrosymmetric substrates, the coherent interference between the physisorbed adlayer and the underlying 2D matrix induces a characteristic Fano-like asymmetry and ranking reversals that are entirely absent on centrosymmetric platforms. By establishing that functionalization topology, dynamic spatial orientation, and substrate point-group symmetry constitute a single, non-separable parameter space, this work provides a systematic blueprint for the rational assembly, predictive discovery, and non-invasive characterization of next-generation low-dimensional hybrid materials for nonlinear optoelectronics.

From the Higgs mechanism to magnetic ordering, spontaneous symmetry breaking organizes physics across scales. Whether an analogous transition governs waves scattered by periodically driven structures has remained an open experimental challenge. Here we demonstrate a universal symmetry-breaking transition in a periodically driven finite scattering system. By measuring the multispectral Floquet scattering matrix of a strongly modulated microwave resonator, we observe a transition from an unbroken symmetry regime with scattering eigenvalues of equal modulus to a broken symmetry regime where their moduli split apart, through an exceptional point. At parametric resonance, this transition culminates in coherent perfect absorption, where a tailored multispectral input state is completely absorbed without outgoing radiation, the singular limit of the underlying transition. Because it arises from the general algebraic structure of the Floquet scattering matrix rather than from implementation-specific details, this transition should occur broadly in such systems. Unlike instability phenomena in bulk driven media, it emerges in the eigenstructure of a finite scattering operator that couples waves across multiple frequency channels. Our results establish Floquet scattering as an experimentally accessible platform for the observation of symmetry breaking and for dynamic wave control in driven photonic systems.

Iterative model-based reconstruction in photoacoustic tomography repeatedly applies the forward operator mapping the initial pressure to the transducer signals, and its adjoint. At the scale of current three-dimensional systems, this operator cannot be stored and must be evaluated matrix-free, while accounting for the finite, focused surface of the transducers, whose spatial impulse response degrades the resolution when ignored. Representing the initial pressure by compactly supported radial functions, we show that the measured signal is exactly a temporal convolution between a system kernel gathering the radial function and the electrical impulse response, and a purely geometric quantity accounting for the portion of the transducer surface reached by the wave emitted from a voxel during one time step. Two implementations are proposed, differing only in how this quantity is evaluated: a quadrature over points of the surface, as in existing works, or a closed-form area, which never discretizes the surface. We derive closed forms for planar and cylindrically focused transducers and provide, in the latter case, two accelerations of the resulting elliptic integrals, a lookup table and a trapezoidal approximation, together with the piecewise planar approximation customary in the literature. These implementations reduce the per-voxel geometric computations and are released as an open-source Python package for graphics processing units. The performance of these operators is first demonstrated on a synthetic phantom, where the lookup-table-based operator reaches the accuracy of the exact evaluation ten times faster and outperforms the point discretization on both accuracy and runtime. A second experiment shows that they enable the processing of a realistic vascular phantom at full scale, with a higher peak signalto-noise ratio and a better resolution than the back-projection counterpart. The released implementations are an important step towards the adoption of three-dimensional modelbased photoacoustic reconstructions with finite and focused transducers.

A generalist vision encoder must capture semantic, spatial, language-aligned, and action-relevant cues within a unified representation, yet softmax attention underlying today's most capable visual backbones becomes prohibitively expensive at high resolution. A natural attempt to address both challenges is to distill multiple specialist teachers directly into an efficient architecture. We find that directly coupling these objectives degrades representation quality, as the student must simultaneously reconcile heterogeneous capabilities and adapt them to a different token-mixing architecture. We introduce IronViT, built on a simple principle: consolidate capabilities before constraining computation. IronViT first distills complementary specialists into a softmax attention capability bridge, then progressively transfers the consolidated representation to a hybrid softmax-linear attention encoder. A purpose-built data pipeline further curates the distillation corpus for higher information density and broader domain coverage. Across recognition, retrieval, dense prediction, multimodal understanding, and robotic learning, IronViT is competitive with leading specialist and generalist vision encoders. The softmax bridge achieves the strongest aggregate performance in multimodal understanding and robotic learning among the evaluated backbones, while the hybrid encoder retains broad transfer performance with an efficiency advantage that grows with input resolution. Together, these results show that consolidating capabilities before architectural conversion can yield a generalist visual encoder without inheriting the prohibitive high-resolution cost of conventional softmax attention.

CAR-bench evaluates whether tool-using agents stay reliable under real-world uncertainty, executing every tool inside the evaluator so that each tool-result exchange is a separate agent round-trip. A conventional next-action agent can batch parallel tool calls, but a chain of dependent calls costs it one model call per round of results. We present a coroutine-bridge harness in which the model's only action is to emit a Python program that blocks and resumes in place across evaluator tool exchanges. This decouples model invocation from tool round-trips: on the public test split the agent uses a median of two model calls against seven agent turns per task, resolving a full multi-turn task in a median of 1.8 s of model latency on Cerebras gpt-oss-120b. Because the action surface is executable code, deterministic CAR-bench policies are encoded directly as logic in the tool layer rather than as prompt rules, enforcing compliance at zero reasoning cost. On the official hidden evaluation the harness won Track 2 with 60.0% Pass^3, 4.5x the organizer baseline, at the lowest estimated cost and the fastest median task latency (3.14 s) of any entry scoring above that baseline; the same unchanged harness reproduced an identical 60.0% Pass^3 on GPT-5.5 in the Open track, matching frontier-model agents. A single static prompt, appended with per-task state at the tail, stays byte-identical across calls and across tasks: the frozen submission prompt served 78% of input tokens from cache (86.6% across its warm tail), against 73% over a three-week development corpus in which prompt edits repeatedly reset the cache. This compounds the few-call design into a small fraction of nominal input compute.

In 1948, Erdös and Straus formulated a conjecture : for any positive integer $n>2$, there exist positive integers $n_1,n_2$ and $n_3$ such that \begin{equation}\frac{4}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3},\nonumber\end{equation} which is still open. It is known that the conjecture holds if one can prove it for any prime $n\equiv 1\;(\mbox{mod}\;24)$. If $n=24m+1$ and $n_1\leq n_2,n_3$, then $n_1=6m+k$ with $1\leq k\leq 12m$. A solution $(n_1,n_2,n_3)$ of the above equation is called a tame solution if $n_2$ and $n_3$ are factors of $(6m+k)(24m+1)$. We call $n=24m+1$ wild if it does not have any tame solution. Based on the information in our earlier work on tame solutions posed in arXiv, Howerton found that there are only fourteen wild primes of the form $n=24m+1\leq 2.4\times 10^{11}$. In this paper, we derive thirty-four families of wild solutions of the above equation, which contain the solvability of the fourteen wild primes. Together with our earlier tame polynomial solutions, numeric test shows that they cover all the primes of the form $24m+1$.

It is standard practice to include covariates in regression discontinuity designs (RDDs) and regression kink designs (RKDs), but the theoretical justification for doing so does not generally extend beyond linear estimands. This paper proposes a novel entropy balancing reweighting approach for covariate adjustment within a general framework of RDDs and RKDs. While conventional regression-based covariate adjustment methods generally fail to deliver consistent estimation for nonlinear estimands such as quantile treatment effects, our reweighting approach achieves consistency while improving efficiency. Moreover, even in settings where the regression-based covariate adjustment method already improves efficiency, our approach can deliver additional efficiency gains. Simulation studies corroborate these theoretical findings. We present an empirical application in which our covariate adjustment yields statistically significant results that would not be obtained without covariate adjustment.

Quantum uncertainty emerged from two strikingly different routes to quantum mechanics. Heisenberg's matrix mechanics replaced the classical description of atomic orbits by relations among observable transition quantities and led, in 1927, to the uncertainty relation and its influential measurement-based interpretation. Schrödinger's wave mechanics grew instead from the Bose–Einstein and de Broglie developments and restored a continuous space-time description through matter waves. The two formalisms were soon shown to be closely related, but neither historical route by itself settles the ontological question of whether particles may possess underlying trajectories. After reviewing these developments, including Einstein's criticism of a simple observability doctrine and Mott's wave-mechanical account of straight cloud-chamber tracks, we distinguish precise quantum uncertainty relations from the stronger claim that quantum mechanics excludes definite microscopic histories. We then compare Feynman paths, Bohmian trajectories, Nelson's stochastic mechanics, and finite-speed persistent Goldstein–Kac dynamics. The Kac process has continuous, piecewise differentiable finite-speed paths; its diffusion limit approaches Wiener kinematics, while analytic continuation of its two-sector dynamics is related to Dirac evolution. These examples show that quantum uncertainty relations constrain observable statistics without, by themselves, uniquely determining an underlying path geometry.

In this work, we present the General Interface for MPI-AMRVAC / Legolas Interconnection (or GIMLI, for short) as a toolkit for in-depth (magneto)hydrodynamic studies combining linear and non-linear methods. Acting as a bridge between the linear (M)HD spectroscopy code Legolas and the non-linear simulation code MPI-AMRVAC, GIMLI facilitates the initialization of non-linear MPI-AMRVAC simulations with linear solutions. We showcase this functionality on both Cartesian and cylindrical setups, covering representative plasma physical and astrophysical scenarios: Parker unstable magnetized atmospheres, interchange modes in a straight tokamak setup, resistive Harris sheet evolutions and thermally modified discrete Alfvén waves in coronal loops. We offer suggestions on how to combine linear and non-linear methods, and demonstrate how to leverage GIMLI in the process.

High-bandwidth flash (HBF) is introduced to address the memory wall, which can co-package a dense NAND stack with the GPU, targeting the performance gap between near-accelerator bandwidth and flash density. HBF, however, is neither a large HBM nor a fast NVMe SSD. Its usable bandwidth depends on how GPU cache-line requests map onto NAND pages, how concurrency spreads across channel-affine die sets, and how media management interacts with the GPU memory pipeline. To our knowledge, existing GPU, SSD, or HBF simulators cannot faithfully model this behavior. We present HBF-Sim, an extensible, reusable, and faithful HBF simulator integrated with simulated GPUs. It closes the loop between GPU issue limits, device queuing, and NAND behavior in one end-to-end request path. HBF-Sim separates a GPU-HBF interaction controller from page-based parallel stack storage, and it models the full GPU-HBF request path. It provides an MSHR-based address mapping table that merges cache-line requests into page-based operations, as well as a page-based multi-stack flash manager for highly parallel reads and writes. Validation tests and device-level microbenchmarks expose performance bottlenecks caused by limited channel distribution and resource conflicts, offering concrete guidance for next-generation HBF architectures.