We study fixed-cardinality minimum Riesz $s$-energy subset selection for ordered point sets on the real line. Given $x_1<\cdots<x_n$, an exponent $s>0$, and a cardinality $k$, the task is to choose $1\leq i_1<\cdots<i_k\leq n$ minimizing $E_s(i_1,\ldots,i_k)=\sum_{1\leq p<q\leq k}(x_{i_q}-x_{i_p})^{-s}$. We prove that the one-dimensional Riesz interaction satisfies a Monge inequality. When feasible subsets are encoded as increasing index vectors, this property implies submodularity on a finite distributive lattice and yields polynomial-time solvability by submodular minimization over such lattices. The structural reduction holds for every real $s>0$; We also derive an explicit minimum $S$--$T$ min cut formulation with $k(n-k)$ threshold variables and $O(k^2(n-k)^2)$ finite pairwise edges. The constructed graph has $N=k(n-k)$ nodes and $M=O(k^2(n-k)^2)$ arcs after an $O(k^2(n-k)^2)$ coefficient-construction step; an $O(NM)$ max-flow bound gives an $O(k^3(n-k)^3)$ cut step, while the conservative $O(N^2M)$ bound gives $O(k^4(n-k)^4)$. By an isometry, the same algorithm applies to $\ell_1$-staircases, including monotone two-dimensional Pareto-front and skyline approximations. The report is accompanied by an open-source Python implementation of the proposed exact algorithm and an appendix with examples and detailed explanations of the underlying theory.

We study finite-order meromorphic functions representable as absolutely convergent sums of squares of Cauchy kernels and having only finitely many zeros. By earlier work of Baranov and the author, such functions admit a representation $f=P/g^2$, where $P$ is a polynomial and $g$ is entire, satisfying the differential equation $ Pg''-P'g'+Qg=0, $ where $Q$ is a polynomial. We show that the zeros of $g$ asymptotically accumulate along the Stokes rays. If $\mathrm{deg}\ Q>\mathrm{deg}\ P$, they approach these rays in the Euclidean metric, whereas in the borderline case $\mathrm{deg}\ Q=\mathrm{deg}\ P$ one obtains in general only localization in logarithmic neighborhoods of the Stokes rays, and this is sharp. We then characterize the existence of a decomposition $ P/g^2=\sum c_n (z-t_n)^{-2} $ in terms of the sectorial behavior of $g$ and, equivalently, in terms of the Laine condition for the corresponding Schwarzian equation. Finally, for fixed $P$ and fixed order, we identify the resulting families, modulo the natural equivalence relation, with finite-dimensional affine algebraic varieties.

This paper investigates the creative process of automated design and artistic evaluation using an evolutionary system. We consider how a multimodal artificial intelligence (AI) model can communicate and guide a combined generative and evolutionary computational system. This creates a framework for the evolution of aesthetically pleasing complex 3D organic forms by integrating genetic algorithms with the visual reasoning capabilities of large-scale AI foundation models. The framework shifts the artist role from that of intensive direct selection to one of system design; transferring detailed step-by-step curation to an AI agent capable of multimodal aesthetic judgement. This framework enables the human artist/designer to rapidly traverse large areas of multi-dimensional evolutionary parameter space to find creative outcomes based on their semantic targets. Detailed audit trails of the AI's aesthetic reasoning are generated for each experiment. Interactive visualisation tools, together with AI-generated summaries and evolutionary narratives, enable deep exploration into each evolutionary experiment and providing a transparent insight into the AI-guided process.

We investigate the entropy of a dynamical black hole arising from second-order perturbations of a general stationary background with a bifurcate Killing horizon. Using Gaussian null coordinates, we study the geometry of the apparent horizon perturbatively up to second order. Within the covariant phase space formalism, to explore the contribution of matter fields, we introduce a new modified canonical energy, and establish a balance law relating the second-order variation of the entropy to the energy flux entering the black hole. We show that the entropy is given precisely by the area of the apparent horizon at second order when the null energy condition holds for the infalling matter, and that the variation of the entropy also obeys the second law. We also discuss the possibility that the area law continues to hold when the null energy condition is violated.

Owing to rapid recent progress, ultracold atomic lattice systems for simulating topological phases are now at a pivotal stage, evolving from established paradigms into increasingly versatile and programmable quantum simulators. In this review, we survey recent experimental advances across four major classes of platforms: optical lattices, including optical lattices with laser-assisted tunneling and optical Raman lattices; synthetic lattices in momentum or internal-state space; Floquet-engineered lattices; and optical tweezer arrays, all of which offer distinct capabilities for realizing and probing topological matter. For each class, we highlight representative experimental breakthroughs, the topological models that have been realized, and the advanced detection and characterization techniques employed, emphasizing how these complementary approaches collectively expand the frontier of quantum simulation. We also discuss emerging directions in strongly correlated and nonequilibrium topological phases, and conclude with an outlook on future prospects.

Cryogenic hydrogen isotope fuel layers with high structural integrity and atomic-scale smoothness are prerequisites for symmetric implosion and ignition in inertial confinement fusion (ICF). Using deuterium (D$_2$) as model fuel, we perform large-scale molecular dynamics simulations with a Feynman-Hibbs corrected Silvera-Goldman potential to describe nuclear quantum effects at low temperatures, systematically investigating D$_2$ crystallization inside spherical ablator capsules. By varying substrate lattice constant from 3.1 angstrom to 3.9 angstrom, we demonstrate that lattice matching dictates the transition from coherent epitaxial growth to polycrystalline formation, establishing it as the primary design principle for high-performance targets. When the substrate lattice closely matches the equilibrium hexagonal-close-packed (HCP) spacing of cryogenic D$_2$ (approximately 3.5 angstrom), D$_2$ forms coherent layer-by-layer epitaxial growth consistent with Ostwald's stepwise nucleation theory, yielding HCP-dominated near-single crystals with minimal dislocations and ultra-smooth inner surfaces. In contrast, large lattice mismatch destabilizes coherent growth and causes island-like growth, producing polycrystalline structures with mixed HCP/FCC phases, elevated defects, and greatly increased surface roughness. Radial stress analysis shows that interfacial stress from mismatch localizes within 2-3 molecular layers near the interface, triggering subsequent defect-mediated growth. These findings highlight substrate lattice matching in regulating confined solid growth and crystallization quality, establish it as a key principle for ablator inner-surface engineering in ICF cryogenic targets, and offer atomic guidance for growing high-quality single-crystal deuterium-tritium (DT) fuel layers with optimal smoothness.

Fault-tolerant quantum computing fundamentally relies on the accurate characterization of circuit-level noise to optimize decoding algorithms. However, extracting complex multi-body error correlations remains challenging. Contemporary greedy inference algorithms can suffer from statistical distortion, discarding true physical mechanisms while introducing many unphysical false positives. Here, we introduce the Correlation-Analysis-based Hypergraph Reconstruction (CAHR) algorithm, a globally consistent framework to invert experimental syndrome statistics directly into discrete physical hypergraphs. By coupling exact algebraic correlation equations with a top-down concurrent-pruning strategy, CAHR recovers the fault topology without false positives for both $d=5$ rotated surface codes and dense 8-body 2D color codes in our benchmark settings. Furthermore, we show that exact continuous parameter extraction in dense codes is limited by a \textit{variance cascade}, where absolute statistical variance accumulates linearly from high- to low-degree mechanisms. This motivates a two-stage inference paradigm: utilizing CAHR to extract the fault topology, followed by continuous probability optimization. This provides a practical approach for characterizing and decoding highly correlated noise in realistic quantum hardware.

Fluid and charge flow through interstitial volumes among impermeable randomly placed grains in porous materials ceases to occur at a critical concentration where networks of void volumes are disrupted at macroscopic scales. This critical density for void percolation can be difficult to calculate due to the irregular shape of the void regions. We develop and implement a geometrically exact method, scaling only linearly in the system volume, for identifying the shape and size of contiguous voids. In this manner, we calculate percolation thresholds for both grain cluster percolation (where system spanning networks of overlapping grains begin to appear with increasing density) and void percolation at much higher grain concentrations where networks of interstitial volumes no longer exist on macroscopic scales. For both the former and the latter, we calculate critical concentrations for inclusions in the shape of the Platonic solids (as well as truncated icosahedra) for both aligned and randomly oriented grains. In the case of critical densities for void percolation, the accuracy of our results is significantly improved relative to prior benchmarks. We also incorporate structural disorder of inclusions by considering impermeable grains in the form of cubes subject to a series of randomly placed and oriented fracture planes to mimic aggressively fractured inclusions found in nature. As the number of sustained slices becomes large, we find that the critical porosity for void percolation tends to 5%

Adiabatically eliminating the quantum degrees of freedom in a mixed quantum-classical system produces an effective force in the classical equation of motion. The elimination can be made to any order in the adiabatic parameter, generating a series of higher order forces. By applying a sequence of near-identity unitary transformations to the quantum state, we derive a hierarchy of increasingly accurate effective actions for the classical variables. The third order Euler-Lagrange equation is non-Newtonian as the force depends on the jerk, the third order time derivative of position. We find that the third order terms induce a special kind of Kawaguchi geometry on the space of classical variables. This geometry is characterized by an almost symplectic structure and a differential line element that depends on the acceleration in addition to the velocity. Our results can be used to efficiently capture higher order nonadiabatic effects in molecular dynamics simulations.

We present a quantum-enhanced Markov chain Monte Carlo (QE-MCMC) method to sample turbulent acceleration vectors from a joint target distribution that depends on all three components and height to model the transport and dispersion of massless Lagrangian tracer particles in two turbulent shear flows. A homogeneous shear flow, characterized by a uniform shear rate S, is considered as the starting point. Secondly, a turbulent boundary layer, which forms in both halves of a plane turbulent channel flow at friction Reynolds number Re_tau = 1000, is considered, where the mean shear rate S(y) varies with distance from the wall y. In this hybrid quantum-classical method, the proposal distribution Q for the first of two Metropolis-Hastings sampling substeps is constructed by a parametric quantum circuit. The algorithm generates synthetic tracer particle tracks. The resulting scaling laws for tracer-particle pair dispersion, a central quantity to probe turbulent mixing from a Lagrangian perspective, agree with a stochastic transport model consisting of coupled Langevin equations and with the classical MCMC counterpart. Differently from the classical sampling method, QE-MCMC uses a tempered target distribution. Due to the height dependence of the tracer dynamics in turbulent channel flow, an effective height-weighted spectral gap between the first and second eigenvalue of the Markov-chain transition matrix is introduced. The latter is found to significantly exceed the one of classical MCMC when sampling from a multivariate distribution with cross-correlations at the highest qubit numbers and thus resolutions. Consequently, our results support the applicability of this one-shot algorithm as a generative Lagrangian quantum-computing module, possibly embedded in a complex fluid-flow problem. Our module is found to work reliably for a relatively small number of qubits per spatial dimension of Nq <= 6.

Asthma causes expiratory airflow limitation and is clinically assessed using spirometry, which provides the FEV1/FVC ratio representing the proportion of air exhaled in the first second relative to total forced vital capacity. Prior studies suggest that respiratory sounds recorded at posterior sites (Left Lower, Left Upper, Right Upper, Right Lower) reflect regional airflow patterns. In this study, we investigate the relationship between the expiratory-to-inspiratory (E/I) spectral power ratio and FEV1/FVC in 141 participants aged 20-60 years using Spearman correlation across frequency subbands. The 100-200 Hz and 200-400 Hz bands showed significant correlations. Overall, lower posterior sites showed stronger associations; younger adults showed stronger correlations at the Left Lower site, whereas older adults showed stronger correlations at the Left Upper site. Gender-stratified analysis showed stronger Left Lower correlations in males and stronger Left Upper correlations in females.

A game of information concerns two players transmitting messages that are obscured by noise. A receiver digests the combination of the two information sources and makes an assessment rationally. The aim of the players is to generate opposing assessments for the receiver by choosing signal-to-noise ratios of their information. It is shown that this problem can be reduced into an elementary infinite game on the square, thus admitting a complete equilibrium solution. Three generalisations of the game are proposed.

Coding agents are increasingly used to automate software engineering tasks. To guide their behavior, these agents commonly rely on configuration files, typically named AGENTS.&zwnj;md or CLAUDE.&zwnj;md, which provide instructions about architecture, workflows, coding conventions, and testing practices. Despite their growing importance, little is known about common problems affecting the definition and maintenance of these files. In this paper, we present the first catalog of smells for coding-agent configuration files. To identify such smells, we first conducted a grey literature review and a repository mining analysis. As a result, we identified six configuration smells and proposed automated heuristics to detect them. To evaluate the prevalence of the proposed smells, we analyzed 100 popular open-source repositories containing either an AGENTS.&zwnj;md or a CLAUDE.&zwnj;md file. Our results show that configuration smells are widespread. Lint Leakage was the most common smell, affecting 62% of the files, followed by Context Bloat (42%) and Skill Leakage (35%). We further show that several smells frequently co-occur, particularly Context Bloat, Skill Leakage, and Conflicting Instructions.

TxGraffiti conjectured in 2023 that every nontrivial connected graph $G$ satisfies $μ^*(G) \le H(G)$, where $μ^*(G)$ is the saturation number and $H(G)$ is the harmonic index. The conjecture is false. As first shown by B$\imath$y$\imath$koğlu (2026), the ratio $μ^*(G)/H(G)$ can be made arbitrarily large. That refutation is complemented here in three ways. The friendship graph $F_4$ is a counterexample on nine vertices, and an exhaustive enumeration confirms that nine is the smallest order admitting any counterexample. The conjecture fails even on trees, and hence on triangle-free graphs and on bipartite graphs more generally. The subdivided star $S_k$, a central vertex joined to $k$ paths of length two, is a counterexample for every $k \ge 5$, and a further enumeration confirms that eleven is the smallest order of any triangle-free counterexample. On this family the ratio $μ^*(S_k)/H(S_k)$ exceeds $1$ but stays below $3/2$, and in fact every nontrivial tree $T$ satisfies $μ^*(T) < \frac{3}{2} H(T)$ with the constant best possible, in contrast to the unbounded separation possible without the tree restriction. The conjecture does hold for every graph in which all vertices have the same degree, in which case $H(G) = n/2$.

The classical expected utility (EU) axioms are not sufficient for finite datasets. There are a number of anomalies (violations of EU) where axioms are satisfied. This paper studies axioms that are immune to this problem and definitively delineate between EU and non-EU. We discuss implications for experimental design and explore the automatic generation of anomalies.

In this work, a systematic investigation of the production of high-orbital-excitation kaons in $K^{-}p$ reactions is carried out within an effective Lagrangian approach. The relevant $t$-channel processes are constructed, and the model is calibrated using a single adjustable parameter determined from existing experimental data. With this parameter, the measured production cross sections for the $K_3^*(1780)$, $K_2(1820)$, $K_2(1770)$ and $K_4^*(2045)$ states are successfully reproduced. Employing the same framework, the production cross sections for other high-orbital kaons are predicted. The results indicate that these states possess sizable cross sections and exhibit characteristically forward-peaked angular distributions, which is a typical feature of $t$-channel exchange, highlighting their great potential for observation in future experiments.

Answering statistical queries over sensitive data under differential privacy (DP) is a common task in many settings, including databases, mobile computing, and data markets. In these scenarios, multiple analysts may issue the same query, while receiving answers generated under different privacy budgets due to differences in trust levels or willingness to pay. Existing approaches for such multi-tier DP queries either incur excessive cumulative privacy loss or suffer from suboptimal utility. In this paper, we propose a framework for multi-tier DP query release that simultaneously bound the cumulative privacy loss by the maximum privacy budget among all queries and achieve optimal utility comparable to that of single-tier mechanisms. Our framework applies to different classes of DP mechanisms. For noise-adding mechanisms (e.g., count queries with the two-sided Geometric mechanism in the curator model), we develop a general solution based on the characteristic functions of noise distributions. For other mechanisms (e.g., count queries under the local DP model with the Subset mechanism), we design mechanism-specific primitives for budget transformation and introduce a template-based strategy that attains optimal utility across different privacy regimes. Experimental results demonstrate the effectiveness of our framework.

We present a performance and portability evaluation of three well-established astrophysical production codes, namely iPIC3D, PLUTO, and OpenGadget3, on a Sophgo SG2044 RISC-V processor (part of the Monte Cimone cluster), with comparisons to AMD EPYC 9554 (x86) and NVIDIA GH200 Grace (ARM) systems. These applications represent memory-bound, compute-bound, and hybrid workloads, respectively. Numerical correctness is verified across all platforms, confirming portability. RISC-V shows consistently lower performance, with slowdowns of about $3-6\times$ relative to x86 and $5-9\times$ relative to ARM. The gap is mainly due to limited memory bandwidth, shared cache constraints, narrower 128-bit vector units, and lower clock frequency, but also less-mature auto-vectorization capability of the GNU compiler suite. Memory-bound kernels are the most affected, where early bandwidth saturation and L2 cache contention reduce scalability at higher thread counts. Hybrid MPI+OpenMP configurations reveal a trade-off between memory contention and communication overhead, with intermediate configurations achieving the best performance. These results suggest that RISC-V is capable of supporting scientific workloads; however, additional improvements in both hardware and compiler technology, particularly in auto-vectorization, are required to achieve competitive performance.

Classical general relativity predicts a singularity at the center of every black hole. We argue that this singularity is never reached. Operating purely within the standard framework of quantum mechanics and the Feynman sum over geometries, we demonstrate that the gravitational functional integral loses support at the Planck curvature threshold ($\mathcal{K} \sim \ell_P^{-4}$). This forms a quantum boundary, $\mathcal{B}_Q$, that truncates the spacetime manifold at a finite, positive radius ($r_\mathcal{B} \approx 10^{-22}$\,m for a solar-mass black hole). The suppression is driven by the mathematical Sobolev failure of the Einstein-Hilbert action; at Planck curvature, Heisenberg uncertainty in the ADM conjugate variables dictates that quantum metric fluctuations render the manifold non-differentiable, making the action mathematically undefined. Because the phase amplitude is undefined, the wavefunctional evaluates identically to zero ($Ψ= 0$), formally marking where physical spacetime cannot exist. For realistic rotating black holes, we demonstrate that $\mathcal{B}_Q$ acts as a quantum-geometric cutoff for the mass-inflation instability, capping the internal mass parameter at a finite amplification of $n_{max} \approx 0.67\,(r_g/\ell_P)^{1/5}$ and $r_B^{\rm max\, Kerr} = 1.67 r_g^{2/5} \ell_P^{3/5}$ for a maximally spinning black hole, and dynamically enforcing a universal, sphericalized core. Evaluating the Gibbons-Hawking-York boundary term over this terminal spacelike slice yields a finite, macroscopic interior action per boundary segment, $S_{GHY}^{\mathcal{B}} \approx \frac{3}{2}Mc^2\,Δt$. Operating without injecting novel trans-Planckian degrees of freedom, these results suggest the classical singularity is not a physical event, but the natural terminal boundary of the geometry's domain of definition.

Quadratic Unconstrained Boolean Optimization (QUBO) problems are widespread in both industrial applications and scientific studies. A QUBO problem corresponds to the optimization of a system of Ising spins defined on a generally sparse and heterogeneous graph. When the QUBO problem contains conflicting requests, the corresponding Ising system is frustrated, generating a complex energy landscape, which is hard to explore and optimize. Despite extensive algorithmic and hardware developments, finding low-energy configurations in these systems remains challenging (e.g., local-update heuristics typically become trapped in metastable states), especially when the (possibly frustrated) interactions generate extended correlated domains. We introduce CluMP (Cluster-based Message-Passing), an algorithm that performs collective updates on connected clusters of spins using information from Belief Propagation (BP). By controlling the amount of frustration within clusters, CluMP enables BP convergence on large subgraphs and proposes nonlocal rearrangements involving up to hundreds of spins in a single move. We benchmark CluMP against state-of-the-art local-update heuristics on spin-glass models defined on several graph topologies, including random regular graphs and lattice regular graphs in two and three dimensions. Cluster moves consistently bypass local trapping and reach lower energies with fewer effective operations than single-spin dynamics. These results demonstrate that frustration-tolerant cluster updates can be implemented efficiently on sparse graphs. The CluMP framework provides a scalable strategy for large-scale combinatorial optimization and inference problems, where exploiting medium- and long-range correlations is key to navigating complex energy landscapes.

Strong light-matter coupling between molecules and optical or plasmonic cavity modes has emerged as a promising platform for advancing photonics, materials science, and chemistry. However, optical cavities and plasmonic resonators in particular are inherently lossy systems characterized by finite photon lifetimes. Accurate theoretical descriptions of molecular dynamics under strong coupling therefore require a proper treatment of cavity losses. In this work, we compare three theoretical approaches for modeling dissipative molecule-cavity dynamics within a realistic parameter regime: the Lindblad master equation, the stochastic Schrödinger equation, and the non-Hermitian Schrödinger equation. As an example, we consider the two lowest energy state of Na2 molecule coupled to a cavity mode and analyze the time evolution of the excited-state population and the mean photon number. Our results demonstrate that the stochastic Schrödinger equation provides an accurate and computationally efficient alternative to the Lindblad master equation, while the non-Hermitian Schrödinger approach is found to be applicable only within a limited range of conditions. Furthermore, we show that inclusion of molecular rotation leads to rotational-vibrational-photonic coupling and gives rise to pronounced nonadiabatic dynamics through light-induced conical intersections. These findings highlight the importance of both dissipation and rotational degrees of freedom for a realistic description of molecular dynamics in strongly coupled molecule-cavity systems.

We prove that every natural number is a finite sum of distinct unit fractions whose denominators are semiprimes (products of two distinct primes). This is the $ω=2$ integer case of a problem of Erdős and Graham, stated only as a conjecture by Butler, Erdős and Graham (Integers 15 (2015), A51), who proved the $ω=3$ analogue. Counterintuitively the problem hardens as $ω$ decreases -- the induction's feed thins -- so $ω=2$ is the hard case; our proof adapts the Butler-Erdős-Graham induction to this thin-feed regime, where the entire content of the induction step reduces to an explicit onset inequality $Y_0(N)\le\min\{β(N),β'(N)\}$, proved for all $N\ge10$ by Olson's addition theorem and elementary Chebyshev bounds above a finite, machine-checked base range. The same engine extends to the rationals: for every squarefree $b$, every $a/b$ above an explicit threshold $\min\{B_{N_b}/6,\,1/5\}$ is $ω=2$ representable, unconditionally. As an application we give the first complete proof of the rational $ω=3$ statement -- every $a/b$ with squarefree $b$ is a sum of distinct sphenic unit fractions -- that Butler, Erdős and Graham conjectured but left unpublished; a descent settles every $ω\ge3$. What remains open is the $ω=2$ regime below this threshold, which we reduce to a single explicit conjecture -- that the gap-free floor of a semiprime subset-sum set tends to zero. This work is a human-AI collaboration: AI tools (notably Anthropic's Claude, used through Claude Code) contributed substantially to the Lean formalisation, the experiments, and the writing; correspondingly, every result is machine-checked in Lean 4 / Mathlib (no sorry; two cited classical axioms, plus the native_decide compiler-trust base for the finite computations), so its correctness is independent of the tools used.

We demonstrate that all anti-self-dual Einstein metrics with non--zero cosmological constant $Λ$ locally arise from solutions of a single second order PDE introduced by Lipstein and Nagy. We show how this equation fits into the hyper--heavenly formalism of Plebański, and establish a Lax pair. Finally we show how Plebański's second heavenly equation arises in the limit as $Λ\rightarrow 0$.

We analyze a two-dimensional Bose-Fermi mixture at zero temperature in the presence of a tunable Bose-Fermi attraction. We adopt a diagrammatic T-matrix approach and study the behavior of several thermodynamic quantities for the two species as functions of density, mass ratio, and coupling strength. These include the chemical potentials, the boson momentum distribution function, the condensate density, and Tan's contact parameter. We analytically demonstrate that the present T-matrix formalism recovers the correct second-order perturbative expansion of the chemical potentials in the weak-coupling regime, and test it numerically. The near-universal behavior of the condensate fraction already found in prior work for the mass-balanced case is confirmed for different masses and becomes even more accurate when the boson mass is large. The mass imbalance emerges as an additional control parameter that qualitatively affects the bosonic momentum distribution. In particular, we found that it can be used to allow for the experimental observation of a peculiar peak in the boson momentum distribution at finite momentum.

Large Language Model (LLM) coding agents have achieved strong results on software engineering tasks, yet repository exploration remains a major bottleneck: locating relevant code consumes substantial token budget and pollutes the agent's context with irrelevant snippets. In most agents, the same model explores the repository and solves the task, leaving exploratory reads and searches in the solver's history. We present FastContext, a dedicated exploration subagent that separates repository exploration from solving. Invoked on demand, FastContext issues parallel tool calls and returns concise file paths and line ranges as focused context. FastContext is powered by specialized exploration models spanning 4B--30B parameters. We bootstrap them from strong reference-model trajectories and refine them with task-grounded rewards for broad first-turn search, multi-turn evidence gathering, and precise citation generation. Across SWE-bench Multilingual, SWE-bench Pro, and SWE-QA, integrating FastContext into Mini-SWE-Agent improves end-to-end resolution rates up to 5.5% while reducing coding-agent token consumption up to 60%, with marginal overhead. These results show that repository exploration can be separated from solving and handled effectively by specialized models. Code and data: https://github.com/microsoft/fastcontext

We present updated atmosphere models designed for calculating the post-formation evolution and cooling of giant planets with masses between $0.3$ and $10$ $M_J$. Our tables provide the entropy in the convective region at the base of the atmosphere, temperature ($T$)pressure ($P$) profiles, and emergent spectra for atmospheres calculated using the radiative transfer code \texttt{CoolTLusty} for $T_{\mathrm{eff}}$s over the range 100 to 1400 Kelvin and log$_{10}$($g$) from 2.8 to 4.4 ($cgs$) with the latest opacities and equations of state. Each spectrum and thermal profile is calculated using line-by-line opacity sampling. We construct tables at 3 different metallicities ($Z = 1, 3.16, 10 Z_\odot$) and 2 different helium fractions ($Y=0.15, 0.275$), with the improvement that we adopt a metal-inclusive EOS that treats heavy elements consistently with the opacity metallicity (rather than folding it into an effective $Y$). The result is tables that accommodate both changes in $Y$ due to helium rain and potential variations in $Z$ during envelope evolution. We present a comparison between TP profiles, modeled spectra, and evolutionary tracks, and find that on-the-fly interpolation of boundary conditions in atmospheric composition has a notable impact on the late stages of giant planet evolution, altering the timing of helium rain and therefore the subsequent cooling history and atmospheric helium depletion. We also provide an available toolkit that generates spectra and boundary conditions via efficient interpolation across the 4D parameter space $(T_{\rm eff}, \log_{10} g, Y, Z)$, which is useful for post processing evolutionary tracks to produce fully time-resolved spectral evolutions.

We present James Webb Space Telescope (JWST) results of a morphological study of galaxies in the CAnadian NIRISS Unbiased Cluster (CANUCS) and Technicolor surveys, observed in 19 medium- and broadband NIRCam filters in five CANUCS NIRCam Flanking Fields with rest-frame wavelength coverage between $\sim 0.2 - 3.2μm$. Using GALFIT, we measure the morphological parameters of $\sim$ 4,100 star-forming galaxies at $0.6 < z \leq 4$ with stellar masses of $8.5 < \text{log}(M_*/M_\odot) \leq 11.5$. This enables us to concurrently examine how galaxy size varies as a function of stellar mass, redshift, and rest-frame wavelength to provide a novel parametrization of the galaxy size-wavelength relation. Additionally, we analyze the evolution of the galaxy size-mass relation in the rest-frame optical and NIR with the introduction of wavelength as a free parameter. We report a gradient in the slope of the size-mass relation with respect to rest-frame wavelength with a critical crossover mass at $\sim 10^{9.5} M_\odot$. We propose this characteristic mass as the stellar mass at which galaxies transition between diffuse and compact morphologies. We concurrently present the data release of morphological measurements of the five CANUCS-Technicolor NIRCam Flanking Fields in which we provide structural parameters for $\sim$ 41,000 galaxies in up to 29 JWST+HST filters.

We prove a growth dichotomy for infinite approximate groups, and more generally approximate semigroups, in hyperbolic groups. If \(G\) is a finitely generated hyperbolic group and \(A\subseteq G\) is infinite with \[ A^2\subseteq AX \] for some finite \(X\subseteq G\), then either \(\langle A\rangle\) is virtually cyclic, or \(A\) has positive exponential growth in the ambient word metric. We also introduce a product-growth criterion for the existence of growth rates of approximate semigroups. The criterion applies to hyperbolic groups: if \(G\) is hyperbolic with finite generating set \(S\), then there is a constant \(c_{G,S}>0\) such that \[ |UV| \geq c_{G,S}\,\frac{|U||V|}{n+k+1}, \qquad U\subseteq B_n,\; V\subseteq B_k. \] The linear loss is optimal in order whenever \(G\) contains an element of infinite order. In the free group with its standard generating set one may take \(c_{G,S}=1/4\). We also prove that, in a free group, if \(U\subseteq S_n\) and \(V\subseteq S_k\), then \[ |UV|\geq \left(\frac{2}{3}+\frac{1}{3\cdot 4^{\min\{n,k\}}}\right)|U||V|, \] and this constant is sharp for all \(n,k\).

We study the moduli space of non-Hermitian Yang--Mills connections over a compact Kähler manifold. Using normalized harmonic metrics, we construct a natural Hermitian metric on the unobstructed locus and show that, near the Hermitian locus, the unobstructed locus carries an almost hypercomplex structure which is compatible with the associated Riemannian metric.

We extend the application of the Guillemin--Abreu formalism to holomorphic sectional and bisectional curvature on $\mathbb C^n$, $\mathcal O(-\ell)$, and Hirzebruch manifolds $M_{n,\ell}$, and further apply it to the total spaces of certain higher-rank vector bundles. The resulting formulas recover known positivity criteria and we show that, when the slope is sufficiently close to $1$, the extremal metrics on $M_{n,\ell}$ have positive holomorphic sectional curvature. We construct complete scalar-flat Kähler metrics on $ \operatorname{Tot}\bigl(\mathcal O(-k)\oplus\mathcal O(-k)\to\mathbb{CP}^n\bigr), $ and identify the Ricci-flat case, which occurs precisely when $2k=n+1$.