Papers

Objective. Gamma Knife cone-beam computed tomography (CBCT) images suffer from distinct cone-beam artifacts for some patients, due to the conical X-ray beam which is oriented to intersect the detector perpendicularly at its inferior edge. The use of an exotic scan trajectory which provides more complete sampling across the field of view than the current arc can reduce cone-beam artifacts. In this study, the feasibility of a line-arc-line scan trajectory for the Gamma Knife CBCT is assessed through a proof of concept. Approach. Using a customized research Gamma Knife, a Catphan 503 and an anthropomorphic head phantom are imaged for different exotic scan trajectories, consisting of combinations of arcs and lines. The CBCT images for each trajectory are then reconstructed with an iterative algorithm. Main results. A line-arc-line trajectory provides the largest image quality improvement among the investigated trajectories, with no noticeable cone-beam artifacts in the CBCT images: the axial interfaces between modules of the Catphan are well defined, and the superior edge of the phantom on the axial axis is sharper by 92%, compared with the current arc trajectory. For the head CBCT images, the proposed trajectory removes most of the cone-beam artifact on the superior side of the skull, characteristic of the current Gamma Knife CBCT images. The artifact reduction also leads to a visual improvement in terms of uniformity in both phantoms. Significance. A line-arc-line CBCT scan trajectory would be feasible on the Gamma Knife with limited changes to the current configuration, and could produce images with improved image quality.

Exclusive photoproduction is an important probe of nuclear parton distributions at low Bjorken-$x$. The Good-Walker paradigm relates coherent photoproduction to the average nuclear configuration, giving access to the transverse distribution of gluons in a target, while incoherent photoproduction is sensitive to fluctuations such as gluonic hotspots. Efficiently separating coherent and incoherent interactions is a key challenge for experiments at the future Electron-Ion Collider (EIC). In this article, we study nuclear de-excitation via photon emission, and see how the finite photon detection efficiency leads to misidentification of incoherent emission. We compare the detection efficiency for incoherent $J/\psi$ production using the BeAGLE event generator for Ag-107, Au-197, and Pb-208 targets, for two different forward photon energy thresholds: 50 MeV and 200 MeV. The shell structures of the three species exhibit different incoherent tagging efficiencies due to differences in the lifetimes and energy levels of their excited states. Some of the low-lying states live long enough so that they decay outside the EIC detectors. Especially for the lower photon energy threshold, lead allows a higher tagging efficiency than gold, due to its lack of low-lying and/or long-lived excited states.

Audio language models pass speech and text through a single decoder. We ask whether that decoder represents a distinctive feature in the same direction when a phoneme is heard and when it is read. For minimal pairs of phonemes differing in one feature, we take the offset between the two members' mean representations. Averaging those offsets gives a direction for each stream, and we measure the cosine between the two. Because the two streams already agree about arbitrary phoneme pairs, we compare every measure against a reference built from random pairings rather than against zero. We apply this to 6 models, 7 features and 15 languages from 11 families. Only voicing in the two Qwen2.5-Omni models exceeds that reference after correction for multiple testing, and the reference varies by a factor of seven between models. In three of the six models, voicing has one direction in audio across the 14 languages with enough minimal pairs to measure it, and every language pair agrees in two of them. The model family, not the model size, predicts which stream represents a feature.

Micro-computed tomography (micro-CT) is increasingly applied to imaging scenarios in which object motion, deformation, truncated fields of view, continuous rotation, or unconventional scanning protocols violate assumptions underlying classical reconstruction pipelines. Existing reconstruction frameworks efficiently support standard geometries and workflows but offer limited control over how projection operators are discretized and evaluated. This restricts methodological exploration when accuracy depends on ray sampling, interpolation, or operator coupling. We introduce CTrex, a research-oriented, GPU-accelerated iterative reconstruction framework that exposes the projection-correction-backprojection pipeline down to the kernel level. Rather than treating these operators as fixed black boxes, CTrex represents them as editable computational building blocks within a unified iterative structure. This allows non-ideal acquisition effects to be incorporated directly into the numerical operators rather than treated as external corrections. CTrex combines GPU-level accessibility with an extensible geometry formulation based on homogeneous-coordinate view matrices, allowing rigid and affine transformations, detector misalignments, and time-varying geometries to be expressed consistently. It supports circular, helical, offset, and conveyor-belt trajectories while keeping GPU kernels agnostic to the trajectory definition. Applications in motion- and deformation-aware reconstruction, event-based 4D imaging, cylindrical-coordinate reconstruction, and extended-field-of-view CT illustrate how operator-level adaptations enable strategies difficult to realize in conventional frameworks. CTrex provides a flexible platform for CT reconstruction research under realistic and unconventional imaging conditions.

We develop the thinning–sprinkling technique, a general method for proving robustness of graph properties under random vertex sampling. Using it, we show that random induced subgraphs of tough graphs, high-degree connected vertex-transitive graphs, and nearly regular sublinear expanders retain strong connectivity or expansion properties with very high probability. We also prove that every $k$-connected graph with $k=\omega(\log n)$ contains a spanning bipartite subgraph that is $\Omega(k)$-connected. Using these robustness results, we further develop a general framework for constructing almost Hamilton cycles from randomly sampled highly connected subgraphs. As a consequence, we show that tough graphs, connected vertex-transitive graphs and nearly regular expanders contain a cycle of length at least $(1-o(1))n$ whenever the toughness or degree is polylogarithmically large. This gives asymptotic solutions of longstanding conjectures of Chvátal and Lovász on Hamiltonicity of tough and vertex-transitive graphs.

We report spectroscopic observations during a prominence eruption on 9 October 2025 from the Sun's west limb, associated with an M2.0 flare that commenced at 12:11 UT. The event was captured in sit-and-stare mode by the Visible Emission Line Coronagraph (VELC) onboard Aditya-L1, providing continuous observations of the Fe XIV 5303 Åcoronal greenline. The spatially averaged green-line emission exhibits a clear correspondence with the EUV late-phase (ELP) emission observed in multiple SDO/AIA channels. In particular, an enhanced 5303 Åemission peak at 15:24 UT coincides with secondary peaks in the AIA 211, 171, 193, and 335 Åpassbands, occurring $\sim173$ minutes after the X-ray peak. The 5303 Åline-width information provides important constraints on the mechanism responsible for the ELP. The line-width decreases progressively by about 28% toward the ELP peak, broadly consistent with the cooling of post-flare coronal loops. This behavior suggests that the ELP is predominantly associated with plasma cooling, with relatively weak additional energy input from magnetic reconnection, which does not produce a significant enhancement in line-widths. The estimated non-thermal velocity decreases from $\sim$36 km s$^{-1}$ during the impulsive phase to $\sim$21 km s$^{-1}$ during the gradual phase, indicating a reduction in turbulent plasma motions. And doppler velocities evolve from predominantly positive values during the eruptive rise phase to negative values during the later gradual phase, implying upward and subsequent downward plasma motions. To our knowledge, this study provides the first space-based spectroscopic evidence linking coronal green-line emission with the ELP and its origin during a solar flare.

Dual-mode consensus protocols are fast when the network is partially synchronous and remain live under asynchrony. We introduce Steelhead, a dual-mode mechanism that composes a partially synchronous and an asynchronous commit rule over one DAG: every k-th round is decided by the asynchronous rule, whose leader a common coin reveals after the votes, and all other rounds by the partially synchronous rule. Every interval, validators replay the committed DAG under each candidate period, adopt the one with the fewest expected message delays, and fall back to k = 1 when the output stalls; the asynchronous rule applied to the coin rounds alone keeps the protocol live. Steelhead sends no message beyond the DAG's blocks, not even to agree on the period, and opens a coin only on the rounds that need a hidden leader. It is generic over pairs of DAG commit rules that share a committee; we instantiate it with Mysticeti and Mahi-Mahi at n >= 3f+1 and with the two variants of BlueBottle at n >= 5f+1. We prove it safe and live, and provide mechanized proofs in Lean 4. In simulation, Steelhead matches the partially synchronous protocol in a healthy network, stays close to the asynchronous one when network conditions stall the partially synchronous one, and adapts quickly in both directions.

We study the spin-1/2 nearest-neighbor Heisenberg model on the breathing pyrochlore lattice in the mixed ferro-antiferromagnetic regime, where one tetrahedral sublattice is antiferromagnetic and the other ferromagnetic. The classical ground-state manifold is then that of the nearest-neighbor face-centered-cubic (fcc) antiferromagnet built from composite tetrahedral moments. Classical Monte Carlo simulations and the self-consistent Gaussian approximation show that thermal order-by-disorder lifts its subextensive degeneracy and selects the collinear Type-I state with wave vector $X=(1,0,0)$ through a strongly first-order transition. Pseudofermion functional renormalization group calculations for $S=1/2$ and $S=1$ reveal a nonmagnetic window adjacent to the decoupled antiferromagnetic-tetrahedron limit, beyond which $X$ order reappears. Density matrix renormalization group calculations show that this window is not featureless: the antiferromagnetic tetrahedra develop nearly ideal tetramer correlations, with four bonds carrying $\langle\mathbf{S}_i\cdot\mathbf{S}_j\rangle\simeq-1/2$ and the two opposite bonds $\simeq+1/4$, while the structure factor retains broad maxima at $X$. A third-order effective Hamiltonian in the tetrahedral-singlet manifold explains this: reversing the sign of the inter-tetrahedron coupling converts Tsunetsugu's dimer selection into a uniform tetramer selection, as confirmed by exact diagonalization. A dynamic high-temperature expansion traces how local tetrahedral excitations give way to low-energy $X$-centered spectral weight. Finally, we place density-functional parameters for eight structures of spin-3/2 breathing chromium thiospinels in the classical phase diagram. The mapping reproduces the $\mathbf{k}=(1,0,0)$ order of CuInCr$_4$S$_8$, accounts for the absence of order in LiGaCr$_4$S$_8$, and predicts Type-I order for LiInCr$_4$S$_8$.

This paper introduces a novel semiparametric testing framework for localized point-impact effects within a spatial semi-functional linear regression model. We address an intricate inferential problem that simultaneously accommodates three distinct sources of complexity: an infinite-dimensional global functional slope, an unknown smooth spatial nuisance surface, and data-dependent, unobserved impact locations. To isolate the point-impact coefficients, we construct a robust residualized cross-moment estimator after regularizing the functional component via Tikhonov inverse and estimating the spatial nuisance surface through local-linear smoothing. We establish a multivariate central limit theorem under the null hypothesis of no point-impact effect. We develop two operational test statistics: a general formulation whitened by the long-run covariance matrix to handle arbitrary spatial dependence, and a simpler chi-square calibration valid under short-range spatial dependencies in regression errors. Rigorous finite-sample simulations and an application to Canadian weather data demonstrate the superior power and size control of our methodology.

Automatic speech recognition is typically trained assuming that the reference transcript is the only valid labeling of an utterance, yet even nominally verbatim transcripts contain localized differences in pronunciation, spelling, or lexical realization that the acoustics do not uniquely determine. Omni-temporal Classification (OTC) tolerates such noise by adding wildcard paths to the connectionist temporal classification (CTC) alignment graph, but its word-level arcs are too coarse, since bypassing one unsupported token discards supervision for the whole word. We move wildcard arcs to token granularity so unsupported tokens can be bypassed while the rest of the word stays supervised, and we combine token- and word-level arcs as complementary escape paths. Across 19 languages and three corpora, token-level OTC improves over CTC on all 25 tasks. We also replace epoch-indexed relaxation of the wildcard weights with a predictive-entropy-indexed schedule, which performs comparably while reducing dependence on training length. Combining this schedule with the hybrid graph gives the lowest mean word error rate (WER) on every corpus and a 9.45% average relative WER reduction over CTC. Independent validator transcriptions show that token-level models place significantly more wildcard-bypass probability than CTC on disputed characters, indicating that token-level tolerance targets localized transcript ambiguity.

Non-Abelian quantum codes connect quantum error correction, phases of matter, and computational resources. In this work, we develop a general framework for constructing non-Abelian quantum low-density parity-check (qLDPC) codes by gauging sheaf codes via cup products and use it to establish code families with constant encoding rate and linear distance, simultaneously achieving optimal asymptotic scaling in both parameters. In particular, we characterize explicit logical representatives of the full gauged code space, and provide a fundamental treatment of non-Abelian code distance in the sense of Knill–Laflamme based on combining expansion with cleaning to establish protection against arbitrary errors. We further construct an almost-good family with entire code spaces exhibiting long-range magic. Moreover, we use linearly addressable cup product to directly generate linearly many encoded magic states from gauging measurements of Clifford operators. These results extend good qLDPC codes beyond the Pauli stabilizer setting, lay the foundation for pursuing the no low-energy trivial magic conjecture and shed light on non-Abelian quantum phases and orders beyond geometric locality.

This note record a finitely generated extension of Caprace's example of a non-inner-amenable group is also not properly proximal, which answers the original question by Boutonnet, Ioana and Peterson. The extension is an explicit ICC subgroup of $\operatorname{GL}_4(\mathbb{F}_2(t))$, which has no property (T). Failure of proper proximality follows from the work of Ishan-Peterson-Ruth and the passage of proper proximality to co-amenable subgroups. Non-inner-amenability follows from a property-(T) subgroup and an elementary centralizer computation.

Future quantum networks will make use of entanglement to perform numerous tasks, such as sending quantum information over long distances, distributed quantum computing, and quantum sensing. In general, these tasks will need to be performed simultaneously in various regions of a network, while minimizing resources and latency. We will thus require policies for scheduling link-level entanglement resources, and using the link-level entanglement to create various forms of multipartite entanglement required for every task. In this work, we address this problem using reinforcement learning. We formulate a Markov Decision Process for the problem and use double deep Q-networks (DQN) with Message Passing Neural Networks (MPNNs), experience replay buffers, and curriculum training to obtain policies. The key physical parameter is the probability of link-level entanglement generation, i.e., the link activation probability. We show that our policies maintain 100% success for up to 71% lower link activation probability than the baseline heuristics for a set of physically relevant network topologies. We then examine an additional constraint where experiment (task) placements are restricted to specific hardware types and demonstrate a similar advantage in performance over heuristics, with our policy maintaining at least an 80% success rate for up to a 59% lower link activation probability. Finally, we explore methods to interpret the learned policy by defining metrics enabling conclusions to be drawn about the model's behavior and by tasking a large language model (LLM) to derive a novel heuristic given example actions taken by the DQN-trained policy. We find that the LLM heuristic performs similarly to the DQN-trained policy in performance, indicating a promising method for interpretable policy extraction for large quantum networks, where direct training becomes computationally expensive.

Let $(M, g)$ be an $n$ $(\ge 3)$ dimensional, non-collapsed compact Riemannian manifold and $\operatorname{Ric}^-$ be the negative part of the Ricci curvature and $\beta \in (\frac{2n}{n+2}, 2)$. We prove a relative volume comparison theorem when $|\operatorname{Ric}^-|^\beta$ is in the Kato class (cf. Definition 1.1), which results from a new integral Laplace comparison theorem in the spirit of \cite{PW} for a suitable conformal metric. This partly addresses an expectation in \cite{TZZZZ}, where the same result was proven when $|\operatorname{Ric}^-|^2$ is in the class.

Sustained ICRF operation in a fusion power plant may require low edge densities to mitigate plasma-wall interactions, a regime which was recently achieved in WEST with very little impurity sputtering. Cold plasma theory, however, predicts singular radiofrequency electric fields in this regime, both at the lower hybrid resonance and along the resonance cones, raising the question of whether standard collisional cold plasma models suffice to describe low-density edge ICRF at all. Collisions in principle remove these singularities, replacing them with finite but sharply peaked fields. We derive these peak length scales analytically and confirm them with a 2D finite-element simulation using exponential mesh refinement, achieving micrometer resolution where needed. We conclude that edge collisions in cold plasma do not remove the need to resolve length scales ordinarily associated with hot-plasma and Bernstein-wave physics.

The stability of an ecological community is conventionally defined through species interactions, which quantify how species affect one another. Interaction strengths are notoriously difficult to measure in species-rich assemblages. Long-term monitoring of species-rich communities, however, provides species abundance time series, increasingly available across habitats and taxa but not yet connected to the stability properties of the communities they describe. Here we develop a statistical framework that infers stability regimes in large ecological communities directly from abundance time series. We study stochastic Generalized Lotka–Volterra dynamics with random interactions and environmental fluctuations using dynamical mean-field theory, reducing the multispecies system to an effective stochastic process for a representative species. The theory predicts three stability regimes (stable coexistence, intermittent dynamics close to extinction, and unbounded growth) separated by analytical boundaries, and shows that environmental stochasticity systematically destabilizes coexistence by promoting intermittent low-abundance dynamics. The resulting steady-state species abundance distribution is a Gamma law that ties the dynamical phases to the variability-based stability metrics used in empirical studies. Recasting the effective dynamics as a multivariate regression model, we infer interaction statistics, environmental variability and the characteristic timescale of the dynamics from community data, without reconstructing the interaction network. Applied to natural communities spanning a broad range of habitats and taxa, the method resolves contrasting stability regimes and yields quantitative estimates of species extinction risk.

Let $(X_i,d_i,\mathfrak m_i)$ be compact $\mathrm{RCD}(K,N)$ spaces converging to a space $X$ of rectifiable dimension $m$. Their first Betti numbers can drop by at most $N-m$. When equality holds, the maximal abelian covers have a non-collapsed limit $Y$ carrying a free isometric $\mathbb{R}^{N-m}$-action. We turn this limiting symmetry into fibrations of the approximating spaces. More precisely, after passing to a subsequence, there is an open full-measure set $G\subset X$, containing every regular point, on which $X$ is a topological orbifold and the $X_i$ admit local Seifert fibrations with $(N-m)$-torus fibres. Each finite local group acts on the fibre by translations. If the $X_i$ have no boundary, then $X\setminus G$ has Hausdorff codimension at least two. If $Y$ has no bubbling and $X$ is a smooth closed Riemannian orbifold, the local fibrations may be chosen as restrictions of a single global Seifert fibration. An affine replacement on the smooth manifold cover shows, in addition, that a finite cover of $X_i$ is homeomorphic to a product with $\mathbb{T}^{N-m}$; here we use the classification of affine torus bundles at the Betti number equality of Peng, Wang and Wang. When the base is a closed Riemannian manifold, the maps are torus bundles, confirming a conjecture of Zamora and Zhu for possibly singular RCD total spaces. The new ingredients are a pointwise linearization of the collapsing action at regular orbits, an invariant harmonic transverse coordinate compatible with finite isotropy, and an exactly equivariant orbit coordinate built from an elementary rounding-and-doubling argument in the collapsing deck group.

A paired dominating set of a graph $G$ is a dominating set $D$ such that $G[D]$ has a perfect matching. The minimum size of such a set is the paired domination number $\gpr(G)$. Desormeaux and Henning conjectured that every cubic bipartite graph $G$ of order $n$ satisfies $\gpr(G)\le n/2$. We prove the conjecture in the sharp integer form $\gpr(G)\le 2\lfloor |V(G)|/4\rfloor$ for every finite simple cubic bipartite graph $G$. The proof combines a directed contraction along a perfect matching, switching arguments based on dominator trees, a four-symbol boundary calculus for two-edge cuts, and the Gallai–Edmonds decomposition. Equality is attained by $K_{3,3}$ when $|V(G)|\equiv2\pmod4$ and by the cube $Q_3$ when $|V(G)|\equiv0\pmod4$.

Asked to choose between candidates and explain the choice, a language model often rejects a rival by naming a fact its profile lacks: no director, no date of death. That sentence is a claim about the text in front of the model, and it can be tested without any judge. We insert a real corpus sentence stating the named fact into the rival's profile and ask again under greedy decoding. Two controls separate content from placement: a length-matched irrelevant sentence at the same profile, and the same two sentences at a third option the model never mentioned. In the largest of three runs, six open models on 2WikiMultihopQA, supplying the named fact at the profile the model named moves its choice more than the irrelevant control does, odds ratio 3.57 [1.54, 8.26], Holm p=0.0210, and this survives dropping any single model. The contrast the design was built to detect, the same fact at the option nobody named, does not clear correction, Holm p=0.2428. The strongest result in the family carries no content claim at all: the identical irrelevant sentence moves the choice more at the named rival than at the third option, Holm p=0.0008. Repair and control also differ in co-candidate mentions, relation template and fluency; post-hoc matching on the first two preserves the content effects' direction, matching fluency weakens one, so the content contrasts bound an effect rather than establish one. A forced single-token probability read disagrees in direction with the free-text choice on that same contrast, and three candidate explanations for the disagreement find no support. Every measurement is a string rule, so each was validated against the records it reads; validation caught eight defects. The largest, a choice-parsing rule that returned the option a model had just rejected in 17.1% of adjudicable responses, would have reported six surviving contrasts instead of four.

Modern infrastructure asset management constitutes a complex sequential decision-making problem, characterized by long planning horizons and system-level interactions, such as spatial deterioration correlations and economies of scale. While deep reinforcement learning has shown promise in optimizing maintenance policies, scaling to real-world networks remains challenging. Centralized approaches become computationally intractable in large-scale systems, whereas decentralized approaches often fail to capture essential coordination mechanisms. To address these challenges, we propose a graph-based framework that integrates accurate environment modeling with scalable decision support. First, we employ a hierarchical Bayesian model leveraging a Gaussian Process on Graph kernel to infer a realistic, spatially correlated networked environment of railway maintenance planning from real-world data provided by the Swiss Federal Railways. Second, we introduce a topology-aware Multi-Agent Reinforcement Learning (MARL) framework by integrating graph neural networks and graph Transformers to optimize network-level policies. A central contribution of this work is the demonstration of scalability through zero-shot transfer learning: graph-based agents, trained only on small network portions, are successfully deployed in a zero-shot manner on large-scale unseen networks without any retraining. Numerical results indicate that the proposed method significantly outperforms optimized heuristics and standard MARL baselines, reducing computational training time while maintaining superior performance on large-scale networks.

We determine the exact universal high-temperature separability threshold for Pauli Hamiltonians of bounded degree $\Delta\ge2$. If every coefficient in the Hamiltonian has magnitude at most one and each term has overlapping support with at most $\Delta$ other terms, the Gibbs state is a mixture of product Pauli eigenstates whenever \[ \beta \le z_\Delta := \operatorname{arctanh}\left[\max_{0\le x \le 1}x\left(\frac{1-x}{1+x}\right)^{\Delta-1} \right]. \] For every $\beta>z_\Delta$, a finite commuting Hamiltonian with maximum overlap degree at most $\Delta$ has an entangled Gibbs state. At any fixed $\beta<z_\Delta$ strictly below the threshold, a classical polynomial-time algorithm produces samples from a distribution over product Pauli eigenstates approximating the Gibbs state in trace distance.

We establish proper agnostic learning of matrix product states and tree tensor networks. Given copies of an arbitrary quantum state $\rho$, our algorithms return a state $|\psi\rangle$ of chosen bond dimension such that $\langle\psi| \rho |\psi\rangle$ is within $\varepsilon$ of the optimum over the model class, without assuming that $\rho$ itself belongs to or is well approximated by that class. The main idea is to use improper learning to compress the mixed-state objective, reducing proper agnostic learning to optimization against a finite collection of explicitly specified pure states. We then introduce a comparator-dual compression procedure that reduces the bond dimension of these targets while uniformly preserving their overlaps with all bounded-bond comparators, with an error independent of system size. For matrix product states, this gives polynomial copy complexity in the system size, local dimension, bond dimension, and $1/\varepsilon$, together with polynomial runtime in the system size for fixed local dimension, bond dimension, and accuracy. The same framework yields proper agnostic learning of tree tensor networks on bounded-degree trees, with both copy complexity and runtime polynomial in the system size when the remaining parameters are fixed.

Large Language Models (LLMs) typically exhibit a performance profile where reliability degrades as task complexity increases. We address the challenge of generating high-quality natural language executable plans for complex tasks by introducing $\textbf{GRASP}$, a strategy-aware, multi-stage planning framework. GRASP decouples the planning pipeline across specialized, context-isolated modules: it pre-compiles global macro-guidelines (GenPlan), explores alternative localized strategies within isolated context windows (RevPlan), and independently evaluates trajectories using a multi-criteria discriminator (VerPlan). Empirical evaluations show that GRASP consistently establishes a new state-of-the-art frontier across diverse datasets, yielding substantial accuracy gains over direct LLM planners on Natural Plan Calendar Scheduling ($\sim$12.4$\%$$\uparrow$), ZebraLogic ($\sim$30.8$\%$$\uparrow$), and SciBench Math. Crucially, under multi-task scaling-where standard planners suffer immediate performance collapse-GRASP completely flattens the multi-task degradation penalty. In interleaved dual-task environments, GRASP achieves an absolute accuracy gain of up to 16.7$\%$ over direct LLM planners. Furthermore, by isolating context and enforcing strict macro-regularization, GRASP outperforms frontier reasoning models (such as GPT-5-mini) by a margin of 14.5$\%$.

For a compact connected Hamiltonian $T$-space (with $T$ a torus), the components of the set of (relative) regular values of the momentum map are open convex polytopes, whose closures (called the chambers) form a polyhedral decomposition of the momentum polytope. In a previous paper we showed that there is a canonical affine stratification of the momentum polytope with the property that, while varying through a stratum, the fibers of the momentum map do not change as $T$-spaces. In this paper we show that the strata of this stratification are the relative interiors of the faces of the chambers. In doing so, we also give a proof of the fact that these faces form a polyhedral complex, which (it seems) was missing from the literature. We further extend the above to Hamiltonian $T$-spaces whose momentum map is proper as map into a convex set and, in the compact Kähler case, we point out a description of the above strata in terms of the $T_\mathbb{C}$-orbit closure polytopes.

JWST has increased both the number of high-redshift galaxies with high-quality spectral energy distributions (SEDs) and their information content. In parallel, wide-area surveys from Euclid, Rubin's LSST, and Roman will increase galaxy samples by orders of magnitude. Analysing these datasets requires stellar-population models that are both flexible and computationally efficient. We present CERIDWEN, a GPU-native SED fitting framework written in JAX, with an end-to-end differentiable forward model spanning stellar populations, nebular emission, dust attenuation and emission, and projection into the observer frame. Its vectorised, compiled architecture lets nested sampling replace a batch of live points in parallel on the GPU, which makes flexible stellar-population models tractable under full Bayesian inference. Automatic differentiation also provides exact gradients for the gradient-based samplers in the package. We jointly infer time-dependent chemical-enrichment histories instead of a single stellar metallicity, and demonstrate non-parametric star-formation histories (SFHs) with $\sim$120 age bins. Using $\alpha$-enhanced stellar libraries from FSPS, CERIDWEN can sample stellar [$\alpha$/Fe] jointly with [Fe/H], mass, and SFH, so that the joint posterior represents the [Fe/H]-[$\alpha$/Fe] degeneracy explicitly. In controlled mocks, CERIDWEN recovers parameters with well-calibrated posterior uncertainties, while fits to real JWST observations reproduce posteriors from the established Prospector framework: on a single GPU, CERIDWEN completes a fit in a median sampling time of $\sim$4 min, $\sim$134$\times$ faster per fit than equivalent CPU-based Prospector runs. CERIDWEN therefore makes full Bayesian inference practical for larger galaxy samples and more flexible stellar-population models, reducing computational constraints on the physical complexity explored in SED fitting.

Most benchmarks hand the model a question. EnigmaForge hands it a stack of old documents and no question at all. Buried in the letters, receipts, and logbook margins is a small logic puzzle whose solution is unique - proved by a SAT solver at generation time, with an ablation certificate showing every clue is load-bearing. Because instances are generated rather than collected, the corpus renews forever. The headline measure is intuition: task success when handed only the story, with world reconstruction as the secondary axis. Twenty-five frontier models ran over 600 instances (17,400 scored records) under three matched conditions. Intuition reshuffles the leaderboard: a 22x spread where fact recovery spans 1.6x, the second-best fact-recoverer ranks fourteenth, one model is indifferent to being told the question, and another is significantly better without it. Several models were blocked by their own content filters before reaching the puzzle - any benchmark scoring refusals as failure is quietly measuring filter behavior.

Excitations of the neutron star (NS) fundamental mode (f-mode) during a binary NS inspiral or from a glitching pulsar can produce gravitational waves (GWs) that will be detectable with the next generation of detectors, opening the door to GW asteroseismology of neutron stars. There exist approximately equation-of-state (EOS)-insensitive, or "universal," relations that relate the f-mode to other NS properties. These universal relations have typically been identified with relatively small, selective EOS samples. To more thoroughly explore the parameter space, we examine the f-modes for a large sample of piecewise-parametric EOSs by solving the linearized fluid perturbation equations for the f-mode frequency and damping time in full general relativity. We utilize our sample to evaluate the EOS-sensitivity of previously-proposed universal relations (URs) for both the f-mode frequency and damping time. We find that URs that depend on combinations of only NS mass and radius have significant residuals, as previously reported; but that these residuals are strongly correlated with the overall stiffness of the EOS. We account for this residual dependence on the EOS by introducing linear correction terms that depend on the characteristic radius predicted by the EOS and the slope of the mass-radius curve at intermediate masses. To assess the impact of our new correction terms on observables, we consider the case of GW emission due to a glitch in a Vela-like pulsar and demonstrate that the predicted signal-to-noise ratio for such an event is over/under-estimated by up to ~10% when using an existing, single-parameter UR, but is recovered nearly exactly with our improved 3-parameter UR. In contrast, we find that URs between the f-mode and tidal deformability exhibit only minimal EOS-dependent correlations in their residuals and overall remain highly EOS-insensitive.

The topological order of the Kitaev toric code is insensitive to disorder in its couplings since all star and plaquette operators commute; consequently, the stabilizer ground-state manifold is independent of the individual coupling strengths, and the phase remains stable against weak local perturbations. This insensitivity, however, is a property of the eigenstates and not of the dynamics they generate, and we show that the disorder sensitivity of a probe prepared outside that eigenbasis can be a metrological resource. In particular, we investigate the estimation of the strength of three topological-order-breaking perturbations, the nonlinear Castelnovo-Chamon deformation, nearest-neighbor Ising interactions, and a magnetic field along horizontal edges, encoded on an initially separable probe through unitary evolution under the disordered toric code Hamiltonian. We demonstrate that the quenched average quantum Fisher information (QFI), a figure of merit for metrological precision, exceeds that of its ordered counterpart in suitable regimes of perturbation strength and encoding time. For the ordered case, we further identify optimal product probes, for which the quadratic and cubic terms of the short-time expansion vanish identically, leaving a transient quartic scaling of QFI. Interestingly, this window persists as long as the multipartite entanglement generated by the encoding continues to increase, and it survives under local dephasing, bit-flip, and amplitude damping noise acting independently on each site, with the non-unital channel being the least detrimental.

Circuit cutting enables quantum computations to be decomposed into smaller subcircuits at the cost of additional sampling overhead. Gate-cutting provides one such approach by replacing nonlocal gates with quasiprobability decompositions of local operations. Starting from the known optimal two-qubit gate-cutting formula, we derive complete sharp lower and upper envelopes relating the quasiprobability extent $\gamma$ to five established descriptors: entangling power, gate typicality, operator entanglement, Schmidt strength, and maximum product-input concurrence. We recast $\gamma$ as a Rényi-$1/2$ functional of the operator-Schmidt spectrum and show how the physical constraints on two-qubit spectra sharpen generic entropy bounds and select a small set of recurring extremal Cartan families. None of the five descriptors generically determines $\gamma$ alone, but each imposes exact constraints, revealing how substantially the optimal gate-cutting cost can vary between gates with similar nonlocal characteristics.

In this paper, we study the joint selection of an environmental support contact and a whole-body configuration for a prescribed loco-manipulation task. A contact may provide greater physical support while restricting the motion required for the task. We formulate this problem through three capability measures: residual wrench, end-effector reach, and base mobility available after satisfying the task requirements, and we balance them against contact acquisition cost. Evaluating these capabilities for every candidate requires repeated whole-body optimizations. To reduce this computational cost, we propose Capability-Tradeoff Contact Selection (CTCS). CTCS screens candidates for contact and task feasibility, groups similar candidates within each surface, and predicts their capabilities from exact anchor evaluations using local sensitivity analysis. It checks these predictions through selective exact evaluations, ranks candidates by capability, and evaluates a shortlist exactly for final selection. We evaluate CTCS in simulations and hardware experiments using a Unitree Go2 quadruped with an AgileX NERO arm across $392$ task conditions with nine available support surfaces. Results show that CTCS outperforms ground-only and fixed-contact support, as it can select support surfaces that provide favorable capability trade-offs for the task. Compared with evaluating every candidate exactly, CTCS achieves approximately $3\times$ speedup while closely matching the resulting mean objective value.