Papers

Diffusion Transformers (DiTs) can generate high-quality images and videos, but generating each sample requires multiple costly DiT forward passes. Two common ways to accelerate DiT sampling are step distillation, which reduces the number of sampling steps, and caching, which skips some DiT evaluations by reusing a tensor computed at an earlier step. Most caching methods decide in advance which tensor to reuse. After distillation, adjacent sampling steps are farther apart. Reusing a tensor across this larger gap introduces more error, so choosing what to cache becomes especially important. We therefore introduce AutoTarget, a method that chooses the cached tensor for a given model, solver, and reuse schedule. AutoTarget uses a small set of runs without cache reuse to measure the error caused by reusing each candidate tensor, then selects the candidate with the lowest error. We also analyze how an error at one reuse step affects the final sample. For Euler sampling, we identify cache targets that produce the same trajectory and show why a stored solver update may not. Experiments on distilled image and video DiTs show that the best cache target changes with the model, image resolution, and solver. AutoTarget reduces DiT evaluations and retained cache storage. Generation quality remains close to the corresponding uncached run. On the tested PixArt-LCM and FLUX.1-schnell settings, its calibration ranking matches the ranking from held-out cached runs. To help others reproduce the method, we provide its core implementation on GitHub at https://github.com/wali1024-offical/AutoTarget.

We derive sharp lower bounds on the energy cost of Page-like entanglement entropy excursions in two-dimensional conformal field theory. For states satisfying the primary quantum null energy condition (QNEC), the positive null energy $E_+$ obeys a sharp lower bound with two branches separated by the threshold $\Delta S=(c/6)\ln 2$. We also derive a sharp lower bound on the net energy $E_{\rm net}$, with a coefficient larger by a factor of two than the value quoted by Abdolrahimi and Page [Phys. Rev. D 92, 083005 (2015)] and, in the QNEC-saturating sector, we obtain a sharp lower bound on the negative energy $E_-$. The constants are sharp as infima over smooth conformal vacua. We determine the entropy profiles that minimize $E_+$ for general QNEC states and the one that minimizes $E_-$ in the saturating sector. Finally, for an excursion containing an infinite sequence of small sub-excursions within a finite duration, we derive a necessary condition for the total positive energy to remain finite, which is stronger than requiring the entropy to have finite total variation.

We study a physics-informed neural network (PINN) approximation of a coupled PDE system that models the interaction between fluid and elastic dynamics. The canonical heat-wave model considered here couples a parabolic and a hyperbolic equation through transmission conditions on a fixed boundary interface, and serves as a prototype for the Stokes-elastic systems that arises in real world applications. This coupling makes the error analysis more delicate than that for a single PDE. We bound the error between the exact and PINN solutions by the associated PINN residuals, and we moreover prove that the generalization error is controlled by the training error, the number of quadrature points, and the size of the network. {To the best of our knowledge}, these are the first error estimates for a PINN approximation of a coupled fluid-structure interaction PDE system. We also show that numerical experiments with respect to a given test problem.

We introduce HyperBrowseComp, a multilingual and multimodal browsing benchmark comprising 423 manually authored and human-validated questions across 13 languages, written by native or highly proficient speakers. Questions are designed to be extremely challenging. Each question targets a concise, publicly verifiable answer whose discovery requires locating obscure evidence, following multi-step clue chains, or inspecting heterogeneous sources such as videos, scanned documents, images, or maps. Easier questions are filtered out by evaluating them with models without internet access to reduce the likelihood that they can be answered with parametric knowledge alone. We evaluate several models using provider-native search and a shared external retrieval harness under a common agent protocol. To contextualize model performance and effort, we also conduct a human evaluation on a sample of the questions. HyperBrowseComp provides a challenging testbed for persistent information seeking across languages and evidence modalities, with difficulty arising from discovering and connecting evidence on the open web.

Non-recurrent epidemics on complex networks, such as the paradigmatic susceptible-infected-recovered (SIR) model, are often studied by mapping the model to bond percolation. However, the conditions under which this identification is justified have not been fully understood, except in specific cases. Here, we systematically determine when this mapping can be applied, starting from minimal assumptions on the epidemic model and the underlying network. Specifically, we discuss the conditions for three different forms of equivalence between a general non-recurrent epidemic model and Bernoulli bond percolation: isomorphism, equality of marginal infection probabilities, and equality of expected epidemic size. We numerically demonstrate the validity of our findings and examine how epidemiological outcomes are affected when these equivalences are not upheld. Our results establish the methodological basis and limitations of a common tool for analyzing epidemic processes on networks.

Green Pea galaxies (GPs) are a class of rare, extreme star-forming galaxies whose physical properties closely resemble high-redshift Ly-{\alpha} emitting galaxies. Their high equivalent width [O III] emission lines make them readily identifiable in surveys of emission-line galaxies like the on-going deep, narrowband Star Formation Across Cosmic Times (SFACT) survey. In this study, we use broadband gri colors and [O III] equivalent widths derived from narrowband images to select a new sample of ~120 GP candidates from a catalog of [O III]-detected galaxies identified in the SFACT survey. All SFACT GP candidates have spectroscopically confirmed redshift in the range z = 0.31-0.51. The median apparent magnitude of our sample is g = 22.9. We compare the properties of our GP candidate sample to other samples of known GPs. We find that the excellent depth of SFACT allows us to detect GP candidates to lower luminosities than these comparison samples. This is the first catalog of SFACT GP candidates; additional candidates will be added as the spectroscopic follow-up of the SFACT survey is completed.

The increasing diversity of parallel hardware challenges existing compilation flows. While OpenMP provides a portable abstraction for shared-memory parallelism, existing compilers tightly couple the frontend semantics with fixed lowering strategies. This design limits performance portability across different runtimes and architectures. In this paper, we present a modular approach to parallel code generation based on the Multi-Level Intermediate Representation (MLIR) framework. Our approach combines an OpenMP frontend with a domain-specific language (DSL) that specifies how OpenMP constructs are lowered for a target. We call this approach OpenMP meta-lowering, treating lowering as a programmable component rather than compiler-specific logic. This design provides explicit control over code outlining, data sharing, and runtime interfacing across diverse targets. We evaluate our approach on PolyBench/C-OMP across general-purpose and embedded multicore targets. Our results show that the proposed method matches the performance of state-of-the-art compiler toolchains with negligible code-size overhead (< 0.7%). Preserving OpenMP constructs until late lowering stages enables both general-purpose and OpenMP-specific MLIR optimizations. By decoupling lowering from compiler internals, our approach expresses the same OpenMP subset in 5,182 lines of code, ~32% fewer than the corresponding lowering code in Clang and ~76% fewer than in GCC, while supporting the pmsis runtime costs only a few specification lines, enabling rapid support for new runtimes without modifying the compiler.

Contactless heart-rate sensing with millimeter-wave (mmWave) radar requires assessing whether individual measurements support reliable estimation. We study learning to assess heartbeat observability, defined as the readability of the heartbeat component in an acquired phase spectrum, for selective heart-rate estimation. Coherent superposition of scatterer returns can suppress this component even under similar macroscopic observation geometry, motivating assessment directly from acquired measurements. To obtain training supervision across different observability conditions, we develop a controllable multi-scatterer frequency-modulated continuous-wave (FMCW) simulator. Agreement between the dominant heartbeat-band peak and the known heart rate provides an automatic observability label for each simulated measurement. We propose HEAR (Heartbeat Estimation with Assessed Reliability), a compact dual-task Transformer that jointly predicts an observability score and heart rate. Its input combines spectral magnitudes with frequencies relative to the respiration fundamental, providing context for respiratory harmonics. Trained solely on simulated observations, HEAR transfers zero-shot to two public real-world datasets collected at 60 and 120 GHz from 134 subjects. The same learned score supports selective prediction with both HEAR's own heart-rate head and multiple existing estimators. On the 120 GHz dataset, score-based selection reduces the HR head's mean absolute error from 17.9 BPM at full coverage to 1.6 BPM at 50% coverage. The complete pipeline achieves an end-to-end processing latency of 50.8 ms on an edge device. Project page: https://yuxuanhu9.github.io/HEAR/.

Many-body perturbation theory is a powerful framework to calculate spectroscopic quantities, as well as the total energy. However, the field suffers from the fact that different flavors of approximations lead to a wide range of results. We present several in principle exact expansions and discuss how to use them consistently. We concentrate on the first two orders in the respective screened Coulomb interaction. Of special interest is a consistent expansion around the Kohn-Sham system. We illustrate the performance of the various choices using the symmetric Hubbard dimer over a wide range of correlation strength. In particular, the expansion based on exact Kohn-Sham ingredients stands out as a promising route towards good energies and good spectra.

A Hardy space approach to the Nyman-Beurling and Báez-Duarte criterion for the Riemann Hypothesis (RH) was introduced in [7]. It states that the RH holds if and only if the span of a particular sequence of functions $(h_k)_{k\geq2}$, denoted $\mathcal{N}$, is dense in the Hardy space $H^2$. In this note we construct a bounded operator $T$ on $H^{2}$ such that if the closure of $\mathcal{N}$ is $T$-invariant, then either the RH holds or there exists an infinite progression of $\zeta$-zeros. In particular, this yields an operator-theoretic criterion for the Riemann hypothesis as an invariant subspace question.

We describe the Writerslogic team's participation in the CLEF 2026 SimpleText shared task, addressing Task 1 (text simplification) and Task 2 (complexity spotting). For Task 1, we develop a multi-candidate generation pipeline using GPT-4o-mini that produces five simplification candidates per sentence at varying temperatures, then selects the best candidate using a reference-free scoring heuristic that rewards compression, source word retention, Cochrane Plain Language Summary vocabulary usage, and lexical simplicity. On Task 1.1 (sentence-level simplification), our Claude Sonnet 4 submission achieves SARI 47.43 and BLEU 14.21, the top-ranked sentence-level system (3rd on the combined Task 1 leaderboard, behind two document-level submissions). For Task 2, we fine-tune a DeBERTa-v3-large NLI model on 350K labeled (source, sentence) pairs, framing hallucination detection as natural language inference. The model reads the most relevant source sentence as premise and the candidate as hypothesis, directly learning to distinguish grounded from hallucinated content. On Task 2.1 (binary overgeneration identification), our fine-tuned DeBERTa system achieves 0.8081 document-level macro F1 (0.8085 in our best ensemble), the top-ranked entry within the identification track and 2nd among teams overall, behind AIIR Lab (0.8197). On Task 2.2 (multi-class error classification), our best submission reaches 0.804 multiclass accuracy, ranking 2nd among unique teams behind AIIR Lab (0.827). We evaluate both tasks on English and multilingual biomedical text from Cochrane systematic reviews.

We propose a Gibbs state preparation algorithm that exploits algebraic structure in the Hamiltonian. Our starting point is Hamiltonian Decoded Quantum Interferometry (HDQI), a recent algorithm that reduces Gibbs state preparation for Pauli Hamiltonians to decoding error-correcting codes. We introduce quantum decoding HDQI (QD-HDQI), replacing HDQI's coherent classical decoder by a quantum decoder that can exploit interference between different errors. For commuting Pauli Hamiltonians, our reduction is efficient and the associated quantum decoding problem corresponds to transmitting the associated symplectic code over i.i.d. pure-state classical-quantum channels. For uniformly random Hamiltonian signs, the vanishing-error threshold of an efficient decoder directly determines the lowest temperature that our algorithm can reach. Even using only classical decoders, this improves upon HDQI's achievable inverse temperature from linear to square-root in the correctable error fraction; quantum decoders can improve further by tolerating still stronger noise. A similar picture extends to the noncommuting regime previously handled by HDQI, where now the noise is correlated within small, independent blocks. We study two such quantum decoders in our QD-HDQI Gibbs sampling framework. The first, based on unambiguous state discrimination, works efficiently for arbitrary binary linear codes. However, we "dequantize" this strategy for commuting Hamiltonians, contributing a classical rejection sampler that matches its temperature threshold. The second is belief propagation with quantum messages (BPQM), a quantum generalization of classical belief propagation. We show that for certain dilute spin glasses, BPQM's decoding threshold exceeds the Shannon limit for classical decoding, reaching temperatures inaccessible to any classical decoder within our framework.

We describe the Writerslogic systems for three PAN at CLEF 2026 shared tasks (Reasoning Trajectory Detection, Voight-Kampff Generative AI Detection, and Multi-Author Writing Style Analysis), unified by a shared analytical framework: feature robustness under distribution shift is governed by support overlap between training and test distributions, not by training-set effect size. This yields a taxonomy (domain-anchored, domain-portable, domain-invariant) that explains why generator-specific features die under domain shift while vocabulary fingerprints (hapax ratio, Yule's K, Heaps' exponent), compression measures, and character n-grams survive. On Reasoning Trajectory Detection, where training was entirely mathematics and 84 percent of test was unseen domains, the framework guided system design to 1st place in source detection (0.85 macro F1 via Opus-Sonnet agreement) and 3rd place in safety classification (0.66 macro F1 via query-refusal decomposition). For Voight-Kampff, we built a calibrated ensemble of DeBERTa-v2 (ONNX), multi-seed LightGBM with 44 domain-portable stylometric features, and SVM on n-gram TF-IDF, combined via learned stacking with isotonic calibration; the best configuration achieved 0.891 on the PAN 2026 test set with balanced sub-metrics (0.853 to 0.902 across all evaluation dimensions). For Multi-Author Writing Style Analysis, we describe a system fusing spectral clustering over character n-gram similarity graphs, normalized compression distance for local boundary detection, and SmolLM-135M perplexity for neural change-point detection; a platform mix-up meant our run never reached the official evaluation, so we report the design and its a priori predictions. Across all three tasks, features measuring generation process properties are designed to outperform features measuring generated content properties under domain shift.

Financial AI agents must do more than retrieve facts: investment workflows require correct quantitative execution, reliable use of procedural resources, and auditable structured outputs. We introduce FinSkillBench, an evaluation suite of 2,603 point in time episodes across 12 subtasks in portfolio construction, risk management, and fundamental analysis, with hidden regenerable ground truth and task specific deterministic verifiers. Executing 17,820 episodes across 9 models and 3 resource conditions, the paired analysis across 8 models shows that curated skill packages raise mean scores by +16.2 points (0.366 to 0.528), whereas skills generated within a single episode add only +0.5 points while consuming more tokens and turns. We then decompose the curated premium by granting human authored procedural documents and executable domain tools separately: documents alone add +5.6 points, tools alone add +19.5 points, and their combination is subadditive. The premium is strongly workflow dependent: executable tools dominate numerically intensive workflows, documentation matters more when procedural or output schema guidance is the bottleneck, and interpretive tasks benefit from both. The effects are sign stable across 10 scoring variants and cluster bootstrap analyses, and an independently implemented second harness reproduces the directional pattern while showing that effect magnitudes depend on how tools and data are exposed. Overall, a measured "skill premium" is a property of the full model, resource, and harness system rather than of the underlying model alone.

Sampling-based model predictive control (MPC) is a powerful approach to trajectory optimization, but its performance depends on an informative cost function that often requires substantial domain knowledge to design. An alternative is to derive objectives directly from the system dynamics. Empowerment, defined as the channel capacity between an agent's inputs and its future state, provides such a goal-agnostic objective and has been shown to produce useful behaviors across a range of domains. However, existing empowerment-based controllers have two key limitations: empowerment is estimated using a virtual probing policy distinct from the executed control policy, obscuring its connection to the resulting behavior; and its computation typically requires second-order derivatives of the dynamics, limiting compatibility with standard MPC methods. We formulate empowerment using a single policy for both probing and acting, directly linking the empowerment objective to the executed behavior. The resulting objective requires only first-order derivatives and can be optimized with standard MPC solvers, either alone or in combination with a task-specific cost. We evaluate the proposed approach on classical control tasks and show that combining empowerment with task costs matches or exceeds the success rate achieved by either objective alone. Our formulation provides a practical bridge between standard MPC and intrinsically motivated control.

Recent studies have shown that most commercial direct time-of-flight (dToF) LiDARs can be spoofed by injecting high-frequency laser pulses into the receiver, which can erase pedestrians from the point cloud. This paper presents the first dToF LiDAR system-on-chip (SoC) with integrated sensor-level hardware security against spoofing attacks. We propose Dual-Domain Fingerprinting (DDF), which emits laser pulse pairs whose time interval and amplitude ratio are both randomized and authenticates received echoes in this two-dimensional space, so that spoofed signals are rejected before they corrupt the ranging result. An Event-Driven AFE (ED-AFE) activates the ADC only around pulse peaks: it digitizes three samples around each peak with a triggered ADC at 1-GHz sampling and applies parabolic interpolation, achieving 1-cm distance resolution with a 99% reduction in ADC power. A time-modulated laser driver controls the laser amplitude from 10% to 100% by modulating the charge time of a laser capacitor, providing the microsecond-order amplitude modulation required by DDF. A LiDAR system with a 16-channel 65-nm CMOS prototype SoC demonstrates up to 120-m ranging and an AFE power of 3.1 mW per channel, 60% lower than prior art. In a proof-of-concept experiment in which the dual-domain authentication is applied to measured sensor data, 73% of the point cloud is protected under spoofing attack, compared with 0% without DDF.

This is a very first draft of a manuscript about existence of solutions of differential inclusions involving chattering.

Constant-frequency oscillation is usually tied to the broken phase of a spatially coupled PT-symmetric dimer, where the eigenfrequencies form a complex-conjugate pair with a fixed real part. This work shows that an analogous locking can instead come from Floquet hybridization in a synthetic frequency dimension. Periodic gain–loss modulation folds the spectrum into replicas spaced by the drive frequency $\Omega$. Coupling between neighboring replicas opens an additional real-part degeneracy at the edge of the Floquet Brillouin zone. The hybridized Floquet mode at $\omega_0\pm\Omega/2$ requires the minimum gain and is therefore selected for the self-oscillation. A Floquet PT-symmetric circuit with a JFET time-varying negative resistance confirms the prediction. The observed constant-frequency oscillation contains two frequency components of comparable amplitude, separated by the modulation frequency, which identifies its origin from Floquet hybridization rather than ordinary PT-symmetry breaking or dispersion flattening. More broadly, once a suitably symmetry-constrained spectral degeneracy is established, self-sustained frequency pinning can arise beyond the conventional spatial PT-broken phase.

Why are some dynamic lot-sizing problems polynomial? We address this question by introducing Grid Theory, a structural framework based on cumulative production and the additive structure of production bounds. For a general single-item dynamic lot-sizing model with lower and upper production bounds, there exists an optimal extreme solution in which, within each regeneration interval, all but at most one production quantity lie on a boundary value. This induces additive grids, and the Main Grid Theorem establishes that an optimal cumulative production trajectory can be restricted to these discrete sets. Although the resulting grids may be exponentially large, we introduce the notion of additive dimension to capture production-bound profiles whose boundary sums admit a low-dimensional representation. We show that bounded additive dimension yields a polynomially constructible grid envelope and a polynomial time grid-based dynamic programming algorithm. The framework extends to separable concave costs and establishes polynomial solvability of several families, including constant capacities, minimum order quantities, a fixed number of capacity levels, fixed-degree polynomial capacities, periodic capacities, and piecewise polynomial capacities. In particular, polynomiality may hold even when the number of distinct capacity values grows with the planning horizon. Grid Theory thus identifies additive structure, rather than the number of distinct resource values, as a sufficient mechanism for polynomial solvability.

Cephalonauts One is a whole-brain 3 Tesla (3T) functional magnetic resonance imaging (fMRI) dataset recorded while subjects listened to audio podcasts. Three healthy subjects underwent multiple scanning sessions, each consisting of five 15-minute runs, while listening to podcasts in their native language. With 30 hours of fMRI data per subject, the current release is the deepest available fMRI dataset using naturalistic speech stimuli. The dataset pairs brain activity with the corresponding podcast audio, transcript annotations, and derived stimulus embeddings. Furthermore, we introduce a brain decoding benchmark formulated as audio segment retrieval: given fMRI activity from a held-out session, the decoder must identify the corresponding time-aligned podcast audio segment among candidate segments. We provide standardized splits, evaluation metrics, and baseline decoders for this task. Finally, a scaling analysis shows that decoding performance improves continuously with the amount of training data per subject.

Exactly solvable models are often identified from structural features of their interactions. For quantum spin Hamiltonians, these are captured by the frustration graph of anticommuting Pauli terms. The frustration graph characterizes broad families of spin models that map to free fermions for arbitrary, or generic, values of their coupling strengths. Nevertheless, there exist non-generically solvable models that admit free-fermion solutions only at finely tuned couplings. In this work, we characterize a family of such models in terms of graph structures. Given an arbitrary instance of Fendley's free-fermions-in-disguise (FFD) chain, we construct a set of operators, called Krylov currents, that are exactly quadratic in its effective fermionic modes and thus extend it to a linear family of free-fermion solvable Hamiltonians. As the Krylov currents are nonlinear in the FFD Hamiltonian terms, the elements of this generated family are non-generically solvable, and they accordingly fail the known conditions for generic solvability. We prove that every Krylov current admits an expansion in terms of induced paths of the frustration graph and that they generate the full special-orthogonal algebra of Gaussian transformations. Our results identify path support as a signature of non-generic solvability, and they provide a systematic route to finding exactly solvable many-body Hamiltonians.

Empirical claims about the connection between over-squashing and long-range interactions in GNNs, can only be trusted if the benchmarks used to validate them genuinely require long-range interactions. The de-facto standard, the Long Range Graph Benchmark, has been repeatedly shown to be saturated by tuned short-range models, with existing synthetic alternatives being tied to specific topologies. As such, there is a lack of principled certificate of long-rangedness on arbitrary graphs. This state reflects the absence of a precise characterization of long-ranged benchmarks. We address this fundamental gap by introducing four verifiable axioms: Predictability, Tightness, Strictly $k$-Range, and Topology-Invariance, that any task claiming to test $k$-hop interactions must satisfy. We formally prove that violating any one of them admits failure modes that undermine conclusions drawn from the task. Based on these axioms, we introduce TRIP (Truly Ranged Interactions Problem) and its generalisation GRIP (Generally Ranged Interactions Problem), constructive procedures that turn any graph into a provably long-ranged task by drawing features from stable distributions. Moreover, by construction, GRIP admits a closed-form, per-range Maximum-Likelihood oracle that yields the first a priori per-range lower bound on test error available on any benchmark. Using our framework, we: (i) audit 4 common long-range benchmarks and identify their failures modes with respect to our axioms; (ii) on TRIP-instantiated topologies, we find a popular notion of curvature is uncorrelated with GNN performance, supporting topological-vs-computational bottleneck distinction; and (iii) we show that a novel benchmark's over-squashing measures factors beyond pure long-rangedness. Code to use the framework and reproduce experiments is released https://github.com/ferranhernandezc/graph-grip.

Let $\mathcal{C}_\varepsilon$ denote the time it takes a Brownian motion to come within distance $\varepsilon$ of every point in the two dimensional torus $\mathbb{T}^2$ of unit area. We prove that for an explicit non-random centering $m_\varepsilon$, the variables $\{\sqrt{\mathcal{C}_{\varepsilon}} - m_\varepsilon \}$ converge in distribution as $\varepsilon \to 0$, to a randomly shifted Gumbel law.

We propose a formulation of a quantum field theory within the framework of the unfolded dynamics approach, originally developed in higher-spin gauge theory. We construct an unfolded system that describes a hierarchy of Schwinger-Dyson equations for vertex functions of a scalar QFT in terms of unfolded first-order equations. A distinctive feature of the constructed system is the appearance of two additional evolution parameters responsible for the WKB and RG behaviors. As an illustration, a one-loop analysis of the theory with quartic self-interaction is carried out.

We demonstrate that form factors evaluated with momenta analytically continued into the complex plane can be accessed directly from position-space Euclidean correlators such as those computed numerically in lattice quantum field theory, without continuing the correlators themselves or solving an inverse problem. The method applies a bilateral Laplace transform to lattice data, yielding the form factor throughout the transform's domain of convergence. For the pion form factor in Quantum Chromodynamics (QCD), this domain contains all complex values of the invariant $Q^2$ satisfying $\mathrm{Re} \, Q^2>-4m_\pi^2$, where $m_\pi$ denotes the pion mass. This extended kinematic reach could improve charge-radius determinations and provide more complete input for fits based on conformal mappings. After developing the method for infinite-volume correlators, we discuss several finite-volume estimators suitable for realistic calculations, including position-space fits and the use of a spatial chemical potential implemented through boundary conditions with an imaginary twist angle. Finally, we test the method in the two-dimensional $O(3)$ nonlinear sigma model using Monte Carlo data.

We are developing an experimental platform at Lawrence Livermore National Laboratory's Jupiter Laser Facility to characterize X-ray emission from highly charged ions in the high-density ($n_e > 10^{23}$ cm$^{-3}$), high-temperature ($T_e \sim 1$ keV) regime, leveraging the recently upgraded frequency-doubled short-pulse Titan laser. These measurements will provide experimental benchmarks for high electron density effects on atomic structure, including Stark broadening, ionization potential depression, density-dependent line shifts, and suppression of dielectronic recombination, effects that are relevant to spectral modeling packages used by both the high-energy-density and astrophysics communities. Here, we describe the current status of the platform and present results from first experiments using the upgraded frequency-doubling capability, including calibrated K-shell spectra acquired from five time-integrated X-ray channels. Comparisons with MERL line shape calculations and with spectra recorded at AWE's Orion Laser Facility indicate that the upgraded Titan laser reliably produces the necessary plasma conditions, establishing a foundation for systematic benchmarking of high-density atomic physics in future campaigns.

Large language models (LLMs) have reached expert-level performance on competition mathematics largely through the volume of search placed around them: candidate solutions are sampled in quantity and retained only when an external criterion accepts them. Such a procedure improves the outcome that survives it while leaving untouched what the model represents. We examine that question where no external criterion exists: translating statements between the dialects of neighbouring subfields, where fidelity turns on the level of generality at which content is asserted. The source leaves that level implicit in its vocabulary, so a faithful translation must recover it from the relation between the theories. We introduce an instrument that codes truth, content and scope in separate blind queues, with a judge-free measure of whether a rewrite states the hypothesis implicit in its source, and establish its sensitivity with a planted-positive control. Across seven models from four families, translating towards the general framing widens the domain of quantification in 60.6% of rewrites and narrows it in none; translating towards the concrete framing narrows it in 28.3% and widens it in 0.3%. The hypothesis that would prevent it is stated in 21.6% of model rewrites and 4.2% of human statements. Capability does not govern the asymmetry: it appears in every model tested, and the most capable widens least. It replicates on the half of the benchmark held out by a pre-registered rule, and on statements written by mathematicians. Instructing a model to state every hypothesis it requires raises that rate but not its sensitivity to direction. We argue that these systems have acquired an object-level correspondence between subfield vocabularies without the constraint under which a translation between theories carries hypotheses to hypotheses.

We refute the Strong Roberson Conjecture, which asserts that adding any graph outside a graph class closed under minors and disjoint unions strictly increases the distinguishing power of homomorphism counts from that class. More precisely, we construct connected graphs $H$ for which homomorphism counts from graphs excluding $H$ as a minor determine the number of homomorphisms from $H$ to any target graph. We also refute the analogous conjecture with immersions in place of minors. The proof introduces a method for deriving exact homomorphism count dependence from modular equivalences. We obtain these modular equivalences for infinitely many primes using prime-order automorphisms and the corresponding orbit quotients. We complete the refutations by proving that suitable circulant graphs with two jump lengths and related cubic bipartite graphs exclude their corresponding orbit quotients as minors and immersions, respectively.

We introduce a global frequency function for harmonic functions on rotationally symmetric Cartan-Hadamard manifolds. In real hyperbolic space, we also identify a different frequency function associated with the normalized spherical $L^2$-mass of a hyperbolic harmonic function and prove its monotonicity. As a consequence, we obtain a logarithmic convexity theorem for the normalized spherical $L^2$-mass and a hyperbolic analog of the classical three-sphere theorem.

Generating progressively harder reasoning problems requires synthesis procedures that adapt as the task distribution evolves. Existing task-level recursion reuses generated problems as seeds but leaves the construction harness unchanged. We present task-harness co-evolution, a framework for recursive harness self-improvement (RSI) in reasoning-data synthesis. Online self-improvement converts intermediate solver failures into reusable skills during generation. Post-task self-improvement revises skills, prompts, and workflows after each batch, adopting candidates only when they generate harder valid tasks within a bounded cost increase. Model weights and verification criteria remain fixed. Across mathematics, coding, and science, mean solver accuracy decreases from 100.0% to 54.8% over fourteen evolution rounds. Ablations show that combining both update schedules produces harder tasks than fixed-harness recursion or either schedule alone. The resulting data improves downstream SFT and GRPO performance. In particular, a 27B student fine-tuned on 10K synthesized mathematics examples achieves 62.5% mean-16 accuracy on APEX, competitive with selected frontier-model references. These results support adapting the synthesis harness alongside the tasks to generate increasingly challenging data with downstream training value.