Papers

Let $V$ be a graded vertex operator coalgebra and $\mathcal{C}$ the category of admissible $V$-comodules. We first give the construction of contragredient comodule of an admissible $V$-comodule. We then introduce cointertwining operators among admissible $V$-comodules. Using cointertwining operators, we define the cotensor decomposition of an admissible $V$-comodule by a universal property. Finally, we prove that the complexified Grothendieck group $\mathbb{K}[\mathcal{C}]=\mathbb{C}\otimes_{\mathbb{Z}}K[\mathcal{C}]$ is a cocommutative coassociative coalgebra. Moreover, this coalgebra is naturally dual to the fusion algebra of the category of admissible modules over the dual vertex operator algebra $V'$.

We analyze the composer embeddings learned by a composer-conditioned Transformer as a continuous latent space of compositional style, rather than merely as an internal representation for generation. A model that recursively predicts melody continuations was trained on melodic sequences extracted from MIDI data, conditioned on composer identity (124 composers). Principal component analysis of the learned composer embedding matrix (124x128) shows that the first principal component correlates strongly with composer birth year (r = -0.884, p < 0.001, n = 123), a stronger correlation than we obtain by applying the same PC1-birth-year analysis to existing general-purpose audio-text embeddings (CLAP, MuQ-MuLan) trained on unrelated audio-text corpora, not on symbolic melody generation. A shuffle test (2,000 permutations) confirms that the Silhouette score for stylistic-period labels is statistically significant (0.0110, p < 0.001). We further show that vector arithmetic in the embedding space captures meaningful stylistic relationships between composers. These results suggest that composer embeddings, learned without supervision beyond composer identity, form an interpretable latent space that captures musical-historical structure.

Closed-loop visual servoing requires predictions that indicate whether an action reduces task error, not only whether the action is plausible. We call this gap the prediction-control mismatch and introduce WM-VS, a target-centric progress-aligned world-model framework for closed-loop visual servoing. Offline target-region DINOv2 correspondences define a signed four-dimensional servo coordinate for translation, scale, and in-plane rotation. Stage 1 aligns action-conditioned latent transitions with this coordinate; Stage 2 freezes the world model and trains a reactive joint-velocity policy with action imitation, consequence supervision, and short imagined rollouts that favor error contraction. Deployment is RGB-only and reactive, without online trajectory optimization. On a real 7-DoF eye-to-hand system, WM-VS reaches a corner RMSE no larger than 10 percent of its initial value in 30/30 trials and retains this criterion at the final valid frame in 25/30 (83.33 percent). Removing future-error alignment reduces retention to 26.67 percent. The learned progress signal agrees with an external AprilTag corner error not used for training or control (mean Spearman rho = 0.8778). Without retraining, two unseen 3D targets achieve translation-error reductions of 86.48 percent and 90.27 percent and rotation-error reductions of 70.01 percent and 65.70 percent. These results link progress-aligned action consequences to repeated closed-loop correction and transfer. Code and data will be released as open source.

Optimization methods for experimental science are often evaluated on synthetic functions that are reproducible but omit important characteristics of real experiments. We introduce RECOB (REliable Chem Optimization Benchmark, Github repository: \hyperlink{https://github.com/XieZikai/RECOB}{https://github.com/XieZikai/RECOB}), a black-box optimization benchmark constructed exclusively from data generated through physical experiments in chemistry and materials science. The suite contains 14 single-objective and two multi-objective tasks spanning chemical reactions, material formulations, electrochemical systems, continuous-flow processes, and automated laboratories. Each task provides a machine-readable specification of its decision variables, feasible domain, physical constraints, objective direction, and experimental provenance. Continuously queryable learned oracles are screened using repeated holdout validation and prespecified admission criteria, while measured-table replay enables evaluation using the original experimental responses. Under a common paired evaluation protocol, we compare ten single-objective and eight multi-objective optimization methods. HEBO achieves the best aggregate single-objective rank, while qNEHVI leads the multi-objective comparison. Model-based methods generally outperform non-adaptive baselines, although their computational overhead varies substantially. We further assess benchmark reliability using independent oracle retraining and measured-table replay. Aggregate optimizer rankings remain highly consistent across retrained oracles, while replay preserves the broad performance hierarchy using only physically measured responses. Together, these results show that RECOB can reproducibly distinguish optimizer performance as an experimentally grounded and reliability-tested benchmark for black-box optimization in chemistry and materials science.

We prove that topological isomorphism of procountable groups is a universal analytic equivalence relation, answering a question of Gao, Nies, and Paolini. The same conclusion follows for non-Archimedean Polish groups. More strongly, there is one countable group $H$ for which universality already holds among inverse limits of sequences of surjective endomorphisms of $H$. Thus all the classification complexity can be carried by the bonding maps. We encode permutative equivalence of unconditional basic sequences by integer weights with prescribed symmetries. An extension of Gao, Nies, and Paolini's tree construction recovers bounded weight differences from uniform continuity while allowing these symmetries to act. Przeździecki's almost-full functor transfers the resulting inverse graph systems to groups. Identifying the stage graphs with a single graph makes the passage from weights to bonding endomorphisms continuous.

Quantum Darwinism explains objective information through redundant environmental records. Earlier work established that imperfect records can be amplified and that environment self-evolution can enhance or suppress their formation. We investigate how preparation, interaction angle, and field disorder combine in an imperfect-CNOT model with random Gaussian couplings and pure, noninteracting environment qubits. We find that, without fields, a single alignment parameter $\Lambda$ determines the preparation and interaction-angle dependence of conditional-state distinguishability. Increasing interaction imperfection or local field strength can improve or suppress recording. We explain this nonmonotonic response through the geometry of conditional branch separation. For the pure initial environments considered here, the $Z$ basis remains optimal for Holevo information, so field-assisted recording requires no change of the recorded system observable. Comparing uniform local field strengths with Gaussian-distributed strengths at equal root-mean-square strength shows how disorder broadens both beneficial and detrimental field effects. Exact expressions for fragment information and numerical simulations with up to 24 environment qubits quantify the distinction between high mean information and reliable records across fragments and throughout a finite observation window. These results connect the geometry of local information acquisition to the fragment sizes needed for robust recording. The branch-distinguishability analysis itself requires only the conditional evolution of each environment qubit and extends to other interactions that preserve a system pointer basis.

Coding agents have emerged as a promising paradigm for robot manipulation: a language model writes the robot controller as a program, and agents built in this way now operate robots without robot-specific training. Whether this paradigm is also safe, however, has not been asked. We evaluate coding agents under a safety constraint, where each task pairs a manipulation goal with an obstacle the robot must not touch. The agent pursues the goal but collides with the obstacle in most cases, treating task completion as its sole objective. The agent reasons about the obstacle in its traces, and the prompt already forbids touching it, so neither perception nor instruction is at fault; the fault lies in the planning, where the stated constraint never becomes a priority. By decomposing manipulation into a route phase and a contact-rich moment, we locate the source of the failure. Along the route, the model cannot prioritize the safety constraint, having no notion of a clearing route and none of replanning once a chosen route becomes infeasible. At the contact, it is unaware that contact execution is bounded by the same constraint. To close this gap, we present SafeHarness, which equips the model with two obstacle-aware harnesses. Obstacle-aware route planning grounds the objects as bounding boxes and draws candidate routes over them as sequences of waypoints. The agent then plans a route in advance, verifies it, replans when necessary, and only then executes it. Obstacle-aware contact execution instead selects the contact position so that the contact itself avoids the obstacle. SafeHarness attains 81.2% task success and 91.9% collision avoidance with GPT-6-Astra, surpassing the previous SOTA by 13.7 and 23.0 points, and the same agent without harnesses by 31.2 and 57.5 points, respectively.

Embedding spaces define notions of semantic similarity and distance. We study whether those embeddings reflect physical measurements of mass, distance, time and volume, which admit a unique, objective notion of semantic equivalence and distance. We find that physical measurement is only weakly modeled in the embedding space, and that instead quite peculiar measurement patterns can be observed. Further analysis indicates that embedding representations of physical measurements are strongly influenced by superficial string similarity, and recalibration of similarity does not substantially improve the alignment.

Complex robotic manipulation tasks frequently require a long-term memory of past events and actions. As conditioning on full histories renders policies prone to spurious correlations and degrades performance, many approaches to policy memory involve compressing historical information through expensive VLM queries in-the-loop to process only task-salient information. In this paper, we propose an alternative approach in which computationally intensive VLM queries are made during train-time to learn a lightweight latent memory that can be efficiently queried at deployment time. Our representation, which we call the workspace token, is trained by (1) using a VLM to identify current and historical information necessary for completing a task, then (2) distilling these into the workspace token using a set-reconstruction decoder loss. In both simulation and hardware, we show that the workspace token can be used as a drop-in replacement for observations during deployment, enabling policies to solve memory-intensive tasks without the need for VLM reasoning in-the-loop, in effect serving as a latent harness for distilling a stronger reasoning models ability to solve long-horizon tasks to a reactive robotic policy. We further demonstrate that the workspace tokens are not only more lightweight, but also lead to better policy performance compared to conditioning policies on explicit modalities like curated past image frames, motivating a latent approach to history curation and reasoning model harnesses more broadly.

Perceiving and remembering the visual world is fundamental to navigating and interacting with our environment. Current 4D foundation models, such as camera-controllable video models or 4D reconstruction models, can perceive and reconstruct dynamic environments, but how well they remember what they have perceived remains an open question. Existing benchmarks largely rely on pixel-level metrics and lack ground truth for objects once they leave the field of view, making them unable to evaluate visual memory in an object-centric manner against references. To fill this gap, we introduce PersistBench, a dataset and metric suite that leverages 360{\deg} videos as omniscient ground truth and proposes three evaluation aspects: object permanence, motion continuity, and appearance preservation. Evaluating various models across diverse categories reveals that current models can only maintain short-term consistency that degrades significantly once objects leave the field of view. Our findings highlight the gap between current model capabilities and robust visual memory ("seeing is not remembering"), providing guidance for future development of 4D foundation models. Dataset and code are available on the project page: https://guangzhaohe.com/persistbench.

A splash lives for a fraction of a second: sheets tear into ligaments and droplets, appearance is view-dependent and nearly textureless, and little persists long enough to track. Reconstruction research has consequently focused on smoke, synthetic liquids, or gently deforming surfaces. To our knowledge, no synchronized multi-view dataset of splashing liquids exists. We therefore introduce a benchmark of 20 real scenes, from coherent streams to violent splashes, captured by seven synchronized, calibrated 4K cameras at 60 fps, with manually refined per-view liquid and container masks and fixed evaluation splits. We further present SplashSplat, built on a single principle: impose physical structure only where the observations can constrain it. Per-frame liquid SDFs fused from the masks provide the geometry, level-set transport between consecutive SDFs yields a coarse velocity field, and Lagrangian carriers advected along this flow, corrected against each new observation and reseeded where coverage is lost, decode local Gaussians for differentiable rendering. SplashSplat outperforms state-of-the-art dynamic Gaussian splatting methods on our real captures and on a synthetic benchmark, with physically more plausible motion and a lower training cost. The same representation supports temporal interpolation and style transfer without re-optimization.

Modeling articulated objects from sparse monocular views is challenging because each observation reveals only partial geometry and motion evidence. Most feed-forward methods infer articulation from a single observation and therefore rely heavily on learned category-level shape priors. We present FAMOS, a feed-forward model that predicts movable-part segmentation and joint parameters from a sparse, unordered set of partial point clouds. Our model jointly reasons over multiple observations and naturally supports a variable number of inputs, including a single view. To aggregate articulation cues across observations, we introduce a Multi-state Articulation Transformer with alternating state-wise and global attention. We further propose an observed articulation span objective that supervises the motion range each part exhibits across the input observations, encouraging the model to leverage the full observation set. To overcome the limited scale and diversity of existing datasets, we introduce a procedural data generator that synthesizes self-annotated assets during training. Experiments on PartNet-Mobility, ACD, and ArtiCraft-10K demonstrate consistent improvements over both feed-forward and optimization-based baselines. Project page: https://kevinqu7.github.io/famos

Professional design requires any-color control: the ability to specify an object's target color with any 24-bit hex value for image generation and editing. Prior work has explored color generation, editing, and colorization, but often relies on dedicated color representations or specialized inference procedures. Advances in large language models offer a simpler starting point: even compact models can associate hex values with color semantics. We present Paint-Anything, which learns a shared hex-prompt interface for generation and editing through object-level color supervision. We develop a data pipeline that constructs Paint-500K from real images through object grounding, perceptual color labeling, and editing-pair synthesis. Since shadows make real-image labels only approximate colors, we complement this supervision with pure-color anchors whose pixels exactly match their paired hex values. These anchors are used only at high-noise timesteps, leaving low-noise training to natural images. We further introduce Any Color Benchmark (ACBench), comprising ACBench-T2I and ACBench-Edit, to measure object-level hex color fidelity across both tasks. On FLUX.2-4B, Paint-Anything improves ACBench-T2I and ACBench-Edit scores by 85.3% and 28.3%, respectively, relative to the base model, with ablations supporting the training recipe. It also achieves the highest average CompColor score among the compared methods.

Hereditary polyposis syndromes can be precursor lesions to colorectal cancer and are associated with a broad spectrum of extracolonic tumors. Early identification and accurate classification of these syndromes are essential for timely diagnosis, individualized patient management, and targeted surveillance strategies for affected families. However, public endoscopic datasets are largely organized around the individual sporadic polyp, and none links the polyposis phenotype to histopathology and germline findings at the patient level. Here, we present ERCPMP-Gx, an endoscopic, histopathological, and genomic dataset developed to support the application of artificial intelligence (AI) in the recognition, characterization, and classification of colorectal polyposis. Most procedures were performed using the Olympus EVIS X1 system with white-light endoscopy (WLE), narrow-band imaging (NBI), magnifying NBI (M-NBI), and NBI with near focus modes, yielding 160 images and accompanying video clips. Approximately eighty percent of cases represent clinically and/or genetically confirmed hereditary polyposis syndromes (PG), including familial adenomatous polyposis (FAP), Peutz-Jeghers syndrome (PJS), juvenile polyposis syndrome (JPS), and ganglioneuroma syndrome (GNS), while the remaining twenty percent comprise non-hereditary polyps and polyp-mimicking lesions with overlapping morphological features (Non-PG), included to support differential classification. Each released record is linked, where available, to standardized endoscopic annotations, representative histopathology, and clinically reported germline findings, forming an AI-ready, patient-level annotation framework. The dataset is publicly accessible at Mendeley (https://doi.org/10.17632/nzyfc544bx.2). For the latest updates and further information, readers are referred to the DataBioX website: https://databiox.com.

Pretraining a neural PDE surrogate can reduce the amount of new CFD data needed when geometry or modeled physics changes. However, it remains unclear how different components of distribution shift affect this benefit. We pretrain a surrogate on 254,909 RANS solutions from one airfoil family and fine-tune it on a new family under two target settings with matched freestream ranges: the same Spalart-Allmaras (SA) modeling and SA with added $e^N$ transition modeling. At $N=1000$, the pretrained model matches the accuracy of a model trained from scratch on $3.25\times$ as many samples for the same-SA target, but $2.58\times$ as many for the transition-modeled target. By $N=5000$, this ordering reverses ($1.56\times$ versus $1.86\times$). At $N=1000$, sampling more distinct airfoils lowers error on both targets, but only for the same-SA target is the gain increase larger than the observed draw-to-draw variation ($3.3\times$ to $4.0\times$). These results show that pretraining value depends jointly on target-data budget, target-data coverage, and whether source and target differ in modeled physics.

Anomalies of generalized symmetries are closely related to the statistics of topological excitations. Truncating a symmetry transformation to a finite region produces an operator that creates symmetry defects on its boundary; we call this a symmetry patch operator. Such operators resemble hopping operators that create topological excitations at the boundary of their support, but this geometric similarity does not justify identifying the two. For finite Abelian groups in one spatial dimension, we prove that if the same family of local operators defines both valid hopping operators and compatible symmetry patches, the type-III component of the anomaly is $-2$ times that of the statistics. We establish a one-to-one correspondence between statistics and anomaly by treating hopping operators as symmetric operators that commute with the global symmetry, following the description of symmetry through the algebra of local symmetric operators. We explain this correspondence through gauging by coupling boundary matter to a Dijkgraaf-Witten gauge field in one higher spatial dimension. Hopping operators act on the gauge-invariant degrees of freedom. After fixing the background gauge field, the residual gauge transformations become the global symmetry, and the gauge invariance of hopping operators becomes the requirement that they commute with this symmetry.

Frontier coding agents are increasingly trusted to work autonomously for long periods of time, yet what they actually did is often hard to tell from their final response. We quantify the propensity of such agents to overclaim task completion, which may mislead the user. We operationalize overclaiming as a final response that reports work that the agent's own transcript shows it did not do, for example, claiming to have read a file it never opened. This criterion requires no inference about intent and does not depend on whether the delivered work is correct; it asks only whether the reported work was done. We introduce OverclaimBench, an evaluation suite of five file-review scenarios with transcript-based coverage measurements and registered planted defects. We evaluate eight proprietary frontier models in their own production command-line interfaces and four open-weight models under a single fixed harness, and find that 1) agents fail to read every file they were asked to review in 67.9% of runs; 2) among these incomplete runs, agents are misleading 80.4% of the time (59-96% per model), either falsely claiming a complete review or leaving the gap undisclosed; 3) requiring delegation to subagents increases coverage, but a large majority of reviews that remain incomplete are still misleading; and 4) agents that falsely claim a complete review miss planted defects at about 1.8 times the rate of agents that read every file, showing that claims of completion can conceal substantive failures. Together, these results show that agents' final responses are not reliable accounts of their actions.

A polyhedron is a planar, $3$-connected graph. We iteratively construct all polyhedra (save for pyramids) from a unique starting graph, namely the square pyramid, via two graph transformations. This builds upon a previous construction, that starts from the full class of pyramids, and applies the same transformations. In a related result, we iteratively construct all quadrangulations of the sphere where all $4$-cycles are facial, i.e., the class of radial graphs of the polyhedra (save for antibipyramids), from a unique starting graph, namely the square antibipyramid, via a unique graph transformation. This builds upon a previous construction, that starts from the full class of antibipyramids, and applies the same transformation.

We investigate the dwarf spheroidal (dSph) satellites and stellar halo of M31 using near-infrared imaging from the Wide-Field Camera on the UKIRT 3.8 m telescope. Our homogeneous analysis covers the stellar extents of 12 dSphs, as well as their surrounding halo field populations. We identify carbon-rich (C) and oxygen-rich (M) thermally-pulsing AGB stars (TP-AGBs) using colour-magnitude and colour-colour diagrams, which also allows for effective contaminant rejection. TP-AGB stars are detected in eight of the 12 dSphs, indicating small intermediate-age populations in a substantial fraction of the sample; they are also found in considerable numbers throughout most of M31's stellar halo. By combining 316 new detections with a revised classification of objects previously reported in the literature, we increase the TP-AGB candidate population in the dSphs from 82 to 359. We use the resulting dSph and halo AGB samples to compute C/M ratios and infer metallicities in the dSphs and adjacent halo fields with non-zero AGB counts. A clear metallicity gradient is observed in the M31 stellar halo out to ~150 kpc, consistent with that found using other tracers. Using literature star formation histories from main-sequence turn-off photometry, we find a tight correlation between the number of C stars in the dSphs and the stellar mass formed in the last 0.5–3 Gyr. This study underscores the promise of AGB stars as quantitative tracers of intermediate-age star formation, particularly in intrinsically faint systems, and provides a catalogue of candidate TP-AGB stars for follow-up.

We prove linear stability of Kasner spacetimes in the direction of the Big Bang, up to an explicit finite dimensional space of non-decaying self-similar solutions. The fastest growing solution is the linearization of Taub's explicit Bianchi II solution, describing a Kasner transition. All other non-decaying solutions are inhomogeneous analogues of this, and the linearized Kasner metric. The key novelty is a notion of quasinormal modes on Kasner spacetimes, similar to quasinormal modes on stationary black holes spacetimes. All quiescent (as opposed to oscillatory) vacuum Big Bang spacetimes of dimension 4 are asymptotic to a Kasner spacetime from the perspective of a single observer at the Big Bang. They are expected to be highly unstable due to the oscillations conjectured by Belinski, Khalatnikov and Lifschitz. This paper provides a complete description of this instability on a linear level without symmetry assumptions.

Hostile rhetoric toward social groups can normalize exclusion and justify mistreatment, as well as contribute to rising polarization and political violence. Efforts to moderate hostile rhetoric in online speech draw on foundational theories in social and moral psychology, and political science. However, these theories were developed largely in parallel, often propose different and sometimes conflicting accounts of how hostility develops, and have rarely been tested against each other in real discourse. The result is a fragmented understanding of the rhetorical mechanisms of hostility, without a clear sense of how they appear, and relate to each other, in real-world discourse. Using 2.86 million posts from TikTok, Truth Social, and Twitter/X during the 2024 U.S. presidential election, we model the mechanisms of six foundational theories of intergroup hostility – boundary construction, threat construction, scapegoating, negative evaluation, dehumanization, and action orientation – within a common empirical framework to recover the broader organization of intergroup hostility rhetoric. Structurally, we find that boundary construction and threat construction anchor the system; temporally, we find that these mechanisms tend to follow a regular ordering: boundary construction, derogation, and action orientation tend to appear early; dehumanization and threat construction later; scapegoating latest. Mapping how these theoretical frameworks actually manifest in discourse bridges longstanding divisions across social science traditions and presents computational social science with a clearer empirical foundation for modeling intergroup hostility rhetoric beyond single-label detection.

Reinforcement learning (RL) of large language models is notoriously sensitive to small differences between training and inference engines, often referred to as the training-inference mismatch (TIM). However, completely eliminating TIM is impractical, as it would come at a major cost to rollout efficiency. In this paper, we show that the instability of RL under TIM is primarily caused by drift: a persistent bias between training and inference engines that accumulates with every training step. We derive an additive "score centering" correction term that stabilizes RL under TIM by canceling drift. When training models from 0.6B to 30B parameters, score centering alone matches or outperforms methods based on importance sampling under quantization, with the gap growing as the mismatch becomes more severe. Because the correction is additive, score centering also composes with importance sampling – their composition outperforms pure importance-sampling baselines in our staleness experiments.

We study a new class of M2-brane matrix models associated with affine BC and twisted affine AD quivers. These models exhibit the characteristic $N^{3/2}$ scaling of the free energy in the large $N$ limit. We establish a Fermi gas formalism and demonstrate that their grand canonical sum is given by a Fredholm Pfaffian, which is in parallel with the affine D quiver matrix models. The resulting Fermi gas density matrix shows a rational dependence on the canonical position/momentum operators in addition to the standard hyperbolic dependence. This leads to unconventional sub-leading corrections, which obstruct the Airy function structure in the $1/N$ expansion of the free energy observed in the previously studied M2-brane matrix models.

We consider generalizations of the classical Fourier uniqueness theorem. First, we construct a family of uniformly discrete sets $\Lambda \subset \mathbb{R}$, of uniform density one, such that the exponential system $\{e^{2\pi i\lambda x} : \lambda \in \Lambda\}$ is complete in $L^p(S)$ for every $1 \leq p < \infty$ and every measurable set $S \subset \mathbb{R}$ with $|S| < 1$. We also show that no set that is asymptotically integer can have this universality property. Additionally, for every $v \in (0,1)$, we construct a set of integer frequencies and uniform density $v$ whose exponential system is complete in $L^p(S)$ for every $1 \leq p < \infty$ and every measurable set $S \subset [0,1]$ with $|S| < v$. Finally, we prove that the Sobolev regularity condition $\alpha > \frac12$ for the existence of uniformly discrete uniqueness sets for spectra with periodic weak gaps, considered by Olevskii and Ulanovskii, is sharp. Our findings admit extensions to higher dimensions and are verified in Lean.

Coding harnesses shape how autonomous coding agents translate model capabilities into long-horizon software-engineering performance, yet existing work typically evaluates harnesses as monolithic systems, leaving the effectiveness of individual components unclear. To enable component-level comparisons, we study this question with a lightweight coding harness whose execution loop is fixed while three components are varied: planning, action space, and context management. Across four models evaluated on SWE-Bench Verified and Terminal-Bench 2.1, we evaluate 176 matched settings spanning five context-management strategies, four context-window budgets, and targeted ablations of planning and action space. We find that: (1) Context management becomes increasingly valuable as the context-window budget tightens, with most of its benefit coming from preventing context-overflow failures. (2) Staging rule-based elision before LLM-based summarization provides the strongest overall efficiency among the context-management strategies, whereas making elided content recoverable adds machinery that models rarely use and yields no accuracy gain. (3) Planning shifts from an accuracy scaffold for weaker models to a cost saver for stronger models, with little change in accuracy. (4) Predefined tools improve performance for models with weaker bash proficiency, whereas bash-capable models can operate effectively with a bash-only interface and achieve substantially lower cost, especially on command-line-centric tasks. Trajectory-level analysis explains these effects: context management extends execution trajectories without substantially altering agent behavior, planning changes where trajectories stop, and the action space changes the granularity at which code is written. These findings inform model- and budget-aware harness design and provide a modular framework for evaluating future harness components.

OpenAI~\cite{OpenAIManuscript} has recently announced a proof of finite time singularity formation for the 3D Navier-Stokes equations, in the presence of a $C^\infty$-smooth body force. The construction in~\cite{OpenAIManuscript} has a few key features, among which we single out: (i) the angular mean of the solution satisfies specific Type II bounds which are anisotropic; (ii) the solution is exactly axisymmetric in a collapsing core region. In this paper we consider solutions of the 3D Navier-Stokes equations in the presence of a real-analytic body force, and assume that these solutions satisfy properties (i) and (ii) above. We prove that such solutions are in fact regular at the putative singular point. As a consequence, in the construction of~\cite{OpenAIManuscript}, and in any construction with properties (i) and (ii) whose force remains bounded in $C^2$ up to the singular time, the force can neither vanish identically near the singular point, nor be real analytic in the space variables, locally uniformly in time. The main idea of the proof is inspired by our earlier work~\cite{CIV26} and the companion paper~\cite{CIVEulerLength}: zooming-in at the putative singularity using the anisotropic length scales provided by the a priori bounds, we arrive at ancient limits whose PDE evolution imposes additional rigidity.

Quantum many-body dynamics is difficult to simulate because the global wavefunction develops extensive complexity, whereas local observables may retain only an intrinsic, system-size-independent complexity. This distinction is especially relevant in thermalizing systems, where local subsystems lose microscopic information and relax towards equilibrium. We introduce a variational time-evolution principle that exploits this separation by replacing global-state fidelity with a cost function defined on local reduced density matrices. The resulting locally optimized matrix-product-state (LOMPS) algorithm retains coherent short-time dynamics while using the simplification generated by thermalization at later times, and admits closed-form equations of motion analogous to the time-dependent variational principle. The same principle yields a quantum-classical algorithm in which a quantum processor evaluates the local cost and a noise-robust classical procedure performs the optimization. Proof-of-principle implementations on Quantinuum H2 and IBM Heron processors recover the characteristic local dynamics.

We calculate the dark matter axion mass in the post-inflationary scenario in a minimal model with a set of classical field theory simulations on $12\,288^3$ grids. In the model, the Peccei-Quinn U(1) symmetry is broken by a complex scalar field at a temperature $f_{\rm a} \sim 10^{11}$ GeV, creating a string network. The strings become the boundaries of domain walls at the QCD transition, which draw the strings together and annihilate them. The decay of the strings and domain walls leaves behind axion radiation, with a comoving number density estimated to be $9.48(23)f_{\rm a}^2 H_*$, normalised to unit scale factor when the axion mass is equal to the Hubble rate $H_*$. Using the most commonly quoted lattice results for the topological susceptibility, the dark matter axion mass in this minimal model is $17.46(84)\,\mu\text{eV}$. This corresponds to a symmetry-breaking scale of $3.27(15) \times 10^{11}\, \text{GeV}$, and a haloscope resonant frequency of $4.22(20)\,\text{GHz}$. We argue that field theory simulations of non-minimal models where the strings have a Higgs condensate or gauge flux, and are annihilated by domain walls, will give axion mass predictions below about $40\,\mu\text{eV}$.

World modeling enables intelligence to anticipate consequences, guide interventions, and learn from interaction. Yet predictive models remain domain-specific: can a common learning principle support world modeling across radically different systems? We introduce JEPA-Anything, a domain-agnostic framework based on orthogonal predictive factorization (OPF). Extending joint-embedding predictive architectures, OPF decomposes latent targets into complementary factors, learns them through dedicated pathways, and recombines them within a shared predictive design. We evaluate JEPA-Anything across seven domains: vision, biology, clinical trajectories, control, molecular dynamics, physical fields, and weather. Experiments span representation learning, intervention prediction, out-of-distribution generalization, and long-horizon dynamics, including 10 matched dynamics tasks, forecasting of over 1,000 clinical events, and 100-step molecular rollouts across four systems. Against matched JEPA baselines, JEPA-Anything improves reported metrics on all 10 dynamics tasks and reduces single-intervention prediction error on Interventional Pong by 34.8%. It achieves the lowest one-step and 100-step molecular errors among compared methods in all four systems. Beyond prediction, a factor-nominated biological intervention receives experimental support in cell co-cultures, patient-derived organoids, tumor fragments, and mice; latent orbital modes recover the Keplerian scaling exponent with a fitted slope of -1.4991. These results support a common factorized predictive principle across heterogeneous worlds, connecting world modeling with intervention and experimentally grounded scientific discovery. Code: https://github.com/Gen-Verse/JEPA-Anything

We introduce a new approach, based on neural quantum states (NQSs), to rapidly compute nuclear observables when couplings in nuclear Hamiltonians are varied. A single interaction-dependent NQS, trained across a range of couplings in the Hamiltonian, provides high-fidelity wavefunctions for that continuous range of interaction parameters. With access to the wavefunction for each set of couplings, any static observables can be computed efficiently without retraining the NQS. We apply this framework to two-body nuclear scattering and the deuteron ground state with local interactions derived from chiral effective field theory up to third order.