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arXiv2026

New Formalism for Modelling Flowing Plasmas in a Magnetic Field

A new formalism for modelling a flowing plasma in a magnetic field, having potential for application in plasma thrusters, materials processing, space plasmas, etc., is developed. In this framework, the plasma expands downstream from the source region into an expansion chamber along an axisymmetric magnetic field. For plasma flowing along a magnetic field, the ion velocity parallel to the magnetic field lines is much greater than the perpendicular velocity. This characteristic permits a unique ordering of the relevant flow variables when the flow equations are transformed into a magnetic coordinate system (MCS), in which the coordinate axes are parallel and perpendicular to the field lines. The ordering of the flow variables in the MCS further simplifies the flow equations by allowing them to be split into sets of reduced equations. As a specific implementation, the proposed formalism was validated by using data (for boundary conditions) from a small volume plasma system experiment (Ganguli et al 2016 Plasma Sources Sci. Technol. 25 025026). The model shows favourable agreement with the experiments and is used to predict various physical quantities relevant for applications. The corresponding physical implications are discussed in detail.

physics.plasm-ph↗
arXiv2026

From Answers to Policies: Efficient In-Context Learning System through Emulating Expert Investigation

Pretrained large language models offer a practical foundation for learning useful behavior from few task-specific examples. We argue that current prompt and context optimization methods underuse the extensive knowledge and reasoning capabilities of trillion-parameter models. These capabilities can make adaptation more sample-efficient, more compute efficient and at no performance loss when organized around how human experts investigate failures. We formalize Policy Iteration with Human Feedback (PIHF), which makes this implicit procedure explicit for LLM agents to execute, and build its automated implementation, PIHF-MCP. Initialized from clinician feedback on rare-disease diagnosis, PIHF-MCP supplies the expert procedure, testing tools, review and persistent inquiry records to develop reusable task policies. Across general reasoning benchmarks (BIG-Bench Extra Hard, HoVer and LiveBench-Math), PIHF-MCP improved performance of the baseline model by 16.9, 22.2 and 4.7 percentage points, respectively. With a matched baseline model, development used about 1/5 of the labelled examples and 4% of the task rollouts reported by a previous SOTA in-context optimizer, making it about 9 times faster and 3 times cheaper at comparable or higher scores. In a low-data rare-disease diagnosis setting, policies developed from previous SOTA prompt optimizers trailed a previously published PIHF-developed system on every held-out cohort (on average 16 percentage points). These findings support a route to more efficient inference-time scaling: PIHF-MCP develops reusable policies from a few examples that improve performance on unseen cases and across models. Because each policy comes from an explicit, recorded investigation, the process also keeps humans in the loop and enables ownership and learning, making it well suited to high-stakes decisions.

cs.AI↗
arXiv2026

LadderTeam: Dual-Agent Laddering Elicitation Framework

Eliciting detailed and actionable software requirements from end-users is a critical phase in the iterative development of a software product or application. To ensure the feedback collected is detailed and actionable, software teams can leverage the laddering interview technique. While effective for ensuring granular and actionable items from the software feedback, these interviews are subject to several limitations. They are traditionally a manual process associated with a time and financial burden, limiting scalability; interviewers must balance probing for depth while managing interviewee behavioral and cultural constraints. To address these limitations, we present \textbf{LadderTeam}, an open, reproducible framework that automates UX wireframe interviews using a dual-agent Large Language Model (LLM) architecture. An active interviewer agent executes one of three probing strategies (ACV, 5-Whys, and JTBD) to elicit actionable software requirements from usability feedback comments, while a concurrent background Judge agent evaluates probe-response pairs and triggers real-time guardrails to prevent topic drift. To rigorously evaluate LLM laddering without participant variance confounds, we introduce a controlled simulation methodology utilizing scripted ground-truth transcripts to isolate probe quality as the sole experimental variable. Across 216 interviews, \textbf{LadderTeam} achieved 99.1\% chain convergence and an 81.0\% ground-truth actionable response match (86.1\% reluctant personality, 75.9\% terse personality) with zero drift across all runs. All evaluation code, all transcripts, inputs, and a live demonstration platform will be open-sourced upon acceptance.

cs.SE↗
arXiv2026

Universal CKM for Environment-Aware Wireless Networks: Enabling Cross-Device and Cross-Task Channel Knowledge Transfer

Channel knowledge map (CKM) is a promising technology for environment-aware sixth-generation (6G) wireless networks. However, existing CKMs are tightly coupled with wireless devices and downstream tasks, which limit their scalability and reusability in wireless networks. To address these limitations, this article proposes the concept of universal CKM (uCKM) as a foundational wireless environment prior, which aims to enable cross-device and cross-task channel knowledge transfer for environment-aware wireless networks. We first revisit the representative CKMs and discuss their limitations. Then, the uCKM-enabled new paradigm for environment-aware wireless networks is introduced, and its benefits are highlighted from the perspectives of uCKM construction and utilization phases, for which we propose the visions of ``All for uCKM'' and ``uCKM for All'', i.e., the data acquired by all devices and tasks should contribute to the construction of uCKM, while the constructed uCKM, in turn, can be utilized to support all devices and tasks. Subsequently, we discuss the main challenges of uCKM and propose potential solutions. Last, we provide simulation results to demonstrate the feasibility and performance gains brought by uCKM and outline future research directions.

cs.IT↗
arXiv2026

Exponential Growth of Mean Multiplicities in Length Spectra of Semi-Arithmetic Surfaces of Arbitrary Arithmetic Dimension

For a semi-arithmetic Fuchsian group $Γ$ of arithmetic dimension $r$ with a generalized modular embedding, EGMM holds for $r\leq2$, and for $r\geq3$ under an explicit \emph{strong contraction condition}, via a multi-dimensional Schwarz-Pick bound and a geometry-of-numbers estimate. A covering construction turns every known example into an infinite explicit family with the same exponent via principal congruence towers. We add new $r\leq2$ examples (genus-$3$/$4$ Prym eigenform loci, a different commensurability class from the known triangle groups and McMullen genus-two family) and attempt a direct flat-geometric bound on the contraction constant $δ$ for the latter via its Lyapunov exponents ($δ=2/3$ on ergodic average, by Bainbridge exact computation), explaining why an average bound does not yet certify the pointwise one \eqref{eqstrong-contraction} needs.

math.FA↗
arXiv2026

Finitely Related Clones: Action Algebras and Applications to Free Algebras

For finite-domain constraint satisfaction problems (CSPs), the polymorphism clone provides an algebraic framework for studying the associated constraint language. A central question in clone theory is whether a clone is finitely related, that is, whether it is determined by the operations preserving a finite set of relations. Here, we study this question through the action algebra of a clone on its own $n$-ary part. We prove that a clone $\mathcal{C}$ on a finite domain $C$ is finitely related if and only if its action algebra $\widetilde{\mathcal{C}} = \mathcal{C} \curvearrowright \mathcal{C}^{(n)}$ is finitely related, provided that $n \geq |C|$. We also apply natural clone isomorphisms to obtain a finite-relatedness criterion for free algebras: a finite algebra is finitely related if and only if its free algebra of sufficiently large finite rank is finitely related.

math.LO↗
arXiv2026

Entity tracking emerges in sub-billion parameter language models and exceeds human performance in naturalistic narratives

Understanding language requires tracking entities across discourse - i.e., knowing where things are and how they change, even when not explicitly stated. Whether language models perform such tracking in a human-like fashion remains unclear, in part because existing evaluations rely on artificial tasks, far removed from natural language comprehension, and lack comparisons to humans. Here, we evaluate entity tracking in both language models and humans (N = 48) using naturalistic narratives at multiple levels of complexity. In humans, we find that entity tracking degrades specifically with narrative complexity, not narrative length. In language models, we find that human-level entity tracking is already present at 410 million parameters - well below the multi-billion parameter, code-specialised models identified by prior work - and improves with scale, with contemporary models far exceeding human performance. Together, these results demonstrate that entity tracking, a core component of language understanding, emerges at model scales far smaller than previously thought.

cs.CL↗
arXiv2026

Curvature-induced phantom mimicry and cosmological bounces without violating the Dominant Energy Condition

We explore the active geometric contribution of spatial curvature in a closed universe, distinguishing between kinematic superacceleration and the strict violation of matter energy conditions. We demonstrate that for pressureless matter obeying the Dominant Energy Condition (DEC), positive spatial curvature does not induce a phantom regime, but leads to a decelerating expansion that culminates in a late-time turnaround ($\dot{H}<0$). At this finite-scale moment, the expansion ceases and the apparent horizon stays regular, signaling the beginning of an eventual Big Crunch. We contrast this behavior with the genuine phantom case ($ω<-1$), where positive curvature introduces a distinct, early finite-radius expansion bounce ($\dot{H}>0$) that cannot prevent the inevitable late-time Big Rip singularity. Finally, we contextualize these results, discussing how positive spatial curvature can dynamically mimic phantom phenomenology and permit geodesically complete cosmologies without relying on exotic, energy-condition-violating matter.

gr-qc↗
arXiv2026

The Road Taken: The Role of Optimizers at the Edge of Stability

The edge of stability refers to a phenomenon in deep learning with gradient-based optimizers where the Hessian eigenvalues of the loss remain stable above a threshold that the classical descent lemma predicts to be unstable. Previous works formulate the edge of stability with respect to the maximum Hessian eigenvalue and the learning rate. However, we observe that many first-order methods, including gradient descent, significantly violate the stability bound predicted by these theories by a factor as large as $\times 21.1$. Moreover, this deviation turns out to be systematic and highly dependent on the underlying optimizer, which is not captured by previous formulations. This calls for a new formulation of the stability threshold, which we derive from the directional Hessian and the gradient-alignment score with respect to the actual update taken by the optimizer, rather than the maximum curvature mode. Our new formulation of the realized edge of stability not only removes optimizer-dependent offsets and provides more consistent predictions of the stability threshold, but also introduces new diagnostic tools that reveal the unique role of the optimizer in actively balancing between the temporal and spatial budgets in first-order optimization.

cs.LG↗
arXiv2026

Realizing Logical Diagonal Gates via Transversal Physical $Z$-Rotations in CSS Codes

Calderbank-Shor-Steane (CSS) codes, constructed from nested classical codes $C_2 \subseteq C_1$, are typically optimized for good code parameters. However, practical quantum computing equally demands fault-tolerant logical gates. In this work, we characterize nested pairs $(C_1, C_2)$ whose resulting CSS codes realize a target logical diagonal gate via transversal physical $Z$-rotations. In doing so, we recover a result of Camps-Moreno et al. that CSS codes can realize only logical single-qubit $Z$-rotations and multi-qubit controlled-$Z$ rotations via transversal physical $Z$-rotations. Building on our characterization, we develop the ''appending construction'', that takes as input an $[[n',k']]$ CSS code $Q'$ and a target logical $Z$-rotation (single-qubit or multi-controlled) $U_L$, and extends $Q'$ by systematically appending $n''$ physical qubits to obtain an $[[n,k]]$ CSS code $Q$ with $n = n'+n''$ and $k=k'$. The target logical gate $U_L$ is realized in $Q$ by applying a well-chosen physical transversal $Z$-rotation to the $n''$ appended physical qubits. Moreover, any logical gate realized via transversal physical $Z$-rotations in the input code $Q'$ remains transversally realizable in the extended code $Q$. The CSS code $Q$ may incur a loss in minimum distance, but the loss can be controlled through the parameter choices made in the construction. By repeatedly applying the appending construction, we can extend any CSS code $Q'$ to obtain a CSS code $Q$ that supports fault-tolerant implementations of multiple desired logical $Z$-rotations. The cost to be paid for this is the increased physical qubit overhead as the number of target logical gates grows. To illustrate our methodology, we construct CSS code families that transversally realize addressable logical single-qubit and multi-controlled-$Z$ rotations.

quant-ph↗
arXiv2026

Scaffolding Minds: Optimizing Latent Visual Target Representations for Multimodal Reasoning

Latent reasoning has advanced multimodal reasoning through a two-stage training paradigm: (1) a helper image is encoded into latent tokens to teach visual chain-of-thought during a supervised fine-tuning (SFT) stage, and (2) these latent tokens are further refined with reward feedback during a reinforcement learning (RL) stage. In this paper, we identify two key limitations of this framework, one in each stage. First, the SFT stage typically relies on an off-the-shelf vision encoder to encode the helper image, yielding suboptimal latent representations that may not be well aligned with the downstream reasoning task. Second, existing RL methods treat the latent component only through deterministic regularization, which constrains policy drift but does not create alternative latent trajectories for exploration. To address these limitations, we propose Scaffolding Minds. Our approach learns a dedicated scaffolding encoder that provides an optimized target in latent space, and learns both the mean and variance of the RL sampler. We further show that these two improvements are complementary, together yielding substantial gains over strong baselines. Empirically, our method improves over the strongest latent reasoning baseline by +9.5 points on FrozenLake spatial planning, with the gain widening to +19 points on the 32x32 grids, and by +5.6 points on average across nine visual-centric reasoning benchmarks.

cs.CV↗
arXiv2026

Rethinking Patch Based Multivariate Time Series Forecasting with Semantic Structured Partitioning

Multivariate time series forecasting (MTSF) is a fundamental task in many real world applications. Existing patch based forecasting methods generally fall into three categories: fixed partitioning, multi-scale partitioning, and extendable partitioning. Fixed partitioning often breaks meaningful temporal boundaries, multi-scale partitioning may introduce redundant representations across scales, and extendable partitioning improves flexibility but still lacks an explicit mechanism for organizing semantic structure and modeling interactions among heterogeneous temporal patterns. To address these limitations, we propose SCPaT, a Transformer based framework built on semantic structured partitioning. SCPaT first decomposes input sequences into semantically consistent units through adaptive semantic unit generation, then constructs a dynamic semantic graph to model directed dependencies among these units and organize them into higher order semantic blocks. Based on these structured representations, an importance aware routing mechanism adaptively dispatches different semantic blocks to different experts for customized modeling. Extensive experiments on 12 real world datasets demonstrate the effectiveness of SCPaT.

cs.AI↗
arXiv2026

A Classification of Small MSTD Sets in Arbitrary Fields

A finite set $A$ in an additive abelian group is a More Sums Than Differences (MSTD) set if $|A+A| > |A-A|$. We prove that no MSTD set of size $5$ exists in an additive abelian group. Using a computer program inspired by Hegarty, we then obtain classifications of MSTD sets of sizes $6$, $7$, $8$, and $9$ in arbitrary fields. We also investigate the minimal cardinality of MSTD sets that are multiplicative subgroups of $\Z/p\Z$.

math.NT↗
arXiv2026

Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems

Deep learning surrogates have become powerful tools for simulating and forecasting complex dynamical systems, yet their utility remains limited by catastrophic error accumulation during long-term autoregressive rollouts. This behavior is partly tied to the nature of the underlying systems: chaotic spatiotemporal systems visit phase space unevenly, with dynamics dominated by recurrent, low-dimensional quiescent states and characterized by rare and dynamically complex regime transitions. Trained under a sample-wise uniform objective, standard neural surrogates allocate their finite capacity to the statistically more numerous low-dimensional quiescent states, systematically under-representing the transient regimes that trigger disproportionate, localized errors. Existing imbalanced-regression methods tackle this issue by reweighting samples according to target-space density. However, statistical target-space rarity does not coincide with the intrinsic dynamical rarity encoded in the recurrence geometry of the attractor. To address this, we introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework. Using the local dimension $d$ from dynamical systems theory as an a priori measure of a state's dynamical complexity, DAW reshapes the loss landscape to allocate representational capacity toward the sparse, high-$d$ regimes where forecast errors are systematically large. On the chaotic KS equation, DAW consistently outperforms uniform training as well as weighting based on target-space rarity, and its randomly permuted ablation, reducing long-term autoregressive error relative to all baselines. Event-level analysis shows that DAW achieves this by suppressing the localized error amplifications incurred during sharp jumps in the local dimension $d$, which typically accompany complex physical processes such as wave-merging in the KS system.

cs.LG↗
arXiv2026

Functional compatibility as a determinant of persistent neural learning

Neural networks can acquire new capabilities while damaging existing ones, but what determines whether new learning persists remains unclear. We identify functional compatibility, the extent to which incoming learning can coexist with behaviour that must be preserved, as an experimentally manipulable causal determinant of persistence. From identical neural states, we vary compatibility while matching unrestricted learning opportunity and imposing a common retention requirement. Persistent learning increases with compatibility across independent directions, convolutional and transformer architectures, vision and text, and a ten-seed replication. Learning rules and retention constraints determine how much compatible opportunity is retained, whereas nonlinear geometry limits the matched intervention at larger update norms. Functional compatibility therefore reframes stability-plasticity from preventing forgetting to determining which new learning can coexist with existing function and persist.

cs.LG↗
arXiv2026

Beyond the $L^{9/5}$ Vorticity Criterion in the Stationary Navier--Stokes Liouville Problem

Let $(v,p)$ be a smooth stationary Navier--Stokes solution in $\mathbb R^3$ with $v(x)\to0$ as $|x|\to\infty$. We prove that $v\equiv0$ if its vorticity $ω:= \nabla\times v$ belongs to $L^{s,\infty}(\mathbb R^3)$ for some $9/5\le s<(2+\sqrt{13})/3$. To the author's knowledge, this is the first global weak-Lorentz vorticity criterion beyond $9/5$ requiring neither smallness nor an additional Fubini-type hypothesis. The finite Dirichlet integral is recovered from the vorticity hypothesis rather than assumed. In particular, $|ω(x)|=O(|x|^{-α})$ implies triviality for $α>\sqrt{13}-2$, crossing the $|x|^{-5/3}$ vorticity-decay scale. The proof combines this automatic finite-energy upgrade with a new variable-denominator Bernoulli--vorticity quotient identity. Its concave level localization produces a vanishing normalized-vorticity trace, which is then coupled to a pressure-weighted Lamb identity and a nonlinear feedback estimate.

math.AP↗
arXiv2026

Transient Dynamics and Duty-Cycle Optimization in a Pulse-Wwidth Modulation Bell--Bloom Pumping

We investigate the duty-cycle-dependent atomic response under full-depth intensity pulse-width modulation in Bell--Bloom optical pumping. A time-domain Bloch model explicitly resolves the pump-on/off spin dynamics, yielding piecewise analytical transient solutions and a periodic steady-state description without cycle averaging or harmonic truncation. An extended free-induction-decay method independently determines the effective dark and pump-on transverse-relaxation rates, $W_0$ and $W$. The predicted lock-in responses agree well with experimental results. We find that for each Larmor frequency $ω_0$, the slope is maximized at a finite pump rate that increases with $ω_0$. These results provide a practical framework for sensitivity-oriented optimization of the duty cycle and pump rate in PWM-driven atomic magnetometers.

physics.app-ph↗
arXiv2026

GeoWAM: Visual Geometry World Action Models for Autonomous Driving

World action models (WAMs) have recently gained increasing attention as a framework for jointly modeling scene evolution and ego actions in autonomous driving. Most existing WAMs learn scene dynamics in pixel space by combining a video-generation backbone for future-observation prediction with an action head for ego-trajectory prediction. Pixels, however, provide only an indirect representation of these dynamics: they entangle geometry and motion with appearance, texture, and illumination, forcing the model to infer three-dimensional transformations from two-dimensional observations. We argue that point-based geometry provides a more natural state space for driving. It explicitly captures spatial structure and both rigid and non-rigid scene dynamics while remaining aligned with the 3D space of driving actions. Building on this insight, we introduce GeoWAM, a visual geometry world action model for autonomous driving. Rather than predicting future images, GeoWAM is pretrained to forecast future scene geometry, yielding representations that jointly encode spatial structure and temporal evolution. A geometry-conditioned action head then leverages these learned geometric dynamics to predict future ego-trajectories. Extensive experiments show that GeoWAM outperforms image-based alternatives, achieving a combined EPDMS of 36.6 on navhard without PDMS supervision and strong zero-shot generalization to nuScenes, with a collision rate of 0.24%. Scaling geometry pretraining with unlabeled data further improves performance, increasing the navhard score by 8.2% to 39.6 and strengthening zero-shot transfer to nuScenes, where the collision rate is reduced by 50% to 0.12%. Together, these results establish geometry as an effective state representation for autonomous driving and geometry pretraining as a general, scalable strategy for downstream planning.

cs.CV↗