Papers

Psychological dynamics unfold across multiple timescales: symptoms and other psychological states can change rapidly, whereas social, environmental, biological, and developmental conditions often evolve more slowly. We formulate this structure as a stochastic slow-fast system in which binary symptom states form a fast interacting network embedded within a slow contextual field. Pairwise symptom coupling governs interactions within the fast layer, while the contextual field shifts symptom-specific activation tendencies and can itself receive feedback from sustained symptom activation. Simulations show that changes in the slow field can shift the macroscopic activation state of the symptom system even when the underlying interaction matrix remains fixed. Perturbations to the field generate transient increases in symptom activation followed by recovery, while feedback between the fast and slow layers delays recovery and, when sufficiently strong, produces dependence on initial conditions. We further show that when between-person variation in the contextual field is omitted from network estimation, the inferred system exhibits stronger total coupling and nonzero couplings between symptom pairs that are uncoupled in the data-generating model. Thus, slowly varying context can alter both the dynamics and the apparent interaction structure of a fast psychological system. The framework connects psychological network models with slow-fast dynamical systems and provides a formal basis for distinguishing changes in activation from changes in coupling.

Large language models (LLMs) increasingly mediate human decisions and communication, yet their behavioural regularities remain difficult to characterize systematically. We develop a cross-linguistic psychometric profiling framework and evaluate nine LLMs using seven psychological instruments, with five repeated administrations per model and language in Chinese and English. Items unresolved after a prespecified retry procedure are retained as NA. Joint analysis of scored and NA responses captures response tendencies and boundaries of self-report applicability. LLMs exhibit structured, model-specific profiles despite a shared alignment-shaped pattern of higher prosocial and self-regulatory responses and lower dominance, disengagement and harmful-intent endorsement. NA responses are structured rather than uniformly distributed, indicating where outputs are treated as inapplicable, refused or cannot be mapped to valid response options. Language condition and provider origin are associated with profile configuration and answerability, whereas repeated administrations show high reproducibility and permit recovery of model identity. Human-reference and prompt-robustness analyses further indicate that these signatures are context dependent. Joint analysis of psychometric profiling and answerability offers a framework for quantifying deployment-level behavioural signatures.

We investigate an inflationary scenario within a modified gravity theory that extends the Einstein-Hilbert action through a non-minimal coupling between the inflaton $\phi$ and the trace of the energy-momentum tensor $T$. This $f(\phi)T$ framework is designed to naturally recover the standard general relativity in the post-inflationary universe. Within this theory, we apply the Woods-Saxon potential. The slow-roll dynamics yields a luminal sound speed $c_s^2=1$ for our specific choice of the coupling function. For the model parameters $a \lesssim 1$ and the modest coupling $\beta=0.1$, we obtain a scalar spectral index $n_s\approx0.959$–$0.966$ and a tensor-to-scalar ratio $r<0.01$, which reveal a good agreement with the latest Planck and BICEP/Keck data on the $(n_s, r)$ constraints. Crucially, we shall demonstrate that the $f(\phi)T$ coupling is essential for the observational viability of the model with respect to the CMB two-point statistics. This work establishes a viable inflationary scenario within the scope of the inflationary observables which are considered here.

Federated learning (FL) enables collaborative model training without centralizing private data, but performance often degrades under feature skew: clients share labels while the conditional input distributions $p_i(x\!\mid\!y)$ vary due to latent, client-specific appearance factors. We propose Joint Domain-Class Federated Learning (JDFL), a lightweight, optimizer-agnostic extension that makes this latent domain variation usable without sharing raw data. JDFL first infers domain clusters called pseudo-domains from brief local update signals. It then expands the classifier head to output $M\times C$, joint (domain-class) logits. This allows the model to represent domain-conditioned appearance while keeping a shared backbone. To train the expanded head we introduce two complementary supervision strategies based on simple intuitions: a similarity-aware soft-labeling that transfers evidence between nearby inferred domains while allowing domain-specific specialization, and a per-sample randomized target assignment that perturbs supervision across the joint outputs and serves as a low-cost training-time regularizer. JDFL integrates with existing standard FL methods (e.g., FedAvg, SCAFFOLD) with minimal changes. Empirically, both supervision modes consistently improve global test accuracy on standard domain-shifted image benchmarks; ablations and sensitivity studies show the gains stem from the proposed supervision and parametrization rather than mere capacity increase.

An acyclic dicolouring of an oriented graph is a vertex partition in which every colour class and every bipartite subdigraph induced by two classes is acyclic. We first prove the Gallai–Roy-type bound $\vec{\chi}_a(D)\leq L(D)$, where $L(D)$ is the maximum order of a directed path. Let $r=\log_2(8/7)$. Bang-Jensen, Picasarri-Arrieta, and Yeo previously constructed tournaments of order $n$ whose acyclic dichromatic number is at least $n-(\frac8r)\log_2 n-\log_2\log_2 n$. We improve the leading logarithmic coefficient by a factor of two: for the uniform random tournament $\mathcal{T}_n$, asymptotically almost surely, $\vec{\chi}_a(\mathcal{T}_n)\geq n-\frac4r\log_2 n+\frac2r\log_2\log_2 n-O(1)$. Finally, if $m(k)$ denotes the minimum order of an oriented graph with acyclic dichromatic number at least $k$, tournament completion shows that the same minimum is obtained over tournaments. We prove $m(3)=5$ and $m(4)=7$ and classify the tournament witnesses at these minimum orders: there is one at order five and two at order seven.

We discuss the pion gravitational form factors at intermediate and large spacelike momentum transfer in a perturbative-QCD factorization framework. The short-distance kernel is supplemented by the one-loop non-Abelian $TJJ$ correlator, where the energy–momentum tensor couples to two off-shell gluons. Its trace sector contains the QCD conformal anomaly and admits a scalar, dilaton-like pole interpretation. A transverse-momentum-dependent pion wave function, combined with Sudakov resummation and a Gaussian intrinsic-transverse-momentum profile, suppresses endpoints and large transverse separations. The projection on the pion form factors exhibits a characteristic hierarchy: the isolated anomaly cancels in the momentum form factor 4A_\pi$, remains important in the mechanical form factor $D_\pi$, and dominates the $TJJ$ correction to the trace form factor. The result identifies a beta-function-controlled short-distance contribution to pion mechanical structure and clarifies the relation between the perturbative anomaly pole and a correlated scalar partonic channel.

We show that a statistical model in the sense of McCullagh, in the form given by Brøns, is a natural transformation between two functors from the category of designs to the Kleisli category Stoch of the Giry monad, provided that its components are measurable in the parameter. The condition is empty for finite models. A design-indexed quantity is a family of morphisms of Stoch defined on the parameter objects, called meaningful if it is natural. We prove that Tjur's criterion, imposed on parameter functions indexed by finite samples with multiplicities, forces the indexing by the support and then coincides with naturality over the insertions. For finite designs we show that a quantity can be corrected to a natural one within a given class of corrections if and only if a class vanishes in the first cohomology group of a Baues-Wirsching complex relative to that class, while its image in the absolute group is always zero. In the one-way layout, marginal dispersion is not meaningful, and within-group dispersion is the unique correction that leaves the merged design unchanged. A prior is a family of states on the parameter objects, called coherent over a class of design morphisms if it is natural over that class. We show that coherence at a merge confines the prior to the image of the corresponding parameter map, that coherence over the insertions is Kolmogorov consistency, and that coherence over the injections adds the exchangeability assumed by the categorical de Finetti theorem. In the finite one-way scheme, the coherent priors form polytopes of known dimension. The analogue of Jeffreys' general rule is not coherent, while the analogue for location-scale families is. Finally, we show that ridge regression is the Bayesian inversion of the Gaussian linear model with respect to a Gaussian prior, which is coherent over the insertions and never over the injections.

The Pfaffian number of a graph is the minimum number of Pfaffians needed to obtain its perfect-matching polynomial by linear combination. In 2009, Norine conjectured that every Pfaffian number is a power of four. Miranda and Lucchesi disproved this conjecture in 2011 by constructing a graph of Pfaffian number six, and conjectured instead that every nontrivial Pfaffian number is even. We disprove their conjecture by proving that the Pfaffian number of $K_{3,3}\sqcup K_{3,3}$ is 13. We also construct a connected cubic bipartite matching-covered graph with Pfaffian number 13.

We give a candidate proof of Conjecture 5 in the third arXiv version of Latala and Strzelecka Operator lp lq norms of Gaussian matrices.

Reach-and-attach of soft robotic arms with passive suction requires accurate targeting and sufficient contact speed, yet geared actuators can impose a speed limit that improved trajectory tracking alone cannot overcome. This paper proposes an embodied snap controller that separates slow servo-driven preloading from rapid elastic release, enabling a compliant arm to move beyond its direct tendon-driven speed limit. Octopus biology motivates the controller's section-wise organizational prior, rather than reproduction of the octopus nervous system. A learned policy shared across three sections selects preloads, aim, tendon slack, and release timing, determining where, how, and when to load and release the body. The policy is optimized offline using a hardware-validated recurrent model within experimentally supported bounds. Across five optimization seeds and 400 unseen simulated targets, attachment success is $(73\pm4)\%$ at a $5\text{ cm}$ lateral tolerance, and the shared policy reaches the matched centralized controller's mean final reward after a median $17\%$ of the common evaluation budget. Hardware characterization achieves tip speeds of 1.56-1.64 m/s, at least $108\%$ above direct tendon-driven release. In 18 open-loop hardware trials across six placements, 17 exceed the 1 m/s snap threshold and nine retrieve the object, with successful retrieval at five placements. These results demonstrate a practical division of responsibility in the control problem: learned control prepares the body, and passive body mechanics execute the rapid movement needed for dynamic reach-and-attach.

Vision-language models (VLMs) provide a compelling foundation for reasoning-driven mobile navigation, offering rich contextual understanding and strong generalization from large-scale pretraining. Most existing navigation frameworks rely on imitation learning and therefore require substantial labeled trajectory data, limiting their scalability and robustness. In this work, we propose a parameter-efficient approach to fine-tune a pretrained VLM for autonomous navigation using an Imperative Learning paradigm. By optimizing against differentiable geometric cost fields rather than labeled trajectories, our model learns to generate collision-free paths exclusively from stereoscopic depth observations. We introduce a unified end-to-end navigation pipeline for natural-language-driven robotic control. This system leverages a shared VLM backbone with task-specific Low-Rank Adaptation (LoRA) modules, effectively bridging the gap from semantic target selection to low-level trajectory planning. Our approach achieves competitive Success weighted by Path Length (SPL) in unseen environments while updating less than 1% of the model's total parameters. Qualitative real-world experiments validate sim-to-real generalization and stable path planning without fine-tuning on real-world data. These results highlight a practical approach for deploying VLM-based agents on mobile robots, enabling high-level semantic navigation without the prohibitive requirement for large-scale, labeled trajectory data.

Given a simply-connected $4$-manifold with boundary the $3$-sphere, we give sufficient conditions for a knot in the boundary to bound a simply embedded locally flat surface in the $4$-manifold of fixed nonzero genus, representing a fixed nonzero homology class. In certain indefinite cases, we also give conditions for these slice surfaces to be unique up to equivalence.

Graph-based ranking methods such as PageRank can amplify structural disparities in networks, motivating fairness-aware ranking mechanisms for sensitive groups. Locally Fair PageRank (LFPR) enforces fairness through local propagation, but exact computation requires repeated iterations until convergence, limiting scalability on large graphs. We develop a scalable analytical framework for approximating Neighborhood Locally Fair PageRank and Uniform Locally Fair PageRank. By introducing a group-aware heterogeneous mean-field representation, the framework aggregates structurally similar nodes into degree classes and derives closed-form approximations of stationary LFPR scores, avoiding repeated propagation over the fairness-aware transition matrix. We develop a One-Step Refinement (ORF) mechanism that applies the fairness-aware propagation operator once to the mean-field estimate, incorporating node-specific neighborhood information without iterative convergence. The fluctuation analysis characterizes degree-dependent variability around the mean-field solution and shows that the coefficient of variation decreases with increasing in-degree. The mean-field approximation reduces the computational cost of exact LFPR from iterative graph-scale propagation to linear-time node-level estimation, while ORF requires one graph traversal. Experiments on six real-world networks show strong agreement with exact LFPR scores and rankings, preservation of group-level fairness, and substantial runtime reductions. The mean-field approximation reduces complexity to $\mathcal{O}(n)$, while ORF improves accuracy with $\mathcal{O}(m+n)$.

In this work, we present a constructive method to derive homogeneous linear differential equations of arbitrary order for Laguerre–Hahn orthogonal polynomials. The approach is based on a hierarchy of structure relations, built recursively from the fundamental structure relation of the Laguerre–Hahn forms. The fourth-order differential equation, which has been extensively studied in the literature, is naturally recovered as a particular case of this general framework. Special attention is devoted to the semiclassical case. The method is fully algorithmic and has been implemented in {\it Mathematica$^{\circledR}$}. We apply it to two Laguerre–Hahn families of class zero analogous to Hermite, providing explicit structure relations and differential equations of orders five and ten. We also examine the classical Hermite sequence, which is recovered as a limiting case of the first family.

We prove Steinness over $\breve{\mathbf{Q}}_p$ for the basic local Shimura tower attached to $G=\mathrm{GL}_n$, $\mu=(1,1,0^{n-2})$, with basic Newton slope $2/n$, for every odd $n\ge3$, at every finite level and for every prime $p$. The proof proceeds by constructing global analytic functions from the crystalline period map, proving compactness of their sublevel sets via a perfectoid normalization of Tate lattices, and showing that the resulting function map to affine space is finite. The key geometric inputs are the Fargues–Fontaine realization of the universal cover, a normalized determinant on the rank-two locus, and an integral PEL realization over $W(\overline{\mathbf{F}}_p)$ used to produce bounded global Hodge generators. The integral constructions include the prime $p=2$.

A non-linear, non-Bayesian method called sequential bound estimation (SBE) derived 100% confidence intervals of location (CIL) for 219 explosions in the ocean from measurements of their time differences of arrivals among five widely-spaced time-unsynchronized receivers on the ocean bottom. The explosion's locations were measured with the global positioning system. A blind evaluation revealed all 219 explosions were within their CIL. The probability this could happen by chance is $4 \times 10^{-116}$. The explosions were detonated in shallow water on the eastern continental shelf of the U.S. over the so-called New England Mud Patch.

Reinforcement learning in real-life applications requires safety guarantees during exploration. Typical reinforcement learning algorithms do not provide such guarantees, and many modifications that do rely on Gaussian processes (GPs), which have a large computational cost. We propose a computationally lightweight algorithm based on the Nadaraya-Watson estimator that safely explores and optimizes constrained Markov decision processes (MDPs). Our algorithm, CoLSafe-MDP, uses an estimator that scales in constant-time with bounds on the estimates, a significant improvement from its GP-based counterparts that scale cubically with the number of data points. We then evaluate its performance in a grid-based environment and on observational Martian terrain data.

Context: Wolf-Rayet (WR) stars are particularly rare in low-metallicity galaxies and remain poorly understood. Detailed studies of the presumably complete population of WR stars in the nearby Small Magellanic Cloud (SMC) galaxy led to perplexing results. Aims: The nearby galaxy NGC 6822 has a similar metallicity to the SMC, and hence provides an excellent laboratory for a comparative study. We aim to derive the stellar and wind parameters of each known WR star in NGC 6822 by means of quantitative spectroscopy. The results are compared with the WR population of the SMC. Methods: New optical and UV spectroscopic observations have been obtained with the Very Large Telescope (VLT) and Hubble Space Telescope (HST). We employ the Potsdam Wolf-Rayet (PoWR) model atmosphere code for our analysis, consistently fitting synthetic spectra to the observed spectral energy distribution, and optical and UV spectra. Results: We spectroscopically confirm all four stars in our sample belong to the nitrogen sequence with early subtypes (WN3-WN6). All stars show indications of binarity. Only one star in our sample has a high fraction of hydrogen in its atmosphere, as typical for the WN population in the SMC, and two other stars in our sample are hydrogen-free. Finally, the spectrum and parameters of the fourth object closely resemble those of the qWR-type strongly magnetic merger-product star in the HD 45166 binary. Conclusions: The stellar properties of our sample are diverse. We have identified the first H-free WN-type stars at metallicities $\sim$ 1/7Z$_\odot$. According to evolutionary calculations, the WR stars in NGC 6822 stem from progenitors with initial masses below 40 M$_\odot$. We report a discovery of a low luminosity stripped qWR star in NGC 6822, and conclude that the WR star population in NGC 6822 and the SMC are distinct despite similar metallicities of their host galaxies.

Non-technical stakeholders frequently cannot write the SQL needed to extract insights from operational databases. We built and evaluated a Text-to-SQL agent that closes this gap end to end: a six-node LangGraph StateGraph checks question relevance, fetches the live schema, generates PostgreSQL, validates it with a dry run, retries on failure, executes the query, and narrates the result set in plain English. The agent uses prompt engineering only; no model was fine-tuned. We evaluated it on the Chicago Crime dataset (approximately 8.5 million records, 22 attributes) against a hand-built benchmark of 100 natural language questions with ground-truth SQL, stratified into 30 Easy, 40 Medium and 30 Hard items. Comparing two prompt revisions of the same agent, the revised system (V2) reached a Valid SQL Rate of 93% (from 87%), an Execution Accuracy of 60% under a hybrid relational equivalence metric (from 47%; 19% from 12% under strict JSON matching), and a mean Synthesis Quality of 4.34 out of 5 (from 3.91). The single largest driver was removing a LIMIT 10 instruction from the system prompt, which had been truncating multi-row answers. Error analysis attributes the residual failures to relevance-checker false rejections, ambiguous question semantics, and free-tier API rate limits rather than to the language generation step. We report no comparison against an external baseline system or a public benchmark; the study is a single-model engineering evaluation.

Generating text-rich images from prompts requires both textual fidelity and the coherent integration of text into the surrounding image. An explicit layout can provide structured guidance about what text should appear and where, but a well-formed plan alone does not guarantee that the renderer will realize it faithfully. Existing layout-based AR-diffusion systems typically optimize planning and rendering separately, preventing the planner's representations from being adapted jointly with image synthesis. We introduce DuetGen, an autonomous visual text generator built on DeepFusion, which jointly learns autoregressive planning and continuous diffusion rendering. DeepFusion conditions a diffusion transformer on the planner's prompt and bbox-content hidden states, allowing rendering supervision to shape the representations connecting textual plans with visual outputs. Its joint objective combines autoregressive plan supervision, text-region-weighted diffusion learning, and auxiliary coordinate supervision to maintain structured planning, emphasize text-bearing regions, and improve the spatial precision of planner representations. During inference, Phase-Aware Attention Modulation strengthens the correspondence between image regions and their matched coordinate and content states, facilitating region-specific execution of the generated plan. With a 2B planner and a 4B single-stream DiT, DuetGen achieves 0.8293 word accuracy on CVTG-2K and 0.938 accuracy on LongText-Bench, closely matching the substantially larger Qwen-Image on both benchmarks. These results demonstrate the value of jointly learned planning representations and region-specific rendering for autonomous visual text generation.

We resolve an existing question concerning dynamical and structural stability of the E {\times} B staircases in magnetically confined fusion plasma. The problem has stirred considerable interest in the literature due to a unique combination of its scientific and practical aspects. Here, we report a new approach to the problem by combining the paradigmatic Hasegawa-Wakatani model of electrostatic drift-wave turbulence with an idea of interaction renormalization, imported from quantum field theory. It is shown based on the Schrödinger-Newton equation with renormalized interaction constant that the plasma staircase is robust and stable as soon as the nonadiabaticity parameter, {\delta}, goes above a certain critical value, and is unstable otherwise. This critical value is an exact result of the interaction model and is found to be {\delta}c = {\pi}. For {\delta} < {\delta}c , the unstable system expands in the radial direction, resulting in a radial second moment that grows with time t as t^(2/3). The results obtained bear important implications with regard to the implementation of arrays of semipermeable transport barriers in tokamaks, suggesting a threshold condition for their generation.

Reproducibility is essential for scientific progress, enabling validation, fair comparison, and building upon prior work. In computational network science (CNS), however, reproducibility remains limited due to missing code, inaccessible datasets, and insufficient reporting of experimental details. This paper presents a taxonomy of reproducibility in CNS, structured around artifact availability, algorithmic clarity, experimental environments, and data processing and experimental pipelines. To systematically examine these challenges, we conduct four case studies spanning diverse methodological settings: topic-based influential user detection (network science and natural language processing-based methods), influence-based community detection (pure network-based methods), influence maximization (classical, heuristic, approximation, and AI-based mixed approaches), and reinforcement learning for network analysis (learning-based methods). Across these domains, we observe a consistent lack of publicly available artifacts, particularly code and datasets, hindering verification and comparison of results. We identify key causes of this reproducibility gap, including limited incentives for sharing artifacts, data access restrictions, incomplete experimental descriptions, and a complex methodological pipeline. Finally, we outline recommendations to improve reproducibility, including mandatory artifact sharing policies, standardized benchmarks, and comprehensive reporting of experimental setups. Addressing these gaps is critical to ensure transparency, comparability, and sustained progress in computational network science.

Talking-head and dyadic models now achieve real-time inference, yet fast motion generation alone does not produce an interactive conversation. A live system must synchronize the model's output with speech from an external voice agent, schedule video frames for playback, and handle interruptions. We introduce AVTR-1, an open stack for real-time interactive avatar conversations, built around a compact 153M-parameter autoregressive flow-matching motion generator conditioned on both participants' audio. We adapt its audio encoder for streaming through self-distillation. The stack turns the model's chunk-based generation into a continuous, synchronized audio-video stream driven by an external voice agent, and we analytically derive its contribution to the user-facing latencies and validate the resulting bounds with two commercial voice agents. Further experiments demonstrate that AVTR-1 leads the compared dyadic systems on all reported visual-quality metrics and most conventional listening-motion metrics while remaining competitive in lip synchronization. Its inference runtime operates in real time on data-center and consumer GPUs. However, conventional listening metrics do not establish whether the paired speaker's speech contributes to generated motion. We therefore introduce the Reference-Based Directed Granger Gain (R-DGG), which measures the additional predictive information carried by speaker speech after accounting for listener history and speaker motion. R-DGG finds statistically supported predictive dependence for recorded listeners and all evaluated dyadic systems, but not for talking-head generators without paired audio or mismatched speaker-listener pairs. We release the model weights, renderer, and serving backend under component-specific licenses.

Machine learning development in Jupyter notebooks is iterative and feedback-driven. Practitioners author statements that reveal information about program execution and use it to decide what to do next. We call these feedback statements and identify two forms: exploratory statements that display values for visual inspection, and validation statements that enforce conditions programmatically through assertions. Many ML failures do not surface as exceptions and thus escape the crash-based analyses that dominate prior work on ML notebooks. This study examines what practitioners check to catch failures that would otherwise pass silently, by characterizing feedback statements that encode the practitioner's mental model of what the code should do and what could go wrong. We mine 297,851 public Python Jupyter notebooks from GitHub and Kaggle and extract 1,092,780 feedback statements. We sample 816 statements through proportional stratified sampling from semantic clusters obtained from CodeBERT embeddings, and apply grounded theory and open coding to label and analyze each one. We contribute a taxonomy of feedback statements in ML notebooks, organized along the functional intent of the statement and the ML pipeline stage in which it appears. The taxonomy reveals that feedback is overwhelmingly exploratory, and that the two platforms host qualitatively different modes of ML work. Mapping our taxonomy to an existing crash taxonomy shows that it captures defensive practices against silent failures that crash analysis cannot observe. Our findings indicate that notebook source should be treated as a confounder in studies of ML developer practice, surface opportunities for notebook tooling, and motivate empirical study of silent ML failures. We release the corpus of 1,092,780 feedback statements and the codebook to support replication and tooling research.

We study finite-time singularity formation for a nonlocal Boussinesq system arising in cold-plasma dynamics. We show that smooth, symmetric initial data with strictly positive total density and a sufficiently negative velocity slope at the origin lead to finite-time blow-up. More precisely, we give an explicit upper bound for the lifespan and show that the velocity gradient becomes unbounded.

Vision-language agents that crop and zoom are trained with rewards that credit a successful tool call, yet a successful call does not show that the model needed to look or used the pixels it received. On our cold-start checkpoint only 10% to 12% of visual calls were both needed and used, and released agents make spurious calls 36% to 87% of the time on individual benchmarks. Outcome rewards, judge rewards, and branch probes each observe one side of this failure, and about two thirds of what an outcome reward pays goes to calls that were neither needed nor used. CounterCredit asks both questions of every image-returning call at its realized pre-call state, using the policy's own gold-answer score. A decision value compares the realized visual branch with answering immediately; an evidence value compares the returned crop with random same-size patches substituted into the same call. A call verified on both earns cashback and every other executed call pays rent; the price is bounded so that every correct trajectory outranks every wrong one, and a dual-channel GRPO advantage keeps the price in its own units. From the same cold start, prompt pool, and budget, CounterCredit reaches 89.5% on V*, 80.2% on HR-Bench-4K, and 76.4% on HR-Bench-8K, 6.3 to 9.4 points above outcome-only GRPO at 1.78 against 1.84 calls per question, and lowers the spurious-call rate to 31% to 36%, the lowest among the agents evaluated. The same recipe lifts a Qwen3-VL-8B base from 75.4 to 80.8 on average.

For an odd prime $p$, let $\Gamma(R)$ denote the zero-divisor graph associated with the finite local ring $R= \mathbb{F}_p[x]/\langle x^4 \rangle$, having $p^3 - 1$ vertices and size $|E(\Gamma(R))| = \frac{1}{2}(3p^4 - 4p^3 - p^2 + 2)$. Using an equitable 4-cell partition induced by the ideal filtration $\langle u^3 \rangle \subset \langle u^2 \rangle \subset \langle u \rangle$, we prove that $\operatorname{Spec}_A(\Gamma(R))$ decomposes into discrete levels $\lambda \in \{0, -1\}$ with multiplicities $p^3 - p^2 - 1$ and $p^2 - 3$, respectively, alongside three irrational roots of an irreducible cubic polynomial $P_3(\lambda) = 0$, yielding adjacency energy $\epsilon(\Gamma(R)) = 4p^2 + \mathcal{O}(p)$. In contrast, the Laplacian spectrum is entirely integral: $\operatorname{Spec}_L(\Gamma(R)) = \{0^1, (p - 1)^{p^3 - p^2}, (p^2 - 1)^{p^2 - p - 1}, (p^3 - 1)^{p - 1}\}$. Consequently, the tree entropy satisfies $z(\Gamma(R)) = \ln p - \frac{1}{p} + \frac{\ln p}{p} + \mathcal{O}(\frac{\ln p}{p^2})$, with small-failure unreliability bounded by $p^2(p - 1)(1 - q)^{p-1}$. In linear consensus $\dot{x} = -Lx$, error trajectories decouple into three modal timescales $\{ (p^3 - 1)^{-1}, (p^2 - 1)^{-1}, (p - 1)^{-1} \}$ with algebraic connectivity $\alpha(\Gamma(R)) = p - 1$ and steady-state $H_2$ error variance $H_2^2 = \frac{Kf(\Gamma(R))}{2n^2} = \frac{1}{2p} + \mathcal{O}(p^{-3})$. Furthermore, the Kirchhoff index yields a vanishing average resistance distance $\overline{r}(\Gamma(R)) = \frac{2}{p} + \mathcal{O}(p^{-3}) \to 0$, while unbiased Markovian random walks induce an asymptotic traffic concentration vector $\Pi = (\frac{1}{3}, 0, \frac{1}{3}, \frac{1}{3})$ with quadratic per-node core routing stress $\pi_{\mathrm{core}}/\pi_{\mathrm{periph}} \sim p^2 + p + 1$.

In this paper, we study the characterizations of Schatten \(p\)-class Toeplitz operators on smoothly bounded convex domains of finite type in \(\C^n\). On one hand, by using discrete Kobayashi lattice, we characterize the Schatten \(p\)-class Toeplitz operators by employing a probabilistic selection method for \(0<p<1\). At the same time, we show that the characterizations obtained by Kobayashi lattice are equivalent to the Berezin transform for \(p > \frac{n}{n+1}\). On the other hand, as an application, the criterion gives a geometric characterization for Schatten \(p\)-class weighted composition operators for \(0<p<2\) and also gives an analytic characterization for \(p>\frac{2n}{n+1}\). Our main results give an answer to the question that find a geometric or analytic characterization of the Schatten \(p\)-class weighted composition operators whenever \(0<p<2\) raised by Xiao-Yang-Yuan \cite{Xiao2026}.

The ground state phase diagram of the Shastry-Sutherland model remains controversial. In particular, the nature of the transition between the plaquette valence bond solid (PVBS) phase and the Néel antiferromagnetic (AFM) phase is still under debate. While some studies suggest a direct transition between the two phases, others propose the existence of a narrow intermediate quantum spin liquid regime. To address this issue, we perform large-scale Density Matrix Renormalization Group calculations to determine the Néel AFM phase boundary in the Shastry-Sutherland model. By applying staggered boundary pinning fields and directly measuring the bulk staggered magnetization, and through systematic extrapolations with respect to truncation error as well as careful finite-size scaling, we find that the staggered magnetization remains finite across the controversial region $0.78 \lesssim J_{1}/J_{2} \leq 0.81$, which was suggested to host a quantum spin liquid phase in some studies. Together with the previously established consensus placing the PVBS phase boundary at $J_{1}/J_{2} \approx 0.78$, these results provide evidence against the existence of an intermediate quantum spin liquid phase and support a direct PVBS–Néel AFM transition in the Shastry-Sutherland model.

This paper investigates the constrained existence problem for subgame perfect equilibria (SPEs) in multiplayer graph games. In the proposed framework, each player has a preference relation over the set of plays, assumed to be $\omega$-recognizable. Equivalently, he has a preference relation over a finite set of payoffs, and the set of plays with the same payoff is $\omega$-regular, for each payoff. This generic framework avoids the need to focus on specific payoff functions. We show that the constrained SPE existence problem is EXPTIME-complete, as well as for Nash equilibria (NEs).