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arXiv2026

Asymptotically Tight Bounds for Generalized Covering Radii of Binary Primitive BCH Codes at All Higher Orders

We study the generalized covering radii of binary primitive BCH codes, which measure how many parity-check columns suffice to span several prescribed syndromes. For the four-error-correcting family of length $2^m-1$, the second radius is exactly $11$ for $m\geq55$, and it is either $11$ or $12$ for $m\geq16$. For every fixed error parameter at least two, we give an explicit stable bound with two adjacent possible values for the second radius and an arithmetic criterion for exactness. At every higher order, we obtain explicit lower and upper bounds whose additive gap is bounded independently of the order for each fixed error parameter, once explicit field-size conditions hold. The bounds are therefore asymptotically tight as the order grows. The higher-order upper bound retains the common-core support count established by Xiong, Yip, and Zullo; our refinement reduces its sufficient field-size threshold at large order. The refinement combines componentwise mixed degrees with the ordinary degree of a multicone. The upper bounds come from constructing syndrome representations with a common set of parity-check columns.

cs.IT↗

arXiv2026

GlanceWAM: Sparse Test-Time Imagination for World-Action Models

Video generative models provide rich physical priors for robot learning, yet existing world-action models (WAMs) face a fundamental trade-off: synchronous video generation at control rate is latency-prohibitive, while abandoning test-time visual imagination sacrifices task success. We show that visual imagination achieves both real-time inference and superior success rates when generated asynchronously off the critical path and consumed directly in latent space. We introduce GlanceWAM, which decouples imagination from control on a single shared video DiT backbone: an asynchronous proposer glances ahead on a slow clock to imagine a single lookahead frame seconds into the future in the background, while an action head decodes action chunks at control rate (48 ms) purely in latent space without blocking. Enabled by a non-interfering attention mask that isolates video representations and staleness-robust horizon training that accommodates asynchronous lookahead aging, GlanceWAM breaks the speed-success dilemma. Trained purely on demonstrations, it attains 72.2% on the 24-task RoboCasa kitchen benchmark (vs. 67.1% for synchronous Cosmos Policy) and 99.0% on LIBERO while cutting per-chunk control latency $24\times$ relative to synchronous world-action models (48 ms on one A100). In single-arm and bimanual real-robot manipulation, it achieves higher average success than $π_{0.5}$ without any robot-data pretraining. Code is available at https://github.com/linhanwang/GlanceWAM.

cs.CV↗

arXiv2026

New RG flows between non-Unitary CFTs from exact massless scattering theories

We construct complete solutions of the massless S-matrix bootstrap equations describing a new infinite family of integrable RG flows from the higher-fusion-level minimal models M(3,2n+3;n) to the non-unitary Virasoro minimal models M(2,2n+3), including a flow from M(3,5) to the Yang--Lee CFT M(2,5) when n=1. We provide strong evidence for this identification by matching conformal perturbation theory around the UV fixed points with the small-volume expansion of the corresponding thermodynamic Bethe ansatz equations. We further show that a family of non-invertible Verlinde defect lines is preserved along the flows.

hep-th↗

arXiv2026

Unified-protocol voxel-level pulmonary embolism annotations for three public CT angiography datasets

Reliable clot-volume quantification and subsequent risk assessment in pulmonary embolism depend on precise segmentation of emboli on computed tomography pulmonary angiography. Deep learning models for this task must be trained on accurate voxel-level labels. The three public datasets that provide such labels were annotated under different protocols, and some of their studies contain unlabeled emboli or labels that are discontinuous across slices. This Data Descriptor presents voxel-level pulmonary embolism annotations for 149 of the 166 studies in these datasets. A primary rater drew all annotations under a single protocol. A thoracic radiologist with more than 20 years of experience reviewed and revised them. Three raters at three different centers independently annotated a subset of 15 studies. The subset was selected by source dataset and embolus location. Technical validation quantifies volumetric agreement with the source annotations, changes in within-mask attenuation, and inter-rater agreement on the subset. The dataset is intended to allow segmentation models to be developed and compared under a common reference standard.

eess.IV↗

arXiv2026

On-policy Distillation with Verifiable Reward

Reinforcement Learning with Verifiable Rewards (RLVR) and on-policy distillation (OPD) have become two widely adopted paradigms for post-training large language models. However, RLVR suffers from sparse task-level feedback, while OPD provides dense token-level guidance but ignores trajectory correctness, limiting its performance to that of the teacher. Combining them is a promising direction: OPD supplies dense supervisory signals, while RLVR provides task-level correctness. Nevertheless, existing integrations often rely on weighted combination or heuristic switching, introducing extra hyperparameters and trade-offs. We propose On-policy Distillation with Verifiable Reward (OPDVR), a simple yet effective method that seamlessly combines OPD and RLVR without adding any hyperparameters. We first reformulate the implicit reward of sampled-token OPD based on trajectory correctness, then apply a ReLU gating mechanism to ensure that correct trajectories receive non-negative rewards and incorrect ones receive non-positive rewards---thereby aligning the distillation signal with task success while preserving the teacher's distributional guidance. Furthermore, our modification transforms sampled-token OPD into a proper RLVR method, making it readily combinable with any policy gradient algorithm, such as GRPO. Experiments on six reasoning benchmarks show that OPDVR consistently outperforms standard OPD. Our code is available at https://github.com/LeapLabTHU/OPDVR.

cs.LG↗

arXiv2026

Solving Robust POMDPs with Omega-regular Objectives via Partially Observable Stochastic Games

Robust POMDPs (RPOMDPs) generalize classical POMDPs to the setting where exact transition probabilities are not known -- rather, they are only known to belong to some uncertainty set of values. In this work, we study the problem of solving RPOMDPs with general omega-regular objectives, which subsume a broad class of objectives such as reachability, safety, and linear temporal logic (LTL) objectives. We show that, for (s,a)-rectangular RPOMDPs with polytopic uncertainty sets, the problem of solving RPOMDPs under omega-regular objectives can be reduced to solving partially observable stochastic games (POSGs) under omega-regular objectives. Moreover, we show for the first time that reductions can be constructed in both directions, establishing the semantic equivalence between (s,a)-rectangular RPOMDPs with polytopic uncertainty sets and POSGs. This allows us to derive a range of new computational complexity results, including both upper and lower complexity bounds, on solving RPOMDPs with different omega-regular objectives. As a corollary, we also derive new computational complexity results for RMDPs.

cs.AI↗

arXiv2026

Resonant Induced Orbital Electron Capture: Novel method for low-energy $\barν_e$ detection

We propose a novel approach to detecting low-energy electron antineutrinos based on the induced capture of orbital electrons by nuclei. This process is resonant, requiring the antineutrino energy to precisely match the energy difference between the final and initial atomic systems. For continuous-spectrum sources, the resonance conditions can be satisfied without fine-tuning, and the effective cross sections depend on the spectral intensity of the $\barν_e$ flux at the resonance rather than on the neutrino energy itself. This opens the possibility of detecting neutrinos of never previously probed low energies. We identify a number of candidate nuclides that allow transitions to excited states of the daughter nuclei corresponding to resonant $\barν_e$ energies below the inverse $β$ decay threshold of 1.8 MeV, and we consider a distinctive atomic-nuclear coincidence signature for background rejection. We discuss implications of the proposed method for detecting low-energy reactor neutrinos, geoneutrinos, and keV-scale thermal solar neutrinos. Applications to neutrino oscillation experiments and to reactor monitoring are also briefly discussed.

hep-ph↗

arXiv2026

Rainbow Turán numbers for paths of length four

Given a set $V$ of $n$ vertices and an integer $k\ge1$, our goal is to maximize the number of edges in graphs $G_1, G_2, \ldots, G_k$, defined on $V$, under the constraint that the union of all graphs, thought of as a multi-graph, does not contain a rainbow copy of the path $P_5$ on $5$ vertices, that is, a copy of $P_5$ with each of its four edges belonging to a different $G_i$. We consider two versions of the problem, in which, respectively, $\sum_i e(G_i)$ and $\min_i e(G_i)$ is maximized. In the former case, we determine the maximum precisely for all $k\le n-1$ (and also for $P_4$). In the latter, we obtain an asymptotic value for $k\in\{5,6,9\}$ and formulate a very plausible conjecture for all other values of $k$. We also solve the problem for $k=4$, but under an additional assumption of completeness.

math.CO↗

arXiv2026

Nonequilibrium Dynamics of Simple Exclusion Processes Across Dimensions

The simple exclusion process (SEP) is a paradigmatic model for nonequilibrium transport, yet its rich dynamics over an exponentially large configuration space remain notoriously intractable. Here, we leverage variational autoregressive networks to characterize the nonequilibrium dynamics of the symmetric (SSEP), asymmetric (ASEP), and totally asymmetric (TASEP) cases in one to three dimensions at any time. We validate the approach against established finite-time 1D and long-time 2D results for the SSEP, and further provide new results on dynamical activity, density fields and nonequilibrium phase transitions for 2D and 3D cases. In 2D, we give a directional-density criterion connecting the bulk-density organization to the 1D TASEP phase diagram, and reveal how boundary and bulk rates separately control the activity and susceptibility. In 3D, we provide the first finite-time characterization of the SSEP active-inactive phase transition, and uncover scaling relations over time. Across dimensions, the critical field follows a trend $s_c\sim L^{-2}$, suggesting tuning strategies by the characteristic diffusive length scale. Overall, this work establishes a unified neural-network framework for characterizing nonequilibrium dynamics of representative transport systems.

cond-mat.stat-mech↗

arXiv2026

Reconstructing the Right Episode: Evaluating Interleaved Conversational Memory Beyond Long Context

Conversations with chat assistants increasingly span many topics in a single long-running thread, challenging memory systems. Existing long-context and memory benchmarks often expose session or topic boundaries, or probe direct personal-memory questions. These settings understate a harder assistant-memory regime: a flat mixed-topic thread where the system must infer which earlier episode makes a later task decision valid. We introduce SCALE-QA, a constraint-grounded task QA benchmark for flat unsegmented threads targeting episode integrity failure. The dataset contains 3,000 audited questions across 10 domains, uses deterministic four-way multiple-choice grading, and includes a deterministic runtime builder; experiments use all 3,000 questions through 128k and a stratified 400-question diagnostic at 1M. SCALE-QA questions are ordinary task-oriented requests whose correct answer depends on causally related evidence introduced earlier in the conversation. We also propose Temporal-Semantic Interleaved Memory Reconstruction (TSIM), which segments the turn stream into coherent episodes and indexes them through a hierarchical multi-view memory stack with deterministic episode-level summary and cluster-routing views. Experiments show that SCALE-QA challenges strong RAG baselines and long-context LLMs alike; across three open-source and proprietary LLM backends, TSIM achieves the highest accuracy in every backend setting, gaining 5.6-17.6 accuracy points over the strongest corresponding baseline.

cs.CL↗

arXiv2026

Comparing Corrupted Constrained Learning Problems

A key result in statistics is the data processing inequality, originally proved by Blackwell (1951) and later refined by DeGroot (1962) in terms of statistical uncertainty. The latter statement claims that the Bayes risk achieved on raw data always undercuts the Bayes risk on a processed version of the same data. This seemingly contradicts empirical findings in machine learning: pre-training, representation learning, feature learning, data augmentation are techniques used to improve performance of machine learning models. We reconcile both worlds by simply accepting that machine learning problems are constrained learning problems: the model class used does not include all measurable functions. We present counterexamples showing that the classical data processing inequality fails to hold in such a setting. Hence, we formulate a generalized data processing inequality, requiring the constrained Bayes risk of a joint distribution (with respect to a loss function and a constrained model class) to lower bound the constrained Bayes risk on the stochastically modified data distribution, regardless of the choice of distribution. We show this inequality to be equivalent to a set containment condition on a specific function set induced by the loss and model class, called the superprediction set. Finally, we exploit our characterization, derive sufficient conditions for this containment and quantify the inequality-gap.

cs.LG↗

arXiv2026

TacForcing: Streaming Action Generation with Execution-Time Tactile Feedback

Contact-rich manipulation requires adapting to contact states that can evolve substantially within an action horizon. However, chunk-based vision-language-action models predict complete action chunks from observations collected before execution, leaving tactile conditioning stale during execution. Existing tactile-reactive approaches typically rely on separate high-frequency controllers, which increase both architectural and training complexity. In this paper, we introduce TacForcing, a streaming action-generation framework incorporating execution-time tactile feedback. TacForcing replaces the standard action expert with a streaming expert that generates action blocks sequentially while preserving intermediate states of unfinished blocks. After each block is executed, the expert resumes generation from these states using newly acquired tactile feedback. To better align tactile conditioning with action execution, we further introduce Execution-Aware Tactile Attention (EATA), which restricts direct access to each tactile update to the next block scheduled for execution. Across six UniVTAC simulation tasks and six real-world contact-rich manipulation tasks on two robot platforms, TacForcing achieves average success rates of 65% in simulation and 66% in the real world, outperforming the strongest baselines by 6 and 15 percentage points, respectively.

cs.RO↗

arXiv2026

Why Cooper pairs live in AdS2: a spectral analysis of the Yukawa-SYK model

We establish the spectral foundation of the geometric formulation of Cooper pairing in the Yukawa--Sachdev--Ye--Kitaev model. Starting from the large-$N$ bilocal effective action, we derive the Gaussian fluctuation kernel in the even-frequency spin-singlet Cooper channel. Following the construction of Maldacena and Stanford, we determine the kernel eigenvalue $k\left(h\right)$ analytically for arbitrary conformal weight $h$ and resolve the pairing fluctuations into the continuous and discrete sectors of the associated de-Sitter space Laplacian. We show that the superconducting instability and the universal low-energy fluctuations near it reside entirely in the continuous scattering sector, while the discrete modes remain non-critical. Expanding the kernel about the lowest continuum mode yields a Klein--Gordon action on ${\rm dS}_2$, restricted to the continuous spectral subspace. This is precisely the subspace on which the inverse Radon transform to ${\rm AdS}_2$ is well defined. The projected bilocal Cooper-pair field can therefore be mapped onto a scalar matter field propagating in ${\rm AdS}_2$, without requiring any further spectral restriction on the bulk theory. Our results provide the missing microscopic justification for the projection implicit in earlier holographic formulations and clarify how a local bulk field emerges from the bilocal pairing theory.

hep-th↗

arXiv2026

Simultaneous Envy and Equitability Guarantees

Recent work in fair division has focused on either simultaneously satisfying closely related fairness notions or achieving a single notion across the ex-ante and ex-post worlds. We study the compatibility of two fundamentally different fairness notions: envy-freeness and equitability. For indivisible goods-only and chores-only settings, we study the existence and complexity of simultaneously satisfying their relaxations, revealing sharp contrasts between the two settings. For normalized binary goods, we give a polynomial-time algorithm for computing an EF1+EQ1 allocation with at most seven agents, but also construct a normalized instance with a larger number of agents for which no such allocation exists. In sharp contrast, binary chores admit the stronger EFX+EQX guarantee for any number of agents, even without normalization. We further initiate the study of cross-notion ex-ante and ex-post guarantees, asking whether randomized allocations can provide ex-ante guarantees for one notion while preserving ex-post guarantees for another.

cs.GT↗

arXiv2026

Alignment Matters Inside and Out in Equivariant Graph Flow Matching

Graphs are invariant under node permutations, motivating permutation-equivariant architectures in generative models. In flow matching, however, symmetry also affects the source-target coupling: one must choose both which graphs to pair and which node representatives to align. We study these two forms of alignment, termed outer and inner alignment, and their effect on equivariant graph flow matching. We connect inner alignment to transport on the graph quotient space, whose Euclidean quotient metric coincides with Gromov-Monge distance, and show that quotient couplings admit aligned representative lifts while symmetrization yields equivariant flow-matching minimizers, including for categorical endpoints. In practice, we compare random augmentation, permutation-blind minibatch optimal transport, approximate Gromov-Wasserstein alignment, and combinations of inner and outer alignment. Across continuous graph and molecular generation, alignment can substantially simplify trajectories and improve few-step generation, while its benefits depend on the alignment and computational budget. Our results highlight that effective graph flow matching benefits from alignment both inside and across graph pairs.

cs.LG↗

arXiv2026

Concavity and other properties of the entropy on manifolds

In this paper, we establish systematic estimates for the entropy and its density on Riemannian manifolds, focusing on the more challenging cases where the Ricci curvature changes sign or the boundary is nonconvex. For example, the refined second law of thermodynamics states that the entropy in a compact domain in $\mathbb R^n$ is increasing in time, furthermore, it is concave if the domain is convex. The concavity property is equivalent to the property that the Fisher information is decreasing, which also holds for convex domains in a Riemannian manifold with nonnegative Ricci curvature (cf. \cite{NiLei}). In view of the wide application of entropy in mathematics, information theory, physics, etc., there is certain desire in the community to extend the property to broader settings, especially to the case with nonconvex boundary (see e.g. \cite[p. 3]{CFM}), even in the Euclidean case. Here, we prove that the refined second law still holds if the domain is not too far from convex and the negative part of the Ricci curvature is not too large, in an explicit, nonperturbative sense, thus realizing some of the expectations. The proof is based on a new, sharp second order log Poincaré inequality that does not require explicit curvature conditions of the manifold. If the negative part of the Ricci curvature is too large, a counterexample to the concavity is given. Some other related estimates for the entropy density (Hamilton type estimates) are also proven.

math.AP↗

arXiv2026

A geometric resolution limit from vacuum entanglement: Topological Structure and Particle-Wave Asymmetry

We establish that vacuum entanglement entropy, regulated by weak spacetime curvature, imposes a fundamental lower bound on radial resolution for quantum excitations. From the area law, weak gravity introduces a natural UV regulator via the perturbative Green's function. Geometric projection yields a minimal radial scale $Δr_{\min} \propto r_s^2/R$, where $r_s$ is the Schwarzschild radius and $R$ the boundary radius. Consistency with the Compton wavelength defines a global mass scale $m_{\text{geo}} \equiv \hbar R/(c r_s^2)$. Particle masses satisfy $m = αm_{\text{geo}}$, where $α$ encodes vacuum structure. For Earth, $m_{\text{geo}} \approx 2.84 \times 10^{-32}$ kg. We determine $α$ via spectral analysis of curvature-induced mode shifts, implemented in Python with $N=3000$ radial points and $n_{\text{modes}}=1000$. The calculation yields $α(2) \approx 33$, matching the electron benchmark without adjustable parameters, ruling out exponential ansätze in favor of slow power-law growth $α(l) \propto l^{1.27}$. Crucially, this resolution limit endows the quantum vacuum with the properties of a granular refractive medium. This elegantly explains a fundamental particle-wave asymmetry: massive excitations with $λ_C \ll Δr_{\min}$ propagate in the geometric optics limit, following macroscopic gradients as classical geodesics. Conversely, photons with $λ\ll Δr_{\min}$ interact directly with the medium's granularity, leading to phase decoherence and anomalous dispersion. This framework reframes mass as a probe of vacuum-imposed resolution limits, yielding distinct, falsifiable predictions for high-energy photon propagation.

hep-th↗

arXiv2026

CultureConverse: A Multilingual Multi-turn Simulation Harness for Culturally Grounded Assistance in East and Southeast Asia

Current cultural evaluations for large language models (LLMs) often reduce culture to single-turn factual recall via MCQs, failing to capture a common use case: users seeking practical help over multiple turns in culturally grounded scenarios. We introduce CultureConverse, a scalable, multilingual simulation and evaluation harness for culturally grounded assistant dialogue that covers 10 East and Southeast Asian regions, 58 subgroup identities, and 7 domains. Each simulated and evaluated episode produces a scored interaction where the assistant assists the user and infers cultural constraints from partial information. The resulting CultureConverse-DS dataset contains 14,610 benchmark (evaluation) episodes and 274,295 oracle-guided (gold-mode) dialogues. In our benchmark evaluation of 18 models, GPT-5 mini achieves the highest assistance quality. Human annotation experiments suggest that our evaluation framework is a sufficient proxy for human judgment. Performance gains from fine-tuning on 27,860 high-quality CultureConverse-DS samples improve in-domain assistance and transfer out-of-domain to cultural MCQ and safety classification benchmarks. We release the harness, both splits, and judge prompts to support interactive evaluation of cultural competency.

cs.CL↗