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arXiv2026

Surface Defects in the $\mathcal{N}=2$ Lens Space Index and Elliptic Integrability

We determine the surface-defect difference operators of the 4d $\mathcal{N}=2$ lens space index for class $\mathcal{S}$ theories of type $A_{N-1}$ on $(\mathbb{S}^3/\mathbb{Z}_r)\times\mathbb{S}^1$. For generic fugacities $(p,q,t)$ and arbitrary rank $N$, orbifold order $r$ and discrete holonomies, their coefficients are finite products of theta functions with nomes $p^r$ and $q^r$. After an explicit gauge transformation, Gaussian in the holonomies, each operator factorizes into two elliptic Ruijsenaars--Schneider-type operators with step $pq$, one with nome $p^r$ and one with nome $q^r$, acting on variables glued along a lattice. Using this factorization and a Wronski-type relation, we prove that all the operators commute. We also establish a sufficient criterion for self-adjointness with respect to the bilinear vector multiplet pairing. It applies to the basic mixed operator and, in suitable parameter chambers, to the pure $p$- and $q$-type operators; for general mixed operators the contour prescription remains open. These results support the expectations from S-duality.

hep-th↗
arXiv2026

Spontaneous chiral-symmetry breaking in four-dimensional QCD with $A_x=A_y=0$ projection in dimensional reduction gauge

We investigate spontaneous chiral-symmetry breaking in four-dimensional (4D) QCD in the dimensional reduction (DR) gauge, defined so as to minimize $R_{\mathrm{DR}}\equiv~\int d^{4}s ~ \mathrm{Tr} \left[ A_{x}^{2}(s) + A_{y}^{2}(s) \right]$. We consider ``$tz$-projection" of $A_{x,y}(s) \to 0$ and ``$xy$-projection" of $A_{t,z}(s) \to 0$, respectively, for the gauge configuration generated in the DR gauge, in a similar sense to Abelian, monopole and photon projections in the maximally Abelian gauge. The chiral condensate is estimated from the low-lying Dirac-eigenvalue density $ρ(λ)$ using the Banks-Casher relation. By the $tz$-projection in the DR gauge, the chiral condensate is largely reserved. In contrast, the chiral condensate becomes zero by the $xy$-projection in the DR gauge. This indicates that $A_{t}(s)$ and $A_{z}(s)$ play a dominant role, while $A_{x}(s)$ and $A_{y}(s)$ play no role, in spontaneous chiral-symmetry breaking in the DR gauge.

hep-lat↗
arXiv2026

ADAPT for Science: A Multi-Agent System for Self-Evolving Scientific Optimization

Scientific discovery often requires identifying a small number of high-performing designs in vast, constrained search spaces. This is difficult when evaluations are costly, feasible solutions are sparse, parameters are strongly coupled, and physical constraints are strict. Recent AI for AI methods can automatically improve algorithms and optimization procedures. However, general purpose approaches are not designed around scientific priors, physical constraints, and limited evaluation budgets. We introduce ADAPT for Science, a multi-agent framework that treats scientific optimization as two coupled decisions: where to search and how to search. ADAPT uses historical designs to identify promising and diverse initial conditions, progressively concentrates computation on favorable search directions, and evolves the optimization procedure from execution feedback. We evaluate ADAPT on the design of gravitational wave detectors using a differentiable physics simulator and eight unseen detector topologies. Under matched scientific evaluation budgets, ADAPT achieves a mean loss of 0.204 +/- 0.101, reducing loss by 54.9% relative to the best classical optimizer and by 62.2% relative to the best general purpose agentic evolution baseline. ADAPT achieves the lowest loss on all unseen topologies among the evaluated baselines. ADAPT provides a step toward scientific optimization systems that continuously learn from prior experience and their own search outcomes.

cs.AI↗
arXiv2026

Stiff source terms inside ADER-DG method

ADER-DG numerical method with the LST-DG predictor, when used to solve hyperbolic equations with stiff source terms, exhibits properties characteristic of IMEX computational schemes. With increasing stiffness, characterized by the parameter $z = ν{Δt}^{n} < 0$, the maximum of the Courant number $\mathrm{CFL}_{\rm max}$ of the ADER-DG numerical method increases. In the region of strong stiffness $|z| \gg 1$, a linear increase in the Courant number $\mathrm{CFL}_{\rm max}(z) \sim |z|$ occurs. In the region of small source terms $|z| \ll 1$, the results $\mathrm{CFL}_{\rm max}(z)$ transform into known results for the problem $\mathrm{CFL}_{\rm max}(0)$ without source terms. In the transition region $|z| \sim 1$, a range of insignificant decrease in the Courant number $\mathrm{CFL}_{\rm max}(z)$ is discovered. In the linear case, instability is violated precisely when one of the matrix eigenvalues reaches $λ= -1$, regardless of the phase $θ$ of the numerical solution. A rigorous stability theory of the ADER-DG numerical method for stiff problems for arbitrary degree $N$ of basis polynomials is constructed. The stability condition is simplified to solving a polynomial equation for the Courant number $\mathrm{CFL}$. Highly accurate dependencies of the Courant number $\mathrm{CFL}_{\rm max}(N, z)$ of the ADER-DG method on the parameter $z$ are obtained. A rigorous direct proof of the approximation of the ADER-DG method is presented. Approximation orders $p = N+1$ for arbitrary degrees $N$ are rigorously derived. A set of numerical experiments is carried out to apply the ADER-DG method to solving both a linear advection-reaction equation and the system of Euler equations for a two-component reacting medium. The results obtained in these calculations confirm the theoretical results well.

physics.comp-ph↗
arXiv2026

Training Mixed-Monotone Neural Networks for Verification Without Set Propagation

Most formal verification approaches for neural networks conservatively enclose the output set of the neural network. However, computing a tight output enclosure is in general computationally hard. We sidestep this challenge with a novel neural network architecture that realizes mixed-monotone functions as the difference of monotone subnetworks. By utilizing the theory on mixed-monotone systems, this reduces the computation of a tight output enclosure from complicated set propagation to two simple forward passes of opposite corners of an input interval. Moreover, because the size of the resulting enclosure is a closed-form function of the weights of the neural network, we can directly minimize it during training. We prove a lower bound on the size of any such enclosure, given by the total variation of the represented function generalized to several inputs, which makes it possible to compare the tightness of the enclosure against the optimum. Our evaluation on regression and dynamical-system benchmarks demonstrates that our training reduces the enclosure size to within 0.5% of the lower bound without sacrificing prediction accuracy. Computing our enclosure is orders of magnitude faster than CROWN and $α$-CROWN and on deep networks it is also tighter than zonotope propagation and CROWN, while its size exceeds that of $α$-CROWN by only 5.1%.

cs.LG↗
arXiv2026

CAVC: Convergence-Adaptive Audio-Visual Cache for Modality-Asymmetric Diffusion Generation

Diffusion-based audio-visual generation methods typically perform joint denoising of audio and video latents throughout the entire sampling trajectory, repeatedly executing modality-specific denoising branches and cross-modal attention at every timestep. However, we observe that such uniform joint computation is not always necessary. The key is a modality-asymmetric recoverability: audio-side drift introduced by mid-stage caching can be substantially reduced by only a few terminal joint denoising steps, whereas video-side degradation caused by caching leads to persistent loss of motion and temporal details. This asymmetry suggests that inference acceleration should selectively cache recoverable audio-side computation while preserving full video refinement. Motivated by this observation, we propose \textbf{Convergence-Adaptive Audio-Visual Cache (CAVC)}, a training-free modality-asymmetric caching framework. CAVC adopts a sandwich-structured computation allocation: after detecting that audio denoiser outputs enter a cache-tolerant regime, it caches and reuses the audio denoiser output to bypass audio denoising and cross-modal attention in the middle stage, while the video branch continues independent spatio-temporal refinement; a few joint steps are then restored at the end to reduce accumulated cross-modal drift and improve synchronization. Experiments across multiple public benchmarks demonstrate that CAVC achieves 1.10--1.35x wall-clock acceleration, improves several visual dynamics and temporal statistics, and maintains competitive audio fidelity and audio-visual alignment.

cs.CV↗
arXiv2026

From Turing Patterns to Spike Self-Replication and Nucleation in a Growing-Domain Tulip Breaking Virus Model

A recently proposed reaction-diffusion model for the tulip breaking virus (TBV) has been shown to generate striped pigmentation patterns on growing tulip petals. In this paper, we investigate the formation of localized spike patterns in this model in the asymptotic limit of small viral diffusivity. It is known that two distinct bifurcation mechanisms can occur which generate new spikes as the domain half-length $L$ slowly increases: spike self-replication and spike nucleation. Self-replication occurs through a saddle-node bifurcation of the inner spike core problem, whereas nucleation is associated with a fold of the nonlinear outer problem. Using matched asymptotic expansions, we derive critical conditions for these mechanisms and construct phase diagrams that predict which mechanism occurs first as $L$ increases, or whether nucleation is absent. We further combine these results with a Turing instability analysis of the homogeneous steady state to obtain a phase diagram of pattern-forming mechanisms. An interesting finding is that, for the TBV model, the Turing-unstable region lies entirely within the parameter regime where spike nucleation is possible. These results provide further insight into the mechanisms underlying the formation and evolution of pigmentation patterns in virus-infected tulips.

q-bio.PE↗
arXiv2026

System-Level Evaluation of Uplink Access Schemes for Ambient IoT

Ambient Internet of Things (A-IoT) devices operate under stringent energy constraints, relying on harvested power in the $μ$W-to-mW range and limited energy storage. The A-IoT air interface for active devices is still under development; we therefore use Narrowband Internet of Things (NB-IoT) as an implementable reference for evaluating autonomous Uplink (UL) access under harvested energy. Under these conditions, the standard NB-IoT contention-based Random Access (RA) procedure incurs substantial per-packet overhead, making UL access in dense A-IoT networks increasingly energy-expensive. Context-retaining UL access schemes reduce this overhead, but their energy-latency trade-offs are insufficiently studied in literature under realistic harvesting and protocol constraints. To address this gap, we extend the LENA-NB ns-3 module with solar energy harvesting, supercapacitor storage, and a hysteretic brown-out mechanism, and propose Hybrid Scheduling Request (HSR), a hybrid UL access scheme combining reserved request occasions with opportunistic contention. We compare RA, Scheduling Request (SR), HSR and an Idealized Fast Uplink Grant (FUG) serving as a performance bound. Results show that HSR reduces mean packet delay by up to 69% and SR reduces energy per delivered bit by up to 24%, both relative to RA.

cs.NI↗
arXiv2026

All-photonic millimeter-wave and terahertz signal core at room and cryogenic temperatures

Millimeter-wave and terahertz technologies offer new opportunities for high-capacity communications, sensing, and quantum systems, but electronic signal chains above 100 GHz are limited by weak sources, noisy receivers, and lossy interconnects. Photonic approaches mitigate these constraints by enabling chip-scale high-frequency components, yet existing implementations generally retain lossy off-chip electrical or free-space links, hindering dense and compact integration for cryogenic or space-constrained settings. Here, we show a monolithic lithium tantalate photonic chip, termed a signal core, which generates, modulates, routes, and detects continuous-wave signals at discrete frequencies between 100 GHz and 2.5 THz. The architecture integrates high-frequency functional modules on chip and uses exclusively fiber-based optical interfaces. Bidirectional coherent electro-optic conversion enables signal generation, detection, and nanosecond-scale amplitude and phase modulation, while micro-coplanar striplines interconnect the modules into an end-to-end signal chain on a single chip. Our modules achieve single-photon electro-optic coupling rates of g_0/2π=10 kHz and peak drive-power-normalized photon-flux conversion efficiencies of 1.0%/mW for generation and 0.5%/mW for detection. It also operates at 4 K in a dilution refrigerator through the same fiber-only optical links. Together, these capabilities establish an all-photonic platform for millimeter-wave-to-terahertz systems and offer a broadly applicable architecture for applications constrained by electrical-interconnect loss, heat load, and footprint.

physics.optics↗
arXiv2026

Joules-to-GDP: How Much Economic Value Do AI Systems Produce per Unit of Energy?

An AI system can produce more economically valuable work while delivering less value for the energy it consumes. We therefore ask: How much economic value does an AI system create per unit of energy consumed? We formalize economic value in two ways: (1) net dollar value, the output's dollar value minus AI-system execution cost, and (2) time saving, the expert's completion time minus the AI system's completion time. Dividing each by measured end-to-end energy yields Net Value per Joule (NVJ) and Time Saving per Joule (TSJ), reported in USD/MJ and hours/MJ. We study 220 public GDPval tasks across 44 occupations, serving five open-weight models locally and evaluating four accelerator types. First, the occupation groups where AI systems succeed most often, deliver the greatest dollar value, or save the most time do not necessarily provide the greatest economic return per joule. For example, among the tested tasks, engineering work delivers about 10% more net dollar value per task than software development. Yet software development delivers about 27% more net value per joule. Second, GLM 5.2 delivers the highest average net dollar value, at $72.27 per task using 0.430 MJ, equivalent in energy to about four hours of active laptop use. By contrast, Gemma 4 31B delivers 56% of that net dollar value using just 23% of the energy, achieving approximately 2.5 times the NVJ and 2.8 times the TSJ. Third, across four single-accelerator deployments, Qwen3.6-27B's NVJ varies by a factor of 4.32 and TSJ by 9.27, with B200 leading both. Additionally, one and eight H100s deliver similar net dollar value, but eight reduce completion time by 22% at 3.24 times the energy. Our framework makes output value and expert time saving under an energy budget explicit objectives for improving models, accelerators, and software, while offering a new basis for assessing AI's potential economic effect on occupational work.

cs.LG↗
arXiv2026

The signless Laplacian spectral Turán problems for disjoint triangles

The classical Turán-type problem for graphs forbidding $k$ disjoint triangles has been resolved firstly by Erdős [Arch. Math. 13 (1962) 222-227] for graphs of sufficiently large order and improved by Moon [Canad. J. Math. 20 (1968) 95-102], who established that the unique edge extremal graph is $K_{k-1}\vee T_2(n-k+1)$ for $n> \frac{19k-11}{2}$. In this paper, we determine the maximum signless Laplacian spectral radius among all $kK_3$-free graphs of order $n$ and characterize the unique signless Laplacian spectral extremal graph $K_{k-1}\vee T_{2}(n-k+1)$ for all $k\ge 2$ and sufficiently large $n$.

math.CO↗
arXiv2026

Synthetic-to-Real Code-Switched ASR: A Spontaneous Nepali-English Podcast Benchmark

Nepali-English code-switched conversational speech presents severe challenges for automatic speech recognition (ASR), chiefly through script confusion (inappropriate mixing of Devanagari and Latin orthography) and elevated error rates at language switch points. Supervised fine-tuning (SFT) can adapt multilingual foundation models, but human code-switched audio is expensive to collect and annotate. We curate a new benchmark of 13,044 spontaneous podcast utterances (15.45 h total; 10,214 test, 2,830 dev), audited and verified to eliminate machine translation leakages and acoustic loops. We investigate a two-stage synthetic-to-real adaptation framework: Stage 1 applies SFT on 0.95 h of speech synthesized via a multi-speaker, dual-engine TTS pipeline; Stage 2 explores Group Relative Policy Optimization (GRPO) with transcription and script rewards. We find that synthetic SFT provides the primary cross-domain transfer to spontaneous human speech, reducing Mixed Error Rate (MER) from 23.40% to 21.52% (-1.88 pp) and switch-point error rate (SPER) from 35.89% to 28.77% (-7.12 pp). Subsequent GRPO yields small, statistically significant adjustments on 173 test utterances (1.69%), driving English script confusion (SCR_en) from 6.45% to 6.36% (p <= 0.001) and SPER to 28.70% (p = 0.022 clustered). Crucially, ablation reveals that in this SFT-converged encoder-decoder setting, an auxiliary script reward term yields performance identical to MER-only optimization because rollout candidate groups exhibit near-zero script variance on synthetic data. On monolingual benchmarks, SFT improves Nepali MER by 2.71 pp (stabilizing at 18.42% after GRPO, a 2.38 pp gain over baseline) while preserving English lexical WER (3.38% vs. 3.33%). Verified transcripts, timestamps, episode metadata, and reconstruction scripts are publicly released.

cs.CL↗
arXiv2026

Direct Forcing: A Single-Stage Training Recipe for Few-Step Autoregressive Text-to-Video Generation

Few-step autoregressive video generation enables low-latency streaming, yet prevailing training pipelines separate causal adaptation from distribution matching. Recent representation-based text-to-video methods retain this separation by starting from ODE-initialized checkpoints, even when the target distribution is defined directly by reference videos. We introduce Direct Forcing, a single-stage framework that uses reference videos both as paired examples of how a history continues and as a target population for self-generated rollouts. Causal Continuation Alignment learns paired spatiotemporal correspondence under reference histories, while Rollout Distribution Matching uses maximum mean discrepancy to align the representation distributions of self-generated and reference videos. Together, these complementary signals allow a pretrained video model to learn causal continuation and the target video distribution in a single training stage. Dynamic Gradient Balancing adapts the relative gradient contributions of continuation alignment and distribution matching during training. Starting from bidirectional Wan2.1-1.3B, Direct Forcing learns a four-step autoregressive generator in 250 updates without a separate initialization stage or online diffusion-score supervision, achieving 84.63 VBench Total and 86.01 Quality. Ablation studies further demonstrate the benefits of dynamic gradient balancing and reveal distinct representation preferences: deeper features benefit continuation alignment, whereas intermediate features yield better performance for rollout distribution matching.

cs.CV↗
arXiv2026

Inverse KLT kernel of AdS string-amplitude building blocks from the intersection matrix

We develop a topological and combinatorial interpretation of the Kawai--Lewellen--Tye (KLT) relations for $n$-point AdS string-amplitude building blocks, which are disk integrals with multivariable multiple polylogarithm insertions and sphere integrals with their single-valued counterparts. Building on the framework of twisted de Rham theory over a noncommutative ring, we reformulate the problem in terms of associahedral chambers of the moduli space loaded with solutions of the Knizhnik--Zamolodchikov equation. We construct regularized twisted cycles and express their intersection pairings through local monodromies and Drinfeld associators, which control transport between fusion-tree normalizations. Organizing the intersection contributions by common boundary faces yields the intersection matrix, which is identified with the inverse KLT kernel by the twisted period relation. The field-theory limit of the inverse KLT kernel is also given.

hep-th↗
arXiv2026

Cross-Spectral Feature Fusion for Multispectral Document Binarization

Historical document binarization remains challenging when faded ink, bleed-through, and background degradation exhibit wavelength-dependent behavior across visible and near-infrared observations. This study investigates whether adaptive cross-spectral feature fusion and targeted structural guidance can improve multispectral document binarization beyond fixed fusion and generic attention mechanisms. Four registered SMADI bands at 500, 600, 700, and 1000 nm are processed using a multi-branch conditional generative adversarial network (cGAN). Visible, NIR, and structural feature streams are fused at encoder depth L = 3 using spatial- and channel-wise softmax gating, while auxiliary edge maps derived from selected VIS-NIR band pairs provide targeted structural guidance. Nine controlled fusion and structural configurations are evaluated using five-fold document-level cross-validation, DIBCO-standard metrics, and Holm-corrected statistical testing. The F3 + NIR edge-guided configuration provides the strongest overall performance among the evaluated models, achieving mean F1 = 0.7916, p-FM = 0.8044, and IoU = 0.6654. Relative to the fixed Mid AVG baseline, it improves F1 by 0.0269, p-FM by 0.0360, and IoU by 0.0321, with all three gains remaining statistically significant after Holm correction. Mean NRM and DRD are also reduced, although these reductions are not statistically significant after correction. Targeted cross-spectral structural guidance provides an effective mechanism for regulating intermediate multispectral fusion, improving primary foreground-overlap performance while retaining the complete four-band observation.

cs.CV↗
arXiv2026

Consensus-Based Distributed Filtering for Angles-Only Tracking in Cislunar Space

This paper investigates consensus-based distributed filtering strategies for multi-observer angles-only navigation in the cislunar space. The objective is to estimate the inertial state of a target spacecraft using only line-of-sight measurements collected by a network of observer spacecraft. This problem is particularly relevant for autonomous cislunar navigation, where ground support may be limited, and centralized fusion architectures may be problematic due to communication and computational constraints, and single-point failure risks. Three distributed filtering approaches are considered: the Distributed Extended Kalman Filter, the Information-Weighted Consensus Filter, and the Kalman Consensus Filter. All methods share the same local prediction and measurement-processing steps, but differ in the way information is exchanged and fused across the network. Their performance is evaluated and compared to a centralized Extended Kalman Filter, adopted as benchmark, and independent local filters in a high-fidelity cislunar scenario. Numerical simulations show that the distributed approaches significantly improve estimation accuracy with respect to independent filters. Monte Carlo sensitivity analyses are then conducted to characterize the robustness of the considered methods to finite consensus iterations and prior misalignment among the agents.

eess.SY↗
arXiv2026

Phases of flux vacua and their quantum symmetries

We present a torsional linear sigma model with (0,2) supersymmetry that realizes, in its large radius phase, a five-dimensional heterotic flux vacuum, and we use the linear sigma model to connect this geometry to a stringy regime realized as an asymmetric orbifold of a Gepner model and a circle. Along the way we develop a number of tools relevant for more general (0,2) gauged linear sigma model constructions of heterotic vacua.

hep-th↗
arXiv2026

Separate Field Scoring Protects Unused Tools When Agents Pool Tool-Use Experience

Agents that call tools from a shared catalog can pool what they learn about which tool serves which request. We measure what pooled usage examples do to tool retrieval, reporting separately the held-out tools, for which no agent has usage, and all other tools. Adding usage examples to the index as extra entries for used tools raises Hit@5 (whether a gold tool is in the top five) for those tools and lowers it for held-out tools, by a large margin on two of three catalogs and with both embedders we tested. Giving used tools the same number of equally long entries filled with other tools' text lowers held-out Hit@5 about as much, but gives little or none of the gain. We call our method of scoring usage as its own field SYNAPSE. On StableToolBench, the held-out gold tool appears in its top five more often than with a router that reserves slots for usage (0.785 against 0.683), and this held-out lead holds on all three catalogs with both embedders. This protection persisted when we replaced each tool's usage with other tools' text, and a constant score offset for tools with usage gives similar held-out Hit@5 in most settings. The gain for tools with usage, in contrast, needs usage about the right tool. The router keeps more of the gain on labeled queries on TOUCAN with both embedders and on ToolRet with one, so the better choice depends on the workload. Splitting the usage among ten simulated agents shows that pooling helps exactly as much as giving one agent the same records.

cs.SE↗