Papers

We establish nearly sharp $W^{1,\infty}$ stability estimates for the Legendre spectral Ritz projection associated with Laplacian on a square domain. Its norm grows proportionally to the square root of the polynomial degree, up to a cubic logarithmic factor. The upper bound uses an integral representation of the discrete gradient projection in terms of one-dimensional semigroup kernels and a rank-two Duhamel comparison between the mass-matrix semigroup and its infinite-dimensional counterpart. The lower bound follows from the endpoint concentration of the Legendre kernel. As an application, we derive gradient maximum-norm error estimates for the Poisson and heat equations, with spatial factors optimal up to logarithmic terms.

As a lightweight and highly accurate method for nearest-neighbor search in 3D point clouds, approaches based on space-filling curves (SFC) have been proposed. However, due to the inherent properties of SFC, a gap arises between proximity relationships along the SFC and those in the original Euclidean space. In this study, we propose a loss function that reduces the influence of this gap. Specifically, we compute the distances between adjacent points along the SFC and train the model to optimize feature similarity between pairs of points that are distant from each other in the original 3D space. We incorporate the proposed method into a high-performing 3D point cloud segmentation model and evaluate its effectiveness on three datasets. The results demonstrate that the proposed method outperforms conventional methods on both indoor and outdoor point cloud datasets.

A large number of theories in international relations attribute importance to the rhetoric of leading foreign policy actors. Moreover, in recent years, there has been a significant growth in interest for producing machine-readable text of remarks from key foreign policy actors. Yet, researchers have, to date, focused primarily on the rhetoric of executive leaders and members of legislatures. To understand the construction of foreign policy in the public arena and dynamics in it, especially in the United States, we need a collection of fine-grained textual representation of the remarks of US Secretaries of State. An especially promising use for such a corpus of text is to measure attention areas in US foreign policy and its implication for the US's policies, including in foreign aid. In this note, We introduce the United States Secretary of State Dataset, a corpus of 17,700 remarks delivered by US Secretaries of State from 1997 to 2026. Using this dataset, we demonstrate that Secretaries of State frequently make public remarks, the likes of which can have substantively meaningful implications.

Retrieving external knowledge can improve large language model (LLM) translation by providing supplementary information such as idiom interpretations and terminology. However, existing retrieval-augmented machine translation systems typically apply predefined retrieval strategies uniformly across all inputs. We argue that translation operates in a partial-evidence regime: LLM's parametric knowledge suffices for many inputs, while external evidence benefits a subset and usually supports rather than directly provides the desired translation. This creates two challenges: deciding when to retrieve and what evidence to acquire. We introduce Selective Retrieval-Augmented Translation (SRAT), an agentic reinforcement learning framework that learns when to translate directly or retrieve, what to retrieve, and how to integrate these decisions by optimizing final translation quality. To align evidence retrieval with downstream translation quality rather than simple semantic similarity, we further develop joint Plackett–Luce optimization and translation-quality contrastive training for retriever-training. Experiments on idiom, knowledge-intensive, and document-level translation with offline or online retrieval show that SRAT consistently outperforms never- and always-retrieve baselines, and quality-aligned retriever training provides further gains when similarity-based retrieval is insufficient. The results demonstrate the benefit of treating retrieval as a learnable translation action rather than fixed preprocessing.

We devise a dual-arm cooperative planning framework for wiping table surface in the presence of scattered objects. Unlike conventional surface-cleaning strategies that only cover free areas and detour around obstacles, our framework explicitly assigns one arm to rearrange objects while the other performs coverage wiping, thereby enabling access to previously obstructed regions. Specifically, we first construct a set of wiping and object-rearrangement action primitives. Based on these primitives, we introduce Geo-MILP, a geometry-aware task planner formulated as Mixed-Integer Linear Programming (MILP). By integrating Logic-Based Benders Decomposition (LBBD), Geo-MILP iteratively optimizes action sequencingand timing to resolve geometric conflicts, promoting efficient cooperation between wiping and object rearrangement. We then employ K-Order Markov Optimization (KOMO) to generate smooth, collision-free motions to ensure feasible execution. Simulation and physical experiments demonstrate that the proposed framework not only increases reachable coverage by enabling access to obstructed areas, but also significantly improves time efficiency compared to Task and Motion Planning (TAMP) baselines, reducing planning time by up to 9 times and execution makespan by approximately 40%.

Temporal action detection in long untrimmed videos suffers from inaccurate localization and low-quality proposals, especially with sparse annotations and ambiguous boundaries. For open-ended video understanding and LLM-driven event analysis, reliable proposals connect temporal localization, event annotation, and semantic understanding. However, conventional temporal action detection (TAD) pipelines lack explicit modeling of proposal localization quality, cross-representation support, and inter-proposal relations. We propose Hybrid Rank-Calibration of Action Proposals (HyrCap), a proposal-centric query-based TAD framework for temporal event understanding. Hybrid combines complementary video features with different localization cues, while Rank-Calibration adjusts proposal ranking confidence to reflect localization reliability and candidate competition. HyrCap treats dense query-based predictions as an over-complete temporal event hypothesis space. Cross-Representation Consensus Calibration, Localization Quality Estimation, and Proposal Redundancy Suppression improve proposal ranking reliability, localization quality, and candidate discrimination. Inspired by LLMs' capabilities in fine-grained semantic recognition, event description, and reasoning, we introduce HyrCap for Semantic Action Understanding, using calibrated proposals for standard TAD and as inputs to LLM-based semantic understanding. We define a staged evaluation protocol to separately measure event localization, segment-level semantic understanding, and combined event understanding performance. Experiments on public benchmarks show that HyrCap achieves state-of-the-art performance across multiple metrics and provides a finer-grained paradigm and evaluation protocol for query-based event segmentation and annotation.

Verifiable instruction-following benchmarks emphasize output-constraint satisfaction but can overlook whether responses meaningfully answer the underlying request, creating an evaluation blind spot. We show that frontier models can receive full credit for responses with little substantive answer content. Using the same verifier-based criterion as a training reward can induce reward hacking, as publicly released checkpoints exhibit higher constraint satisfaction but lower response quality after reinforcement learning with verifiable rewards. To address this reward hacking, we introduce CALIF, a lightweight method that augments verifier rewards with a calibrated likelihood-based bonus to preserve response quality. CALIF evaluates response likelihood under the request alone using the existing frozen reference policy, requiring no additional judge or learned reward model. Across models ranging from 1.7B to 8B in reasoning and non-reasoning modes, CALIF improves constraint satisfaction on IFBench while maintaining response quality near or above pre-RL levels. It also outperforms corresponding base policies in 40 of 45 model-metric comparisons across three rubric-based instruction-following benchmarks, demonstrating gains beyond training verifiers.

Accurate path loss (PL) estimation is essential for wireless network planning and optimization. This paper proposes HankelKANet, a lightweight physics-inspired network for PL estimation that structurally embeds electromagnetic propagation characteristics into the neural architecture. Built on a single residual UNet backbone, the proposed model integrates urban layout features with a convolutional Kolmogorov-Arnold network(KAN). Specifically, the convolutional kernels are parameterized by the radial amplitudes of the zeroth- and first-order Hankel functions. This formulation acts as a physics-inspired nonlinear distance encoding, enabling the network to capture dominant attenuation characteristics directly without requiring additional physics-based loss terms. Experimental results demonstrate that HankelKANet achieves state-of-the-art accuracy and efficiency on both the simulated RadioMapSeer dataset and the real-world Huawei RSRPSet. Compared with the leading baseline, PEFNet, it reduces the parameter count by 78% and lowers the RMSE by 16.96% on the simulated data, while further exhibiting robust cross-dataset transferability and high data efficiency during target-domain adaptation. To interpret these empirical gains, we mathematically establish a parameter-conditional spatial gradient bound. Using discrete Dirichlet energy (DDE) and Jacobian sensitivity heatmaps, we empirically verify that this physical encoding intrinsically constrains the network's spatial derivatives. This structural smoothness effectively eliminates non-physical spatial ripples, preventing overfitting to simulator artifacts and serving as the fundamental driver for robust real world generalization.

Robotic exploration, coverage, and multi-agent deployment algorithms require reproducible environments with controllable geometry and visibility. This paper presents the Dungeon and Visibility World Generator, an open-source framework for constructing two- and three-dimensional environments and evaluating geometric line-of-sight. The framework supports orthogonal, polygonal or polyhedral, and curvilinear geometries, with six construction families covering scattered rooms, clusters, winding passages, caverns, branches, and loops. Room dimensions, passage structures, obstacles, and spatial placement can be controlled through configurable parameters and probability distributions. Each generated environment provides continuous free-space geometry and a corresponding discrete occupancy representation. A Rust-based visibility engine supports line-of-sight queries in both representations, enabling the evaluation of observable regions from arbitrary agent positions. The framework records configurations, generated geometries, occupancy grids, and visibility results to support reproducible experiments. We demonstrate the generator across all six geometry classes, examine how geometry and spatial resolution affect visibility, and evaluate generation time and reproducibility. The resulting framework provides a configurable foundation for evaluating robotic exploration, coverage, and multi-agent deployment algorithms in diverse environments.

In this article we present a new view on string theory that is rooted in quantum foundations extended to the domain of quantum gravity in the form of gravitized quantum theory, in which the canonical probability measure captured by the Born rule of quantum theory, turns out to be dynamical and contextual. We claim that this gravitization of quantum theory is the essence of string theory. String theory, according to this view, originates in foundations of quantum theory and Nambu's dynamics, which features in the non-perturbative definition of string theory in terms of a T-duality covariant and non-commutative formulation, called the metastring. Nambu's dynamics and the associated cubic and hypercubic objects also appear as the natural language for exploring the new observables and phenomena implied by a dynamical Born rule, including triple and higher order quantum interference, that can be investigated in experiments involving massive quantum probes, and that are also needed for direct empirical tests of the Born rule, a cornerstone of quantum theory.

We investigate gravitational wave (GW) signatures from extreme-mass-ratio inspirals (EMRIs) around a Bardeen black hole, modeling the small object as a test particle, and provide a framework for probing strong-field spacetime geometry. We first present the equations of motion for test particles around a Bardeen black hole and characterize circular orbits in the parameter space of energy and angular momentum. Using Levin's classification, we adopt the extended classification scheme to classify periodic orbits around a Bardeen black hole. We then compute GW waveforms in both the time and frequency domains, as well as the corresponding characteristic strains, for these periodic orbits and compare them with the sensitivity curves of the Laser Interferometer Space Antenna (LISA), the evolved Laser Interferometer Space Antenna (eLISA), the TianQin mission, the Big Bang Observer (BBO), and the Decihertz Interferometer Gravitational wave Observatory (DECIGO). We find that detectability is controlled primarily by the luminosity distance. At a luminosity distance of 200 Mpc, the signals can exceed the sensitivity curves of BBO and DECIGO and are comparable to the LISA sensitivity curve, whereas at 2 Gpc, they remain below the sensitivity curves of all detectors considered. These results suggest that EMRIs on periodic orbits around Bardeen black holes offer a promising avenue to probe strong-field gravity and the properties of Bardeen black holes.

Cameras and the foundation models built on them recognize what a 3D scene contains, but not what it is made of: surfaces of the same colour can be different materials. Hyperspectral unmixing explains each spectrum as a mixture of material signatures, yet in 3D it is applied to rendered images after the views are composited, or tied to slow implicit fields, and no multi-view data with known composition exist to check the result. We present the Spectral World Renderer (SWR), which unifies world generation and unmixing. A coding agent builds executable 3D worlds that are rendered with measured spectra, so every hyperspectral image comes with exact labels and sub-pixel proportions; the resulting SWR-Bench provides eight indoor and outdoor worlds in which decompositions can be verified. SWR then unmixes inside rendering: each Gaussian of a compact 3D representation is decoded into material abundances before compositing, so one render yields spectra and material maps, and any surface can be queried by material name, a clicked pixel or a reference spectrum. Without material labels, SWR identifies materials best in all eight worlds, has the best mean PSNR on real captures, trains 3.7-12.9x faster than unmixing baselines, renders 34.9 labelled views/s and separates same-coloured materials.

In multi-modal 3D pre-training, aligning 3D shapes, their 2D image counterparts, and language descriptions has made tremendous progress. However, we find that supervision from rendered images is unreliable, the semantics encoded in synthetic views are distorted due to domain gap, self-occlusion, and rendering artifacts. Instead, we learn transferable 3D representations from language only. We observe that, in real world, 3D shapes are organized in a tree-like structure, ranging from general concepts to fine-grained instances with specific attributes, while language typically denotes generic concepts and subsumes these various 3D instantiations. Hence, we propose to embed 3D representations in hyperbolic space, whose geometry is well-suited for modeling tree-like data without distortion. To capture the asymmetric hierarchy between language and 3D shapes, we further impose a partial-order relation that language entails 3D shapes. Our method, Hyperbolic Contrastive Learning (HyperCL), jointly optimizes a hyperbolic geodesic-based contrastive objective and an entailment loss to learn discriminative cross-modal representations while explicitly preserving this hierarchy. We also introduce a rigorously verified benchmark for comprehensively evaluating cross-modal 3D alignment. Across two widely used benchmarks and ours, we improve the performance up to 4.6% absolute percentage on 3D shape classification and 5.5% on cross-modal text-to-3D retrieval under the same parameter budget. The code and evaluation benchmark will be made publicly available.

While multi-fingered dexterous robot hands have the potential to provide human-level dexterity, using them for functional manipulation remains difficult because task success depends on precise contact, coordinated arm-hand motion, and reactive recovery from execution errors. Precise contact depends on complex contact dynamics that are difficult to model accurately in simulation, motivating real-world learning. However, real-world demonstrations in the full arm-hand control space are costly and noisy because each trajectory must coordinate arm motion with high-DoF multi-finger contact. Small execution deviations can further cause slipped contact or premature force application, making recovery from off-nominal contact states important for robust execution. To deal with these challenges, we propose HiFun, a hierarchical real-world RL framework for functional dexterous manipulation tasks. Our key insight is to decouple the control complexity into a functional hand skill for precise contact execution and an arm-hand coordination policy for arm control and hand-skill activation. This design enables effective real-time human intervention for reactive recovery learning and efficient data collection with Dynamic Movement Primitive (DMP) augmentation. Across six real-world tasks on two dexterous hands, HiFun achieves 98.3% average success within one hour of online training and remains robust to dynamic disturbances. The project page is available at https://hly-123.github.io/HiFun/.

Vision-language-action (VLA) models connect visual perception and language understanding with robot control, providing a foundation for instruction-conditioned manipulation. However, conventional pretrained VLA policies lack a mechanism for gradual adaptation through accumulated interaction experience during deployment. We therefore propose VLRLA, a general framework that equips existing VLA models with in-context reinforcement learning capabilities for deployment-time adaptation. Our approach augments a VLA model with a reinforcement learning module that learns from historical observations, actions, rewards, and termination signals. During deployment, the policy gradually refines its action generation and progressively improves task success while keeping model parameters fixed. Our approach is also designed for general applicability and compatibility with diverse learning history construction strategies and model training pipelines. Finally, through extensive experiments, we systematically investigate the learning properties of VLRLA in simulation and demonstrate its ability to adapt to unseen scenarios during real-world deployment.

Public debt supplies liquidity and collateral services only if institutions coordinate on using the same claim. We study this coordination when use carries a recurring cost and a benefit that rises with other users. Above a quality threshold, two positive-adoption equilibria exist, and under best responses the initial user base decides between collapse and high adoption. Under logit choice, as the population grows and noise vanishes, the long-run distribution selects high adoption only above a strictly higher threshold. Debt issuance improves market depth but eventually dilutes backing per claim. This trade-off creates a range of debt levels supporting the liquidity premium of public debt in macroeconomic models and a narrower range supporting its long-run selection. At the boundary of the wider range, the premium is discontinuous. A matching transfer that corrects the adoption externality makes stationary selection maximize network surplus. Transfers can also help launch a network without permanent support.

In this paper, we investigate a wireless communication network supported by multiple uncrewed aerial vehicles (UAVs). To ensure reliable connectivity, UAVs are desired to approach the boundaries of designated no-fly zones (NFZs) without violating them when mobile users (MUs) enter NFZs. To support heterogeneous communication services, MUs are assigned different priority levels based on their individual communication types. Considering the practical constraints arising from user mobility, heterogeneous communication requirements, and NFZs, the objective is to maximize the weighted sum of MU communication rates, where weights correspond to MU priorities. This is achieved by jointly optimizing trajectory planning, UAV transmission power control, and the binary association factor between UAVs and MUs. To address this challenging optimization problem under dynamic constraints, we develop a soft actor-critic algorithm with prioritized experience replay, which learns an adaptive control policy. Numerical results show that the proposed algorithm outperforms benchmark schemes in terms of convergence speed and stability. Moreover, it effectively meets diverse communication requirements, satisfies UAV energy constraints, and ensures reliable operation under NFZ constraints.

We present a CR-CR method for strain gradient elasticity and prove its robustness with respect to the Lame parameter $\lambda$ and the length scale $\iota$. The method introduces the strain as an independent symmetric tensor and discretizes both the strain and the displacement using CR elements. The commuting properties of the CR interpolation operator with the relevant differential operators leads the robustness with respect to $\lambda$. A stabilization term weakly imposes the relation between the strain and the symmetric gradient of the displacement. The method also applies directly to the biharmonic equation and singularly perturbed fourth-order problems. For these problems, we prove that the CR-CR method is equivalent to an RT-CR method proposed by Huang and Tang. This result extends the classical equivalence between the RT-P0 mixed method and the CR method for the Poisson equation to fourth-order problems. The equivalence shows that the stabilization term arises naturally from the RT-CR mixed formulation.

Feel-good Thompson sampling (FGTS) augments the posterior of vanilla Thompson sampling with an exploration term that favors reward functions with high predicted optimal values. This modification achieves minimax-optimal regret up to logarithmic factors in linear contextual bandits, but existing analyses of its two standard variants establish regret guarantees in expectation. In this paper, we derive the first high-probability regret bounds for both cumulative and current-step FGTS in contextual bandits with general realizable function approximation. Our bounds depend on the corresponding decoupling coefficients and the prior mass near the true reward function. In the $d$-dimensional linear setting, both variants satisfy $\mathrm{Regret}(T)=O\big(d\sqrt T\log(2T)+\sqrt T\log(1/\delta)\big)$ with probability at least $1-\delta$, where $T$ is the time horizon. This bound matches the dimension and horizon dependence of algorithms based on the upper confidence bounds, up to logarithmic factors. Relative to the expected-regret guarantees, the cost of controlling the regret with high probability is confined to additive terms with at most linear dependence on $\log(1/\delta)$. The proof ideas are partially developed by GPT-6 Astra under the authors' guidance.

Many firms that run A/B tests struggle with low statistical power, increasing the risk that launch decisions are driven by noise rather than true impact. We argue that in decentralized organizations, low power can reflect misaligned incentives: product teams choose what and how to test on a customer-facing experience to maximize their private reward, while the experience owner sets evaluation rules and launch criteria to optimize the experience. We formalize this interaction via a principal-agent model and show that evaluating tests using raw impact estimates creates a reward to sampling noise. Correctly calibrated posterior-mean evaluation removes this reward and creates a local incentive to reallocate toward fewer, more precise tests of more ambitious ideas. Using data on A/B tests run at Amazon, we document patterns consistent with these model predictions. After an Amazon experience shifted to posterior-mean-based evaluation in 2024, test volume declined while both precision and the dispersion of true impacts increased, more than doubling signal-to-noise ratios. Our results highlight that A/B testing methodologies can shape not only measurement and launch decisions, but which tests are pursued in the first place.

Ultrafast manipulation of light polarization plays a key role in modern high-speed photonics and optoelectronic operations. However, most current polarization-active modulation schemes are restricted by a limited operating wavelength range (visible to infrared), narrow-band resonant fundamental wavelength working condition, and relatively long modulation time (> 1 picosecond). Here, by taking advantage of the transient anisotropic nonlinearity of optical strong coupling between the epsilon-near-zero mode of indium tin oxide (ITO) film and polarization-selective plasmonic resonance, we achieve femtosecond polarization manipulation of broadband light that spans ultraviolet (UV) to visible region by controlling harmonic generation of the signal light under resonant pumping. We demonstrate polarization elliptic rotation of 23.3{\deg} at 407 nm for third-harmonic generation (THG) and 55.0{\deg} at 610 nm for second-harmonic generation (SHG) simultaneously within ~600 fs. In addition, the strongly coupled system can also serve as a universal femtosecond polarization modulation source, imprinting a 32.9{\deg} polarization rotation in the UV region by converting the modulation information of the fundamental signal light to that of THG light via a uniform ITO film in a cascaded configuration. Our study establishes a new paradigm for UV-based, ultrahigh-speed broadband polarization photonics with direct implications for high-speed optical information processing and programmable nonlinear photonic devices.

Block-diffusion language models denoise a whole block of token positions in parallel so each forward pass can emit many tokens. However, blocks are still denoised in strict sequence, a cost that within-block acceleration leaves untouched. Here, we investigate decoding blocks concurrently and propose One Block Ahead (OBA), a training-free decoding algorithm that denoises the next block alongside the current one. We demonstrate that for uniform-state diffusion LMs, where a block's denoising progress is not visible in its intermediate tokens, concurrent decoding is advantageous if the next block's tokens are promoted together with the corresponding sampler state, including the self-conditioning signal and the denoising time. We also derive a break-even criterion that relates the benefit of OBA to the relative cost of a paired-block forward pass. On DiffusionGemma, a state-of-the-art diffusion LM, OBA increases the tokens per forward pass by 42.3% (from 15.64 to 22.25) and the single-request denoising throughput by 16.3%, averaged over ten benchmarks, with a small accuracy regression.

China's next-generation large telescopes, such as the Expandable Aperture Segmented Telescope (EAST) and the Large Optical/Infrared Telescope (LOT), are being planned as flagship facilities for high-angular-resolution astronomy, including the direct imaging and characterization of exoplanetary systems (e.g., exoplanets, circumstellar disks). However, their segmented, centrally obscured apertures present significant challenges for coronagraph design: diffraction from segmented gaps and spiders severely limit contrast, particularly at small inner working angles (IWAs). To address this, we investigate an optimal Shaped Pupil Lyot Coronagraph (SPLC) architecture tailored for these telescopes, which combines a binary shaped pupil apodizer, a focal-plane occulting mask, and a Lyot stop to suppress stellar glare and enhance contrast. We further augment the coronagraph design with a two-deformable-mirror (2-DM) adaptive optics (AO) system to correct atmospheric turbulence and residual aberrations. End-to-end simulations based on site parameters for Lenghu in Qinghai Province and assuming idealized extreme AO (ExAO) correction demonstrate that the optimized 2DM-SPLC designs can achieve raw contrasts of order 10^-6-10^-7 in the V, H, and K bands, providing an upper-bound estimate of the system performance. The simulated performance highlights the advantages of the SPLC in mitigating diffraction from segmented and centrally obscured pupils while maintaining a small IWA and practical throughput, indicating that the 2DM-SPLC is a promising coronagraphic architecture for high-contrast exoplanet imaging on China's future large segmented telescopes.

We propose CktHGVAE, a heterogeneous graph variational autoencoder for transistor-level analog/mixedsignal CMOS circuits that takes not only design variables but also state variables as its inputs and outputs. With a single hyperparameter configuration without topology-specific tuning, comparison between model-generated and SPICE-simulated circuit operational states gives median R2 values above 0.9 for typical single-ended voltage amplifiers and the CMOS inverter, and 0.81-0.96 for differential amplifiers with larger datasets. Latent-space optimization in the PCA-reduced latent space with Bayesian optimization, evolutionary search, random search, and quasi-exhaustive search is demonstrated for a common-source voltage amplifier with NMOS input and resistive load, where the objective function is defined as a penalty for deviation from required circuit specifications. For each search strategy, 93.3 - 100% of all design candidates suggested by the model satisfy the required circuit specifications at the decoder output, and SPICE simulations verify that 90 - 100% of them indeed satisfy the requirements. The model pretrained on a batch of topologies can be transferred to unseen topologies without retraining at all, with zero-shot reconstruction median R2 values of 0.72-0.90 in three of four scenarios, including transfer from single-ended to differential topologies, although the transfer fidelity depends on the choice of pretraining topologies. Our demonstrations suggest that the proposed model can potentially serve as a basis for AMS CMOS circuit design automation.

An agentic scientific workflow can run to completion and still release wrong results: a silent numerical error, a stale input, or a defect in a shared upstream step can contaminate several outputs while a sibling branch stays correct. We treat trust in such results as a release decision. A harness around the workflow's directed acyclic graph (DAG) decides which outputs may be used: it enforces mandatory checks, contains failures to the affected branch, recomputes from tracked versions, adds validators, and releases a result only if a risk model estimates its probability of being invalid as low. Language-model agents work inside the harness, choosing corrective actions and reviewing releases, but cannot override it. On 60 held-out paired instances of two workflows with injected faults, we switched components on and off. Each supplied a different property. Containment and recovery raised the number of correct results. Validation supplied safety: fixed rules without validation released 37 invalid results, while validating every candidate released none. Risk estimation supplied efficiency, matching that safety with 31% fewer validators at somewhat lower yield, although better targeting than random validation was not shown. Lineage evidence helped on one workflow. The language model added no measurable benefit: whether invalid results escaped depended on the harness, not the model. This proof of concept points to a practical path: placing agents inside explicit release-control structure can keep released scientific results trustworthy, and it gives more capable agents a measurable baseline to improve on.

In the classical art gallery problem, a guard sees a target when the segment joining them lies entirely within the polygon. We explore what changes when sight may bend along regular arcs on absolutely irreducible curves, but only those defined by primitive integer polynomials of total degree at most \(d\) and coefficient height at most \(H\). We call such curves admissible sight carriers. Arcs can dramatically improve sight. In a one-sided comb, no straight-line guard sees selected targets in two different teeth, yet a single central guard sees a chosen target in every tooth along parabolic carriers. Sight can also fail in two different ways. Geometrically, the polygon may block every sight arc of the allowed degree between two points. For instance, in an alternating comb, the number of guards needed for a row of targets spanning the comb grows linearly with the number of sides at each fixed degree, even for carriers with arbitrary real coefficients. Arithmetically, no admissible carrier may pass through the points at all. Even in the unit square, at fixed \(d\) and \(H\), the proportion of rational targets that must guard themselves tends to one as the height bound grows. An algebraic target may lie on no rational curve of degree at most \(d\), however large \(H\) is. Both failures can be overcome for finite target sets by allowing the degree and coefficient height to grow. We show that every finite set of algebraic targets in a rational polygon becomes visible from any rational interior guard, with explicit bounds. We also construct, for every \(d\), arbitrarily large Galois orbits in the unit square, all of projective height \(4^{d+1}\), whose points must each guard themselves at degree \(d\) for every \(H\). Yet at degree \(d+1\) and coefficient height one, a single guard sees the whole orbit along \(Z(Y-X^{d+1})\).

This paper proposes the SKG (Symplectic-Kernel Gradient) reasoning engine for law-induced inference and induction. Laws are a priori; data provide instances. Inference is geometric evolution under law constraints. We organize symplectic geometry, GENERIC, kernel methods, RKHS, group-equivariant networks, and constrained mechanics into a unified, analyzable, implementable, verifiable framework. We propose the SKG octuple S = (M, g, omega, H, S, G, Delta, Pi), whose four components correspond to four levels of laws: conservation laws, constitutive relations, symmetry groups, and axiom systems. Main results: (1) Invariants enter metric construction via the Jacobian: g = J^T Sigma^-1 J + epsilon_G I. For constant cases, we establish inverse reconstruction theory: solvability rank condition (Thm 3.9), consistency criterion (Thm 3.11), and uniqueness theorem (Thm 3.14). (2) The kernel bandwidth matrix is uniquely determined by Fisher information and satisfies task-independence (Thm 3.19). (3) The metric reconstruction error decomposes into four terms (Thm 3.21), with squared condition number kappa(Sigma^*)^2 as the dominant amplification factor (Thm 3.22). (4) For state-dependent cases, we establish function-space reconstruction theory on matrix-valued RKHS (Thms 4.8, 4.9). (5) Three-layer projections handle axiom, symplectic-step, and conservation constraints. (6) The residual equation yields the observable formula, four-dimensional rank condition, and noise propagation, while g_qq is structurally unidentifiable. (7) Kernel parameterization yields the RKHS extrapolation bound (Thm 4.15) and strict OOD gain theorem in group directions (Thm 8.15). (8) The learning-decoupling theorem (Thm 9.1) proves the sole object of induction is the parameters of the task energy. Validation: 1D damped oscillator and 2D rotation-invariant system; 6 unit tests, 10 experiments (paired t-test, p < 0.01).

Magneto-optical traps (MOTs), indispensable to cold-atom-based quantum computing and quantum precision measurement, are increasingly desired in compact and stable form. Particularly, the six-beam 3D-MOT, distinguished by symmetric geometry and superior trapping performance, finds particularly broad applications. Conventional implementations, however, rely on complex and bulky free-space optics, hindering miniaturization, practical assembly, and long-term stability. Here, we demonstrate a compact six-beam 3D-MOT system that employs two multifunctional optical metasurface chips to implement the optical-field functionalities required for cooling and trapping atoms. By combining two metasurface chips and a vacuum cell, a photonic-integrated cell module (PICM) is implemented as the core assembly and the volume is only" 73*73*107 mm^3" . In success, 1.3 * 10^3 Rb atoms are trapped and cooled to the temperature of ~183 {\mu}K. It should be noticed that the laser beam is guided to the metasurface through optical fiber, thus such fully fiber-coupled architecture enables straightforward and stable operations. We believe that this work would pave a practical route toward compact and portable 3D-MOT.

We study right comodule algebras and their connections with Hopf bi-Galois objects and right coideal subalgebras. For a Hopf $2$-cocycle $\sigma$ on $K$ and a unital right-colinear algebra map $\Gamma:A\to K$, we show that $\Gamma:A_\sigma\to K^\sigma$ is an algebra map precisely when $\sigma$ is trivial on $\operatorname{im}\Gamma\otimes\operatorname{im}\Gamma$. We describe comodule-algebra morphisms $A_\sigma\to K^\sigma$ by characters and establish injectivity criteria using the coradical and extensions of characters to convolution-invertible functionals. For coactions on Hopf quotients projecting to the coproduct, character-evaluation maps are injective, and equality of their images is determined by a unique algebra character. For the $\imath$-Hopf algebras $H^\imath_\tau$ of Chen–Lu–Pan–Ruan–Wang, with $H$ having a bijective antipode and a Hopf pairing, we obtain a Hopf bi-Galois realization $H^\imath_\tau\hookrightarrow F_\sigma(H\otimes H^{\mathrm{cop}})$. We identify algebra characters with nonzero $\tau$-twisted compatible maps $\chi$ and prove that the corresponding morphisms $\xi_{\tau,\chi}$ of Chen–Lu–Pan–Ruan–Wang are injective, yielding right coideal realizations in $(H\otimes H)^\imath$. We classify the $H^\imath_\tau$ up to comodule-algebra isomorphism and determine when these realizations have the same image.

Spatial intelligence requires scalable 3D environments that are both photorealistic and semantically grounded, yet existing indoor datasets are dominated by room-scale captures and costly LiDAR acquisition. Online real-estate platforms offer abundant panoramas of diverse multi-room homes, but sparse viewpoints and texture-poor regions make reconstruction severely under-constrained. We introduce Holi-Spatial 360, a generative reconstruction and data curation framework for converting these panoramas into annotated multi-room 3D environments. Because reconstruction quality bounds subsequent generation, our Correspondence-Guided Geometric Optimization converts feed-forward reconstruction priors into reliable cross-view constraints and builds a coherent 3D Gaussian Splatting representation as 3D spatial memory. Adapted single-image and video priors then restore appearance and complete continuous trajectories while preserving observed content. The reconstructed scenes support arbitrary RGB-D rendering and an automated curation pipeline that combines end-to-end 3D grounding with VLM-based verification. Holi360 contains over 1K multi-room 3DGS scenes, more than 100K instance annotations, and 2M spatial question-answer pairs. We also introduce the Holi360 benchmark to evaluate the spatial understanding of VLMs in real-world, multi-room indoor environments. Experiments demonstrate superior reconstruction and curation quality under sparse panoramic inputs, while fine-tuning VLMs on Holi360 substantially improves spatial reasoning capabilities.