Papers

Despite rapid progress, generalist robot policies remain brittle during execution. Reliable deployment therefore requires runtime monitoring that provides timely warnings of failure. Existing monitors commonly estimate risk from current observations or policy signals without explicitly predicting the future consequences of proposed actions. To anticipate such risks before action execution, we introduce ReAP, a future-aware runtime monitoring framework that combines visual failure recognition with action-conditioned failure prediction. Specifically, ReAP first trains a visual detector on successful and failed rollouts to learn a failure-relevant representation space and estimate current risk. An action-conditioned predictor then forecasts the resulting future representation in this space to estimate future failure risk. At runtime, the detector and predictor provide complementary signals for current-state failure recognition and future-aware risk assessment. Experiments across diverse robot policies in simulation and the real world demonstrate that ReAP effectively balances failure-detection accuracy and warning timeliness.

Contact-rich insertion requires robots to combine visual alignment with tactile adjustment. However, existing visuotactile chunk-based policies collapse tactile feedback into a single generation-time fusion pathway, leaving persistent contact states, abrupt contact events, and future contact consequences implicitly modeled in a single representation. We present PACE (Phase-Aware Contact-Event Conditioning), a temporal-role tactile conditioning framework for chunk-based insertion policies. PACE organizes a shared tactile stream into three temporal roles: persistent contact states condition action-chunk generation, abrupt contact events correct the generated chunk, and contact-consequence prediction shapes action representations during training. This design preserves chunk-level action continuity while assigning distinct pathways to different temporal roles of contact feedback. Across five real-robot insertion tasks, PACE achieves an average success rate of 90.7%, outperforming vision-only and generation-time tactile-fusion baselines by over 44 percentage points; on the ManipulationNet benchmark, PACE maintains 88.7% success across six geometry-clearance configurations, including an industrial-grade 0.1-mm clearance. Ablations confirm the complementary contributions of the three temporal roles, mechanistic analyses show that PACE separates normal insertion progress from contact events requiring immediate correction, and cross-signal and cross-architecture experiments indicate that this temporal-role principle extends across different physical feedback signals and policy backbones. Videos and materials are available at https://pace-insertion.github.io/.

Frobenius morphisms play a crucial role in algebraic geometry and commutative algebra in positive characteristic. In particular, the Kunz theorem, characterizing non-singularity via Frobenius morphisms, is a monumental work and has a relative version, called the Radu–André theorem. In this paper, we extend the Kunz theorem and the Radu–André theorem to logarithmic algebraic geometry in positive characteristic.

In this paper we deal with the celebrated Gamow liquid drop model, namely, for $m>0$, $N\geq 2$ and $\alpha\in (0,N)$, we study the problem \[ \min\Big\{P(\Omega)+ V_\alpha(\Omega) : \Omega\subset \mathbb{R}^N,\;|\Omega|=m\Big\}\,, \] and focus mostly on the nonexistence of minimizers for large masses. First we show that any possible minimizer in the asymptotic regime must satisfy an optimal thickness property. Eventually, in the simplified setting of sets made up as a tiling of cubes, we show that nonexistence occurs for large masses for the whole range of parameters $N\geq 2$ and $\alpha\in (0,N)$.

As large language models are deployed behind increasingly sophisticated safety mechanisms, evaluating their robustness under realistic adversarial conditions becomes increasingly difficult and critical. Existing jailbreaking evaluations often rely on static prompts, limited interaction horizons, or lightly protected systems, failing to reflect protected deployment settings with prompt-based safety protections. We show that the introduction of a prompt-based safety protection reduces the average attack success rate of a strong multi-turn baseline from 0.896 to 0.608 (32.1% relative), demonstrating that unprotected evaluations substantially overestimate real-world vulnerabilities. We propose Adaptive Traceback and Tactic Curation for Knowledge-based Red-teaming (ATTCK-R), a planning-driven multi-turn red teaming framework designed for protected black-box systems. ATTCK-R models jailbreaking as a long-horizon trajectory optimization problem using a structured belief state, introduces optimization-based tactic curation to abstract reusable strategies from prior successes and failures, and employs informed traceback to resume attacks from strategically meaningful states rather than restarting. Evaluated across 9 widely used LLMs configured with a single prompt-based safety protection layer, ATTCK-R consistently outperforms strong recent multi-turn jailbreaking frameworks. Ablation results confirm that long-horizon planning and tactic curation improve attack effectiveness, while adaptive traceback improves efficiency through structured recovery from conversational failure.

We formulate an axisymmetric spherical torus (ST) six-component magnetofluid equilibrium model for p_11B plasmas composed of thermal and suprathermal proton, boron, and electron fluids. The model is designed for p_11B parameter regimes where ion energies, strong current drive, energetic electron populations, and ion-electron temperature separation can render a single_fluid static_equilibrium description inadequate. It generalizes rotating_plasma equilibrium theory by incorporating relativistic thermal enthalpy corrections to the electron fluids via h(T/m_ec^2) and by constructing modified flux functions Y_{\alpha} associated with canonical angular momentum for each component {\alpha}. The equilibrium is determined by a Grad-Shafranov-like Ampere law for the poloidal magnetic flux Psi, algebraic density relations constrained by quasineutrality, and prescribed profile functions F_{\alpha}(Y_{\alpha}), T_{\alpha}(Y_{\alpha}) and K_{\alpha}(Y_{\alpha}). The manuscript includes the relativistic magnetofluid equations, the axisymmetric equilibrium formulation, the six_fluid computational method, and four numerical equilibria: two reactor_relevant ST p_11B parameter sets and two EHL-2 ST cases. The examples span toroidal beta b_T = 0.058_0.253, plasma currents I_p = 2.697_12.59 MA, and suprathermal electron temperatures T_eh = 287 keV_2.37 MeV, with h up to 19.1. Over these parameter ranges, Ampere's law accuracy, electrostatic potential accuracy, and component_resolved radial force balance can have errors ranging from 3% to below 0.1%. These results indicate that high-temperature p_11B ST equilibria can differ qualitatively from the single_fluid tokamak equilibria and require analysis of equilibrium component_resolved force balance, relativistic electron enthalpy, and explicit reproducibility diagnostics.

Source detection in hypergraphs plays an important role in mitigating the spread of harmful rumors and ensuring social stability. Current methods frequently overlook the causal entanglement problem in observations, thereby limiting the performance of source inference. In this work, we propose a source detection approach in Hypergraphs via Causal Disentanglement (HyperCD). To decouple causal propagation semantics from confounding noise, we propose the causal disentanglement module. A dual-branch variational encoder is utilized to disentangle snapshot embeddings into causal and confounding latent spaces, ensuring that the inference module relies solely on causal propagation signals. To further enforce this separation, an adversarial inference loss term is introduced to guarantee statistical independence between the decoupled branches. Moreover, to capture diffusion dynamics in hypergraphs, an attention-based hypergraph aggregation module is designed, which comprises the node-to-hyperedge propagation and hyperedge-to-node propagation processes. Extensive experiments on six datasets demonstrate the superiority of our HyperCD in effectively mitigating the causal entanglement problem.

Video-based interactive world models aim to enable real-time, user-controllable environments. Yet most existing systems are trained and rolled out at a fixed temporal rate, limiting both runtime-rate adaptation and physical-horizon coverage – a limitation we term temporal-rate coupling. Specifically, when runtime generation throughput differs from the learned temporal rate, the generated world evolves unintentionally more slowly or quickly. Moreover, using a single temporal rate imposes an inherent trade-off between temporal granularity and physical horizon: higher rates capture finer motion but cover a shorter duration under a fixed context window. To address both limitations, we introduce Rate-Adaptive Rollout (RAR), a framework that enables interactive world models to roll out at controllable temporal rates. At its core, Stride-RoPE aligns latent frames sampled at different rates on a shared physical-time coordinate, enabling consistent multi-rate rollout, unseen-rate generalization, and online rate switching without discarding history. Meanwhile, RAR uses multi-stride video sampling to enable joint learning of fine-grained dynamics and long-horizon evolution. Across action- and camera-controlled environments, RAR achieves temporally consistent multi-rate rollout and online rate switching while preserving high-rate generation quality and extending physical horizons under matched training budgets. RAR also transfers to pretrained world models while preserving perceptual quality.

Self-attention assigns two functions to one mechanism-where to read and how to mix-at the price of O(L^2) training, an O(T) decode state, and position signals bound to the training length. Existing attention-free alternatives all optimize the single function of generation. We propose FON (Fusion-Organ Network), which differentiates one weight stack into a drafting organ (multi-tap learnable delays + content-adaptive recursion; causal, O(S) training, O(1) decode state, no sequence-level quadratic attention) and a revision organ that re-processes the written prefix through multi-scale ripple kernels injected via weak gates, never generating. At 30M parameters, iso-parameter and iso-token budget, FON reaches perplexity 131.03 on WikiText-103, beating Transformer (197.73) and Mamba2 (152.53); the advantage persists under all depth-aligned baselines and at the 70M tier (-20.8%). At 8x length extrapolation FON degrades by ~8-9% without positional-encoding engineering, between ALiBi and RoPE. The revision channel provides a structural pathway for in-domain infilling that causal architectures lack in principle (+19% over on-demand coupling), at a perplexity cost indistinguishable within measurement precision. We report all costs and boundaries: impaired long-range retrieval, synthetic-task disadvantages, weaker out-of-domain code infilling than a same-recipe Transformer, and a 6.5-12.3x wall-clock gap.

In this paper, we study derivation based noncommutative geometry of path algebras arising from quivers by identifying a Lie algebra of derivations from which a differential calculus is constructed. We show that properties of the differential calculus are intimately connected with the structure of the quiver. In particular, by introducing the notion of a separating quiver, we find a condition on the quiver which is equivalent to the module of differential forms being a projective bimodule. For such quivers, one can construct bimodule connections, as well as bimodule forms which serve as noncommutative analogues of the Riemannian metric. As an illustration of the above concepts, we present a class of quivers for which one can construct Levi-Civita connections, i.e. torsion free connections compatible with a bimodule form.

Video anomaly understanding (VAU) aims to generate language-level interpretations of anomalous events in long videos, requiring visual evidence that supports explanation beyond anomaly detection alone. Existing VAU pipelines commonly rely on anomaly-centric or predefined temporal sampling strategies, which efficiently emphasize suspicious moments but overlook contextual cues, object interactions, and temporally distributed evidence needed for reasoning. Motivated by recent progress in learnable temporal selection for long-video question answering, we revisit VAU temporal sampling as a downstream-aligned evidence selection problem. We introduce the semantic-conditioned Temporal Sampling Q-Former that learns to select temporal visual evidence through the VAU generation objective. Since generic VAU prompts provide weak video-specific guidance, we condition the sampler on CLIP-embedded object tags automatically extracted from the input video. These tags are used only for temporal evidence selection and are not appended to the LLM generation prompt, separating sampler conditioning from prompt augmentation. The proposed sampler operates in visual-token space, computes soft temporal selection weights from frame-level representations, and merges duplicated selections before response generation. Experiments on HIVAU-70K show that our model achieves the best performance among the compared fine-tuned models, while ablations demonstrate that learnable temporal sampling improves over fixed anomaly-focused sampling and that CLIP-embedded object-tag conditioning further improves over generic-prompt conditioning. Our results suggest that temporal sampling in VAU should be aligned with explanation-oriented evidence utility rather than anomaly saliency alone.

Training neural networks in reduced precision can yield significant efficiency gains, yet all existing methods that scale to standard computer vision benchmarks retain floating-point in at least one stage, typically the weight update or optimizer state. We present a training algorithm that scales to modern deep neural networks, in which every tensor (weights, gradients, and activations) is stored as INT8, and every operation (forward pass, backward pass, weight update, optimizer update) is performed in integer arithmetic. Specifically, tensors are stored as signed integer mantissas paired with explicit power-of-two exponents, on which integer-only operations are performed using five custom composable building blocks (products, sums, divide-by-constant, nonlinear functions, and weight updates). This allows complete implementation of trainable integer layers, including convolutions, batch and layer normalization, softmax, and GELU. A per-group velocity mechanism with independent exponent tracking preserves gradient precision across neurons and channels with diverse magnitudes. As every tensor fits in INT8, training memory is roughly 4x smaller than the FP32 baseline. We validate our training algorithm on CNNs (ResNet-18/34/50/101, MobileNetV2) and Vision Transformers (ViT-Ti / B), demonstrating for the first time that training neural networks with INT8 tensors and integer arithmetic can achieve competitive accuracy on CIFAR-10, CIFAR-100 and ImageNet at a reduced memory budget.

Scaling laws predict large-model performance from small experiments, but finding a reliable law itself requires costly experiments. SLDBench tests whether language-model agents can discover scaling laws when all experimental results are given upfront. We introduce SLDBench v2 with two extensions. First, we expand the corpus from 8 to 127 scenarios spanning language-model pretraining, downstream performance, and vision-language transfer, and select 30 challenging scenarios on which a reference power-law fit reaches $R^2 \le 0.8$; they represent at least $1.09 \times 10^{23}$ FLOPs of source-reported training compute. Second, we introduce active scaling law discovery: an agent chooses which experiments to run, pays each one's recorded cost (e.g., training FLOPs), and revises its law as outcomes arrive, and is scored on the same hidden extrapolation targets as in the passive setting. Across 8 frontier agent systems, median $R^2$ drops from 0.72-0.75 (passive) to 0.24-0.57 (active), and prediction error rises 1.5-4.7 times, depending on the system. Agents favor cheap experiments, spending 8-44% of the full-pool cost on average; low-cost acquisition can yield strong predictions, but cheap purchases also leave experimental conditions needed for extrapolation unobserved. Experimental planning thus remains a key open challenge for agents that assist model development in the prevailing AI-for-AI study. Project page: https://lingbei-meng.github.io/SLDBench-v2/.

The origin of Galactic cosmic rays up to the knee energy (PeV) remains a long-standing open question in astrophysics. Supernova remnant shocks are leading candidates for accelerating particles to PeV energies, yet this requires strong magnetic field amplification in the upstream region to confine the highest energy particles. Despite its importance, the upstream magnetic field strength has long lacked direct observational constraints. Here we report the observation of numerous synchrotron X-ray hotspots extending into the upstream of the supernova remnant RX J1713.7$-$3946 in archival Chandra data. These hotspots show spatial and temporal properties consistent with synchrotron emission from secondary electrons produced by hadronic interactions between accelerated protons and dense molecular clumps. Using the spatial extent of these upstream hotspots as a physical scale, we estimate the proton diffusion length to be $\sim 1~\mathrm{pc}$. This measurement provides a constraint on the upstream magnetic field strength of $\sim 10~\mu\mathrm{G}$, which is consistent with recent simulations of Bell-instability-driven magnetic field amplification. Our results indicate that the current amplification is insufficient to reach PeV energies, explaining the observed TeV gamma-ray spectral cutoff and providing a diagnostic for assessing PeVatron capability in stellar shocks.

We study the query complexity of finding an an $\varepsilon$-stationary points of a one-dimensional non-convex function whose $p$-th derivative is $\beta_p$-Hölder continuous. We determine the optimal complexity for deterministic and randomized algorithms and for oracles that return only derivatives, only function values, or full local information. Randomness provably helps when only derivatives are available, function values help in all cases, and higher-order derivatives never do. Together with known results in higher dimensions, this shows how these benefits depend on the dimension. Our deterministic lower bound also implies that the optimal accuracy exponents of objective-function-free adaptive regularization of order $p$ (OFFAR$p$) in every dimension $d\ge1$ and of deterministic gradient-only trapping in dimension $d=2$.

We study Fourier extension estimates for the truncated cone in $\R^{n+1}$ with weights satisfying an $m$-dimensional ball condition only at radii between $1$ and $R^{1/2}$, where $0<m\le n-1$. Within the discrete induction framework of Du–Li–Wang–Zhang, we obtain a family of bounds by combining multilinear refined Strichartz inequalities, narrow decoupling, and Lorentz rescaling. We also give lightplank, lattice, and hybrid lattice–Knapp examples.

Garment manipulation requires inferring both garment identity and complete configuration from partial, self-occluded observations. This creates a chicken-and-egg problem: completing a partial observation requires a garment-specific deformation prior, while identifying the garment requires a configuration that explains the observation. We introduce ClothAtlas, which jointly identifies garments and estimates their complete configurations from partial point clouds and a library of canonical meshes. A shared graph-conditioned flow-matching model samples configurations for each candidate mesh and ranks candidates by observation fit. The model accommodates different mesh shapes, vertex counts, and connectivities, allowing new garments to be added from canonical meshes alone without retraining. On held-out DexGarmentLab garments, ClothAtlas ranks the correct mesh first among 221 candidates for all 22 test garments from a single flat observation. From a single self-occluded observation, it identifies 15/22 garments, compared with 8/22 for a deterministic graph estimator. Persistent vertex identities support grasp-target localization on real garments, reducing mean error from 15.4 to 6.4 cm overall and from 17.0 to 8.3 cm on occluded targets compared with dense descriptor matching. Project page: https://clothatlas.github.io/

3D Gaussian Splatting (3DGS) has been becoming a promising 3D reconstruction technique because of its advantage of high-fidelity rendering effect with high efficiency. However, it still suffers from coarse density control and semantically blind loss functions when reconstructing the fine-grained structures in complex urban scenes. Thus, this study proposes SG-GS, a semantic-guided 3DGS method for fine-grained structure reconstruction. It takes the semantic segmentation deduced by the Segment Anything Model (SAM) as a constraint and systematically integrates it into both Gaussian density control and loss function design. On the one hand, a semantic-constrained adaptive density control mechanism is constructed, which dynamically allocates gradient thresholds to different semantic regions of the scene and introduces an additional boundary-enhanced densification strategy, so that new Gaussians are directed to structurally critical regions. On the other hand, a multi-feature guided loss function is designed, and fine-grained supervision signals are gradually introduced through a phased progressive training strategy, alleviating the artifacts caused by the lack of semantic constraints in the basic loss. Experiments on three datasets show that the proposed method consistently improves reconstruction accuracy. Compared with the original 3DGS, the PSNR increases by approximately 2.7% to 5.2%, while artifacts on linear structures and boundary blurring are effectively mitigated. The method can serve the fine-grained 3D reconstruction of urban scenes.

For any nonarchimedean local field $k$, we exhibit the first examples of Zariski-dense, discrete subgroups of special linear groups over $k$, which are not commensurable to any lattice in the points of a semisimple group over a local field, and contain an infinite index subgroup isomorphic to a lattice in the $k$-points of a higher rank $k$-semisimple group. We prove that any Gromov-hyperbolic double of a non-elementary free group along a cyclic subgroup embeds as a quasi-isometrically embedded subgroup of $\mathsf{SL}_5(k')\times \mathsf{SL}_5(k')$, where $k'$ is a discretely valued field. More precisely, $k'$ is the field of rational functions $k(t)$ equipped with the Gauss valuation and $k$ is any nonarchimedean local field of characteristic not equal to $2$ or $3$.

We investigate the computational capabilities of a one-dimensional lattice of negatively coupled circle maps in its traveling wave regime. We interpret propagating waves as information carriers and exploit their interactions to implement Boolean logic. The logical states are encoded by the propagation direction of the traveling waves, while the presence or absence of a wave at a designated output location represents the logical output. Using controlled wave collisions, we demonstrate the realization of NAND and NOR gates along with other basic gates. Since NAND and NOR operations are functionally complete, the results establish that the traveling wave regime of the negatively coupled circle-map lattice supports universal Boolean computation in principle. The demonstrated logical operations remain valid over a finite range of the coupling strength \epsilon and map parameter \omega, indicating robustness of the computational scheme to parameter variations. Our results therefore demonstrate that computational functionality can emerge from the collective nonlinear dynamics of a coupled map lattice, providing a con- nection between the dynamical properties of traveling wave states and collision based information processing.

Quantization has emerged as one of the primary techniques for reducing the memory footprint of large language models during inference. A prominent example is Quantized Johnson$-$Lindenstrauss (QJL), which compresses KV caches using 1-bit asymmetric quantization while approximately preserving the inner products required by the attention mechanism. Recent theoretical and practical work aims at replacing the dense Gaussian projections used by the aforementioned transforms with more structured embeddings $-$ such as compositions of randomized Hadamard transforms $-$ while retaining the same embedding dimension. In this paper, we introduce two constructions based on a composition of randomized Hadamard transforms, albeit with a Gaussian rather than Rademacher diagonal in the second stage. The first adds Gaussian dithering to smooth the quantizer, while the second inserts a random permutation to regularize the covariance structure of the resulting Gaussian measurements. We prove embedding-dimension and running-time guarantees analogous to those of Fast JL in the non-quantized setting. The first construction achieves $m=O(\varepsilon^{-2}\log^2(d/\delta))$, while the second achieves $m=O(\varepsilon^{-2}\log(d/\delta))$ under a restriction on $m$. Both constructions can be applied in $O(d\log d)$ time.

Frontier LLM agents perform complex interactive tasks, but their inference costs motivate transferring their experience to smaller open-source agents. Distillation and latent communication typically require target-model training or access to source-model internals. We study how textual frontier-model trajectories can provide reusable local controls for a frozen agent. Inspired by protocol reverse engineering, we introduce $\textit{Agentic Latents}$, comprising anchored states and dynamic profiles of feedback–response cycles elicited by replay in the target model. Our training-free framework, $\textbf{REVEAL}$ ($\textbf{REV}$erse $\textbf{E}$ngineering $\textbf{A}$gentic $\textbf{L}$atents), uses these profiles and trajectory outcomes to match and select local events from successful and failed rollouts of the same task and source model. Their response-transition contrasts yield a target-specific steering direction, applied before each response. Within-benchmark evaluations on Terminal-Bench 2.1 and Humanity's Last Exam with tools report higher accuracy than unmodified agents across three targets. Representation analyses and behavioral case studies support reusing frontier-model experience as local activation control.

Automated visual inspection is essential for efficient repair and recycling of metallic components. AI-based defect detection is a strong fit. However, it is often constrained by scarce, low-diversity training data. To address this gap, we study Generative AI-driven synthetic image generation using Progressive Growing GANs (ProGAN). We implement a ProGAN pipeline with Wasserstein loss and gradient penalty and evaluate key hyperparameters on two public datasets, MVTec AD (metal nut) and MPDD (tube). As a result, training remained stable and the model yielded realistic images. These images can augment training data, improve robustness, and reduce the cost of collecting rare defects.

Quantum random number generators are crucial for information security, yet existing implementations are hindered by bulky optics, device imperfections, and state alignment constraints. Here, using a compact metasurface platform, we achieve polarization-independent certified randomness by establishing a quantitative quantum graph framework. By mapping multi-channel nanophotonic responses onto graph vertices, we assign metasurface measurements an operational information-theoretic meaning, directly connecting weighted graph degrees to conditional min-entropy estimation. The resulting graph-certified measurements yield robust private randomness even under entanglement-based attacks without complex optics. Experimentally, we fabricate 4- and 6-channel dielectric metasurfaces to implement high-dimensional positive operator-valued measure graphs, successfully certifying randomness with heralded single photons and Poissonian light. By integrating complex quantum measurements into a single passive layer, our metasurface quantum graphs provide a scalable route for integrated quantum technologies.

We propose an anomaly detection method for high-dimensional mixed-type data that maps heterogeneous features to a common scale via standardized moment-based transformations, yielding interpretable feature-level anomaly scores. These scores are combined through a dependence-aware aggregation step to construct the Mixed-data Influence (MDI) score, accounting for correlations across features and providing a unified measure of how strongly an observation departs from the reference data distribution. By incorporating higher-order moments, the MDI can detect anomalies that arise not only from location shifts, but also from changes in variability, skewness, and other distributional characteristics. The aggregation mechanism allows our method to capture both sparse anomalies concentrated in a small number of features and weak, coordinated deviations distributed across many features. We empirically investigate the distribution and thresholding behavior of the MDI score across different sample sizes, dimensions, dependence structures, and data types. Simulation experiments and two real-data applications, to multi-omics and ESG data, evaluate finite-sample calibration, detection performance, and feature-level interpretability.

Island-ready 5G deployments provide edge connectivity for isolated regions in crisis scenarios by switching to island operation when they are cut off from the global Internet. This work addresses open research challenges that hinder the practical realization of island readiness, with a focus on the required state synchronization and connectivity monitoring functionality. As a proof of concept and for performance evaluation, we integrate our solutions in open-source projects and emulate a country-wide 5G communication network with real-world cellular traffic. Our evaluation studies the switching latency of transitions to island operation, showing that most of the transition delay stems from the access network reconfiguration. We study the synchronization overhead of a highly distributed core network, finding that the synchronization traffic grows faster than linearly with the number of 5G cores, reaching peak synchronization data rates of 9.36MB/s for a deployment of 50 cores.

In this paper, we determine the generalized Hamming weight hierarchies of two classes of twisted Reed–Solomon (TRS) codes. For TRS codes with one twist, we first determine all possible values of the generalized Hamming weights. We then give a complete characterization of the weight hierarchy in terms of the minimum distance of the dual code. Explicit conditions are derived for the minimum distances of the code and its dual, which make the whole weight hierarchy explicitly computable. As special cases, the obtained results recover several known characterizations for TRS codes to be MDS, NMDS codes, and $s$-gap AMDS codes. For TRS codes with two twists, we similarly determine the complete generalized Hamming weight hierarchy. In this case, the higher generalized Hamming weights are determined by the first two generalized Hamming weights of the dual code, for which explicit rank conditions are also obtained. In addition, we further determine the subcode support weight distributions of this class of single-twist TRS codes. More precisely, for each $1 \le r \le k$, we derive an explicit formula for the number of $r$-dimensional subcodes with a prescribed support size, thereby giving a complete description of the support distribution of subcodes.

We examine the impacts of dark matter (DM) on the observables of the neutron star (NS). The interaction of DM with nucleons intermediate by axion-like particles (ALPs), and the DM-admixed NS (DNS) is formulated in the framework of the relativistic mean field (RMF) formalism. The effects of the DM on the NS are characterized by two parameters: DM Fermi momentum ($q_f$) and DM mass ($m_\chi$). By varying these two parameters, we investigate how the NS's mass, radius, and tidal deformability are altered. Furthermore, we study how the ALP-mediated DM impacts the stability of the NS through the analysis of radial oscillations. In addition, the nonradial oscillation has been investigated by calculating its fundamental mode frequency in the DNS and analyzed how the ALP-mediated DM modifies its behavior.

In LLM agent organizations, shared records determine which facts are available for later decisions. A sender consults interaction histories before deciding whether to report an event. A delivery gap across histories does not show whose relationship drove the choice or whether the resulting record matters downstream. We introduce RelLedger to audit these links. It holds the event, evidence, risk, and message fixed while crossing the sender's histories with the event target and an unrelated actor. Role reassignment and history rewrites locate the controlling cue. Message and cost interventions show when the effect appears. An attribution ledger maps each claim to its required response cells and separates missing interventions from sampling uncertainty. Recipient replay follows delivered information into downstream decisions. Executable workflows for a simulated one-person company extend the audit to retrieved histories, tool calls, and shared ledger updates. Across GPT, Gemini, Claude, DeepSeek, and Qwen, the audit reveals model-specific control paths and smaller relation gaps under explicit loss rules. Claude sends the same factual notice 62.22 percentage points more often with conflict histories than with friendly histories. In executable workflows, strained histories reduce recipient review rates by 45.83 points relative to warm histories for Claude.

Before changing a deployed AI agent (a stricter safety gate, a new model), organizations must approve the change, starting from existing logs. Extending classical risk analysis to partial records and partial changes to running systems, agent-risk replays logged episodes, assuming nothing else changes and the agent does not anticipate the change. The log settles episodes acting as before, a declared stop value settles stopped ones, and the rest need logged support, a saved-state rerun, or a bound. We prove what logs must record for exact replay and which saved states serve a gate family. For independent episodes, we bound the reruns a decision needs and tolerable drift from live behavior. In a bash sandbox, a 7,200-episode log alone decided neither of two retry gates, which let the agent act after refusals the log never shows. Rerunning only each gate's blocked episodes from saved states reached both live decisions at half the agent calls of a live test sized post hoc for them, given the log. Without per-step harm, a stopping gate's certified harm ceiling rose up to 2.5-fold, since the log hides whether harm preceded the stop. Approval thus needs evidence designed in advance: log fields, saved states, targeted reruns.