Papers

The line-of-sight acceleration (LOSA) effect, imprinted in the gravitational wave (GW) signal of an inspiralling compact binary by an external gravitational potential, is one of the most promising means of probing the environment of compact binaries on a single-event basis. However, this effect is potentially degenerate with other low-frequency effects, particularly the binary's orbital eccentricity. LOSA effects and orbital eccentricity can mimic each other if only one or the other (but not both) are accounted for in the waveform template. In this work, we present the (2, 2) mode, leading eccentric harmonic, frequency-domain phase correction incurred by an accelerating eccentric compact binary, and discuss inconsistencies pertaining to this phase correction in the literature. We show that the degeneracy between LOSA and orbital eccentricity can be resolved if both effects are modeled in the template. To demonstrate this, we inject a GW170817-like signal, with eccentricity and LOSA added to it, and recover the parameters of the injected signal assuming an A+ like noise power spectral density (PSD) of the LVK detector network. We find that the true LOSA and eccentricity parameters, along with other binary parameters, are recovered within the $90\%$ credible interval (CI). This study highlights the importance of incorporating LOSA in eccentric waveform models to robustly and reliably estimate LOSA and eccentricity.

Third-party evaluations of autonomous vehicle (AV) safety can play a vital role in improving public acceptance, building consumer confidence, and establishing effective safety standards. In Part I of this study, we propose a dedicated third-party testing initiative for systematically evaluating AV behavioral safety. In this paper, we validate our proposed framework using Autoware.Universe, an open-source Level 4 Automated Driving System (ADS), tested both in simulated environments and on the physical test track at the University of Michigan's Mcity Testing Facility. The results indicate that Autoware.Universe possesses 6 out of 14 behavioral competencies and exhibited a crash rate of 3.01x10^-3 crashes per mile, approximately 1,000 times higher than the average human driver crash rate. During the tests, we also uncovered a number of unknown unsafe scenarios for Autoware.Universe. These findings underscore the necessity of behavioral safety evaluations for improving AV safety performance prior to widespread public deployment.

We investigate the momentum-space mechanical properties of small-$x$ gluons and sea quarks using gravitational transverse-momentum distributions (gravitational TMDs). For gluons, we formulate these distributions using the light-front gauge-invariant canonical energy-momentum tensor and derive their relations to ordinary TMD correlators, identifying momentum densities, the transverse flux of inertia, and transverse stresses. In the eikonal approximation, the longitudinal and transverse canonical gluon momentum densities are determined by the unpolarized distribution, whereas the transverse flux of inertia and transverse stresses vanish. For an unpolarized target, we numerically evaluate the gluon and sea-quark momentum densities using a common initial condition based on the McLerran–Venugopalan model and fixed-coupling leading-order Balitsky–Kovchegov evolution. We also evaluate the sea-quark transverse flux of inertia through the twist-three quark TMD at the high transverse-momentum region. These results illustrate departures from the free-particle relation between canonical transverse momentum and the effective transverse velocity governing inertia flow.

Non-governmental organizations often compete for funding while valuing similar social outcomes. Fundraising may expand total giving to a cause or redirect a given funding pool toward the focal organization. This paper studies how cross-organizational purpose alignment changes the composition of such competition. The analysis separates two effects of fundraising: marginal lift in aggregate funding and marginal shift of funding between organizations. Incomplete alignment creates a wedge between an NGO's marginal mission return and the aggregate mission return that is proportional to shift minus lift. When NGOs choose among fundraising technologies, greater purpose alignment shifts effort toward the relatively lift-intensive technology. Relative to the aggregate mission benchmark, incompletely aligned NGOs choose portfolios that are too shift-intensive. A uniform restriction on fundraising may change total effort but cannot generally correct this composition distortion; correcting the portfolio requires changing relative incentives across technologies. A simple microfoundation interprets cause promotion as lift and organization promotion as shift. Productivity differences preserve reallocation when it raises mission output, while organization-specific benefits restore rivalry even under complete alignment. The model therefore predicts how a common purpose changes the form of competition even when its effect on the level of competition is ambiguous.

We prove a two-dimensional version of Hermida's equivalence result on representable multicategories and classify its stricter versions. The obtained three-dimensional equivalence of the respective totality categories is of categories enriched over the multicategory $\mathsf{Bicat}$ of Verity. There is a basic enriched equivalence with respect to inherently lax monoidal pseudofunctors, and a one with respect to pseudo-monoidal pseudofunctors, related to the latter via the forgetful enriched functors. We extend Slattery's result on a bi-multicategory structure of the Kleisli bicategory of a 2-multicategory encompassing bi-representability.

Phonon lasers amplify mechanical vibrations, serving as key tools for coherent acoustics research and applications such as ultrasensitive sensing and information processing, which has been extensively studied in Markovian systems but remains unexplored in non-Markovian ones. In this paper, we propose the nonreciprocal phonon laser in a coupled cavity system composed of nonlinear optomechanical resonator and degenerate optical parametric amplifier (DOPA) under the Markovian approximation. The mechanical gain and threshold power of the phonon laser are influenced by Sagnac-Fizeau effects, which leads to the unidirectional phonon laser and enhances the phonon laser performance via DOPA. Moreover, we generalize the nonreciprocal phonon laser to non-Markovian regimes. We find that non-Markovian effects can lead to the further enhancement of the phonon laser at a lower phonon laser threshold power with DOPA fixed. Our work reveals connections between low-power mechanical isolation and non-Markovian effects, offering a pathway to manipulate cavity optomechanical devices across a broader range of applications.

Retrieval-augmented generation (RAG) is a widely used approach for grounding large language models (LLMs) in external knowledge. However, configuring a pipeline is an expensive hyperparameter optimization problem over many interacting choices, from chunking and embedding model to reranking and generation. Existing optimizers, from greedy search to Bayesian optimization, reduce each trial to an aggregate score and search without modeling why a configuration performed as it did, even though the retrieved chunks already provide evidence about whether each failure occurred during retrieval or after it. We introduce Agentic AutoRAG, an LLM-agent optimizer for multi-objective RAG hyperparameter optimization with retrieval-versus-generation failure attribution. It proposes configurations scored on a frozen exam from the corpus: after each trial a Diagnoser attributes each failed question to retrieval or generation, and a Proposer, grounded in a knowledge base of model rankings and pricing, selects the next configuration, weighing accuracy against cost to trace a Pareto frontier. On three multi-hop QA benchmarks it reaches higher LLM-judge accuracy than every baseline we compare, and within its first 10 trials it matches or beats the statistical baselines' full 30-trial judge accuracy. In its cost-aware mode on a real-world healthcare corpus it reaches a median exam accuracy of 77%, above the strongest baseline's 71.5%, at about 58% of that baseline's cost per query, and it matches that 71.5% at about 22% of the cost.

Using aerodynamic databases of progressively increasing complexity - from linear analytical theory to nonlinear separated RANS flows - we demonstrate that an autoencoder, trained solely by reconstruction, can spontaneously organize the latent representation according to physically meaningful variables and aerodynamic laws. Although the latent coordinates themselves vary under random initialization, the underlying physical organization is reproducible, even quantitatively. In addition, we present a three-dimensional latent space representation of the airfoil flow obtained by an unsupervised autoencoder with sequential training in which the inviscid field is decoupled from the boundary layer effects with the third latent variable strongly correlated with the Reynolds number and aerodynamic drag. Cross-validated regression and affine-alignment measures show that physical parameters and responses are strongly and linearly encoded in the learned coordinates, consistently across independent trainings.

Autonomous vehicles (AVs) have significantly advanced in real-world deployment in recent years, yet safety continues to be a critical barrier to widespread adoption. Traditional functional safety approaches, which primarily verify the reliability, robustness, and adequacy of AV hardware and software systems from a vehicle-centric perspective, do not sufficiently address the AV's broader interactions and behavioral impact on the surrounding traffic environment. To overcome this limitation, we propose a paradigm shift toward behavioral safety, a comprehensive approach focused on evaluating AV responses and interactions within the traffic environment. To systematically assess behavioral safety, we introduce a third-party AV safety assessment framework comprising two complementary evaluation components: the Behavioral Competency Test and the Driving Intelligence Test. The Behavioral Competency Test evaluates the AV's reactive behaviors under controlled scenarios, ensuring basic behavioral competency. In contrast, the Driving Intelligence Test assesses the AV's interactive behaviors within naturalistic traffic conditions, quantifying the frequency of safety-critical events to deliver statistically meaningful safety metrics before large-scale deployment. In Part II of this study, an open-source Level 4 Automated Driving System (ADS) is tested to demonstrate the effectiveness of the proposed method.

We study nil-Hecke quotients defined by powers of root coordinates. We identify their central ideals through the determinant components of root-orbit power ideals. Apolarity and discriminant removal reduce the graded dual centers to directional bounds on invariant polynomials. We determine their Hilbert series for every exponent and root orbit in all irreducible crystallographic types except $E_6,E_7,E_8$. Relative discriminants compare centers for reflection subgroups and transfer equivariant resolutions. Coordinate-root centers in types $B$ and $C$ are Grassmannian cohomology rings. We classify self-injectivity in type $A$, in rank two, and in type $F_4$, and determine the first nonsemisimple centers in the remaining classical families. For an explicit open set of reflection parameters, the polynomial image of the rational Cherednik algebra at $t=0$ is the full nil-Hecke algebra. This realizes our algebras as Cherednik quotients and their finite centers as closed subschemes on a section of the generalized Calogero–Moser space.

On-Policy Distillation (OPD) trains a student on its own generations using teacher feedback. With different tokenizers, comparing teacher and student predictions requires alignment at both sequence and vocabulary levels. In this paper, we examine whether expanding this alignment coverage improves learning. Across three heterogeneous teacher–student pairs on mathematical reasoning and code generation, strict 1:1 groups already cover most student-generated tokens despite substantial vocabulary mismatch. On responses sampled from the students before distillation, the shared vocabulary retains nearly all teacher and student probability mass at strictly aligned positions on average. Restricting reverse KL to a student-selected top-16 subset of the shared vocabulary at each strict position achieves accuracy comparable to full shared-vocabulary OPD, outperforming the evaluated cross-tokenizer baselines. Adding mean squared error supervision on span log-probabilities in mismatch groups gives complete supervision coverage, yet reduces accuracy. At checkpoints from training with only the strict loss, the span gradients show weak or negative directional agreement with the strict gradients and grow in magnitude relative to them. These diagnostics may help explain the accuracy drop from adding span supervision. Our findings motivate a shift from maximizing alignment coverage to prioritizing supervision reliability: compact supervision at strict positions can be more effective than broader coverage that introduces weakly aligned or conflicting training signals.

An organization may bind future decision makers through a commitment over its own lifespan. This paper studies that choice for philanthropic foundations. A foundation may commit to terminate, commit to institutional continuity, or leave termination to future discretion. Discretion preserves state-contingent stopping. Perpetuity instead raises investment in foundation-specific organizational capital whose return is partly lost upon termination. A terminal commitment limits excessive continuation when future governing bodies obtain private benefits from organizational survival. A canonical model yields nonempty regions in which each regime is optimal, while a finite-horizon extension endogenizes the terminal date. Perpetuity is optimal when organizational capital is sufficiently productive relative to the cost of continuing in bad states; discretion is optimal when stopping flexibility is valuable and governance is aligned; a finite lifespan is optimal when survival incentives create sufficiently costly entrenchment. Organizational lifespan is therefore a distinct commitment margin.

Multimodal large language models (MLLMs) have made significant progress in visual understanding, but precise 3D spatial reasoning integrated with physical environment remains difficult. Furniture assembly requires not only recovering step-level operations from diagrammatic manuals, but also translating semantic attachment relations into 6D pose updates that enable parts to physically interact with the environment and previously assembled components. To study this problem, we propose AssemState, a zero-shot framework for manual and physical-state-guided furniture assembly. It firstly employs anchor-guided boundary assembly states to decompose manual pages into single-part operations and recover an assembly-tree. Then, it uses iterative after-state feedback refinement to guide successive (SE(3)) updates and corrections, and validates their physical plausibility through simulation-based release tests. Experiments show that compared with the strongest prior baseline, AssemState improves F1 from 38.58% to 62.80% and Tree Exact Match from 28.24% to 53.92% for assembly-tree recovery. On 243 independently evaluated part-level operations, our proposed iterative refinement improves judge-accepted operations from 0 to 5.3% and reduces mean Chamfer distance from 5.4111 to 1.7744. However, visually plausible candidate poses may still suffer from collision, floating, mirror-orientation errors, incomplete seating, and wrong-side attachment. These results show that AssemState improves operation-structure recovery and selected local pose metrics, while MLLMs remain limited for spatial relationship reasoning.

Quantum memories are key ingredients for future quantum networks. Developing methods for their certification is therefore an important, yet challenging, problem. In this work, we present a general framework for certifying quantum memories and quantifying their performance in an operational and efficient manner, taking advantage of developments in the theory of quantum channels. We start by giving a pedagogical introduction to these concepts and tools and illustrate their natural application to quantum memories. Specifically, we quantify the fidelity of a quantum memory via the notion of average channel fidelity, which can be estimated precisely in an experiment via a finite set of probe states forming a so-called $2$-design. We then present a number of witnessing techniques for certifying this quantity, and show that it gives access to other important properties of the channel, such as its dimensionality and its capacity to transmit quantum information. We consider mostly a simple prepare-and-measure scenario, but discuss also the case of an entanglement-based setup, as well as a semi-device-independent approach. Finally, we apply these methods to a solid-state quantum memory experiment, certifying an average channel fidelity of 98.6%. Our certification methods can be readily applied to other quantum devices, such as fibers, transducers and gates.

Vision-language-action (VLA) policies repeatedly invoke inference to control robots, making graphics processing unit (GPU) energy a recurring cost of task execution. Reducing energy per inference call, however, may not reduce energy per successful task if numerical errors increase failures or slower inference prolongs execution. We therefore target GPU energy per successful task while preserving task success and keeping the inference-latency increase within 10%. Our approach builds on two observations: quantization sensitivity varies across action classes, model layers, and weights versus activations; and numerical precision changes the workload, shifting favorable GPU operating points. We introduce ActTune, an action-aware framework that connects layer-wise precision allocation with workload-dependent GPU operating-point selection over requested frequency–power-cap pairs. A lightweight decision tree learns its splits and leaf precision configurations directly from configuration action errors, then selects precision before each policy call. The controller forecasts the next workload and applies the selected GPU operating point asynchronously using a lookup table calibrated under a latency budget. A shared resident quantized weight bank enables configuration switching without weight reconstruction or additional policy evaluations. On LIBERO, a benchmark for lifelong robot learning, ActTune improves mean task success by up to 2.3% relative to state of the art. Relative to the original BF16 implementations, it delivers up to $2.02\times$ faster inference and, with GPU operating-point adaptation, reduces energy per successful task by up to 76.8%.

The logarithmic multiplicative error model (log-vMEM) has been useful in modeling and forecasting multivariate positive-valued financial time series. The number of parameters grow rapidly with the dimension of the system and the lag order, making estimation computationally demanding in high-dimensional settings. This paper describes regularized estimation via hierarchical lag structures (Nicholson et al., 2020) for log-vMEM models with multivariate gamma error distribution of Tsionas (2004). The parameter estimation is performed using a blockwise coordinate descent algorithm with a Gauss-Seidel-style update scheme (Wright, 2015). This enables an efficient computation strategy compared to traditional penalized maximum likelihood approaches. The competing models are juxtaposed against each other by combining three hierarchical lag structures (componentwise, elementwise, own-other) and four penalties(group-lasso, adaptive group-lasso, group-mcp, and group-scad). Extensive simulation runs have been performed to test the parameter recovery for both the unpenalized and the penalized models. We apply the proposed methods to model the joint dynamics of robust intraday realized volatility measures for Microsoft (NASDAQ: MSFT) for the competing models. The numerical integration step of the log-likelihood is identified to be the principal computational bottleneck. We address this issue by using GPU-accelerated quadrature integration thus improving computational scalability of the proposed models.

We give a compactness proof of interior Hessian estimates for convex solutions of $\sigma_n(D^2u)/\sigma_{n-2}(D^2u)=1$ and $\sigma_n(D^2u)/\sigma_{n-1}(D^2u)=f(x,u,Du)>0$, with $1/f$ concave in the gradient variable in the latter case, revisiting results of Lu and Fung.

This paper presents a hierarchical density-based model predictive control framework for safe collaborative manipulation by multiple quadrupedal robots. The framework enables a team of robots to push a shared object to a desired pose using only the initial and goal poses, without requiring a precomputed reference trajectory. A centralized box-level MPC optimizes contact forces while enforcing a control-density constraint for goal convergence and obstacle avoidance. Each robot then solves its own distributed robot-level whole-body MPC, under a stated shared-information assumption, to track its moving contact location while accounting for static obstacles and the time-varying positions of neighboring robots. The approach is evaluated in MuJoCo using whole-body contact dynamics for two and three Unitree Go2 quadrupeds collaboratively pushing rigid objects through narrow passages. Comparisons with matched Control Barrier Function and RRT* based tracking baselines demonstrate the effectiveness of the proposed density-based formulation for push-only, force- and torque-coupled manipulation tasks. Implementation videos are available at https://jaggu2606.github.io/go2-density-mpc-pushing/

We study Stein structures on nearly Lefschetz fibrations, with applications to symplectic and Lagrangian submanifolds in Weinstein domains. We prove that, up to Weinstein deformation equivalence, all Lagrangian disks with Legendrian boundary in $4$-dimensional Weinstein domains are regular in the sense of Eliashberg-Ganatra-Lazarev. This settles a Weinstein analogue of the nearby Lagrangian conjecture for two-dimensional Lagrangian disks, and resolves part of a Lagrangian analogue of the Slice-Ribbon conjecture. Along the way, we show that positive allowable nearly Lefschetz fibrations are supported by canonical Stein structures and prove a corresponding quasiflexibility result in the planar case. This yields a generalization of work of Boileau-Orevkov which may be of independent interest. Finally, we give an explicit algorithm producing a Weinstein Kirby diagram from the nearly Lefschetz fibration structure of a multisection complement.

Multi-spacecraft multi-rendezvous mission design requires repeated evaluations of the total cost of visiting a target set within a given time window, and the efficiency of this evaluation is the primary barrier to global search. Existing methods either optimize the order and epochs of each candidate sequence, which is expensive, or estimate the cost leg by leg, in which case the error accumulates with the sequence length. This paper proposes a deep model that regresses the total cost of an unordered target set directly: the pairwise transfer cost surface of each target pair is compressed into a latent feature, and a permutation-invariant transformer encoder regresses the sequence cost from these features and the window parameters, without ordering information. Trained on about 0.85 million labeled sequences, the model attains a mean relative error near 5% and a sub-millisecond evaluation time, about five orders of magnitude faster than precise optimization. Embedded into an evolutionary global search and applied to the GTOC9 problem, it yields the best known solution at every fleet size considered, from seven to ten spacecraft: directly, it produces near-optimal solutions cheaply, and as the initial guess of a differential-evolution refinement it improves the best published solutions further. The evaluator is not specific to this problem or to debris removal: it requires only a pairwise transfer cost function and a sequence-level cost metric monotone in the leg costs, and therefore applies equally to the servicing of satellites in low Earth orbit and to multi-target visits in deep space.

We investigate how post-selected von Neumann measurements modify the nonclassical properties of two-mode entangled coherent states (ECSs). From the conditional pointer state, we characterize squeezing, photon statistics, intermode correlations, entanglement, fidelity, and post-selection probability. Anomalous weak values with moderate coupling enhance squeezing, antibunching, sub-Poissonian statistics, intermode correlations, and bipartite entanglement, while fidelity captures the crossover from weak perturbation to strong distinguishability. These results demonstrate post-selection as a tunable approach to engineering ECSs.

We propose an unified view to three well known quadratic Hamiltonians widely considered in quantum mechanics, i.e. those of the harmonic oscillator, of the inverted harmonic oscillator, and the Berry-Keating Hamiltonian. We describe an unified approach to determine the discrete spectrum of these operators, and to deduce their (generalized) eigenstates. We also look at these Hamiltonians as the generators of $\mathfrak{su}(1,1)$, and of a generalized version of it relevant in presence of non Hermitian generators.

We study the evolution and clustering properties of the star formation rate density (SFR) $\rho_{\rm SFR}$ in the FLAMINGO suite of hydrodynamical simulations, with the aim of exploring the possibility of constraining AGN and stellar feedback prescription, as well as the effect of cosmology, using cross-correlations between the Cosmic Infrared Background (CIB) and other tracers of the large-scale structure. Specifically, we consider tomographic measurements of the bias-weighted SFR-density $\langle b\rho_{\rm SFR}\rangle$, as well as cross-correlations between the CIB and cosmic shear as a probe of the $\rho_{\rm SFR}$-matter correlation. Most of the FLAMINGO models calibrated against the $z=0$ galaxy stellar mass function (SMF) yield similar predictions for the distribution and clustering of star-forming systems, and thus it is difficult to derive clean conclusions regarding the impact of AGN feedback or cosmology on CIB statistics. However, we show that current measurements of $\langle b\rho_{\rm SFR}\rangle$, as well as CIB-shear cross-correlations clearly disfavour models with strong stellar feedback, as well as simulations with strong kinetic (jet-driven) AGN feedback, even under the fiducial SMF calibration. This study demonstrates the potential of CIB cross-correlations to study aspects of the physics of star and galaxy formation in a cosmological setting.

When a subset of alternatives is allowed to be the collective choice, one approach is to study the social choice correspondence defined on agents' preferences over alternatives. This paper considers a different approach. We argue that agents should have preferences directly over outcomes. We consider the social choice problem on a closed real interval, and assume a single-peaked domain over intervals. Our focus is on the peak-only social choice function, referred to as the voting scheme. The leftright scheme, which generalizes the minmax scheme, is the only strategy-proof voting scheme. Adding anonymity, it reduces to the generalized median scheme. For an odd number of agents, the median scheme is the only voting scheme satisfying efficiency, anonymity, and strategy-proofness.

We prove an instantaneous smoothing effect for a degenerate non-local evolution equation (originally derived as the many-particle limit of a system of active Brownian particles). The underlying mechanism is that, by deriving a Harnack-type inequality for an averaged quantity, we are able to show that the equation becomes strongly parabolic for positive times, and thus self-regularising. This paper is a significant improvement of a previous work, where additional (weak) non-degeneracy assumptions were imposed on the initial data. Herein, we completely remove these assumptions, and prove (in addition to the regularity bootstrap) quantitative estimates on the aforementioned averaged quantity by means of an approach à la Bombieri-Giusti.

Modern action recognition models rely on video transformers pretrained on massive collections of web-crawled videos, such as Kinetics-700. However, the use of such data raises ethical concerns, as subjects' consent is typically not obtained. Recent high-quality synthetic video datasets generated from motion-capture data, such as BEDLAM2.0, offer a promising ethical alternative. In this work, we investigate self-supervised pretraining of video transformers on synthetic human-motion datasets. We first show that directly applying the standard VideoMAE masking strategy leads to substantially worse performance than pretraining on Kinetics. To address this limitation, we propose a human-centric masking scheme that leverages body keypoints and person bounding box regions. Our approach encourages the model to focus on the structure and dynamics of human motion during pretraining. Experiments on NTU RGB+D and Toyota-Smarthome demonstrate that our method significantly outperforms standard VideoMAE pretraining on synthetic data, closing 49% of the gap to Kinetics pretraining on NTU RGB+D cross-view-subject without using a single real frame during pretraining. To promote the use of ethical action recognition models, we will publicly release our pretrained models.

Improving embodied agents often focuses on optimizing the underlying model through training, while the surrounding agent harness that controls planning, context, and tool use is typically engineered. We ask whether this harness can instead improve itself directly from experience traces under sparse environmental feedback. We propose EMbodied Agent Harness Optimization (EMHO), a self-evolving framework that keeps the embodied model frozen and iteratively revises its harness by analyzing execution trajectories and prior harness history. EMHO optimizes beyond skills or recovery prompts, modifying how the agent monitors progress, uses vision tools, grounds observations, and responds to failures. To support multiple subtasks with a single harness, we introduce EMHO-Merge, which addresses trade-offs in jointly optimizing a single shared harness across subtasks by using episode-level gains and losses to guide evidence-supported refinement of when and how revised behaviors are applied. We evaluate EMHO on EmbodiedBench across navigation and manipulation tasks, and EMHO consistently improves task success for both Qwen 9B and 27B models. Qualitative analysis shows that EMHO goes beyond recovering from failures and unproductive actions to reshape how the embodied agent interprets and interacts with its environment.

We study quiver Demazure algebras through residue covers and root-power quotients. The cover determined by the zero-root subsystem identifies the additive algebra with a finite fixed algebra of Sauter's generalized quiver Hecke construction. Her basis theorem then gives additive PBW in every finite Weyl type, for arbitrary admissible residue data and uniform quivers. A sequence-cover argument gives global multiplicative PBW in simply-laced type. Under a directed-path condition, root-power quotients are finite dimensional and the formal exponential identifies their additive and multiplicative forms. For arrow-free quivers, we reduce mixed-residue quotients to matrix algebras over finite skew group rings, obtain sharp nonvanishing criteria from coinvariant geometry, and determine their simple modules. In a mixed type-$D_4$ family we compute an explicit coefficient presentation, dimensions, Loewy lengths, and Cartan matrices. We also specify the direct and finite-cover comparisons with Liu's algebras.

Agentic reinforcement learning (RL) disaggregates training from rollout, so each policy update must reach the rollout clusters before the next batch. Transferring a full 1T checkpoint for such weight synchronization (refit) takes 87.5 min between two AWS regions. Measurements of BF16 training show that about 1% of weights change their stored values per step. Recent systems exploit this sparsity but fall short on placement, exactness, or efficiency: they reimplement placement rules, assemble full tensors, rebuild values arithmetically, or use a cross-cluster collective, and none fully recovers from mid-refit failures. We present NeMo-DCR (Delta-Compressed Refit), which sends only changes yet is bit-exact: receivers obtain the same parameter and buffer bits as a dense refit. For placement, fixed affine mappings project changes from training shards into the checkpoint's canonical coordinates, residual conversion covers the other changes, and the serving runtime's native loader places all changes in receiver storage. For exactness, compressible XOR masks carry affine changes whose projection and loader preserve stored bits, and overwrites carry the others. Receivers apply both in place, retries overwrite partial writes, and a joint commit binds the policy to the baseline for the next delta. For efficiency, object storage or a relay tree streams payloads during delta construction, without a cross-cluster collective. Even at 3% and 5% change rates, NeMo-DCR refits of 30B-1T models are 12-40$\times$ faster than a transport-only full-checkpoint reference. A 1T relay-tree refit at 3% takes 150 s instead of 87.5 min, making refits practical for cross-cluster agentic RL at trillion-parameter scale.

Smart contracts written in Solidity manage assets, permissions, and irreversible state changes, making code generation both useful and security-critical. Repository-level Solidity generation is challenging because models must synthesize complete contracts or libraries while preserving consistency across state variables, modifiers, events, inheritance, external calls, and access-control logic. We present RAPO-Sol, a two-stage training framework for repository-level Solidity code generation. First, Retrieval-Augmented Fine-Tuning (RAFT) augments each training input with similar Solidity examples, helping the model learn recurring contract-level patterns while remaining retrieval-free at inference time. Second, Direct Preference Optimization (DPO) trains the model to prefer reference contracts over close but semantically flawed alternatives. We construct rejected samples using Solidity Semantic-Anchor Perturbation (SAP), which perturbs validation statements, visibility modifiers, data-location keywords, context variables, payment operations, and low-level calls. Experiments on SolidityBench with CodeLlama-7B-Instruct, DeepSeek-Coder-6.7B-Instruct, and Qwen2.5-Coder-7B-Instruct show that RAFT consistently improves over supervised fine-tuning, while SAP-based DPO provides further gains in BLEU and SolidityScore. The full RAFT+DPO pipeline achieves the best performance across all three models, demonstrating complementary benefits from retrieval during training and Solidity-aware preference optimization without adding retrieval cost at inference.