Papers

We study the reconstruction of a directional albedo field from confocal non-line-of-sight measurements. For mirror-symmetric vector fields in Sobolev spaces, radial preprocessing reduces the data to spherical means of the divergence with centers on the relay wall. Full data determine this divergence uniquely, with divergence-free fields forming the entire ambiguity. An explicit Fourier–sine formula recovers the irrotational Helmholtz component and reproduces the data. The Fourier–sine transforms of the model data form a weighted Hilbert space that we characterize exactly, with norm equal to the Sobolev norm of the reconstructed field. This weighted range remains well defined even when the preprocessed data fail to belong to standard Sobolev spaces. For Schwartz fields in the model class, such Sobolev regularity holds exactly when the divergence has zero depth integral. Measurements on an open subset of the relay wall, for all radii $0<r<R_{\max}$, uniquely determine the divergence in the union of the corresponding balls. An FFT-based algorithm with Stolt interpolation implements the reconstruction in $O(N^3\log N)$ operations on an $N^3$ grid. Tests on explicitly defined fields assess reconstruction accuracy and invariance under divergence-free perturbations. We present imaging examples of potential and vector-field reconstruction from model-generated, rendered, and measured transients.

We present exact analytical solutions to the nonlinear relativistic Boltzmann equation for homogeneous, isotropic massless multi-component systems with non-isotropic scattering cross sections. For a two-component system, we identify three distinct classes of exact solutions, each corresponding to specific constraints among initial energy densities, particle number densities, and scattering cross sections. These solutions comprise the equilibrium state and two novel classes: a hybrid structure featuring a non-equilibrium Maxwell-Juttner distribution coupled with a nontrivial distribution; the former is unprecedented in kinetic theory, while the latter refers to nontrivial dynamics shared by both species, which is novel in the relativistic context.

Deep-blue-emitting CuBr quantum dots (QDs) hold promise as nontoxic and heavy-metal-free optoelectronic materials, yet their efficiency is limited by intrinsic defects. We report Zn doping as an effective strategy to mitigate defect-mediated recombination in CuBr QDs synthesized via an eco-friendly supersaturated recrystallization method under ambient conditions. XRD shows lattice contraction, Rietveld refinement confirms substitutional doping, and XPS verifies Cu$^+$/ Zn$^{2+}$ states without secondary phases. HR-TEM analysis reveals uniform 3.46 $\pm$ 0.12 nm Zn:CuBr QDs with reduced bandgap, after doping, indicating weaker quantum confinement. The dominant emission peaks appear at 406 nm ($Z_f$) and 431 nm ($Z_{1,2}$) under 365 nm excitation. Narrows defect FWHM, elevated band-edge emission, and extends carrier lifetimes, achieving 96.4 % color purity with CIE coordinates (0.1520, 0.0395). These findings demonstrate that Zn doping is a simple, scalable, and environmentally benign strategy for engineering efficient blue-emitting CuBr QDs.

Residual-based adaptive GMsFEM for high-contrast elliptic problems repeatedly evaluates local weighted $H^{-1}$ indicators on every coarse neighborhood, making indicator evaluation a recurring cost in repeated-query settings. We introduce a non-intrusive Gaussian-process (GP) surrogate for the indicator scores used in Dörfler marking. The operational predictor is the GP posterior mean, algebraically equivalent to a kernel ridge regression (KRR) estimator under the stated convention; it uses compressed local solution and spectral features without changing the multiscale solve, local spectral construction, or basis enrichment. A nonuniform perturbed-marking result quantifies how pointwise score errors affect the exact indicator mass captured by surrogate-selected neighborhoods, while a conditional bounded-discrepancy KRR pathway identifies sufficient assumptions for such score bounds. In controlled held-out in-distribution tests, the surrogate-guided method gives error-versus-DoF trends comparable with classical $H^{-1}$-residual offline adaptivity and evaluates the online indicator component 2.0-2.1 times faster, excluding offline data generation and GP training.

We prove Miller's conjectured bound for solvable groups: if $G$ is a finite solvable group and $\chi\in\Irr(G)$, then $\chi(g)$ is zero or a root of unity for at least half of the elements $g\in G$. We also prove the same bound for monomial irreducible characters of arbitrary finite groups.

High-capacity neural network models have achieved state-of-the-art performance across diverse classification tasks, yet they frequently operate as black-box models, lacking the transparency necessary for critical decision-making. Such opacity creates a persistent trade-off between performance and explainability. This paper proposes a solution to address this gap: the NeuroRule knowledge distillation framework that results in explainable rule-sets from neural network models. NeuroRule adapts the EVOTER rule-set evolution infrastructure to treat neural networks as targets for the evolution process, distilling their performance into concise sets of propositional logic expressions. There are three primary contributions: (1) an evolutionary method for distilling black-box neural network models into explicit rule-set models; (2) a method for making rule sets more explainable by including a conciseness objective to evolution; and (3) a demonstration that the distillation is viable even without access to the original neural network training data. The paper thus establishes that black-box neural network models can be made explainable and therefore useful in real-world applications where trustworthiness is paramount.

This paper contains new 80-digit positive-weight Gauss-Hermite and positive-weight interior-node Gauss-Legendre quadrature rules for up to five dimensions and varying polynomial degree accuracy (depending on quadrature type and dimension). Some of these rules improve on the best available rules in the literature and some offer rules where none (other than the tensor product) existed. The results were produced by combining methodology developed by previous researchers with new approaches. The full precision rules themselves are at https://doi.org/10.5281/zenodo.22881864. Software in Julia, Python, and R providing the rules is available via a package registry and/or GitHub: Quadriceps.jl (both 64-bit and 128-bit; https://github.com/NittanyLion/Quadriceps.jl), quadriceps-py (64-bit only; https://github.com/NittanyLion/quadriceps-py), and quadriceps-r (64-bit only; https://github.com/NittanyLion/quadriceps-r). The software used to create these rules is available via PositiveWeightQuadratureSolvers.jl (https://github.com/NittanyLion/PositiveWeightQuadratureSolvers.jl). The replication package is at QuadricepsReplicationPackage.jl (https://github.com/NittanyLion/QuadricepsReplicationPackage.jl). A snapshot of all five packages is archived at https://doi.org/10.5281/zenodo.22883240.

Post-hoc probability calibration is usually evaluated under an optimistic assumption: the held-out calibration labels are clean. In many AI deployment settings, however, labels come from weak annotators, historical decisions, heuristics, or distant supervision, so the same label noise that corrupts training also corrupts calibration. We study this overlooked failure mode for tabular classifiers and propose LWCal, a CPU-only post-hoc calibrator that down-weights calibration examples whose noisy labels are contradicted by the base model's held-out probability. LWCal requires no clean validation labels, no noise-rate estimate, and no retraining of the base classifier. A second variant, Gated-LWCal, adds a conservative disagreement gate that backs off toward the raw score when the calibration split appears extremely inconsistent. On nine local binary tabular tasks, six random seeds, symmetric and asymmetric label corruption, and three tree-based base learners, LWCal obtains the lowest average calibration error while Gated-LWCal obtains the best average proper-score tradeoff. In the main random-forest study over 432 noisy cells, Gated-LWCal reduces expected calibration error from 0.188 to 0.122 and negative log likelihood from 0.438 to 0.396 relative to the raw classifier. Paired bootstrap intervals for Gated-LWCal versus raw, Platt, isotonic, and beta calibration exclude zero on ECE, Brier score, and NLL. The artifact contains all scripts, result tables, figures, and the compiled paper.

Diffusion Large Language Models (dLLMs) have recently emerged as a promising alternative to autoregressive LLMs by enabling non-autoregressive text generation. However, their practical deployment remains limited by inefficient inference, largely due to the absence of effective Key-Value (KV) caching and scalable parallel decoding mechanisms. Existing acceleration methods typically study KV caching and parallel decoding in isolation, overlooking the I/O bottlenecks that arise when cache reuse and parallel token verification are jointly applied. In this work, we introduce $\textbf{Flash-dLLM}$, a training-free inference acceleration framework for fast and memory-efficient dLLMs. Flash-dLLM first identifies GPU memory I/O as a dominant bottleneck in KV-cache-enabled dLLM inference and addresses it with an I/O-aware fused KV-cache kernel that reduces redundant memory movement. Building on this optimized cache mechanism, Flash-dLLM further proposes an efficient KV-cache-driven draft-and-verify decoding strategy, where the dLLM itself serves as both drafter and verifier without requiring an auxiliary model. This unified design enables faster decoding while preserving generation quality and improving scalability to longer sequences and larger batch size. Extensive experiments on mathematical reasoning and code-generation benchmarks demonstrate that Flash-dLLM consistently outperforms existing state-of-the-art dLLM acceleration methods in both inference speed and memory efficiency. In particular, it achieves $5.1\times$ and $11.0\times$ speedups over prior strongest baseline Elastic-Cache on GSM8K and HumanEval, respectively.

3D Gaussian Splatting (3DGS) can reconstruct a captured scene photorealistically, but the resulting representation does not by itself support physical interaction. Robot simulation instead requires object-level change, i.e., objects must move independently, make contact, and reveal previously occluded surroundings. This gap arises because object appearance may remain entangled with the background, while hidden object geometry and occluded background content may be unobserved. To address this challenge, we present \phi-RIE, a Gaussian-native pipeline that converts selected objects into movable simulator assets while preserving the remaining reconstruction. Our key observation is that asset construction and source removal should be coupled, i.e., one object identity should define the movable asset and the scene content to remove and complete. Accordingly, Scene Observation supplies shared evidence to Coupled Scene Construction, which creates registered assets and completed background Gaussians for simulator-driven rendering in an Interactive Environment. This coupling preserves unedited Gaussians while aligning visual and physical state. On 50 ScanNet++ scenes, evidence-based selection and registration retry increase matched F1 at 20\,mm from 0.336 to 0.383 at fixed retention. Further tests demonstrate asset executability, manipulation gains over a single-generator baseline, and the visual cost of conversion. Together, these results demonstrate that \name\ enables interactive scene conversion.

We present the first blind statistical survey of intervening NaI absorbers over the last $\simeq3$~Gyr using quasar spectra from the Dark Energy Spectroscopic Instrument Data Release~1. We identify 3636 NaI D doublets at $0.01\lesssim z_{\rm abs}\lesssim0.27$ along 214,035 quasar sightlines. We quantify the survey selection function through end-to-end injection–recovery tests and estimate the residual contamination from visual inspection. The completeness reaches 50% at a rest-equivalent width of the NaI $\lambda5891$ line, $W_{5891}\simeq0.95$ Angstrom, and the catalog-weighted purity is $\simeq77\%$. For the fiducial sample with $0.95<W_{5891}<3.5$ Angstrom, we measure the equivalent-width distribution ($f(W_r)$), absorber incidence ($dN/dX$), and cosmic NaI mass density ($\Omega_{\rm Na\,I}$). From $z\simeq0.25$ to $z\simeq0.03$, $dN/dX$ rises by a factor of $\simeq3.4$ in both rest-equivalent-width subsamples, split at the median $W_{5891}=1.41$ Angstrom, while $\Omega_{\rm Na\,I}$ increases by a similar factor. This corresponds to a smooth increase in the product of the comoving number density of NaI-absorbing hosts ($n_{\rm com}$) and the cross-section of the NaI-bearing gas ($\sigma_{\rm eff}$) with cosmic time. The similar evolution of $\Omega_{\rm Na\,I}$ and $dN/dX$ indicates little change in the mean measured NaI column density per absorber. We also find preliminary evidence that NaI absorbers are associated with foreground galaxies at relatively small projected separations and that their quasar sightlines are redder than matched controls. These results support a picture in which NaI traces dense neutral gas in and around galaxies. Dedicated galaxy surveys and CGM/ISM simulations can test the inferred incidence and cross-section, while spectral stacking can probe the associated gas and dust.

Compositional 3D scene reconstruction has recently been explored from two directions: agentic reasoning that provides semantic understanding of spatial relationships but lacks precise alignment with input images; and visual geometry foundation models that predict dense point maps from input images but the reconstruction quality is limited. Therefore, recovering a complete 3D scene from a single monocular image with accurate inter-object relationships and high-fidelity reconstruction quality remains challenging. In this paper, we present HARMONY, a hierarchical chain-of-thought framework that leverages both agentic reasoning and visual geometry foundation. Given an image of an indoor scene, starting from an empty 3D floorplan, HARMONY first calibrates the camera against the reference image to establish a semantically-grounded spatial frame, then uses agentic VLM reasoning to recover the 3D room layout and an initial placement order. It then places the objects in a hierarchical order, from wall-mounted elements, free-standing furniture, to dependent decorations on top of furniture. We also use depth-first traversal for furniture so each placement conditions on previously resolved structure and a reflective feedback loop to avoid error accumulation. After each object placement by VLM, we use the point cloud estimations to perform geometry-based refinement so that the rendered image aligns better with the input. HARMONY can produce 3D scenes that are semantically consistent and perceptually aligned with the reference image, extending single-image compositional reconstruction to complex indoor scene images. Experiments on synthetic and real-world images demonstrate that HARMONY outperforms the evaluated reconstruction baselines, while qualitative comparisons with GPT-6 Astra suggest more faithful object arrangements and better preservation of scene details.

Faithfully evaluating end-to-end driving policies in simulation requires observations that are not merely photo-realistic, but preserve the scene features a policy relies on to make decisions. Existing platforms, however, exhibit a sim-to-real visual gap that corrupts policy perception, undermining their ability to assess a policy's closed-loop decision-making. To this end, we propose DreamStream, a generative, closed-loop simulator that achieves policy-oriented fidelity using a simulator-grounded autoregressive video model. Our video model is distilled from a large pretrained video model via traffic layout guidance, varying visual appearance while preserving policy-relevant features such as scenario layout and the temporal consistency of dynamic objects. We further observe that perceptual metrics like FID misrank how well these features are preserved. To tackle this, we introduce FD$\pi$, a new multi-representation metric that measures the sim-to-real gap as the Fréchet distance over scene-context features from public E2E policies. Under FD$\pi$, DreamStream improves over the strongest prior closed-loop simulator by $1.6\times$ on nuScenes and $4.7\times$ on NAVSIM, and induces the least perturbation to policy's perceptual observability. Based on DreamStream, we construct Navhard-CL benchmark, which turns non-reactive real-world benchmark NAVSIM into interactive testing environments with adversarial driving behaviors and weather variations. This benchmark exposes many failure modes of driving policies, such as scorer bias and lack of recovery behaviors, that prior closed-loop benchmarks overlook. Code and data are available at https://github.com/VAIL-UCLA/DreamStream.

We establish a fully discrete weak-to-strong (W2S) multi-entropy stability theory for arbitrarily high-order finite-volume and discontinuous Galerkin (DG) approximations of the ideal compressible magnetohydrodynamics (MHD) equations on general polytopal meshes, whereby a single numerical update simultaneously satisfies discrete entropy inequalities for any prescribed finite family of convex Harten entropy pairs. Because physical entropies are defined only for positive density and pressure, the central analytical difficulty lies in reconciling discrete entropy stability with positivity preservation, the magnetic divergence constraint, and the nonconservative Godunov–Powell coupling. Building upon the provably positivity-preserving MHD framework of Wu and Shu, we develop a weak multi-entropy analysis of the common cell-average evolution of finite-volume and DG methods. Through convex decomposition and relative entropy, we establish two sufficient criteria for this weak stability general polytopal meshes. Compatible magnetic corrections and locally divergence-free approximations cooperatively offset the nonconservative Godunov–Powell coupling and provide the discrete cancellations essential to both positivity-preservation and entropy stability. A W2S lifting then unifies positivity and entropy limiting into a single cellwise scaling limiter, achieving strong multi-entropy stability while strictly preserving cell averages and the locally divergence-free magnetic field. High-order temporal accuracy follows from variable-step strong-stability-preserving multistep methods. Numerical experiments confirm the theoretical findings and demonstrate computational robustness. This framework provides a rigorous, fully discrete foundation for unifying physical admissibility, magnetic divergence control, and multi-entropy stability in high-order MHD approximations.

In a recent preprint (arXiv:2511.09556), we exhibited an inverse energy cascade for the 3D Navier-Stokes equations which results in "instantaneous" Type I blow-up and failure of uniqueness in certain sharp regularity classes. Our purpose here is to elucidate this phenomenon further in the setting of the Obukhov dyadic model, and to compare it to the better-known phenomenon of finite-time blow-up. When intermittency is low ($\alpha\leq 2$), we recover our previous result from the Navier-Stokes setting; in the energy-supercritical case where intermittency is high ($\alpha>2$), we show that the same can occur in the class of finite energy solutions. We present two different proofs: a soft approach using a Lyapunov function and an explicit multiscale construction. For the inviscid system we illustrate that a similar phenomenon occurs at lower regularity. Finally, we state a finite-time blow-up theorem for a mixed Desnyansky-Novikov-Obukhov model, in which a forward cascade from finitely supported data and no force produces a singularity that is of Type II only by a small margin, with features comparable to the recent forced Navier-Stokes blow-up of OpenAI.

We study asynchronous collective tree exploration, where $k$ agents with unrestricted communication start at the root of an unknown tree and discover edges online. At each step, an adversary chooses which agent moves. We give a deterministic algorithm that explores any tree with $n$ nodes and depth $D$ in at most \[ 2n+O\left(k\log^2(k)D\right) \] moves, matching known lower bounds up to a constant factor. As a direct consequence, we obtain a near-optimal competitive ratio of $O(\log^2 k)$ for synchronous collective tree exploration, where all agents move at each round. The proof relies on a multiscale power regularizer that may be of independent interest.

We present a distributed quantum algorithm that $3$-colors cycles in $O(1)$ rounds, with high probability. It follows that all locally checkable labeling problems (LCLs) that have round complexity $O(\log^* n)$ in the classical LOCAL model can be solved in $O(1)$ rounds in the quantum-LOCAL model, with high probability; this includes problems such as maximal independent set and maximal matching in bounded-degree graphs. This presents the first natural examples of graph problems with an asymptotic distributed quantum advantage for the LOCAL model; all prior examples that separate LOCAL and quantum-LOCAL are artificial problems constructed merely for the sake of demonstrating quantum advantage.

Robin's inequality reformulates the Riemann hypothesis as a bound on the sum-of-divisors function $\sigma$. We introduce a finite-truncation version of Robin's inequality determined intrinsically by the arithmetic structure of $n$, \[ \frac{\sigma(n)}{n} < e^\gamma \sum_{j=0}^{\omega(n)} \frac{(\ln\ln\ln n)^j}{j!}, \qquad n>5040, \] where $\omega(n)$ denotes the number of distinct prime factors of $n$, and $\gamma$ is the Euler-Mascheroni constant. The resulting bound is pointwise stronger than Robin's inequality and we prove it unconditionally for integers with $\omega(n)\le 6$, primorials, odd integers and square-free integers. We also prove that this inequality is equivalent to Robin's inequality, and hence to the Riemann hypothesis. Consequently, the Riemann hypothesis is equivalent to the truncated inequality holding for all colossally abundant numbers. We further show that if the inequality fails, its minimal counterexample must be a superabundant number, placing any obstruction within a rigid extremal class of integers.

Using Soundararajan's resonance method, we obtain extreme values of the central derivatives \[ L^{(r)}(1/2,f\otimes\chi_d), \] where $f$ is a normalized newform and $\chi_d$ ranges over primitive real characters associated with negative fundamental discriminants. The twisted first moment estimate used in the proof may be of independent interest. Applying Gross–Zagier-type formulas, we obtain correspondingly large Néron–Tate heights of Heegner points on elliptic curves and large absolute values of Beilinson–Bloch heights of Heegner cycles attached to modular forms.

We present BRIDGE-I, a metallicity survey of \HI-selected absorbers probing “CGM-like” gas ($16.4\leq \log N_{\rm HI}<20.3$) at Cosmic Noon ($1\leq z \leq2.2$), the epoch of peak star formation and AGN activity. Combining archival HST UV spectra with Keck/HIRES and VLT/UVES optical spectra, we estimate metallicities and physical conditions for 105 absorbers. The Cosmic Noon metallicity distribution (median $[\rm{X/H}]=-1.19$) is statistically indistinguishable from that at $z<1$ ($-1.18$) but differs significantly from $z>2.2$ ($-2.02$). This plateau is driven by the most diffuse absorbers ($16.4\leq \log N_{\rm HI}<17.2$), which reach their $z<1$ enrichment level by Cosmic Noon, whereas denser absorbers remain more metal-poor than their $z<1$ counterparts and continue to be enriched at later times. Unlike at $z>2.2$, no absorber falls below $[\rm{X/H}]=-3.5$, indicating no pristine CGM-like gas at Cosmic Noon. Absorbers in BRIDGE-I trace overdensities of $400\lesssim \delta_b\lesssim2200$, higher than at $z>2.2$. Mean $N_{\rm HI}$ differs by a factor of 400 across absorber types, but mean total hydrogen column by only 2.5, as higher $N_{\rm HI}$ is offset by a higher neutral fraction. The absorber classes thus differ in ionization state and metallicity rather than the total gas content. A metallicity floor of $[\rm{X/H}]\sim-2.0$ emerges for $\log N_{\rm HI}>19.0$ absorbers, indicating that denser, more ISM-like gas is well mixed as a population, while more diffuse gas retains a metal-poor population that is not yet fully mixed.

Distributed quantum computing requires fault-tolerant operations across inter-QPU links that can be substantially noisier than local gates. Uniformly increasing code distance provides additional protection but also enlarges data patches used for local storage and computation. Here, we introduce distributed heterogeneous-distance lattice surgery using an eight-data-patch ancilla-mediated (8-DAM) architecture, which will be useful for near-term quantum devices with less qubit overhead. In this architecture, the central ancilla spanning the inter-QPU boundary is enlarged while the data patches retain distance $d$. The protocol uses traveling stabilizers to suppress hook errors during merge and split operations between these unequal-distance patches. Circuit-level simulations of rotated surface codes at fixed local depolarizing noise show that logical-readout error rates depend only weakly on link noise. The resulting advantage over conventional lattice surgery grows as link errors increase. Comparisons with uniform distance implementations demonstrate comparable logical error suppression with reduced physical-qubit overhead. We also demonstrate how 8-DAM layouts support two simultaneous distributed logical CNOT operations between four logical data qubits using a single enlarged ancilla. At higher link noise, this construction yields lower logical error rates and more stability than two independent distributed logical CNOTs. These results support selective ancilla enlargement as a resource-efficient approach to fault-tolerant distributed quantum computing.

We study decentralized partially observable team decision problems with low-rank latent dynamics and unknown system models. The proposed framework combines team-theoretic equivalence with low-rank model representations to address cooperative decision-making in partially observable Markov decision processes without prior knowledge of the transition model. Each team member makes decisions based on local private information and delayed common information shared across the team. Using only this available information, each member learns an approximate low-rank Markov decision process and applies least-squares value iteration to compute its policy. This yields a fully decentralized learning and planning algorithm that requires neither a centralized coordinator nor centralized training. We show that the resulting member-side solutions approximate the centralized team solution: despite partial observability, unknown dynamics, and delayed common information, each member recovers the corresponding component of an approximate team-optimal policy. We further establish finite-sample performance guarantees and derive a corresponding sample-complexity bound for the proposed algorithm.

Phylogenetic trees offer a hierarchical representation of chemical similarities among stars, from which their evolutionary histories can, in principle, be reconstructed. Simulation-based work suggests that phylogenetic trees built under different chemical evolution scenarios carry distinguishable structural imprints, but whether existing methods can detect this signal in practice is unclear. We evaluate distance measures, both classical tree-based and graph-theoretical, for comparing phylogenetic trees, seeking measures robust to observational noise that separate trees built from populations with distinct chemical enrichment histories. We construct Neighbor-Joining trees from chemical abundance vectors of solar twins and of stars associated with the Milky Way (MW) disk, Gaia-Sausage-Enceladus (GSE), and the Sagittarius dwarf spheroidal galaxy (Sgr). Two benchmark tests assess stability under input perturbations within the same evolutionary history and discriminative power between distinct stellar populations used as proxies for different evolutionary histories. Tree metrics rapidly saturate under perturbations of order the typical uncertainty ($\approx2\sigma$, or $\approx0.05$ dex per element) and fail to distinguish trees when leaf sets differ. In contrast, spectral distances vary smoothly with perturbation amplitude and provide a label-invariant method for comparing trees built from disjoint sets of stars. Among the spectral measures evaluated, the Laplacian spectral distance shows the most consistent separation across population pairs, while the normalized variant is weakest. Applied to MW, GSE, and Sgr stars, spectral measures recover a distance ordering consistent with their known chemical enrichment histories. This framework also provides a route to comparing observed enrichment histories against simulations to identify those that best reproduce the observed tree structure.

A multi-agent system can reduce latency on complex tasks by executing work concurrently. Several pioneering harness frameworks support multi-agent systems. However, the scalability of current multi-agent harnesses is often constrained by a central orchestrator's capacity to allocate tasks and coordinate workers. To address this limitation, we introduce Agensh, a scalable self-organized multi-agent harness without a central orchestrator: concurrent workers execute a multi-agent cooperation loop, continuously gathering context, claiming and self-assigning sub-tasks, taking action and sharing findings, verifying results, and merging progress in an asynchronous manner. The loop is supported by the agentic organization infrastructure comprising three components: a shared workspace holds proposed, ongoing, and completed work; a message interface lets workers communicate; and shared context retains reusable findings and work intentions. To test the scalability of Agensh, we evaluate it on the five hardest ProgramBench tasks with GPT-5.6-sol (high). Scaling from 1 to 128 agents raises the mean final test-pass rate from 19.31% to 28.78%, an approximately 49% relative improvement. Larger organizations reach comparable test-pass rates earlier. On pandoc, scaling from 1 to 1,024 agents raises the final test-pass rate from 33.89% to 55.06%. Worker trajectories further show that different forms of self-organized cooperation gradually emerges and standardizes as the organization grows. These results reveal the number of agents as a new scaling dimension for multi-agent organizations to expand the frontier of general intelligence, offering a practical solution for complex tasks under hard latency constraints or time budgets.

Long-term conversational memory in multi-party settings requires more than retrieving relevant content from long-term conversations: it must distinguish who said what, whom each statement concerns, how individuals perceive one another, what information is shared by the group, and how states change over time. Recent studies on multi-party dialogue benchmarks show that existing general-purpose LLM memory systems tend to lose person and group relations or struggle to integrate clues distributed across members, groups, and time. Together, these issues reveal two core bottlenecks: message attribution and relational understanding in multi-party dialogue, and state reconstruction from interleaved histories. To address both, we propose $\textbf{SpeakerMem-R1}$: its dual-track memory stores speaker-labeled verbatim messages and derived states organized into person-level and group-level views, then combines evidence from both tracks by entity, event, and time at query time. To reduce attribution and update errors during structured memory construction while enabling local deployment, we train Writer-R1 with SpeakerLevenshtein and speaker-conditioned GRPO. On GroupMemBench, SocialMemBench, and EverMemBench, SpeakerMem-R1 achieves binary accuracies of 47.9%, 69.2%, and 61.9%, respectively. On the publicly reported EverMemBench leaderboard from EverMind-AI, we achieves 62.33%, the best reported result among the latest state-of-the-art frameworks. It also achieves 70.85% on all 1,986 LoCoMo questions, which we use as a two-person long-term conversation boundary test. In a controlled evaluation of 305 questions, RL raises the SFT Writer's mean accuracy from 57.38% to 68.20%. We report both binary accuracy and token-F1, and ablations show that the verbatim and structured tracks, as well as person-level and group-level views, are complementary under the standardized evaluation interface.

Agents often work on complex problems that require millions of tokens of context, which necessitates compacting across sessions due to limited context windows. We develop CliffCompaction, an autocompaction technique that reduces cost by up to 50% under a bounded context while maintaining or improving performance on Terminal-Bench and achieving new levels of efficiency for test-time scaling and state-of-the-art results on KernelBench. The per-rollout savings of CliffCompaction make the performance–cost trade-off of test-time scaling more efficient, adding over 10 percentage points on Terminal-Bench for less than the cost of two full-context runs. Under parallel test-time scaling, CliffCompaction lets Kimi K2.6 match Opus 4.7, and exceed Opus 4.6 and GPT-5.3 Codex at lower cost. The key to CliffCompaction's effectiveness is that it keeps compacted information faithful by only truncating or dropping content, never rephrasing or rewriting it. We never compact a compaction—each pass operates only on original content, and prior compacted output is discarded, preventing context drift from accumulating. These properties sustain continual learning over sessions exceeding a million tokens: on KernelBench, CliffCompaction reaches CUDA kernel speedups of $2.23\times$ after 200 steps and $3.58\times$ after 400 steps, surpassing specialized search algorithms and trained agents despite being a general-purpose compaction technique. We open-source a scaffold-agnostic API-proxy implementation of CliffCompaction usable with Claude Code, Codex and other harnesses.

Three-variable first-order logic ($\mathrm{FO}^3$) and the calculus of relations (CoR) define the same binary queries, an equivalence that goes back to Tarski's work in the 1940s. The classical translation from $\mathrm{FO}^3$ to CoR is single-exponential, but it has remained open whether this blowup is necessary. We prove that it is, even over finite structures and even for circuits that share subterms. Our proof introduces a new technique: we modify a single finite structure in exponentially many local ways, each changing the answer of a short $\mathrm{FO}^3$ formula $\varphi$. In any CoR circuit $C$ equivalent to $\varphi$, only compositions of binary relations can notice these modifications, and each composition can notice at most two; thus, $C$ requires exponentially many compositions. The same technique gives an exponential succinctness gap between $\mathrm{FO}^3$ and $\mathrm{FO}^2$, and exponential lower bounds for matrix query languages over the Boolean and tropical semirings, where the analogous question was also open.

We introduce SWE-Serve, a benchmark for evaluating agents on production inference engineering tasks. Implementing an inference feature can require coordinating multiple changes across the serving stack, including model support, runtime execution, and public APIs. Existing benchmarks provide limited coverage of production inference engineering: repository-level software engineering benchmarks do not target inference, while general terminal-agent benchmarks include only a few inference tasks. Dedicated inference benchmarks, meanwhile, focus primarily on isolated kernel generation or performance optimization rather than repository-scale production feature implementation. SWE-Serve provides 53 repository-grounded tasks derived from recent production changes to SGLang, spanning six inference engineering families. Each task executes on either CPU or a single GPU (H100) and is evaluated with hidden functional and regression tests, including, where applicable, end-to-end (E2E) serving tests and calibrated performance gates. Executable no-op and oracle controls, adversarial verifier review, and closed-book execution support task validity and evaluation integrity. Across 11 models and 31 model-effort configurations, the best-performing configuration achieves 75% mean pass@1. SWE-Serve exposes a substantial gap between completing tasks locally and achieving production correctness. On 19 tasks with end-to-end coverage, model-serving E2E tests reject roughly one-third of patches that pass every other test (45.9% under the verifier versus 69.4% with E2E tests excluded from scoring), with pass rate increasing for each model's best-performing configuration. By making the production correctness gap directly measurable, SWE-Serve enables the field to track whether future agents move beyond completing tasks locally to achieving production correctness.

Birnbaum's theorem states that the sufficiency and conditionality principles jointly imply, and are implied by, the likelihood principle. To enable formal certification of the results in Lean, we make the conditionality relation explicit through a finite-sample formulation based on \cite{Evans2013}. We reformulate the theorem as a statement about classes of statistical procedures that preserve statistical relations, and show that the proof reduces to the propagation of evidential equality along chains of conditionality-related inference bases (experiment–observation pairs). The main results are illustrated by Venn diagrams, and a worked finite example exhibits two pairs of inference bases: one related by conditionality but not by sufficiency, and the other related by sufficiency but not by conditionality. For finite parameter spaces with at least two points, the class of likelihood-invariant procedures with codomain $[0,1]$ is strictly contained in the class of sufficiency-invariant procedures.

Spectroscopic frequency shifts due to residual motion of the probed atoms significantly contribute to the uncertainty budgets of state-of-the-art optical ion clocks. For clock transitions with second-order Doppler and quadratic Stark shifts of opposite signs, it is possible to configure electrodynamic ion confinement such that these two shift effects become anticorrelated causing zero net shift. Here, we introduce a spectroscopic interrogation protocol which leads, for systems with unknown and varying motional energy gain rates, to first-order auto-suppression of corresponding frequency shifts without requiring the opposite-sign configuration. We experimentally demonstrate the proposed method on a new ytterbium ion optical clock probing the 467 nm electric octupole (E3) transition, where the combined fractional uncertainty contribution from motion-induced frequency shifts is reduced from $1.3\times10^{-18}$ to $0.3\times10^{-18}$. An interleaved optical frequency ratio measurement against ytterbium's electric quadrupole transition (E2) at 435 nm delivers an E3/E2 frequency ratio of $0.932 \,829 \,404 \,530 \,965 \, 340 (39)$. Combined with previously published ratio data this leads to a limit for a potential fractional temporal variation of the fine-structure constant of $2.4 (2.7) \times 10^{-19}/$yr, in agreement with existing bounds.