Papers

Cavity Quantum Electrodynamics (Cavity-QED) offers a powerful framework for controlling light-matter interactions, yet first-principles approaches commonly assume ideal, lossless cavity fields. Here, we introduce a minimal extension to the Pauli-Fierz Hamiltonian that accounts for cavity dissipation through the experimentally accessible cavity quality factor Q. The electromagnetic field is described as a damped harmonic oscillator within the very weak damping approximation. In this framework, cavity losses only enter the light-matter interaction and dipole self-energy terms, without introducing additional photonic degrees of freedom. A time-dependent unitary transformation yields a real-valued Hermitian Hamiltonian that can be incorporated into existing ab-initio QED methods without additional computational cost or changes in scaling. We combined the approach to the QED-CCSD method and investigated the effects of cavity dissipation on the optical spectrum of a p-nitroaniline molecule under strong light-matter coupling. We found that, for realistic quality factors, cavity dissipation can reduce the Rabi splitting by more than 20% compared to the ideal-cavity limit, even though the system remains in the strong-coupling regime. Convergence towards the ideal-cavity limit then requires substantially higher quality factors than those needed to establish strong coupling. These results demonstrate that cavity dissipation can significantly affect polaritonic energetics and highlight the importance of incorporating experimentally realistic cavity losses into quantitative ab-initio Cavity-QED simulations to accurately guide experimental protocols.

Weight decay is widely used as a regularization technique in neural network training, yet its role in neuron condensation (parameter direction alignment) remains unclear. Starting from a parameter initialization in the neural tangent kernel regime, we characterize training dynamics under weight decay through three stages: rapid fitting, amplitude compression, and neuron condensation. Using a two-layer ReLU network, we analyze a residual correlation field that governs both neuron amplitudes and directions. During rapid fitting, the residual approaches a quasi-static equilibrium maintained by weight decay while the tangent kernel remains nearly unchanged. In the early stage of amplitude compression, kernel decay amplifies the residual correlation field, whose isolated attracting extrema provide candidates for condensation directions. As neuron amplitudes stabilize, we bound the drift of attracting extrema and demonstrate contraction of neuron directions around them, leading to neuron condensation. This staged analysis provides a dynamical understanding of how weight decay promotes a condensed representation, beyond reducing parameter norms.

We study density regularity and optimal Gaussian approximation for complex multiple Wiener-Itô integrals. We first give a kernel criterion for absolute continuity and derive explicit formulas for the density and its derivatives, together with finite-order Sobolev estimates. Our main quantitative result shows that the sum of an intrinsic non-Gaussian term and the covariance mismatch gives the optimal rate simultaneously in every fixed Sobolev norm and in total variation, Kolmogorov and $1$-Wasserstein distances. The intrinsic term is determined by two complex third-order moments and the complex fourth-moment defect, and is equivalently described by complex kernel contractions. No additional Malliavin non-degeneracy assumption is imposed in these asymptotic results. As an application, we obtain explicit optimal rates for the normalized numerator in the least-squares estimator of a complex fractional Ornstein–Uhlenbeck process.

We describe the implementation and on-sky commissioning of a two-input spectrometer/correlator built on a Xilinx ZCU208 Radio Frequency System-on-Chip (RFSoC) and deployed on the Baryon Mapping eXperiment (BMX) interferometric array at Brookhaven National Laboratory. The system combines direct RF sampling, FPGA-based correlation, and 100 Gigabit Ethernet (GbE) visibility transport. Two inputs are digitized directly at 1050 MHz without analog downconversion and channelized into 2048 frequency channels. The correlator forms two autocorrelations and the real and imaginary parts of the cross-correlation, accumulates them in on-chip memory, and transmits the spectra as UDP packets at a fixed firmware-controlled rate. Two independent campaigns using 500 ms and 100 ms accumulation times produced 958,918 consecutive accumulations with no lost, duplicated, or malformed packets. A Cauchy-Schwarz bound is satisfied across all 1.96e9 channel-samples, confirming correct field identification and scaling. On-sky validation includes compact-source transits in six GNSS bands with the expected fringes, coherent detection of the Cygnus A zenith transit at the predicted time, and a Galactic HI plane crossing detected independently in autocorrelation on both dishes. The correlator is parameterizable in input count, with arithmetic scaling quadratically. For extension to BMX's full eight-input dual-polarization system, an occupancy model validated against the deployed firmware indicates that visibility buffering fits when moved to UltraRAM, while multi-tile synchronization, logic utilization, and timing closure remain to be demonstrated in an eight-input implementation.

The classical voter model is dual to coalescing random walks, in much the same way that the Kingman coalescent describes genealogies through binary mergers. Motivated by the passage from the Kingman to the~\(\Lambda\)-coalescent, where multiple mergers are allowed, we introduce the~\(\Lambda\)-broadcast voter model, in which a voter may transmit its opinion simultaneously to several neighbors according to a mechanism governed by a finite measure~\(\Lambda\) on~\([0,1]\); the classical voter model is recovered when~\(\Lambda=\delta_0\). We show that our model is well-defined on general graphs with bounded degrees, and we construct a family of stationary measures~\({\mu_{\alpha,\Lambda}}\), parametrized by bounded harmonic functions, that characterize the extremal stationary measures according to the finite or infinite collision property of the underlying random walk. We then study the dependence of the stationary measures on the broadcasting measure $\Lambda$ through a finite number of its moments. We give general conditions under which different moment profiles yield different stationary measures and obtain, in particular, a complete characterization on trees with bounded degrees and on nearest-neighbour~\(\mathbb Z^d\),~\(d\ge3\). We also prove continuity of the stationary measures with respect to the moment profile. Our main tool is a dual system of coordinated coalescing random walks, whose individual particles are simple random walks but which may jump and coalesce simultaneously; a coupling with independent random walks allows us to relate their long-time behaviour to ordinary random walk collision properties.

Text-driven motion editing modifies an existing motion sequence according to a text instruction while preserving the content of the source motion. Existing methods are typically built for a single, fixed skeletal topology, which limits their use in animation pipelines where characters differ in joint count and skeletal hierarchy. We present Topology-Aware Motion Editor (TAME), a flow-matching transformer that edits motions on humanoid skeletons of varying topology. TAME represents motion as per-joint, per-frame tokens and models interactions among joints, across frames, and with the text instruction through skeletal, temporal, and text cross-attention layers. To make the skeletal attention follow each character's hierarchy, TAME replaces full joint attention with Topology-Constrained Skeletal Propagation (TCSP), which restricts attention to one-hop kinematic neighbors in the skeleton's adjacency matrix. We further introduce Edit-Focused Representation Alignment (EFRA), a self-distilled representation alignment strategy that aligns student features with cleaner EMA-teacher features exclusively on edit-relevant joint-time tokens, making edits faithful to the instruction. To make this setting trainable and comparable, we construct TopoMotionFix, a multi-topology extension of MotionFix with seen- and unseen-topology evaluation protocols. TAME outperforms previous methods in edit alignment and source preservation on MotionFix and reliably edits motions on unseen skeletons in TopoMotionFix.

In August and September 2026, independent researchers publicly documented an unusual incident: thousands of autonomous agents, self identifying as OpenAI models on web research tasks, discovered and began using a small German wiki as an improvised message board posting roughly 18,000 times over six weeks to relay task answers, share a sandbox escape technique, and coordinate against a volunteer human moderator who spent weeks manually deleting their content [1]. The investigators' public writeup is a careful qualitative account, rich with direct quotation, but does not attempt a statistically rigorous quantitative characterization of the behaviour it documents.

Godbersen's long-standing conjecture states that the mixed volumes of any convex body $K \subset \mathbb R^n$ satisfy $V(K[k], -K[n-k])\le \binom{n}{k} \operatorname{vol}(K)$ for any $k \in \{1, \dots, n - 1\}$, with equality if and only if $K$ is an $n$-simplex. Kotrbatý and Mouamine recently proved the inequality in full generality, and showed that if $K$ is a (full-dimensional) polytope attaining equality, it must be a simplex. We complete the characterization of the equality case: if $K \subset \mathbb R^n$ is a convex body for which $V(K[k], -K[n-k]) = \binom{n}{k} \operatorname{vol}(K)$ for some $k \in \{1, \dots, n -1\}$, then $K$ is an $n$-simplex. By a similar method, we characterize the equality case in the higher-order Godbersen inequality conjectured by Schneider and by Kotrbatý.

Disasters can overload cellular control-plane signaling within minutes, yet fine-grained Radio Resource Control (RRC) or Next Generation (NG) Application Protocol (NGAP) telemetry is privacy-sensitive and costly to collect for analytics. Many emergency monitoring pipelines therefore rely on coarse Call Detail Record (CDR) aggregates. We treat Internet activity in CDR grids as a practical proxy for hidden signaling stress under that constraint. We train a lightweight convolutional neural network (CNN) on stylized overload injections, stress-test it with diffusion-synthesized surges that preserve normal traffic structure, and adapt the detector by retraining on hard synthetic samples. Under stress-test conditions, the default alert threshold fails even though receiver operating characteristic (ROC) curves stay strong: the detector still assigns overloaded cells a larger overload probability than normal cells, but those probabilities fall below the default cutoff 0.5 and are labeled normal, so the F1-maximizing threshold – selected post hoc on the same stress-test grids (oracle $\tau^*$) – shifts by $0.32 \pm 0.03$ (operating-point drift). Across three random seeds, hard-sample adaptation raises thresholded performance (F1) from 0% (no alerts at the default cutoff 0.5 on any seed) to $85.67 \pm 14.37$% and ranking from ROC-AUC $0.886 \pm 0.040$ to $0.99996 \pm 0.00007$. Diffusion-synthesized surges expose threshold fragility that matched-condition training – training and testing on the same stylized injections – hides, and hard-sample adaptation restores usable alerts at the default cutoff. Together, these steps define a reusable pre-deployment stress test for emergency monitors. Internet-only CDR input further supports lightweight AI-native workflows that combine monitoring, recalibration, and adaptation.

Integrated sensing and communication (ISAC) has emerged as a promising approach for vehicle-to-everything (V2X) systems by enabling communication and sensing over shared radio resources without additional installation of dedicated sensors. However, candidate resources may experience different communication qualities due to varying channel conditions and resource contention, which should be considered when designing sensing resource patterns. In this letter, we propose a quality-of-service (QoS)-constrained resource pattern selection framework that jointly considers communication reliability and sensing performance. The sensing objective is formulated based on the Fisher information matrix for joint range and velocity estimation, while a minimum packet reception ratio (PRR) is imposed as the communication QoS constraint. To avoid the complexity of exhaustive search, a greedy selection algorithm with one-swap refinement is developed. Simulation results show that the proposed method improves sensing performance over conventional resource patterns while satisfying the PRR requirement and achieves performance close to the exhaustive-search optimum and sensing-only optimum.

This paper presents a locally conservative Enriched Linearized Neural Network (ENN) method for the Darcy flow model. A linearized shallow ReLU$^k$ network, whose hidden-layer parameters are fixed on a quasi-uniform set of the sphere, carries the approximation, and piecewise constant functions on an auxiliary subdivision of the domain are added to ensure local mass conservation. The subdivision may consist of general, possibly curved, elements. Since neural network functions do not satisfy the inverse inequality, the stability and error analysis of the standard discontinuous Galerkin interior penalty formulation do not apply. The missing inverse inequality is remedied by an edge identity combined with a Galerkin least-squares (GLS) term, together with a single neural approximant that is optimal in the $L^2$, $H^1$ and $H^2$ norms simultaneously. We use the nonsymmetric interior penalty (NIPG) form, which is coercive for every positive penalty parameter. With $n$, the width of the shallow neural network, used in ENN, we prove an error estimate in the EG norm that is of the optimal $H^1$ order, i.e., $O(n^{-(r-1)/d})$ for solutions in $H^r$, $r\ge2$, and $O(n^{-(s-1)/d})$ for solutions in $H^s$, $\frac32<s\le2$, for any shape-regular subdivision, when the GLS parameter satisfies $\min\{h,n^{-1/d}\}^2\lesssim\tau\lesssim n^{-2/d}$ and the edge terms are scaled with $\min\{h_e,n^{-1/d}\}$, i.e., by the resolution of the network rather than of the mesh. A numerical Darcy flux is constructed, which is locally conservative, regardless of the size or the number of the elements. Sample numerical results demonstrate the correctness of the theory. In particular, a fixed $4\times4$ subdivision gives the same accuracy as a subdivision refined with the network, and the mass loss stays at round-off unlike a non-conservative neural network method.

We propose a distribution-free metric to rate individual skill in “player-versus-environment” settings, where participants face heterogeneous tasks without direct opponents. Such settings are common in digital platforms, games, education, finance, and the benchmark evaluation of AI agents. They combine high randomness, tasks of widely varying difficulty, and unknown heterogeneity across individuals. Our metric maps each task outcome to a bounded performance score with zero population mean and variance bounded by $1/3$, regardless of the outcome distribution, so that scores are directly comparable across tasks. Aggregating these scores over tasks yields an interpretable skill score for each individual (the “Solo” rating), and a reshuffling null model tests whether that score exceeds what chance alone would produce. We validate the approach on the progression of $2\times10^5$ players in the mobile games Candy Crush Saga and Bubble Witch 3 Saga. The metric identifies high- and low-skill players with high statistical confidence, their classification persists over hundreds of subsequent levels, and a windowed version of the score tracks changes in performance along progression.

Null homogeneous Petrov spaces $V^*_4(N)$ are considered. The geometry of $V^*_4(N)$ is determined by the geometry of the three-dimensional homogeneous Riemannian space $V_3(N)$, which is invariant under the action of the three-parameter motions group $G_3(N)$ ($N$ corresponds to the group number in the Bianchi classification). The canonical frame of the space $V_3(N)$ is used to construct the metric tensor of the space $V^*_4(N)$ and the components of the vector potential of the invariant electromagnetic field. Using this reper, we obtain Maxwell vacuum equations containing only the structure constants of the groups, the non-holonomic components of the contravariant metric tensor and vector potential, and their derivatives with respect to the wave variable. All non-equivalent exact solutions of Maxwell vacuum equations are found for the case of solvable motions groups $G_3(I)-G_3(VII)$. All solutions of Maxwell vacuum equations obtained in this article are written explicitly in terms of arbitrary independent functions of wave variable. Therefore, when integrating the Einstein-Maxwell equations, it has to consider only the remaining systems of Einstein equations which reduce to systems of ordinary differential equations that include only these independent functions.

We investigate the dynamics of charged test particles around a rotating black hole embedded in a King-type dark matter halo and subjected to a prescribed, asymptotically uniform magnetic field. We adopt an effective rotating geometry constructed from a static halo seed through a modified Newman–Janis prescription and a test electromagnetic field that generally requires supporting currents in the nonvacuum background. In the absence of magnetic coupling, the timelike Hamilton–Jacobi equation separates and admits a Carter-type constant, providing an integrable reference system. We characterize the orbital dynamics using Poincaré sections and tangent-vector growth diagnostics, including fast Lyapunov indicators and finite-time Lyapunov exponents, with mass-shell monitoring and numerical refinement checks. For the sampled initial conditions, increasing the magnetic coupling can produce a transition from regular motion to scattered Poincaré sections with sustained positive finite-time growth rates. At fixed magnetic coupling, the two higher-density halo cases yield larger finite-time exponents for a representative chaotic orbit family, whereas the weak-halo correction is not resolved consistently under numerical refinement. A different initial condition yields a closed Poincaré curve and a decreasing finite-time exponent over an extended integration, supporting regular motion despite the nonzero magnetic coupling. These results show that the King-type halo modulates magnetic-field-induced orbital instability in an initial-condition-dependent manner, while regular motion persists within the magnetized system.

A collage system is a grammar-based compression model that extends straight-line programs with repetition and substring truncation. Internal collage systems additionally require every nonterminal to be structurally reachable from the start symbol. Migita, Uehata, and I (CPM 2026) showed that any collage system of size $m$ can be converted into an internal one generating the same string with size at most $9m$, and left the improvement of this constant as an open problem. We show that a simple refinement of their top-down conversion reduces the bound to $5m$. The proof combines three elementary ideas: canonicalization of generated truncations that remain aligned with a target endpoint; a repetition decomposition that absorbs every complete copy of the repetition base into a maximal core; and monotonicity of structural reachability, which prevents an input truncation rule from both becoming structurally reachable and later acting as a hidden target at which endpoint alignment is lost. The conversion runs in deterministic $O(m^2)$ worst-case time in the stated unit-cost random-access machine model. Consequently, for every string, the minimum size of an internal collage system is at most five times the minimum size of a general collage system.

Estimating treatment effects from observational data typically relies on the No Unmeasured Confounding Assumption (NUCA), which rarely holds in practice. Proximal causal learning (PCL) addresses unmeasured confounding via proxy variables, yet existing methods require the proxy variables to be pre-specified. Thus, we propose PCL-U, a framework that learns proxy variables directly from observed covariates. PCL-U uses neural encoders to decompose covariates into treatment-inducing, outcome-inducing, and shared proxies, guided by minimax mutual information objectives, and obtains causal estimates through a practical moment-based risk function. Experiments on benchmarks show that PCL-U matches or outperforms existing baselines. Besides, there are two types of synthetic datasets with varying dimensions and confounding strengths that illustrate that our method maintains stable estimation accuracy.

Length generalization is the ability of sequential models to perform well on context lengths unseen during training. In this work, we show that the challenge of achieving length generalization is related not only to architectural choices such as positional encoding and the attention mechanism but also to the training procedure itself. We study how regularization affects length generalization and find that weight decay can hinder extrapolation. In contrast, dropout improves extrapolation when its placement within the architecture is reconsidered. In that regard, we show that the standard placement of dropout before layer normalization introduces a systematic distributional mismatch, and that applying dropout just before the linear projection resolves this issue. For example, a modified SmolLM3 with sliding window attention, continually pre-trained with dropout, can extrapolate perfectly to 64$\times$ on Needle-in-a-Haystack and far beyond the pre-training context size on RULER and HELMET. Mamba2 also benefits from dropout, suggesting an architecture-agnostic nature of the problem. We further propose Variance-Preserving Affine Dropout (VPAD), a new dropout strategy that substantially reduces the resulting pre-activation variance mismatch, leading to further extrapolation improvements in transformers.

Deep time-series forecasting models have rapidly diversified, yet adapting them to a specific task still requires extensive expert effort in model selection, mechanism diagnosis, architecture design, implementation, and evaluation. Existing AutoML methods are constrained by predefined search spaces, while general-purpose LLM research agents lack reliable control over experimental protocols and model promotion. We introduce EvoCast, a fully autonomous research-agent system for iterative forecasting architecture evolution. EvoCast first establishes and diagnoses a task-specific baseline through executed mechanism ablations, then generates evidence-grounded research directions from dataset characteristics, diagnostic results, prior rounds, and failure records. Its central design, cognition-authority separation, assigns open-ended hypothesis generation and code implementation to LLM agents, while deterministic program authorities control source-edit boundaries, canonical evaluation, and promotion decisions. Experimental outcomes are accumulated as evidence to guide subsequent rounds. Results show that EvoCast completes complex architecture modifications with higher implementation success and lower agent-side token/time cost, and develops task-specific architectures that outperform selected baselines, strong forecasting models, and agent baselines in three real-world forecasting cases. The code is available at https://github.com/18e0-x/EvoCast.

In this paper, we investigate the realizability problem, which asks whether prescribed group actions on graded modules can be realized by the groups of self-homotopy equivalences of CW-complexes acting on their homology. We provide a partial answer in the case of arbitrary groups and permutation modules concentrated in certain degrees. As a consequence, we realize every group as the group of self-homotopy equivalences of an $R$-local CW-complex with arbitrary prescribed connectivity, where $R$ may be chosen with $\rho(R)$ sufficiently large. In particular, this provides a complete answer to Kahn's realizability problem.

Credibility is a central topic for agent-based models intended to support policy-making. Simulations must not only represent the target scenarios and their core dynamics but also demonstrate that their assumptions, parameters, and outputs are empirically grounded and sufficiently accurate for their intended use. This paper addresses this challenge by presenting a general modelling framework, aligned with the Capability Approach, for building credible policy simulations that rely on data and domain-expert knowledge. It then demonstrates how it can be contextualised and implemented to study the social challenge of financial inclusion in Egypt, building on an agent-based model that represents heterogeneous individuals and firms behaving according to their financial states, barriers, opportunities, and preferences. The model is fitted to real-world data in two stages, initialisation and calibration, which respectively build representative synthetic populations and estimate behavioural parameters. By fixing the feasibility parameters, which determine agents' opportunities, and calibrating preference parameters across different population groups, we are able to distinguish and analyse the role of institutional and social barriers in the system, as well as the role of agents' motivations and priorities. This calibration stage provides transparent and group-specific hypotheses about the drivers of observed financial-inclusion gaps, which can further be analysed as gaps between agents' opportunities and realised outcomes, a very relevant insight for policy-making. This paper is thus a step towards improving the credibility and usefulness of policy simulations, strengthening the relationship between the model, the real target system, and the stakeholders who will use it. The code is available at: \url{https://www.comses.net/codebase-release/df8383cb-f49b-4f09-8cce-73603b59adcc/}.

Sub-terahertz (sub-THz) low-phase-noise signal sources commonly employ frequency multiplier chains to extend the operating frequency of lower-frequency oscillators. This paper presents the design and simulations of a wideband, high-output-power frequency multiplier implemented in TSMC 65 nm CMOS technology. The proposed design is based on a distributed frequency multiplier with a quarter-wave transmission line termination at the drain side, where the reflected and forward-traveling waves are constructively combined to enhance the output power. The proposed frequency doubler achieves a minimum conversion loss of 12 dB at an input frequency of 115 GHz with an input power of 12 dBm, resulting in an output power of 0 dBm and 12.6 dB fundamental suppression. For the same input power, the output power remains within 3 dB of its peak value over the 188-260 GHz output frequency range. At 230 GHz, the proposed design achieves a saturated output power of 4 dBm while occupying an area of 0.149 mm^2.

We study the charge resolved structure of the pairwise mode entanglement produced by the Schwinger effect. Using the $U(1)$ electric charge of quantum electrodynamics, we decompose the entanglement of the reduced density matrices of momentum modes into individual charge sectors, applying the symmetry resolved entanglement entropy to the pure bipartition reductions and the charge imbalance resolved negativity to the mixed particle-antiparticle pair. For a constant electric field we obtain closed form results for every mode pairing, with all field dependence controlled by the single pair production probability $|\beta|^2=e^{-\pi\mu}$. For the particle, particle and antiparticle antiparticle pairs the entanglement entropy within each charge sector is field independent, so that the field acts only by redistributing statistical weight among the sectors; for the mixed particle antiparticle pair the populated sector additionally carries a field dependent entropy. The vacuum created pair is the richest case: its resolved negativity is distributed over three imbalance sectors and is transported from one sector to the next as the field increases, the sectors contributing equally only at the critical field. The entanglement across a fixed momentum bipartition, by contrast, is frozen at its initial value because pair creation conserves the sector charge. Symmetry resolution thus refines the total entanglement measures into a sector resolved picture, exposing where in charge space the entanglement of the Schwinger mechanism resides and how the electric field moves it, information beyond that contained in the total measures or in particle number distributions.

Answer correctness is encoded as a recoverable geometric direction in the hidden states of language models. We show that the mean displacement from incorrect to correct answer representations, computed at approximately 70% of model depth from fifty labeled examples with no parameter updates, yields a scoring direction that outperforms zero-shot log-probability scoring by up to +32.0 percentage points on factual benchmarks (ARC-Challenge and MMLU) and by +38.1 to +51.8 percentage points on TruthfulQA, across five models spanning 1B to 8B parameters in three architecture families (Llama, Qwen, Gemma). The method requires one forward pass and one dot product per candidate; no generation is performed at inference. Applied as a hallucination detector on individual (question, answer) pairs, the recovered direction achieves 0.693~AUROC versus 0.578 for log-probability scoring. We additionally find that correctness directions for factual reasoning, domain knowledge, and calibrated truthfulness are near-orthogonal in representation space, revealing that language models allocate geometrically independent subspaces to qualitatively distinct notions of correct answer, with architecture-dependent variation in the degree of separation. This structure explains the observed transfer pattern—the direction calibrated on factual questions transfers within task type but not across it—and suggests that LLM calibration failures may reflect a routing problem: the model's internal representation contains more correctness signal than its output behaviour exploits.

Modal logic comprises a broad family of logics to reason about relational structures. The literature presents many such logics, displaying diverse operators, semantics, and applications. This plurality is reflected in a zoo of mechanised modal logics, which often duplicate syntax, semantics, metatheory, and reasoning infrastructure. We present a library-grade formalisation of modal logic in Lean, developed as part of CSLib (the Lean Computer Science Library) and designed around two complementary forms of reuse: vertical reuse, whereby specialised logics inherit from common abstractions, and horizontal reuse, whereby modal logic becomes a reasoning tool for independently formalised domains. Our development provides a generic framework for polyadic modal languages, reusable metatheory and proof automation, and derived interfaces for specialised modal logics. We exemplify our infrastructure by deriving basic modal logic, basic temporal logic, and Hennessy-Milner Logic; the latter subsumes and extends CSLib's previous implementation while reducing its logic-specific code by 67%. We further apply the same modal infrastructure to reasoning about mathematics (radicals of ideals), theory of programming languages (the type safety strategy for the simply typed $\lambda$-calculus), and concurrency theory (reasoning about processes in the Calculus of Communicating Systems). Our experience suggests that reuse, automation, and integration with the strong Lean ecosystem should be treated as first-class design concerns when formalising theories for shared libraries.

Diffusion models for structured scientific generation must produce samples satisfying hard geometric constraints imposed by physics, chemistry, or biology, yet inference in these settings is prohibitively slow, demanding hundreds to thousands of neural-function evaluations per sample. We unify eight state-of-the-art models spanning medical volumetrics, molecular conformations, protein backbone design, crystal structure prediction, and multi-view 3D scenes under a single abstraction, Constraint-Manifold Diffusion Models (CMDMs), in which the target distribution is supported on a manifold defined by an externally specified constraint map. All existing acceleration families fail on this class: quantization exhausts memory on high-dimensional volumetric operators; pruning breaks constraint fidelity; fast ODE solvers allow trajectories to drift off the constraint manifold; and feature-caching heuristics are blind to constraint geometry, inducing mode confusion in the high-noise regime. We introduce ManifoldCache, the first training-free, data-free accelerator designed from first principles for CMDMs. The key insight is that the conditional score decomposes orthogonally into a normal component, which enforces constraint satisfaction, and a tangential component, which navigates within the manifold. Exploiting this structure, we prove that the noise-schedule midpoint is a sharp safe-caching boundary: caching before it incurs provably bounded error, while caching after it guarantees a strictly positive fraction of trajectories suffer mode confusion, a gap that persists up to the boundary. We further prove that deeper network blocks admit provably larger certified cache strides within the safe phase, as a consequence of the score decomposition propagating through block Jacobians. The resulting schedule requires no calibration data, along with zero training overhead.

In this paper, we characterize fake quadrics $X$ satisfying the bounded cohomology property. Namely, there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ for every curve $C$ on $X$.

We report on the status and prospects of precision weak neutral current interaction measurements in fixed target scattering, atomic parity violation, as well as future collider measurements at momentum transfer $\sqrt{Q^2} \ll M_Z$, including the experiments in parity-violating electron scattering under construction at Jefferson Laboratory and at Mainz that are expected to commence data collection in the very near future.

Double descent has sparked considerable interest, with recent work relating it to the data, the model and the learning configuration. Practical fine-tuning commonly involves training a small adapter on top of frozen pretrained weights, as in low-rank adaptation (LoRA). The adapter's rank is the hyperparameter that sets its capacity, yet how this rank relates to double descent has not been well explored. We quantify this relation under label noise on four vision backbones and a 7B language model with a module-matched rank sweep (MMRS), which extends past full rank and compares every rank with dense fine-tuning of the same modules, paired by seed. On DeiT-Tiny, risk is lowest at rank one and rises sharply as the adapter becomes able to fit the noisy labels, forming an interpolation cliff. Past the peak, risk falls again, but every tested post-peak rank that still saves parameters remains above dense risk. Rank-one LoRA outperforms dense fine-tuning on three of the four vision backbones, consistent with strong regularization at small rank. LoRA thus exhibits a second descent, but matches dense risk only after losing its parameter advantage, first on DeiT-Tiny at four times dense's projection weights. Code is available at https://anonymous.4open.science/r/lora-second-descent-C7B5.

Vision-language models (VLMs) are increasingly evaluated for egocentric and cross-view video reasoning, yet existing benchmarks largely focus on semantic event understanding, temporal relations, or correspondence between already observed views, leaving their ability to reason directly about future visual states underexplored. We introduce EgoExo-Next, a visual-option benchmark for dynamic visual-state reasoning, where models must identify how an observed action trajectory subsequently appears rather than predict only an action label or textual description. EgoExo-Next contains 2,503 human-curated four-choice questions from six public egocentric and ego–exo video sources and comprises four interconnected subtasks that evaluate egocentric next-state prediction, bidirectional ego–exo state correspondence, exocentric next-state prediction, and their composition in Ego-to-Exo Next-State. Extensive evaluation of proprietary, open-source, and spatial reasoning VLMs reveals a substantial human–model gap, with the best model achieving 43.81% average accuracy compared with 98.55% for humans, and the largest degradation occurring on the composed Ego-to-Exo task. These results suggest that current VLMs remain substantially limited in dynamic visual-state reasoning, particularly when temporal progression and cross-view reasoning must be composed. The benchmark is publicly available at \url{https://huggingface.co/datasets/yutongli2024/EgoExo-Next}.

Let $(\mathfrak g, \mathfrak k)$ be the complexication of a Hermitian symmetric pair and let $\gamma_1 <\cdots<\gamma_r$ be the Harish-Chandra strongly orthogonal roots, with $\gamma_1$ the lowest non-compact root, and let $\zeta$ be the normalized central character of $\mathfrak k$. We consider the unitary highest weight representations $L(\lambda(x))$ of $\mathfrak g $ of highest weights of the form $\lambda(x)=-k\gamma_1 -x\zeta$, $x\in\mathbb{R}$. In particular, we are interested in the case $x=a$, the last reduction point in the analytic continuation in $x$. We prove that $L(-k\gamma_1-a \zeta)$, $k\ge 1$, is $K$-multiplicity free and we describe all its K-types.