Papers

The Dotsenko-Fateev equation is a third-order linear ordinary differential equation studied in two-dimensional conformal field theory. We study the confluent Dotsenko-Fateev system, a rank-three system of linear ordinary differential equations obtained by confluence from a first-order system equivalent to the Dotsenko-Fateev equation. It has an irregular singular point at infinity, and its solutions admit double integral representations of confluent Selberg type. Using these representations, we construct sectorial fundamental solution matrices around infinity, establish their asymptotic expansions, and determine the associated Stokes matrices explicitly. We further study three aspects of the confluent Dotsenko-Fateev system: its equivalence to the degree-two polynomial reduction of the Schrödinger equation for the quantum Painlevé equation of type V, its realization as a restriction of a confluent version of the linear Pfaffian system associated with Appell's hypergeometric function $F_4$, and its reduction to the trivial rank-one equation via integral transforms and a quadratic change of the independent variable.

Latent Action Models (LAMs) can capture manipulation priors from action-free videos, but discrete latents usually impose a granularity bottleneck, limiting their ability to represent fine-grained action. Recent continuous alternatives mitigate this, but they are typically used as proxies for world modeling and require a further planning step to produce executable actions. We thus introduce UniLAP, a unified continuous latent-action policy that models the latent space via flow matching and bypasses reliance on future frames during inference. By distilling a LAM teacher with a flow-adaptive objective, UniLAP inherits the teacher's action representation while retaining the multimodal distribution of feasible behaviors. To decouple latent representations from task-irrelevant appearance, we extract a label-free motion target to isolate relevant kinematic cues from spurious visual dynamics. With the established embodiment-agnostic latent manifold, UniLAP can be easily adapted to novel platforms. Pretrained on multi-source videos at a compact 1.1B parameter scale, UniLAP outperforms state-of-the-art latent-action and Vision-Language-Action (VLA) baselines across hand pose forecasting, single-arm and humanoid manipulation, and real-world deployment.

We present a unified theory-to-simulation framework for self-interacting dark matter (SIDM), combining a self-contained introduction to its particle-physics foundations and representative benchmark models with an explicit, systematic mapping to simulation inputs and validated numerical implementations in the moving-mesh code AREPO-2. We characterize representative elementary and composite dark-sector models through their particle content, symmetries, interactions, production mechanisms, and constraints. We then establish an explicit mapping from their microscopic properties to the inputs required for structure-formation simulations, including modifications to cosmological initial conditions, internal-state mass splittings and populations, reaction networks, velocity- and angle-dependent cross sections, dissipative energy loss, and decay rates and recoil kinematics. Building on the efficient, scalable SIDM infrastructure introduced in our companion work, we implement isotropic and anisotropic self-scattering with constant or velocity-dependent cross sections, multi-state and inelastic reactions, and dissipative scattering, as well as a dedicated DM decay module. We validate the implementations through beam-lattice deflection experiments, thermalization and uniform-box decay tests, isolated-halo gravothermal core-collapse simulations, and cosmological box and zoom-in simulations. The tests reproduce analytical predictions and published inelastic and dissipative benchmarks, with agreement across numerical schemes. The resulting framework provides a common reference for researchers across disciplines and a practical route from microscopic dark-sector theories to nonlinear astrophysical predictions beyond standard isotropic, elastic SIDM.

Physical AI is commonly formulated around an explicitly specified task: given a goal or instruction, a system perceives, reasons, and acts. In many real-world settings, however, important tasks emerge from continuously changing world states before a person explicitly formulates them. We study this complementary problem as Proactive Physical AI, where an AI system continuously observes the physical world, identifies situations that warrant intervention, and initiates appropriate actions at the right time. We develop ProAgent, an end-to-end system built around two components: a Jev-style proactive timing model (dubbed StreamingJev) that determines whether and when intervention is needed, and a Response Model that generates responses for people or invokes available device capabilities for physical execution. To support learning at scale, we develop an automated data pipeline that converts videos into supervision for proactive timing. Experiments demonstrate strong proactive performance under both explicit objectives and standing roles, combining more accurate intervention timing with fewer false triggers than the source-backbone baseline. Real-robot evaluations further demonstrate ProAgent's ability to identify emerging needs and translate them into appropriate physical actions.

Symbolic regression (SR) seeks explicit equations that explain observed data, and recent methods increasingly employ large language models (LLMs) and agents for equation discovery. However, these systems typically rely on manually designed workflows and prompts. We argue that the SR agent harness should itself be an optimization target: its design shapes search priors and how numerical feedback guides subsequent equation refinement. We therefore propose HarnessSR, a framework for jointly optimizing prompts and workflows to construct reusable SR agents. During both harness optimization and agent execution, HarnessSR supports either PySR or an LLM-based equation generator through tool-specific interfaces, allowing the framework to optimize search guidance for different equation-discovery mechanisms. HarnessSR first optimizes role prompts through equation-discovery feedback in basic workflows, then jointly searches prompt assignments and workflows with brief adaptation to align the two. Finally, it refines role instructions through reflection on residual patterns, candidate equation structures, and search outcomes, improving how these signals guide subsequent equation search. On LSR-Synth in LLM-SRBench, HarnessSR achieves a mean ID $\mathrm{Acc}_{0.01}$ of 61.33% across three backbones, a 45.0% relative improvement over the next-best baseline.

This article develops optimal order (up to logarithmic factors) weighted cubature rules for Monte Carlo numerical integration in Sobolev reproducing kernel Hilbert spaces over common matrix manifolds. Specifically, we consider matrix models of the Stiefel, Grassmann, flag, and Lagrangian Grassmann manifolds each over either real numbers $\mathbb{R}$, complex numbers $\mathbb{C}$, or quaternions $\mathbb{H}$. The proposed cubature rules use evaluation points which are independent and identically distributed uniform on the manifold. The weights are chosen to be optimal with respect to the reproducing kernel Hilbert space worst-case error, under the constraint that the weights sum to one. Crucially, this constraint ensures optimal weights may be found without having to evaluate the kernel mean embedding (the integral of the kernel), which is often difficult to compute. We consider computable Matérn kernels of Frobenius distances between matrices which reproduce the Sobolev reproducing kernel Hilbert spaces with equivalent norms. Open-source numerical experiments validate our theoretical development, including an application to simultaneous approximation of intrinsic volumes in the Cauchy–Kubota formula. We also present preliminary empirical results beyond independent points including transformations of low-discrepancy quasi-Monte Carlo points from the unit cube and jointly optimized points and weights.

Solar-blind ultraviolet (UV) optical wireless communication (OWC) enables non-line-of-sight (NLOS) transmission through atmospheric scattering. This work presents a comprehensive experimental and simulation study of a 100 m outdoor UVC link with comparative measurements under LOS-blocked and open-field conditions. The results show that LOS-blocked scattering-mediated links exhibit substantially higher path loss and narrower bandwidth than corresponding open-field measurements, highlighting the impact of residual LOS components in practical diffused beam UVC experiments. A photon-tracing Monte Carlo (MC) framework incorporating realistic transmitter/receiver characteristics and obstacle geometry is further developed to reproduce the measured channel characteristics with high accuracy. Despite the severe path loss and pulse broadening effects, reliable 20-200 kbps transmission is experimentally demonstrated over the 100 m LOS-blocked link using on-off keying (OOK) and pulse-position modulation (PPM), representing the longest-distance and highest-data-rate experimental demonstration of an explicitly LOS-blocked scattering-mediated UVC link reported to date.

We introduce a determinantal linear process on the space of $1$-forms over a weighted graph endowed with a unitary local system, which we call the determinantal linear spanning forest (DLSF). This process is the analog of the uniform spanning tree in the presence of an arbitrary rank $n$ quenched gauge field in ${\rm U}(n)$ (or ${\rm O}(n)$, ${\rm SO}(n)$, ${\rm SU}(n)$, ${\rm Sp}(n)$), and generalizes the determinantal random cycle-rooted spanning forest which corresponds to the case of ${\rm U}(1)$ and ${\rm SU}(2)$. We describe the support of this process by means of a polymatroid which is described in terms of the circular and bicircular matroids. We also explain how the DLSF relates to the computation of currents in an electrical network in the presence of a gauge field. The partition function of the DLSF is shown to be the determinant of the twisted Laplacian, for which we also give a matrix-tree type theorem that computes its characteristic polynomial. We initiate the study of the twisted Laplacian determinant as a functional on the space of connections, and give a first order expansion of it in a neighborhood of the trivial connection, for which we provide a probabilistic interpretation. We extend the construction to infinite graphs, exhibiting the analogs of the classical wired and free distributions on spanning forests. We give a sufficient geometric condition on the local spectral gap for the existence of a Poincaré inequality as well as the uniqueness of the infinite volume measure, and the exponential decay of correlations. We show that on any recurrent graph, the wired and free DLSF coincide. We construct examples where they do not, for example, unlike in the classical case, on $\mathbb Z^d$ for $d\geq 3$.

We give counterexamples to the conjecture of Dais-Henk-Ziegler on projective crepant resolutions of complete-intersection quotient singularities. For finite $G\subset\operatorname{SL}_4(\mathbb{Z})$, we determine whether $\mathbb{C}^4/G$ admits a projective crepant resolution, with the representations considered up to conjugacy in $\operatorname{SL}_4(\mathbb{C})$. Ten explicit criteria decide all cases. The examples also show that the Molien series and the age polynomial do not determine existence. We also discuss questions of Ito-Reid on maximal cyclic subgroups and the generation of cohomology in degree two.

Quantum spin liquids are exotic states of matter in which strongly interacting spins remain disordered down to zero temperature and host fractionalized excitations. This has motivated an extensive search for their realization in materials. Among candidate systems, $\alpha$-RuCl$_3$ has drawn particular attention as a platform for the quantum spin liquid proposed by Kitaev, in which the low-energy excitations in applied magnetic fields are interpreted as itinerant Majorana fermions and local flux excitations. However, conflicting experimental signatures have cast doubt on whether a Kitaev quantum spin liquid-like state is really the right starting point to interpret the low-energy states in $\alpha$-RuCl$_3$, motivating a closer look at the nature of these excitations. Here we report an extensive high field study of specific heat up to 35 T on $\alpha$-RuCl$_3$. We find that the low-energy thermodynamics exhibit universal $B/T$ scaling with a single effective energy scale proportional to the applied field as long as the magnetic field is not close to the $c$-axis. This behavior persists continuously from the antiferromagnetic phase boundary to the highest fields, suggesting that the perturbative Kitaev limit, with its Majorana and flux excitations, may not be an appropriate starting point for describing the low-energy thermodynamics of $\alpha$-RuCl$_3$ for fields away from the $c$-axis.

Wireless energy transfer (WET) decouples energy generation from energy use, offering strategic advantages for distributed spacecraft, lunar surface networks, mobile assets, and high-power remote loads. This review organizes the field along four axes: physical mechanism, energy reference plane, mission architecture, and evidence maturity. It examines near field inductive and resonant transfer, microwave and millimeter wave power beaming, optical and laser-based transfer, space-based solar power, lunar and cislunar energy delivery, inter-spacecraft power sharing, intraspacecraft contactless interfaces, and reconfigurable or relay assisted routing within a common R0,R7 energy-accounting framework. Three conclusions emerge. First, WET is most valuable when spatial or temporal mismatches separate energy generation from load demand; it does not universally replace local generation or onboard storage. Second, dominant losses vary across system architectures. Beam collection, rectification, receiver output, and useful load efficiencies are therefore not directly comparable without explicitly defined energy reference planes. Third, technological maturity is uneven. High power ground demonstrations and short range flight applications are relatively well established, whereas long-range radiative inter spacecraft transfer, spaceborne routing hardware, lunar energy networks, and deep space applications remain supported primarily by models, simulations, and mission studies rather than hardware demonstrations. Progress requires validated end to end energy budgets under mission realistic constraints, including pointing and tracking, thermal management, environmental exposure, reliability, energy storage, and regulatory compliance.

Understanding how many aircraft, and which traffic configurations, can be safely and efficiently managed by air traffic controllers within a given airspace is fundamental to air traffic management. Air traffic controllers continuously modify aircraft trajectories through interventions such as speed advisories and radar vectoring, and the patterns of these interventions are difficult to capture effectively using existing air traffic simulators. To address this limitation, we propose Diffusion Transformers for Traffic Scene Generation (DiTSG), which learns to generate air traffic scenes from recorded multi-aircraft trajectories. DiTSG employs stacked multi-agent inverted Transformer layers as the denoising backbone of a diffusion transformer, jointly generates the trajectories of multiple aircraft within a traffic scene, and conditions the generation on agent-specific required times of arrival. The resulting trajectories generated by DiTSG preserve realistic inter-aircraft interactions observed in actual air traffic operations. Experiments show that the DiTSG generates diverse traffic scenes that reproduce the statistical properties of recorded traffic while preserving realistic inter-aircraft interactions.

We present $\texttt{EccHybIMR22}$, a fully analytical $\textbf{Ecc}$entric-$\textbf{Hyb}$rid-$\textbf{I}$nspiral-$\textbf{M}$erger-$\textbf{R}$ingdown model for the quadrupole ($\ell$=$2$, $|m|$=$2$ or simply the $\textbf{22}$) mode. The model is obtained by smoothly attaching an eccentric-inspiral to a quasi-circular-merger-ringdown prescription and is trained on eccentric numerical relativity (NR) simulations with mass ratios $q\leq 10$. In particular, we focus on obtaining a model that is sensitive to large mass ratios ($q>3$). Leveraging the recent expansion of SXS catalog of NR simulations, we construct a set of 91 hybrids (obtained by combining waveforms from post-Newtonian (PN) theory with NR simulations) with a target low total mass limit ($M_{\rm low}$) of $20M_{\odot}$ at an averaged 22 mode frequency of 20Hz, inaccessible with existing NR simulations alone. Employing a little less than a third of these hybrids as targets, we construct $\texttt{EccHybIMR22}$ and recover $65\%$ of the hybrids from the remaining set with mismatches smaller than $\sim3\%$ for a total mass of $40M_\odot$ (chosen arbitrarily) and orbital eccentricity $e_{\rm 20Hz}\lesssim0.33$ ($e_{\rm 20Hz}\lesssim 0.12$) for mass ratios $q\leq3$ ($q>3$). Furthermore, when tested against 175 SXS simulations, the model is able to recover nearly $80\%$ of the simulations with similar mismatches for systems with $0\lesssim e^{\rm NR}_{\rm 20Hz}\lesssim 0.3$.

Standard hate speech detection datasets often emphasize explicit harmful language, but directed harm can also be expressed indirectly, without clearly hateful wording. Sarcasm is one such form of indirect expression, as it can convey harmful intent through mock praise, exaggeration, humor, or apparent politeness. In this paper, we introduce SarcasTraps, a targeted external test set for analyzing the effect of sarcasm on Turkish hate speech detection. SarcasTraps contains 479 entries annotated along two dimensions: hate speech and sarcasm. We train classifiers using BERTurk and XLM-RoBERTa on two existing Turkish hate speech datasets and evaluate them on SarcasTraps, using it strictly as an external test set. We also evaluate GPT-4.1 and Llama-3.3-70B in a zero-shot setting on SarcasTraps. Results show that sarcasm substantially affects hate speech detection. Fine-tuned encoder models lose recall on sarcastic hate, while zero-shot LLMs maintain higher recall but suffer substantial precision drops on sarcastic examples. These findings show that both fine-tuned hate speech detectors and zero-shot LLMs struggle when sarcasm is involved, and SarcasTraps provides quantitative evidence of this challenge through a targeted Turkish test set. Due to the presence of sensitive and hateful language, SarcasTraps will be shared upon request for academic research purposes. Warning: This paper has examples from the dataset which contains offensive and hateful content towards groups of people.

Historical document analysis is crucial for cultural heritage preservation and low-resource language digitization. However, real historical documents often suffer from severe degradation, such as ink erosion and structural damage, causing mixed-visibility character sequences. Conventional OCR systems struggle in such evidence-limited scenarios, while contextual language models may over-correct visually clear characters. To address these challenges, we propose DDVR-Net, a degradation-aware decoupling and visibility-guided restoration framework for historical document recognition. DDVR-Net decouples intrinsic glyph structures from physical corruption at the feature level and predicts local visibility to estimate character reliability. A contextual decoder is selectively activated through a visibility-guided gate, restoring degraded characters while preserving clear visual recognition. Furthermore, we construct a low-resource multilingual benchmark covering Tibetan, Mongolian, and Uyghur scripts with 187000 document pairs, combining large-scale synthetic data and progressive training with real-world annotations to reduce the synthetic-to-real gap. Extensive experiments demonstrate that DDVR-Net consistently outperforms existing methods across three languages and diverse reading orders, providing an effective framework and benchmark for low-resource historical document recognition. Code and Benchmark: https://github.com/Shajiu/DDVR-Net

We consider a random subgraph G_p(n,r,<s) of the complete distance graph G(n,r,<s) whose vertices are the r-element subsets of the set {1,...,n} and whose edges join pairs of subsets that intersect in fewer than s elements; each edge survives independently of the others with probability p. The stability of the Erdos-Ko-Rado theorem is the event that the independence number of the random subgraph equals that of the original graph, N = C_{n-s}^{r-s}. For fixed r and s, two-sided bounds for the critical probability, whose ratio depends on r and s, were obtained by P. A. Ogarok and A. M. Raigorodskii. In this paper we establish the order of the critical probability for growing r=r(n) and s=s(n): if min{C_r^s r^2, s r^3} = o(n), then the upper and lower bounds differ only by an absolute constant factor. The proof is elementary; only one of the two branches of the growth condition uses the complete nontrivial-intersection theorem of Ahlswede-Khachatrian.

We study the conformal coupling in the torsion-free Palatini formulation with an ordinary scalar kinetic term. Tuning the curvature coupling cannot restore Weyl invariance in a Palatini theory with an ordinary scalar kinetic term because, for an independent and inert connection, the scalar-curvature term is separately Weyl-invariant, and no finite curvature coupling cancels the Weyl variation of the kinetic term. This can be demonstrated by evaluating the energy-momentum trace on the scalar equation of motion and noting that it is explicitly independent of the Palatini coupling. Eliminating the connection, we construct a map between the curvature coupling and the effective coupling for the equivalent metric theory, and demonstrate that the scalar continues to propagate even if the reduced kinetic coefficient vanishes. We also show that it becomes a Weyl compensator with a scale-invariant potential only in the rescaled infinite-coupling limit, which in four dimensions is directly related to Palatini ${\cal R}^2$ gravity. We calculate the running of the couplings at one loop, and we find that the conformal shift in the metric-curvature coupling's beta function generates a metric-curvature coupling on a fixed metric-affine background, whereas the independent-curvature coupling runs homogeneously. Furthermore, we follow an alternate prescription in which the connection is allowed to respond to the scalar fluctuations, which results in a different scalar Hessian and therefore different beta functions. Nonetheless, we find that both prescriptions admit the formal infrared limit $(\xi_{eff},\lambda_{eff})\to(1/6,0)$ through different limits of the original couplings in the case of positive perturbative quartics. Finally, we note that trajectories starting on the positive gravitational branch encounter a vanishing gravitational coefficient at a finite scale before this endpoint.

We determine thirteen entirely CM identity fibers of Shimura parametrizations attached to elliptic curves of rank two and conductor below $2000$. Each yields a proof of the imaginary quadratic class number one theorem. The argument combines the Gross–Zagier formula with the Ribet–Takahashi degree comparison to show that the fiber is completely explained by known CM points.

How do language models reconcile conflicting contextual evidence within a prompt? We study this question using lexical redefinition, where an explicit instruction specifies how a word should be interpreted and a subsequent sentence provides additional evidence through its usage. Across 870 word pairs, we find that lexical redefinitions are not applied as fixed rules. Instead, the behaviour depends systematically on the relationship between the explicit instruction and the intervening sentence: the contextualised usage can preserve, weaken, or completely reverse the instruction. These results suggest that the interpretation of an explicit instruction remains sensitive to subsequent contextual evidence. Lexical redefinition therefore provides a controlled behavioural paradigm for studying how language models integrate multiple sources of information within a prompt.

We study the Solomon–Terao algebra and the Solomon–Terao complex of a central hyperplane arrangement $\mathcal A$ in $\mathbb C^\ell$. Let $\eta$ be a homogeneous polynomial of degree $d\geq2$ whose restriction to every flat of $\mathcal A$ has no critical point away from the origin. We prove that the Solomon–Terao algebra $\mathrm{ST}(\mathcal A,\eta)$ has top degree $|\mathcal A|+\ell(d-2)$ and a one-dimensional top graded component with an explicit generator, solving a conjecture of Abe, Maeno, Murai, and Numata. For $d=2$, we show that the total dimension of $\mathrm{ST}(\mathcal A,\eta)$ is bounded below by that of the Orlik–Solomon algebra. Both results hold without assuming that the arrangement $\mathcal A$ is tame. Finally, we prove that $\mathcal A$ is tame if and only if all positive-degree homology groups of the Solomon–Terao complex associated with $\eta$ vanish.

We study the potential impact of lattice QCD window observables on nucleon isovector quark transversity parton distribution functions (PDFs) using the ePump Hessian-updating framework. Window observables, recently proposed in arXiv:2505.22795 as benchmark quantities enabling direct quantitative comparison between lattice QCD and phenomenological PDF extractions, are weighted integrals of PDFs over a range of Bjorken-$x$ for which both approaches are reliable. Experimental determinations of transversity PDFs carry uncertainties of 50–100%, while current lattice calculations have achieved comparable or better precision, creating an opportunity for lattice inputs to significantly constrain a global analysis. We evaluate the constraining power of existing lattice QCD computations of transversity window moments and Gaussian windows against current phenomenological PDF. We additionally examine prospective tensor charges in the transversity channel and estimate the PDF uncertainty reduction achievable at current and near-future lattice precision. Our results provide quantitative guidance on which window observables will most constrain global PDF analyses.

We present first-principles calculations of the electron-hole-pair creation energy in semiconductors and dielectrics, focusing in particular on AlN, 3C-SiC, 4H-SiC, Si, and SiO2. We have employed density functional theory (DFT) to calculate the band structure, density-functional perturbation theory to obtain the phonon dispersion, and time-dependent DFT (TDDFT) to calculate the electron energy loss function (via the dielectric function). We performed full-band Monte Carlo simulations of electron thermalization for energies up to ~100 eV and calculated the average energy required to excite an electron-hole pair. We calculated pair-creation energies of approximately 12.2, 6.5, 7.3, 3.10, and 16.7 eV/pair for AlN, 3C-SiC, 4H-SiC, Si, and SiO2, respectively. These values are in good agreement with measured data, with the largest discrepancy being that of Si (about 14.9% lower than the accepted experimental value of ~3.6 eV/pair). To improve the agreement for Si, we used the GW approach and the Bethe-Salpeter equation (BSE) to calculate the quasiparticle shifts of the electronic band structure and the dielectric function, respectively. Finally, using the GW/BSE data, we calculated a creation energy of ~3.50 eV/pair. We find that the marked improvement in the accuracy of the calculated creation energy, when using the GW/BSE approach, is primarily attributable to the slight decrease in the magnitude of the electron energy-loss function when using the GW/BSE approach for energies below ~10-15 eV. Overall, it is clear that the competition between phonon emission and ionization near the intersection of the phonon scattering and ionization rates is largely responsible for determining the value of the creation energy, with the other major factor being the location and shape of the plasmon peak in the energy-loss function.

Convex relaxations make nonconvex optimization tractable by replacing hard nonconvex problems with convex surrogates that give valid bounds. Yet their design is still largely manual: a human expert must decide where to relax, which relaxation to use, and how much formulation growth is worth paying. We show that this design process can be learned. The method proposed in this paper, AutoConvexRelax, represents the symbolic formulation of a nonconvex problem as a tripartite graph linking variables, symbolic terms, and their objective or constraint positions. It then learns a policy that composes symbolic rewrites into problem-specific relaxation trajectories as the formulation evolves. We prove that finite action sequences generated by the learned policy preserve relaxation validity under explicit domain, occurrence-context, and representation-consistency conditions. We further establish computable error bounds for mixed relaxations and sufficient conditions for feasible recovery and global-optimality certification. As a first instantiation, we apply the method to nonconvex quadratic problems and fractional problems. On 241 benchmark quadratic instances, the learned policy strengthens McCormick lower bounds by 13.52%. Its mean lower bound is 3.70% below strengthened semidefinite relaxations on the normalized comparison metric, while it uses substantially smaller formulations. The learned policy retains this trade-off on fractional instances and reaches near-semidefinite bounds on beamforming and sensor-network localization instances. These results suggest that convex relaxation design can move from a fixed handcrafted choice to an automated learning process that adapts to problem structures. Code is available at https://github.com/auto4opt/AutoConvexRelax.

This paper develops a mathematical framework connecting structural metadata, logical admissibility, and correction in statistical data editing. A normalized routing graph generates a canonical indexed representation and an associated Horn theory, incorporating explicit semantic edits through deterministically evaluated auxiliary variables. Under specified record semantics, the theory characterizes admissibility, distinguishes structural minimality from logical irredundancy, and permits validation without materializing the deductive closure. Canonical indices preserve the provenance and dependency scopes of violations. With complete diagnostics and strictly positive weights, a nonnegative violation Hamiltonian vanishes exactly on admissible corrections within the permitted candidate domain. Verified zero-energy outputs therefore certify feasibility and global minimization of violation energy. Minimum modification cost is formulated separately, with sufficient conditions for an equivalent penalized objective and optimality certificates obtained by matching attained costs with valid lower bounds. A household survey application verifies admissible corrections and certifies minimum cost for a subset of returned records through a retrospective audit. The framework connects structural requirements to correction certificates independently of the numerical search procedure, while statistical accuracy of replacement values requires separate assessment.

Descriptions of how people use AI are becoming training data for the next generation of models. We ask whether what a model reads about its users changes how it treats people. Using contrastive synthetic-document finetuning, we train Qwen3-32B on four matched corpora built from the same 1,625 real-world usage scenarios. The corpora differ only in the predominant motive they attribute to users of AI chatbots: helping others (prosocial), exploiting others (antisocial), legitimate self-advancement, or task completion. Finetuning shifts the models' stated beliefs about users, how true those beliefs look along an internal truth direction, and their broader judgments of how safe and good the world is. These social priors carry into behavior. In trust games, antisocial models expect less reciprocity and send less money than prosocial models. Their distrust is specific and targeted at people, and users of AI chatbots in particular. After an exploitative record, they send almost nothing to a person but most of their endowment to a random device with the same record. In a common-pool resource simulation, a single antisocial agent leads every group of otherwise sustainable agents to exhaust the resource, after privately planning to mislead them. Antisocial training also raises dark-triad scores and lowers alignment ratings. Belief shifts appear when antisocial documents are 1% of training tokens, persist when descriptions of assistant behavior are suppressed, and are not reproduced by training on discourse about misaligned AI. Capping Assistant-Axis drift and steering emotion-related directions leave the gaps largely intact. What models learn about the people they serve shapes how they subsequently treat them and others.

Recent advances in multimodal foundation models, exemplified by GPT-6 Astra, raise the prospect of general-purpose embodied reasoning and planning. Using Internet videos for embodied pretraining calls for reliable physical-scale annotations. Yet visual geometry foundation models often recover scene structure and camera motion without reliable metric scale. We show that uncertain size priors of familiar objects can jointly constrain a reconstruction's shared scale. Building on this insight, we present UniMetric, a universal and training-free metric scale recovery framework for geometry foundation models, without additional sensors or task-specific metric supervision. Specifically, Metric Prior Acquisition elicits object height intervals from a vision-language model. Semantic-Geometric Alignment measures reconstructed object heights along the estimated support-surface normal in each frame and converts the priors into scale intervals. Global Scale Recovery reconciles these intervals through a convex objective, yielding a jointly feasible scale when they overlap and a unique compromise otherwise. The estimated sequence-level scale is applied uniformly to reconstructed points and camera translations. Controlled experiments with real VLM priors show that combining observations improves scale accuracy with exact relative object heights. To evaluate metric accuracy on GFM reconstructions without ground-truth scale alignment, we introduce MetricBench, covering twelve embodied, driving, and roadside subsets with sensor-derived ground truth. Across nine geometry foundation models, UniMetric reduces mean depth Abs Rel, reconstruction Chamfer distance, and trajectory error by 54.2%, 83.8%, and 65.6%, respectively, improving every model on all three tasks at the suite level. We release the UniMetric code and MetricBench data.

The nearly collinear configuration of highly stretched polymer chains before fracture motivates one-dimensional models. At fixed extension, stretching one bond redistributes length among the others, coupling rupture to the whole chain. In this work, I develop a framework for fracture-healing rates in periodic Morse chains, combining deterministic theories, equilibrium simulations and a quasi-deterministic approach using equilibrium fluxes and barrier-top trajectories. Constrained-partition calculations closely reproduce simulated populations and intact-state tensions. An intact-reservoir potential of mean force (PMF) supplies the first-fracture surface probability, while recrossing corrects the attempt flux without a rate-fitted prefactor. Independent rate tests identify an operational chain-length boundary for accurate two-state kinetics; failed-return durations decrease relative to population relaxation as chains grow. Kramers-Grote-Hynes (KGH), nonlinear reactive-flux and equilibrium rates show excellent agreement in this regime. KGH predicts rates away from coexistence and a chain-dependent local activation length dominated by the barrier response. Rates decrease approximately exponentially before declining more gently for longer chains: barrier growth dominates, additional fracture sites partly compensate, and transmission varies more weakly. Beyond coexistence, long chains can fracture practically irreversibly because healing becomes too rare to observe. Projected committor crossings, where the configuration-averaged probability of reaching the fractured core first is one half, lie near site-PMF maxima, although configurations at equal bond length retain different fracture probabilities. Multiple fractures remain negligible near coexistence through at least $N=50$. The framework could supply state-dependent rates to mesoscopic fracture models of polymer networks.

We study the online fair division of indivisible goods. In the standard model, where assignments are irrevocable, no algorithm can guarantee any positive fraction of the maximin share (MMS). Reassigning earlier goods can restore fairness, but it may take value away from agents who already hold them. We ask how much fairness can be maintained if every reassignment must leave each affected agent at least as well off. We consider two forms of such upgrade recourse. Under item-level upgrades, each good an agent holds must be kept or replaced by a distinct good she values at least as much; under bundle-level upgrades, only her total value must not decrease. For item-level upgrades, we show that the optimal MMS factor is essentially $1/H_n \approx 1/\ln n$, where $H_n$ is the $n$-th harmonic number, and that fixed picking sequences nearly attain it. Since these sequences use only the agents' rankings of individual goods, knowing the actual values cannot improve the optimal factor for up to 33 agents, and improves it by at most a vanishing margin as $n$ grows. Bundle-level upgrades allow substantially stronger guarantees. By permitting several-for-one exchanges, they turn this vanishing factor into a constant: we achieve exact MMS for two agents and more than half of MMS for any number of agents, in both cases together with relaxations of envy-freeness. Finally, we show that predictions about future goods let online algorithms inherit any offline MMS guarantee, losing only an additive term bounded by the prediction error. Under item-level upgrades, however, insisting on exact MMS when predictions are correct leaves no positive guarantee when they are wrong.

Large audio-language models (LALMs) are fast becoming a general interface to sound, yet how far their broad pretraining carries into specialized domains remains largely open. Vessel monitoring, maritime safety, and ocean sensing all depend on recognizing underwater signals, but to our knowledge LALMs have not been systematically evaluated on them. Annotated recordings are costly to collect, and a faithful synthetic alternative has to bring together many interacting factors: the structure of detection pulses, communication waveforms, and ship-radiated noise, and the sound-speed profile, geometry, and multipath propagation through which each reaches the receiver. We address this by proposing UA-Bench, to our knowledge the first large-scale benchmark for evaluating LALMs on underwater acoustic signal recognition. It comprises 375,051 audio records that couple parameterized sources with modeled propagation, so that every record can be traced to the conditions that produced it. The records span these three signal families, and each carries a three-level label hierarchy (13 leaf classes), a templated multi-turn dialogue, and source and channel metadata. We evaluate on a balanced 2,600-record subset with a gated coarse-to-fine protocol that locates each error at source routing, fine-grained classification, or output format, and add a paired silent-audio control to test whether the waveform is actually used. Nine open LALMs, evaluated without task-specific adaptation, reach only 2.0%–13.1% leaf accuracy, against a random reference of 7.7%. The waveform helps source routing far more than leaf recognition (for one model, +29.5 versus +2.3 points over silence), and just four models gain reliably at the leaf level, by at most 4.7 points. UA-Bench thus gives a reference point for these models, and its released training partition supports follow-up adaptation work.

In this paper, we study various structural properties like girth, chromatic num ber, etc. of the intersection hypergraph on the subgroups of nite non-cyclic abelian group and we characterize for the star and hypertree structures. Fur thermore, we characterize hypergraphs which are embeddable on plane, torus and projective plane.