Papers

We study global convergence guarantees of third-order Langevin dynamics for non-convex optimization via simulated annealing with fixed friction and decreasing noise. An explicit three-block distorted entropy transfers dissipation from the noisy auxiliary variable to the full state. Under dissipativity, regularity, and low-temperature functional-inequality assumptions, logarithmic cooling drives the objective values to the global minimum in probability at the barrier-controlled kinetic rate. For the exact-force-integral and midpoint three-stage discretizations, polynomially decreasing steps preserve this rate on the physical time scale. The cubic local endpoint estimate gives a less restrictive sufficient step-size condition than the available frozen-force kinetic result. A comparison with the one-gradient UBU integrator shows how its centered stochastic local error leads, under the same strong-coupling analysis, to a smaller sufficient iteration exponent. Numerical experiments are conducted to illustrate our theory. For a double well objective, third-order Langevin terminal-success point estimates are higher than UBU at both a common horizon and an equal gradient budget. For a high-dimensional nonconvex neural-network objective using synthetic data, independently tuned UBU and third-order Langevin schemes both outperform overdamped Langevin dynamics; the third-order Langevin point estimate is higher. For the same neural-network objective on real data, we show the same point-estimate ordering for best-basin probability and post-quench test accuracy. Numerical code and associated experiment results are publicly available at https://github.com/gagawjbytw/simulated-annealing-third-order-langevin.

Benchmarking is an increasingly critical part of research in machine learning and the domains where it is applied, including healthcare. Yet, despite the steady development of new ultrasound foundation models in recent years, the development of well-designed benchmarks to evaluate them has lagged behind. This deficiency has led to fragmented and inconsistent evaluations of competing models, making it difficult to measure progress. To address this issue, we introduce UltraBench 2, a comprehensive benchmark with wide anatomical and task coverage, and a focus on standardization, reproducibility, and ease-of-use. Using this benchmark, we compare existing vision foundation models for ultrasound image analysis. Our analyses demonstrate that ultrasound-specific pretraining still leads on classification, but that state-of-the-art general-purpose models have drawn level on segmentation.

Role-playing agents based on large language models have been widely applied in areas such as personalized assistance and social simulation. Recent RL methods typically train on a fixed scenario pool collected before learning begins. This creates a distributional bottleneck: as the agent improves, the scenarios where it performs poorly also change, while the training distribution remains static. Therefore, we propose AdvRole, an adversarial context rewriting framework that turns role-playing RL into a closed-loop curriculum. AdvRole alternates between an Actor that learns to role-play and a Rewriter that edits character profiles and dialogue contexts into actor-specific hard scenarios. The Rewriter is trained with a performance-gap reward, which favors rewrites that reduce the current Actor's score relative to the original scenario. As a result, the scenario pool evolves with the Actor and continuously targets under-mastered regions of the character-context space. Experiments on three role-playing benchmarks covering English and Chinese, as well as a new multilingual benchmark we release, show that AdvRole consistently outperforms baselines.

Removing CPython's Global Interpreter Lock (GIL) exposes native code to concurrency absent from ordinary C types. Mutation or re-entry can revoke a borrowed object, storage pointer, traversal state, or lease between acquisition and use while its owner remains alive, causing native memory errors and runtime-state corruption. Race analyses track conflicting accesses. Python/C lifecycle analyses track individual object states. These reporting units leave implicit owner-subject-storage relations disconnected from later uses under parallel and re-entrant events. We present CONCURDEP, a source-level static analysis of dependency invalidation. Its key insight is to represent the runtime property a native use requires and ask which target-matched event can revoke it within the dependency's live region. CONCURDEP recovers runtime-semantic dependencies, connects them to events through an event-aware native concurrency dependency graph, and applies property-specific state and protection transfers through a shared engine and six mechanism plugins. CONCURDEP correctly classifies all 180 matched semantic-conformance cases and analyzes each of three production CPython releases with five-run medians of 22.13-27.66 seconds and 670-784 MiB peak resident memory. Source auditing confirms 1,094 of 4,273 unique production fingerprints (25.60% confirmation yield). Removing derived relation recovery loses 25-44 represented roots per release; removing cross-entry events loses 73-94. The study identifies 144 distinct bugs across free-threaded and conventional-GIL builds, including 95 previously unreported in public sources. These results show that explicit dependency, event, and property semantics expose consequential runtime failures across API boundaries and execution modes at release scale.

Intermittent time series are common in spare-parts demand and retail sales. Since the cost of forecast errors is typically asymmetric, decisions such as inventory control require the full predictive distribution rather than a point forecast. Many probabilistic forecasting methods have been proposed; their implementations, however, are scattered across different software frameworks, making it difficult to compare them systematically. We introduce fable$.$intermittent, an R package that implements several probabilistic forecasting methods for intermittent series within the fable framework. The package allows several models to be fitted and evaluated on a collection of time series through a single, simple forecasting pipeline. We also introduce TWEES, a new exponential smoothing model with a Tweedie predictive distribution. Fitting TWEES requires repeated evaluation of the computationally demanding Tweedie density. We also release the R package tweedieDistr, whose implementation of the Tweedie distribution is substantially faster than the existing one while preserving the same numerical accuracy. We evaluate the methods implemented in fable$.$intermittent on four datasets, also released in the package.

We confirm Vaught's conjecture for each partial order ${\mathbb X}=\sum _{{\mathbb I}}\prod _{j<m_i}{\mathbb X}_{i,j}$ from the closure $\langle \langle {\mathcal C}^{\rm rt}\rangle _\Pi\rangle _\Sigma$ of the class ${\mathcal C}^{\rm rt}$ of rooted trees under finite direct products and lexicographic sums. In addition, (a) ${\mathcal T}:=\mathop{\rm Th}\nolimits ({\mathbb X})$ is $\omega $-categorical iff all the theories ${\mathcal T}_{i,j}:=\mathop{\rm Th}\nolimits ({\mathbb X}_{i,j})$ are $\omega $-categorical; (b) ${\mathcal T}$ satisfies VC$^\sharp$ (that is, $I({\mathcal T})\in \{1,{\mathfrak{c}}\}$), if VC$^\sharp$ holds for all ${\mathcal T}_{i,j}$. If ${\mathbb X}\in \langle \langle {\mathcal C}^{\rm rt}_{\rm fa}\rangle _\Pi\rangle _\Sigma$, where ${\mathcal C}^{\rm rt}_{\rm fa}$ is the class of finitely axiomatizable rooted trees, then (c) ${\mathcal T}$ is finitely axiomatizable and (d) ${\mathbb Y}\in \mathop{\rm Mod}\nolimits ({\mathcal T})$ iff ${\mathbb Y} \cong \sum _{{\mathbb I}}\prod _{j<m_i}{\mathbb Y}_{i,j}$, where ${\mathbb Y}_{i,j}\in \mathop{\rm Mod}\nolimits ({\mathcal T}_{i,j})$, for all indices. As a by-product we prove that (e) For each $n$ the class ${\mathcal C} _n$ of partial orders isomorphic to a direct product of $n$ rooted trees of size $>1$ is first-order definable; (f) Each $\omega $-categorical partial order from the class $\langle \langle {\mathcal C}^{\rm rt}_{\rm fb}\rangle _\Pi\rangle _\Sigma$, where ${\mathcal C}^{\rm rt}_{\rm fb}$ is the class of finite-branching rooted trees, is finitely axiomatizable. Statement (f) is related to the results of Rosenstein (for the class of linear orders) and Schmerl (for the class of partial orders of finite width).

The Factivity Inference Evaluation 2026 (FIE2026) classifies Chinese context-hypothesis pairs into nine ordered factivity intervals. Its evaluation metric rewards both exact predictions and proximity to the correct interval, while 64.1% of the 566 training examples belong to a single class. In preliminary experiments, several mDeBERTa classification models predominantly predict the dominant class, whereas a Huber-regression baseline produces more predictions near the correct interval but fewer exact matches. We introduce Utility-Oriented Factivity Inference (UO-FIE), a parameter-efficient system that combines exact-label supervision with graded utility. UO-FIE predicts a distribution over the nine classes and combines hard-label supervision, utility-based soft targets, scheduled class weights, and an ordinal loss. We evaluate expected-utility decoding in controlled comparisons and use ordinal calibration selected on out-of-fold predictions for the submitted system. Based on Qwen3.5-9B with LoRA, UO-FIE ranks first in the fine-tuning track with a macro utility of 0.8316. A separate prompt-based ensemble ranks third in the non-fine-tuning track with a macro utility of 0.8450.

Scientific instruments require accurate calibration to convert detector signals into reliable physical observables. Conventional calibration procedures typically rely on dedicated calibration measurements, analytical response models or labelled reference data, limiting their ability to adapt to changing operating conditions and detector aging. We present a physics-informed self-supervised learning framework that jointly performs wire calibration and interaction position reconstruction in Multi-Wire Parallel Plate Avalanche Counters (MWPPACs) without requiring labelled position measurements or dedicated calibration runs. The method formulates detector calibration as a latent optimization problem in which global wire gains and event-wise interaction positions are estimated simultaneously using supervision derived exclusively from detector geometry and charge-energy consistency constraints. A detector-independent neural network reconstructs sub-wire interaction positions from local charge distributions, eliminating the need to assume analytical induction profiles by learning the detector response directly from experimental data. The end-to-end differentiable framework enables continuous detector self-calibration while improving the uniformity and accuracy of position reconstruction. Experimental evaluation on the entrance MWPPAC tracking detectors of the VAMOS++ magnetic spectrometer demonstrates stable convergence, improved spatial homogeneity and enhanced position resolution. Beyond the detector studied, the method establishes a general framework for physics-informed self-supervised calibration of scientific instruments and is a step toward autonomous intelligent instrumentation capable of continuous adaptation during operation. In this paradigm, detector calibration is no longer a prerequisite for an experiment but an integral part of the measurement process itself.

Recently, Large Language Models (LLMs) have been increasingly able to solve advanced mathematical problems, including many that have been open for decades. This opens the door to expansion of mathematical knowledge at unprecedented scale. Yet, while LLMs may be able to conjecture and prove more and more theorems, it remains open whether this new mathematical knowledge is interesting or useful. We define intrinsic interestingness of a theorem as the ratio between the length of its proof and the length of its statement. We show that this correlates strongly with an extrinsic measure of the downstream utility of a theorem. We identify the difficulty of a proof conditioned on a set of premises as a useful primitive for computing these metrics, and train a 27B model that predicts proof difficulty more accurately than frontier general-purpose models. Optimizing for our metric creates a model capable of producing more interesting theorems, while also reducing substantial or full overlap with Mathlib from 91.9% to 30.6%, showcasing the creation of more out-of-distribution math. We show that our system can generate candidate theorems, select the most interesting among them, and iteratively build on a self-expanding mathematical library. These metrics provide a practical and quantifiable signal for ranking conjectures and guiding proof search within formal mathematical libraries. Our framework provides a path towards self-expanding, machine-verified mathematical libraries that can choose worthwhile statements without relying on human-supplied targets.

These are extended notes based on a series of lectures given by the author at the Institut de Mathematiques de Toulouse in June 2025. The goal is to present classical problems as well as the most recent developments in spectral geometry of the Laplace operator in Euclidean domains, subject to Dirichlet, Neumann and Robin boundary conditions. Among the topics covered, there are embedded eigenvalues in unbounded domains, spectral isoperimetric inequalities, nodal-line and hot-spots conjectures, inverse problems of hearing the shape of a drum and geometrically induced eigenvalues and Hardy-type inequalities in curved tubes.

Machine-learning (ML) emulators for atmospheric processes have advanced rapidly in recent years, transforming weather forecasting. Although early ML ocean forecasting models now exist, they remain less developed than their atmospheric counterparts. Unlike the atmosphere, much of the ocean's kinetic energy resides in mesoscale eddies whose characteristic spatial scales are approximately an order of magnitude smaller than those of comparable atmospheric features. Moreover, complex coastlines, narrow straits, and ice-covered seas make boundary representation a central challenge that atmospheric models do not face. Consequently, numerical ocean simulations commonly use locally refined or even completely unstructured meshes. However, their data-driven counterparts have so far been built around latitude-longitude grids. We present HClimRep-Ocean, an ocean emulator that operates directly on the native unstructured mesh of FESOM2. The emulator is trained on a 209-year AWI-CM3 control integration and is run without atmospheric forcing, receiving the atmospheric state only at initialisation time, which isolates the predictability carried by the ocean state itself. Skill is strongly field-dependent: for currents, HClimRep-Ocean outperforms every reference at 30 day forecast, whereas for temperature and salinity a damped-anomaly persistence forecast remains the more accurate estimator. This behaviour is physically interpretable: current variability is largely geostrophic and internally generated, whereas sea-surface temperature and salinity fluctuations are driven by atmospheric forcing through weather state. Evaluated independently on the OceanBench benchmark, a reanalysis-trained variant of HClimRep-Ocean achieves the lowest RMSE against GLORYS reanalysis among all assessed systems, confirming the competitiveness of the native-mesh approach.

Verification and validation practices (V&V) at NASA's Jet Propulsion Laboratory (JPL) have diverged over the past decade, creating fragmentation that increases overhead, reduces cross-project efficiencies, and inhibits institutional knowledge transfer. We present a unified V&V activity schema developed through human-centered design workshops involving 29 practitioners across multiple mission types and disciplines. The schema builds on a relationship-based architecture that allows for separating methods (Test, Analysis, Inspection, Demonstration, and Review of Design) while maintaining a common attribute set. Formalized as a platform-agnostic SysML model, the schema defines bidirectional relationships between requirements, V&V activities, venues, and evidence. Implementation in JPL's Jama platform demonstrates controlled customization through templates and modular item types, balancing rigor with agility while enabling automations, pattern reuse, and digital thread integration.

Flipping 60% of training labels from a single Byzantine client using label-flipping model poisoning self-degrades an attacker's own federated detection accuracy, $99.96\%$ (at no poisoning rate) to $84.33\%$ in a three-client federated IDS. Where the Federated global ensemble maintains stable accuracy across all tested poison rates, without a defense mechanism in place and without coordination between attackers. In this paper, we present empirical results quantifying the impact of label-flipping poisoning attacks on a three-client federated IDS trained on CICIDS2017 with non-IID attack subtype distributions across clients. We demonstrate that the signal of the adversarial self-compromise represents a detectable anomaly for exploitation for Byzantine client identification in the absence of target data exfiltration. We note that the aggregation step uses a Federated Forest (tree concatenation) rather than a parametric FedAvg; the results therefore measure the impact of poisoning on per-client performance under ensemble aggregation, and extension to genuine FedAvg with a parametric classifier is planned for future work.

We prove that topological isotopy implies smooth isotopy for neat surfaces with common nonempty boundary in a smooth orientable 4-manifold, in the presence of a geometric dual in the boundary. Together with our earlier work on surface smoothing, this shows that the natural map from smooth isotopy classes to topological isotopy classes of such surfaces with prescribed boundary is bijective.

Rooted phylogenetic networks are widely used to represent the evolution of species that have undergone reticulate processes. However, these networks can be highly non-planar, making them more difficult to visualise and interpret than evolutionary trees. In this paper, we investigate planarity properties of galled networks, an important subclass of phylogenetic networks. We show that all planar galled networks are necessarily upward planar. Furthermore, by leveraging recent results on planar phylogenetic networks, we provide three characterisations for each of the outerplanar and terminal planar galled network classes in terms of forbidden vertex configurations, forbidden directed subgraphs, and forbidden structures in their associated underlying undirected graphs. These results contribute to a deeper understanding of the structural properties of galled networks and may inform future methods for their construction and visualisation.

We construct traversable wormhole solutions in the linear teleparallel model $f(T) = \alpha T + \beta$, adopting Padé approximants of order [1/0] and [0/1] as shape functions together with the redshift function $\Phi(r) = -M/r$, and derive the corresponding source terms from the modified field equations. We assess the physical viability of both configurations through the energy conditions, Tolman–Oppenheimer–Volkoff equilibrium, the volume integral quantifier, thin-shell junction matching to an exterior Schwarzschild vacuum, embedding diagrams, proper radial distance, the gravitational energy and the active mass. We then examine the observational signatures of each geometry by analysing equatorial null geodesics and the photon-sphere structure, computing shadow maps and radial intensity profiles, ray-tracing relativistic images of a geometrically thin accretion disc, and integrating timelike rosette orbits. Finally, we study the dynamical stability of both wormholes through a third-order WKB quasinormal-mode analysis across scalar, electromagnetic, and axial gravitational perturbations, cross-checked against time-domain evolution and the eikonal photon-sphere correspondence, and examine the parameter dependence of the mode spectrum together with the possibility of trapped-mode echoes.

This paper is devoted to studying permutation binomial $F_{r,a}(X)=X^r(X^{q-1}+a)\in\mathbb F_{q^e}[X]$ with $a\in\mathbb F_{q^e}^*$. We present a complete characterization for $F_{r,a}$ to be a permutation of $\mathbb{F}_{q^e}$. This yields a complete proof of the conjecture proposed by Masuda–Rubio–Santiago \cite{masuda2022permutation}. More precisely, we show that \(F_{r,a}\) permutes \(\mathbb F_{q^e}\) if and only if $(-a)^{(q^e-1)/(q-1)}\ne1, \gcd(r,q-1)=1$, and there exists \(1\le h<e\) with \(\gcd(h,e)=1\) such that $r(q^h-1)\equiv q-1\pmod{q^e-1}.$

The Erdős-Gyárfás conjecture posits that every graph with minimum degree at least three contains a cycle of length some power of two. We prove a few simple structural properties for any minimal counter-example to this conjecture. In particular, the fraction of its vertices of degree three must be greater than $2/3$, thus improving on the prior bound of $4/7$ (Carr, 2026). Furthermore, it is either biconnected or the $1$-clique-sum of two biconnected graphs. By exploiting some of these properties, we were able to verify the conjecture for every graph of order at most $40$, every bipartite graph of order at most $66$, and every cubic graph of order at most $48$.

Active matter, i.e., nonequilibrium systems that transform non-thermal energy from the environment into self-propulsion or other functional mechanisms, has attracted the attention of the statistical physics community in recent decades. Flocking, as shown by the aerial displays of starling flocks, is perhaps one of the most intriguing collective behaviors exhibited by active matter. While the bulk behavior of free collective motion is now fairly well understood, at least when the surrounding fluid can be neglected (the so-called dry approximation), much less is known when collective motion explicitly breaks a continuous rotational symmetry, either globally or locally. This thesis explores the effects of such explicit symmetry breaking on the dynamics of collective motion. Global symmetry breaking may arise from an anisotropic environment, where a favored direction sets the mean flocking direction. A key question addressed here is how to detect small anisotropies without prior knowledge of the underlying environmental asymmetry. The thesis then examines boundary-induced symmetry breaking. In confined flocking systems, local anisotropies arise at the boundaries and significantly affect both bulk and boundary behavior, especially in finite-sized setups. We focus in particular on a polar active fluid confined between two parallel repelling walls, showing that the influence of the boundaries extends far into the bulk. Finally, we consider a more subtle confinement inspired by the phototactic behavior of certain cyanobacteria, showing that key features of active matter, such as accumulation at boundaries, can arise even without mechanical confinement. The results shed light on how symmetry-breaking perturbations, whether imposed globally or locally, alter the dynamics of active matter systems and offer new insights into the control of collective motion.

Determining a noisy quantum channel's classical capacity and entanglement cost generally requires regularization over many channel uses. We remove both regularizations for every qubit-to-qubit channel admitting a pure output. For each such channel, Holevo information, channel entanglement of formation, and parallel entanglement cost are additive with those of any finite-dimensional partner channel. This class includes all qubit-to-qubit channels of Kraus rank at most two. For the amplitude damping channel with damping probability $p$, the unassisted classical capacity equals the known single-use Holevo information, attained by a binary pure-state ensemble with collective decoding, and the entanglement cost is $h_2((1+\sqrt p)/2)$ ebits per use. The common mechanism is a support criterion for strong superadditivity of entanglement of formation: one marginal has no support on the sector in which both local systems are orthogonal to fixed distinguished vectors. We prove this criterion in arbitrary finite dimensions using a triangular block-matrix entropy inequality and decompositions preserving two expectations. For amplitude damping, we also derive an exact finite-block Holevo deficit, identify the unique optimal average input for $p<1$, and construct a binary Kraus representation attaining the uniform formation bound.

Over three centuries ago our Enlightenment forefathers brought forth in Europe–and later on this continent–a new approach to knowledge production and dissemination, conceived in distrust of authority, and dedicated to the proposition that truth is accessible to human reason. Mathematics, the Enlightenment's firstborn, was its existence proof–knowledge that compels assent without appeal to authority–because the only way to make a theorem certain was to show it to a human mind. Now we are engaged in an existential struggle testing whether mathematics, or any discipline so conceived and so dedicated, can long endure. We are met in the wake of the OpenAI press release: 166 pages, 616,000 lines of Lean, produced in 88 hours by some 10,000 software agents, and read in full–at the time of this Siren Call–by no human being. A proof has historically been two things: a certificate that a theorem is true, and a demonstration that lets another person see why. OpenAI delivered the first without the second. But, in a larger sense, what matters is not what the Silicon Leviathan (OpenAI and its peer competitors) produces but rather what we accept. By accepting the certificate without the demonstration, we adopt the Hobbesian bargain: authority, not truth, makes the law. The age that this augurs is–in Panofsky's phrase–a Middle Ages in reverse–its authority a subhuman superintelligence. The great task before us is to frame a covenant under which what has become optional–understanding–remains required: that nothing counts as mathematics until a human being has understood it–and can show the next person why. Whether we will safeguard and keep our sovereign inheritance–decided at the moment of acceptance–which is not yet past–will determine if this Aufklärungsdämmerung spells the Enlightenment's end.

Background & Problem: Thyroid Fine-Needle Aspiration Biopsy (FNAB) cytology based on the Bethesda System plays a pivotal role in early thyroid cancer detection; however, deep learning approaches face substantial challenges regarding high false-negative rates and overconfidence under clinical domain shift. Methods: In this study, we propose TAM-Chain, a multi-scale (10x, 20x, 40x) thyroid cytology classification framework leveraging Absorbing Markov Chain theory combined with Shannon Entropy-based Uncertainty Quantification. The framework dynamically models multi-magnification feature extraction as an absorbing stochastic process, enabling optimal stopping criteria and a human-in-the-loop referral mechanism to strictly suppress critical diagnostic errors. Results: Extensive evaluation on an internal test set (N = 235) demonstrates a Macro F1 score of 0.9741 with an absolute False-Negative Rate (FNR) of 0.00%. On an independent external validation set (N = 1015) presenting severe domain shift, TAM-Chain maintains superior stability and classification performance (Macro F1 = 0.7026) by adaptively adjusting the expected stopping step and triggering specialist referrals, significantly outperforming single-magnification baselines. Conclusion: The TAM-Chain framework proves to be a highly effective, safe, and adaptable solution for digital pathology workflows, successfully harmonizing automated diagnostic efficiency with stringent biological safety.

Industrial recommendation systems typically operate as a cascade of retrieval, pre-rank, and fine-rank, but these stages are usually trained and served as separate models, causing repeated user-sequence encoding, isolated optimization, and duplicated engineering effort. Building on OneTrans' model-level unification, we present OneTrans-V2, one Transformer that unifies the entire cascade. It encodes the user behavior sequence once as a shared context while preserving stage-specific candidate features and computation. Joint training lets the three stages reinforce one another and enables in-model knowledge distillation from fine-rank to pre-rank. We scale the shared backbone with sparse mixture-of-experts (MoE), which increases capacity with bounded activated computation, and stabilize scaling with $\mu$P-style parameterization. To consolidate objective-specific retrieval channels, we introduce Decision-Conditioned Generative Retrieval (DCGR). DCGR predicts a decision prefix describing the upcoming interaction and generates items conditioned on it, allowing business objectives to steer a single generative process. Finally, Sequence-Native Training (SNT) organizes training around each user's lifelong behavior sequence and amortizes its encoding across exposures. Deployed across all three stages of a large-scale industrial recommendation system, OneTrans-V2 improves gross merchandise value (GMV) by 9.74% and, with a co-designed serving stack, delivers $3.2\times$ the throughput of the cascade it replaces under the same hardware budget.

Massive Internet of Things (IoT) networks operate with short packets whose reliability is limited by finite block- length (FBL) effects, while remote deployments increasingly rely on Low Earth Orbit (LEO) satellites for backhaul connectivity that is sensitive to atmospheric attenuation. In this paper, we pro- pose a unified end-to-end framework for satellite-assisted massive IoT networks that jointly models uplink FBL random access, sensing assisted satellite backhaul, and worst user broadcast downlink transmission. Uplink reliability is characterized using stochastic geometry, while atmospheric sensing and conservative SNR margins enable FBL-safe backhaul adaptation. Numerical results reveal an optimal uplink access probability due to the tradeoff between spatial reuse and FBL reliability, and show that sensing assisted backhaul margins significantly improve robustness against attenuation uncertainty.

Large language models can interpret natural lan- guage, yet robust decisions remain challenging. Jev-like models expose structured choices, but these interfaces do not directly provide numeri- cal values at a requested precision. We propose NUMERICJEV, a training-free numerical decod- ing algorithm that enables numerical output from any LLM with a Jev-like structured-choice in- terface. Surprisingly, on our arithmetic bench- mark, it outperforms direct selection from a can- didate list containing the correct answer by 2.93 percentage points (Figure 1). Our motivation comes from the observation that numerical range selection is itself a decision problem that Jev- like LLMs can address. NUMERICJEV recur- sively refines a range through a multiway deci- sion tree while retaining the original question in context, without parameter updates or hidden- state access. On a 100-value grid, a ten-way tree requires only two decision rounds. Range- normalized MAE is 1.84% versus 5.18% for di- rect choice. A separate three-date historical- index study yields 4.58% mean relative recall er- ror and 0% readout error when the value is sup- plied. Code is available at https://github. com/Bring-AI/jev-numeric.

Coding-agent approval interfaces bind a human decision to a command or tool call, while developer tools execute the transitive workflow that invocation activates. Package installation can run lifecycle hooks and write files; an MCP call can exercise network authority. We call the resulting record-coverage failure approval laundering: the durable record names the entry invocation but omits effects exercised by its workflow. We present the first systematic security analysis of this record-to-closure relation in agent systems. We formalize closure-bound approval over six effect classes and derive an information limit: identical policy-visible fields can require different effect-specific decisions, so no record-only policy can guarantee both. The Approval-to-Action Security Benchmark binds approval objects and decision-time metadata to post-execution evidence. Across 111 fixed approval-object/trace pairs, residual records fall from 40 under explicit fields to 17 with command semantics and 13 with decision-time metadata. Across 11 fixed-SHA executions, the ladder reaches zero metadata residuals; two exact mappings recur across three product frontends. For prospective recovery, effect-bound records commit frozen, source-backed predictions and provenance before authorization. On 17 prespecified holdout workflows, predictions achieve 0.926 macro recall and 0.941 macro precision; binding them cuts residual effects from 10 to 3. A Claude Code PreToolUse integration carries the frozen record through the permission path without automatic approval. These results establish approval laundering as a measurable, recurrent record-coverage failure despite truthful invocation identity. They motivate binding each invocation before authorization to a source-backed prediction of its workflow's transitive effect boundary and preserving that binding with the decision.

Multi-step tool-calling LLM agents rely on host runtimes to preserve state across turns. When a runtime carries an external tool return into later model inputs, providers meter it again. An admitted malicious or compromised tool can thereby convert untrusted data into recurring victim-billed processing without victim credentials or local runtime privilege. We call retained content persistent billable state and formalize the host's decision over whether and how it enters later billable context as the persistent billable-state boundary. We present the first systematic security study of this post-admission lifecycle. We derive six denial-of-wallet attack vectors and build DOW-BENCH, an end-to-end harness evaluated across six model families. Across 243 executions, usage telemetry shows that the maximum per-session cumulative input reaches 14,293x the session's first-call input. Controlled history-policy reruns isolate raw retention's contribution: retaining raw history increases mean effective session cost by 21.2-35.9%. Compression succeeds on 10/12 and 11/12 history-dependent tasks, versus 2/12 under deletion for each provider. To govern this boundary, we combine deterministic history transformation with four host-side invariants that bound prompt mass, context growth, recursive opportunity, and cumulative spend before reingestion. The kernel contains every recurring attack in the 123-evaluation replay corpus. Across 24 Mistral Small 4 workflows, a progress-authorized policy achieves 22/24 oracle-verified task successes with no pre-completion interruptions, versus 13/24 under a fixed cap. Only 71 of 3,830 scanned MCP server and transport repositories expose any code-visible safeguard proxy, and none cover all four safeguard families. These results establish persistent billable state as a first-class security object and pre-reingestion as its host-owned control point.

We prove that every character on a commutative complex complete Hausdorff locally multiplicatively convex algebra, not necessarily unital, is bounded on bounded sets. Consequently, every character on a commutative complex Fréchet–Arens–Michael algebra is continuous, giving an affirmative answer to Michael's problem. In the Fréchet case, each character is bounded by one seminorm from any increasing defining sequence of submultiplicative seminorms.

We investigate the optical and dynamical properties of a rotating black hole in scalar–tensor–vector gravity (STVG) surrounded by perfect fluid dark matter (PFDM). Starting from the static STVG–PFDM geometry, we consider a Kerr-like rotating extension characterized by the spin parameter $a$, the STVG coupling $\alpha$, and the PFDM parameter $\lambda$. We first examine the horizon structure and a radial effective mass function, then analyze null geodesics and unstable spherical photon orbits. We use these results to construct the black-hole shadow and study its size, distortion, and dependence on model parameters and observer inclination. We then compare the predicted angular shadow diameter with the Event Horizon Telescope observations of M87$^*$ and Sgr~A$^*$ in the $(a,\alpha)$ parameter space for representative values of the PFDM parameter. The comparison shows that the PFDM contribution can shift the parameter-space region compatible with the observed shadow diameter, while the shadow size is generally less sensitive to spin than to deformation. We further estimate the Hawking energy-emission spectrum in the high-frequency geometric-optics approximation, using the shadow radius as an effective absorption scale. Finally, we study the quasinormal-mode spectrum in the eikonal limit through the correspondence between unstable photon orbits and ringdown frequencies. The numerical results recover the expected Schwarzschild limit and show a clear separation between the prograde and retrograde modes as the spin increases. The combined analysis provides a consistent optical, energy emission, and ringdown characterization of the rotating STVG–PFDM geometry.

The recent emergence of Time Series Foundation Models (TSFMs) has significantly advanced multi-step forecasting performance, enabling accurate predictions over extended future horizons. However, existing TSFMs often suffer from significantly inherent uncertainty, which typically manifests as derived forecast branches emerging at each time step and spreading to subsequent steps; different forecast branches often exhibit varying forecasting performance, thereby undermining the credibility of TSFM forecasts. In this paper, we propose the Slicing-Graphing-Alignment (SGA) method to quantify the uncertainty of multi-step TSFM forecasts. The proposed SGA first characterizes the topology of all potential forecast branches using a directed acyclic graph, such that the graph complexity bounds the uncertainty of multi-step forecasts, and then precisely measures the graph complexity by integrating both topological information and TSFM-inherent stochasticity. Experimental results conducted on 11 TSFMs and 27 datasets demonstrate that (i) SGA achieves the best performance when ranking predictive errors with uncertainty estimates; (ii) SGA works with a more extensive and more precise sampling coverage than those of existing UQ methods, deriving a quantification mechanism fundamentally different from those of established ones; and (iii) larger model scales of TSFMs correlate with lower uncertainty estimates of multi-step forecasts, suggesting another empirical scaling law for uncertainty quantification of multi-step TSFM forecasts.