Papers

We show that the spectral radius introduced by Shalit and Shamovich uniquely determines the underlying operator space structure: If E_1 and E_2 are operator space structures on C^d such that the corresponding spectral radii \rho_{E_1} and \rho_{E_2} agree on every d-tuple of operators, then the identity map is completely isometric. This answers a question of Scherer, Shalit and Shamovich. Moreover, we obtain an analogous result for the minimal spectral radii, and showcase an application to the completely bounded isomorphism problem for algebras of bounded non-commutative functions on operator space unit balls.

Recent studies suggest that not every token needs to pass through all Transformer layers, motivating token-level adaptive models that selectively skip layers to reduce computation. Our experiments show that these execution choices also affect safety: existing token-level adaptive reasoning models exhibit higher harmful-response rates than their reference backbones. The safety effects depend on which layers are skipped and whether skipping occurs during prompt processing or answer generation. We further find that recognizing harmful requests and producing refusals depend on different layer-wise computations. We introduce SafeDepth, a lightweight, plug-in framework that uses selective layer execution to improve both safety and efficiency. SafeDepth learns to retain computations that support safe responses and bypass those that contribute to unsafe generation. A router selects layer execution based on token representations, layer position, and inference phase, while an adapter supports the skipped paths. We jointly train these modules to reduce computation and harmful responses while preserving performance on benign tasks, targeting a better safety-efficiency trade-off. The pretrained backbone remains frozen throughout, requiring no additional pretraining. Experimental results on Llama-3-8B-Instruct show that SafeDepth reduces computation relative to full-depth inference while largely preserving task performance. Compared with FlexiDepth, it lowers unsafe-response rates across all five harmful-request benchmarks, with the largest absolute decrease on HarmBench-HJ (from 55.44% to 25.25%), while reducing the XSTest false-refusal rate from 12.0% to 4.0%.

Synthetic data are increasingly used to scale LLM training, yet more synthetic data do not necessarily produce better models. Useful synthetic data must add information relevant to the target task without introducing errors that offset their benefit, and the value of an example can change as the training set grows. We develop a linear theory that characterizes this tradeoff and determines where synthetic data are useful, how much should be added, and the marginal value of adding one example to an existing set. The analysis shows the conditions when input coverage alone is sufficient and when synthetic errors must also be considered. Guided by these results, we introduce Training-Aware Target Coverage (TATC), a synthetic data selection method for LLM fine-tuning. TATC identifies candidates whose training effects are beneficial to the target task and selects among them to expand coverage of target-relevant directions not already represented by the available data. Experiments on text and image data verify the linear theory. With mathematical reasoning tasks, TATC selects synthetic solutions for fine-tuning Qwen2.5-Math-1.5B-Instruct and outperforms alternative synthetic-data selection methods on GSM8K across selection budgets. In summary, we provide a principled approach to synthetic data selection by quantifying and maximizing its value to the target task.

Studies suggest that protoplanetary disks around stars with high carbon-to-oxygen (C/O) ratios can produce terrestrial planets with carbon-dominated compositions instead of silicon-dominated ones. While previous work studied the evolution of these disks and the planets that form within them, none analyze in detail how the differences in the surface density profiles of these disks could affect the architectures and iron and siderophile contents of exoplanetary systems. Here, we present a new study that uses the N-body integrator REBOUND and data from a sequential dust condensation model to simulate the formation of planets in systems with varying C/O ratios. We find that bulk density could be used to distinguish between silicon-rich and carbon-rich planets, though it may not be a reliable metric on its own.

Video generation has rapidly progressed from short, low-quality clips to high-resolution, long-duration sequences with complex spatiotemporal dynamics. Despite strong generative priors learned through large-scale pretraining, pretrained video models often fail to reliably follow human intent, maintain temporal coherence, or satisfy physical and safety constraints. Compared with image and text generation, alignment in video generation presents unique challenges, including error accumulation over time, motion-appearance coupling, multi-objective trade-offs, and limited supervision for temporal properties. These challenges motivate systematic post-training strategies that adapt pretrained models without retraining them from scratch. In this survey, we present the first comprehensive review of post-training and alignment in video generation models. We frame post-training as a unifying framework and distinguish between implicit alignment and explicit alignment based on how alignment signals are enforced. From this perspective, we organize existing approaches into four broad categories: supervised fine-tuning methods, self-training and distillation methods, preference- and reward-based methods, and inference-time methods. This taxonomy provides a coherent view of how alignment signals shape model behavior across both training and deployment. Beyond methodological advances, we review commonly used datasets, benchmarks, and evaluation practices, and discuss open challenges such as scalable reward design, long-horizon temporal consistency, stability-expressiveness trade-offs, and safety-aware generation. This survey aims to provide a structured conceptual foundation and practical guidance for advancing controllable and reliable video generation models.

This work introduces a hyperbolic relaxation system designed for the simulation of kinetic equations in the low-Mach number limit. The methodology is built upon a micro-macro decomposition of the scaled BGK model, which reformulates the kinetic distribution function into a coupled system consisting of a macroscopic equilibrium part and a microscopic non-equilibrium remainder. By projecting the microscopic deviations onto a set of orthogonal polynomials, we derive a closed moment relaxation system. The resulting system is a version of Grad's 13 moment system with a linear hyperbolic part and a relaxation adapted to the incompressible limit. We prove the model's structural stability in the incompressible Navier-Stokes limit. Moreover, we develop a high order Asymptotic-Preserving (AP) numerical framework using Implicit-Explicit (IMEX) Runge Kutta schemes for temporal accuracy and finite difference WENO reconstructions as well as central difference approximations for high order spatial resolution. The proposed scheme ensures uniform stability and consistency across different physical regimes, automatically degenerating into a consistent high order discretization of the incompressible thermal Navier-Stokes limit as the scaling parameter vanishes. Numerical experiments in one and two dimensions corroborate the theoretical findings, demonstrating significant reductions in computational cost and robust performance across a wide range of Knudsen and Mach numbers.

Fine features in the Fermi surface geometry, such as nearly cylindrical or nearly paraboloidal strips or local flattenings, are examined as regards their effect on the electronic, mainly galvanomagnetic, properties of metals. It is shown that under certain conditions, these features may significantly change the way a conventional normal metal or a layered structure with metallic conductivity responds to high- frequency external disturbances. All of the effects considered appear to be very sensitive to the disturbance propagation direction and/or to that of the external magnetic field. Experimental possibilities of observing the described effects are discussed.

Vision-Language Models (VLMs) enable video annotation at scale, but costs accumulate quickly: processing a typical 60-second short-form video at one frame per second requires millions of tokens. To reduce costs, researchers rely on heuristics such as sampling a subset of frames, compressing videos into image grids, or using only a single modality. However, it remains unclear which heuristics save cost, and whether they preserve the downstream conclusions these annotations enable. To address this gap, we conduct a systematic evaluation of these heuristics using short-form videos, on two computational social science (CSS) tasks: sentiment and topic classification. We evaluate each configuration along three axes the literature typically treats separately: classification accuracy, validity of downstream inference, and per-video token cost. First, we find that accuracy and validity diverge: the highest-accuracy configuration can produce wrong conclusions. Second, modality value is not guaranteed: text alone can yield strong performance, indicating that adding modalities can add cost without adding signal. Finally, we find that cost can be decoupled from video length when annotating short-form videos: a single $2\times8$ image grid built via simple shot-transition detection approaches full-video understanding ($\kappa$ within~.05), at $\sim 15\%$ of the token cost. Based on these findings, we derive guidelines that can enable cost-aware VLM annotation in CSS.

Let $A$ and $B$ be polynomials with integer coefficients. We study nonzero integer solutions of $$y\mid A(x),\qquad x\mid B(y),$$ using quotient transformations that may change the polynomial pair. We call this process congruence jumping. We establish a general reciprocal-polynomial rule governing such jumps, without coprimality, monicity, or unit assumptions, and give exact criteria for when the resulting polynomial states can be normalized integrally. Companion-surface identities provide a mechanism for constructing infinite integral quotient chains, including an explicit mixed-degree example. The quadratic case is considerably more rigid. We obtain a quantitative denominator bound for finite chains, classify the exceptional nonconstant one-sided infinite chains with nonintegral conic parameter, and show that changing quadratic states reduce to ordinary Vieta dynamics on a fixed conic. We further construct a genuinely nonunit recurrent four-cycle with infinitely many positive integral points and show that its dynamics admits a uniform Pell-type linearization. A motivating nonunit divisibility system is analyzed through Pell orbits and changing-state ladders. Finally, an independent relation-lattice criterion reduces certain solution sets to a finite divisor search.

Motivated by accessing crop plots in a field, where each crop plot can only be visited by a given pair of entry/exit points (we have three different types, each having four cases), we study the corresponding Minimum Spanning Tree (MST) problem of such a planar set of axis-aligned unit squares. It turns out that this crop plot distance does not satisfy triangle inequality, even though the whole setup of the problem is geometric. Hence additional care must be taken. The main results of this paper are as follows: (1) we prove that computing the MST of a set $P$ of unit squares under the crop plot distance is NP-hard, (2) the MST of $P$ can be approximated with a factor-4 approximation.

Forecasting how a newly emerged patent technology will be reused is central to technology intelligence, but reuse-pattern labels do not exist in advance: they must be constructed from the trajectories themselves, and how they are constructed determines what a forecast means. We study $201{,}710$ novel patent technologies (first-time IPC code pairings, USPTO 2002–2022). Our primary labeling applies $k$-means in the latent space of a GRU autoencoder trained on the $20$-year reuse trajectories, using no hand-crafted features; to our knowledge this is the first use of a learned sequence representation for this task. Seven emergence-time features, observable in a technology's first year, recover these labels at a one-vs-rest macro ROC-AUC of $0.914$, but the calendar year of emergence alone reaches $0.874$. A replication on technologies observed for ten full years, none of them right-censored, indicates that this calendar-year effect mainly reflects change over time in what was patented. Separately we cluster the emergence-time features themselves, after Fractal Autoencoder feature selection. That emergence-profile partition agrees with the GRU-based labels only marginally above chance (Adjusted Rand Index $\approx 0.04$), so a partition of emergence-time features is not a reuse-pattern taxonomy and should not be read as one. On a trajectory-shape task following the published construction, GBDT reaches $0.831$ with all seven features and $0.740$ with the selected subset; the published $0.728$, from a different corpus and labeling, is a reference point rather than a benchmark. Two features are additionally left-truncated for the earliest cohorts, which we quantify.

Editing a chest radiograph requires completing the requested change while preserving unrelated content. We study a latent diffusion editor with an instruction-independent source trajectory and an instruction-conditioned editing trajectory. A learned gate mixes their post-sampler candidates at each executed step, and a separate image-space mask composites the decoded proposal with the source. On 2,400 MIMIC-derived requests, 2,244 outputs met the joint target, preservation, quality, and coverage rubric (93.5%), and target completion was 97.4%. Joint validity exceeded a matched composition-only control by 1.7 percentage points (paired patient-cluster 95% interval, 0.6–2.8). At a fixed learned mask, the learned-gate proposal improved joint validity by 1.6 points (0.8–2.4); at a fixed learned proposal, the learned mask improved it by 2.6 points (1.7–3.5). Across three training seeds, mean joint validity was 93.5% with a 0.3-point sample standard deviation. A blinded 240-request assessment yielded adjudicated joint validity of 93.3% for the full editor and 91.7% for composition only. Protected-region mean absolute error decreased from 0.0190 in the raw proposal to 0.0075 after composition. These findings distinguish recurrent-gating effects on the proposal from preservation through final composition in the assessed cohort.

We prove that if $F$ is a noncyclic free group, $R\triangleleft F$ and $S\le F$, then the inclusion $R'\le S'$ implies $R\le S$. Thus the normality hypothesis on the second subgroup can be omitted from the Auslander–Lyndon theorem. No restrictions are imposed on ranks or indices.

Antipodal self-duality (ASD) is a remarkable property that relates an amplitude to itself, after performing a suitable kinematic map and reversing the letters of the symbol (more precisely, acting with the antipode of the Hopf algebra of multiple polylogarithms). ASD has been seen in only one process in planar $\mathcal{N}=4$ super-Yang-Mills theory, and its physical origin is unknown, motivating a search for ASD in other contexts. Recently, ASD was found to hold for square fishnet integrals in a strongly-deformed version of planar $\mathcal{N}=4$. In this paper, we investigate the properties of polynomials in ladder integrals under the ASD transformation that leaves the square fishnet invariant. Our basic building blocks are determinants of certain matrices of ladder integrals, that are labeled by partitions or Young diagrams, and automatically obey the Steinmann relations. We employ integrability-based representations of such determinants, which are essentially matrix-model integrals, and the theory of symmetric polynomials to find many more ASD quantities – linear combinations of determinants whose coefficients are expressed using the combinatorics of partitions. As a byproduct, we provide an alternate proof that square fishnet integrals obey ASD.

This paper develops a distributed adaptive neural interval observer for unknown nonlinear systems with locally incomplete measurements. Each sensor node constructs lower and upper state estimates using its local output and neighboring observer information, while unknown nonlinear dynamics are approximated by adaptive neural models. A distributed adaptation mechanism guarantees bounded estimation and weight errors, whereas a cooperative realization preserves the componentwise interval property. To enhance neural-weight convergence without requiring persistent excitation, a finite experience-replay integral concurrent-learning mechanism is incorporated into the adaptation law. For non-Metzler error dynamics, a Sylvester-based coordinate transformation is introduced to recover a Hurwitz–Metzler distributed realization. The theoretical developments are validated through a nonlinear distributed estimation example.

A robot may lose sight of an object it must later retrieve, need to recall what a person demonstrated earlier, or track which steps of a task it has already completed. Current vision-language-action (VLA) policies often fail once the information needed for action disappears from the current observation, making memory critical for long-horizon robot behavior. Existing approaches typically provide longer histories or learn implicit memory from observation-action trajectories. But action supervision tells a policy how to act, not what to remember: it does not specify which past facts should persist or how they should change as new evidence arrives. We therefore separate maintaining an evidence-grounded account of the past from learning how to act on it. This insight motivates Explicit Concept Memory (ECoMEM), which represents task-relevant history with a reusable library of grounded concepts. An evidence-based Writer selects and updates these records, while a learned Reader turns them into memory tokens that directly condition the VLA. Across 16 RoboMME tasks, ECoMEM leads the evaluated robot policies on 15 tasks. On two new real-robot tasks, the same memory library either transfers directly or requires only one new concept, achieving 86.1% success versus 8.6% for a no-memory VLA. These results show that explicit concepts provide a reusable and extensible memory interface for robot control. Project website: https://ecomem.github.io/

This paper develops an event-triggered fixed-time integral reinforcement learning framework for optimal control of unknown nonlinear systems. An integral data-driven identifier is first used to reconstruct the unknown dynamics, after which an inverse-optimal formulation is employed to construct a fixed-time running cost. A learning law satisfying the practical fixed-time property is then derived. Previously collected data, or data obtained during a finite excitation interval, are stored in an experience-replay buffer and incorporated into the weight-update law. This avoids the persistent-excitation condition, which is often difficult to satisfy in practical operation. To reduce communication and control updates, an event-triggered mechanism is introduced. The paper shows that, under the event-triggered implementation, the closed-loop system still achieves practical fixed-time stability, while the proposed triggering rule guarantees the exclusion of Zeno behavior. Finally, a nonlinear example is presented to verify the theoretical results developed in the paper.

Sensor noise is a fundamental barrier to low-flux astronomical imaging and spectroscopy, where the ideal sensor would unambiguously distinguish individual photon arrivals. While optical semiconductor arrays can reach single-photon sensitivity, comparable performance in the infrared has largely required superconducting detectors. These must be operated at temperatures near absolute zero and require substantially more power, introducing major system-level challenges. HgCdTe avalanche photodiodes offer a semiconductor alternative by amplifying charge before readout, but dark current and tunneling effects have limited their use in the faintest regimes. Here we demonstrate single-photon-resolving operation in a megapixel-format HgCdTe linear-mode avalanche photodiode array operated at conventional cryogenic temperature. Avalanche gain raises photon-induced steps in non-destructive up-the-ramp data above the readout-noise floor while leaving the dark signal largely unamplified, with a false positive rate of approximately 2 false counts per thousand reads per pixel. These results establish LmAPDs as a promising route toward infrared photon-counting focal planes for future low-background astronomical observatories.

We prove that the graph of a standard one-dimensional Brownian motion, $\Gamma_B=\{(t,B_t):t \in [0,1]\}$, is almost surely not conformally removable. This resolves the question left open by Doherty and Miller in their study of the Sobolev removability of the Brownian graph~\cite{DM26}. We also construct non-removable $\alpha$-Hölder graphs for every $\alpha \in (0,2/3)$, including the previously open range $\alpha \in [1/2, 2/3)$. Together with the known removability result for $\alpha>2/3$, this identifies $2/3$ as the threshold for conformal removability of Hölder graphs.

Contextual security defenses prevent AI agents from taking rogue actions by synthesizing a task-specific policy and enforcing it on the agent's tool calls. In multi-step tasks, however, which actions are valid often depends on what the agent has already done and learned. We present Sapien, a policy engine for enforcing stateful contextual policies. A Sapien policy specifies permitted tool-call sequences using a regular expression extended with stateful predicates, deferred policy generation, and scoped semantic checks. We show that Sapien stays within a few percent of an unconstrained agent's utility. Even if the agent is fully hijacked, Sapien's policies rule out 93-95% of attacks on AgentDojo and 62-85% on Toolathlon (twice as many as tool allowlists on long-horizon tasks).

This chapter surveys terrain visibility models, algorithms, and applications. It introduces basic definitions, from line-of-sight, single-viewpoint viewsheds to cumulative and total viewsheds, on both Triangulated Irregular Network (TIN) and regular grid terrains. Reviews exact and approximate algorithms and highlights key application domains including archaeology, visual exposure to greenery, scenic route management, and land conservation.

Objective: To assess the accuracy and efficiency of a large language model (LLM) using two prompt strategies to extract structured data from ophthalmic diagnostic PDF reports. Methods: Twenty deidentified reports across four types (Visual Field, OCT Glaucoma Overview, OCT retinal nerve fiber layer Single Exam, and OCT Thickness Map; n = 5 each) were processed using two GPT-4o-assisted pipelines and compared with a reconciled manual ground truth. Schema-Constrained used Structured Output mode with a predefined JSON Schema; Prompt-Only used a detailed instruction prompt followed by Python conversion to JSON. Outcomes were value accuracy, formatting accuracy, and extraction time. Results: Schema-Constrained value accuracy was 100.00% for Visual Field and RNFL Single Exam, 97.45% for Glaucoma Overview, and 98.00% for Thickness Map; Prompt-Only achieved 100.00% across all four report types. Formatting accuracy was 100.00% for Schema-Constrained across all report types and 100.00% for Prompt-Only except RNFL Single Exam (90.14%). Mean extraction time was 56.51 s per report for manual review versus 5.04 s for Schema-Constrained and 4.70 s for Prompt-Only, an approximately 92% reduction. Conclusions: In this small proof-of-concept dataset, general-purpose LLM-assisted pipelines extracted structured data from ophthalmic diagnostic PDFs with high accuracy and substantially reduced processing time. Prompt-Only achieved the highest value accuracy, while Schema-Constrained produced schema-compliant output with 100% formatting accuracy. These complementary strengths support further evaluation of hybrid, validation-aware workflows for research and clinical data abstraction.

Machine learning interatomic potentials (MLIPs) have advanced rapidly in recent years, yet the majority of models remain semilocal in nature and neglect long-range electrostatic interactions. A growing number of long-range models have emerged to address this limitation, but systematic benchmarks comparing their performance on physically realistic systems remain scarce. In this work, we assess three long-range MLIPs – MACE-POLAR, MACE-LES, and LOREM, against a short-range baseline MACE model, on their ability to capture long-range Coulombic interactions, progressing from idealised synthetic point-charge systems to first-principles data on realistic crystal structures. This progression allows us to isolate model's capability to learn electrostatic interactions from the many competing energy contributions, such as dielectric screening and exchange-correlation, that are present in DFT total energies. As a physically motivated benchmark system, we focus on strontium titanate SrTiO$_3$ with Sr–O Schottky vacancy pairs, a material in which long-range charge interactions play a central role and which serves as a natural stepping stone towards the study of charged polarons and other electronic and optical properties. Building on this benchmark, we further examine oxygen vacancy migration in the presence of the Sr–O Schottky pair, using climbing-image nudged elastic band calculations and molecular dynamics to obtain activation barriers as a function of the vacancy pair separation, providing further extrapolation test of each model's ability to capture the electrostatic effects that govern defect transport.

We consider the estimation of drift, diffusion, and noise covariance from discrete observations of stochastic differential equations driven by Gaussian processes. For a fixed observation horizon $T>0$ and a known initial state $x_0\in\mathbb R$, we study \begin{equation*} dX_t=a(X_t)\,dt+\sigma(X_t)\,dZ_t^{\beta,f}, \qquad X_0=x_0,\quad 0\leq t\leq T. \end{equation*} \smallskip\noindent Here $a:\mathbb R\to\mathbb R$ is the drift coefficient, $\sigma:\mathbb R\to(0,\infty)$ is the diffusion coefficient, and $Z^{\beta,f}$ is a centered Gaussian process from the weighted sub-fractional Brownian family, with covariance \begin{equation*} \operatorname{Cov}(Z_s^{\beta,f},Z_t^{\beta,f}) =\int_0^{s\wedge t} f(r)q_\beta(s-r,t-r)\,dr, \qquad 0\leq s,t\leq T. \end{equation*} \smallskip\noindent Here $s\wedge t=\min\{s,t\}$. The temporal weight $f:[0,T]\to[0,\infty)$ is measurable, bounded, and positive almost everywhere, and $\beta\in(0,2)$ is the covariance exponent. For $u,v\geq0$, the kernel is $q_\beta(u,v)=[u^\beta+v^\beta-(u+v)^\beta]/(1-\beta)$ when $\beta\ne1$. Its continuous extension at $\beta=1$ is $q_1(u,v)=(u+v)\log(u+v)-u\log u-v\log v$, with $0\log0=0$. Using the Euler approximation, we reconstruct the Gaussian driving increments from observed transitions and use their joint density to obtain a trajectory likelihood. Neural and radial-basis representations model the drift, diffusion, and normalized temporal weight, while a likelihood profile estimates the covariance exponent and diffusion scale. We compare the method with two neural alternatives on the same simulated trajectories in twenty coefficient settings.

Weather Jiu-Jitsu is a control paradigm for extreme climatological events, inspired by chaos theory. As a proposition, small, precise, targeted, and cost-inexpensive perturbations can redirect trajectories of a large dynamical system. This strategy has been demonstrated analytically in the Lorenz-63 system, where a naturally chaotic trajectory switching between two attractors can be confined to a single attractor, indefinitely, via arbitrarily small perturbations. This paper examines the feasibility of Microsoft's Aurora – a 1.3 billion parameter global atmospheric model – as a test bed for this strategy. This paper explores three questions: (1) Is Aurora a reliable enough simulation environment to serve as a meaningful testbed? (2) Are the perturbations required to redirect its trajectories small enough to be physically plausible? (3) Does Aurora's learned latent space (the parametric estimators on climatological attributes) yield any apparent, structured, and/or perhaps interpretable features that can convey a geo/atmospheric response to initial conditions? We find evidence consistent with all three: Aurora's modeled trajectories respond to perturbations beyond measurement drift, the perturbation magnitudes required are small relative to the model's own forecast uncertainty, and its latent representations exhibit directional structure that responds to Jiu-Jitsu-type interventions, even though that structure does not separate extreme from normal states outright. These results should be read as feasibility diagnostics rather than a demonstration of control: we do not implement or test an actual steering intervention on Aurora, and several of our findings, particularly around the model's latent-space geometry, are exploratory.

Enterprise information is represented through artifacts shaped by applications, projects, technologies, organizational boundaries, and local requirements. These structures accumulate over time, creating representational complexity that must be maintained by the enterprise and interpreted by information consumers and AI systems. This paper introduces Enterprise Representation Simplification (ERS) as reducing unnecessary representational complexity while preserving required information within a defined scope, and Enterprise Representation Complexity (ERC), a representation-neutral model for comparing complexity across representation states. ERC characterizes representational extent through four dimensions: Representation Objects, Interactions, Behaviors, and Supporting Sources. Objects, Interactions, and Behaviors form dependent categories, while Supporting Sources characterize representation exposure. ERC is defined at representation and task levels, enabling comparison and distinguishing architectural simplification from retrieval optimization. The paper develops two consequences of ERS. First, representational structures create lifecycle obligations for maintenance, governance, dependencies, change, enhancement, and operation. An economic model distinguishes recurring global representation cost, recurring task-level cost, and one-time transformation cost, enabling evaluation over a defined time horizon. Second, reductions in task-level ERC reduce the representational extent an AI system must identify, relate, and interpret. Text-to-SQL research provides evidence that reduced schema and reasoning complexity can improve reasoning accuracy. ERC is not a universal complexity, performance, or cost metric. It provides measurable architectural variables for comparing representational alternatives, transformation effects, economic outcomes, and AI reasoning performance.

Recent advances have linked mixing in porous media to the deformation of infinitesimal fluid elements. However, these Lagrangian frameworks generally neglect or simplify interactions with solid surfaces. We consider transport of thin solute blobs (strips or sheets) near single generic obstacles, in particular along separation lines (separatrices) which connect to stagnation points at solid boundaries. In this case, we demonstrate that the coupling between flow and diffusion is analytically tractable. We provide a complete theory for scalar mixing near upstream stagnation points, which we validate by numerical simulations. We identify a mixing time scale $t_B \sim Pe^{1/3}$, where $Pe$ is the Péclet number, which controls whether scalar decay is driven by fluid stretching or by interaction with the solid boundary. Asymptotically, for times $t < t_B$, we find that the maximum concentration $c_{\rm max}$ decays as $t^{-5/2}$ and that the width $\sigma$ grows like $t^{1/2}$. For $t > t_B$, we find exponential decay of $c_{\rm max}$ and constant width $\sigma \sim s_B \sim Pe^{-1/3}$, where $s_B$ is a mixing length scale distinct from that which appears in shear flows. The asymptotic scalings of $c_{\rm max}(t)$ and $\sigma(t)$, and their dependence on $Pe$, are universal to no-slip stagnation points and qualitatively different from stagnation points in open flows.

We introduce source-anchored algebraic amenability for Hausdorff ample groupoids, a Følner condition formulated in the Steinberg algebra and localized at compact open subsets of the unit space. The unanchored bisectional condition is exactly algebraic amenability of the Steinberg algebra, whereas the anchored version recovers ordinary amenability for one-unit groupoids and detects behavior invisible to the unanchored theory. We establish permanence under isomorphisms, open invariant reductions, disjoint unions, finite products, directed unions and AF approximations, while arbitrary subgroupoids need not inherit the property. For countable transitive discrete groupoids, infinite unit spaces are amenable through range escape, whereas finite unit spaces are amenable precisely when their isotropy groups are. This yields a characterization of hereditary algebraic amenability in terms of isotropy.

In this paper we define the ascending number and bridge number for virtual and welded spatial graphs. We prove that the former admits a lower bound in terms of the latter. This relationship allows us to compare different notions of unknotting virtual spatial graphs by crossing changes.

A correctly governed LLM agent can reach a state in which neither continuing execution nor automatically halting is admissible: the system has detected a persistent failure of its observability or drift-detection layer, but cannot itself decide who has the authority to resume, deny, or recalibrate the deployment. We call this an identity-bound governance event and formalise the mechanism that resolves it. We introduce the Accountability Proof Block (APB): a system-constructed evidence block, a human-supplied decision block, and an ed25519 signature binding both to a registered principal. The system cannot forge the signature, and the principal cannot alter the evidence undetected. We prove four theorems: Protocol-Bounded Governance Completeness, Non-Repudiability, Impossibility of Anonymous Re-Authorization, and Finite-Time APB Construction Termination. The implementation uses RFC 8785 JSON canonicalization and a UUID4-based replay predicate. Empirically, governance completeness holds over 3,812 halt events with zero unresolved cases; the verifier detects 100% of 1,800 attacks across 9 adversarial vectors; a k-of-n multi-principal variant shows 0 false acceptances in 2,000 single-key capture attempts. A study of six open LLMs finds the drift threshold T* stable within model (sigma/T* < 2%) but varying across models, refuting size-monotonicity: the largest model did not drift. T* must therefore be measured per deployment, and the APB is the vehicle by which that threshold yields accountable authority transfer.