While machine learning (ML) software necessitates effective quality assurance, ML engineers still encounter silent semantic faults, such as imbalanced datasets, that degrade prediction performance without apparent symptoms. These faults are typically detected after expensive training cycles, causing significant resource waste. We propose a data-informed static analysis technique to detect silent semantic faults in ML scripts that use the popular random forest classifier. Our approach extracts ML pipelines into directed acyclic graphs and evaluates them against formalized API contracts to detect structural, data, and hyperparameter faults. Our analysis uses aggregated data properties, enabling fault detection even when datasets are inaccessible due to confidentiality restrictions. We implemented this technique in an open-source tool, dille, and evaluated it on real-world Kaggle notebooks that use the random forest classifier. Our results demonstrate that the tool identifies relevant semantic faults with 91% precision and sub-second runtime overhead, making it suitable for integration into integrated development environments, agentic workflows, and continuous integration pipelines. Our empirical study reveals that 12% to 18% of existing ML notebooks that use the random forest classifier are affected by silent semantic faults, highlighting the immediate practical utility of data-informed static analysis in reducing the burden of ML debugging.

We point out three inaccuracies in paper [M.V. Moreira, T.C. Jesus, and J.C. Basilio. Polynomial time verification of decentralized diagnosability of discrete event systems. IEEE Transactions on Automatic Control, 56(7):1679-1684, July 2011]. First, the authors wrongly claimed that their algorithm for verifying (co-)diagnosability of labeled finite-state automata (LFSAs) did not depend on assumptions. We give an LFSA that is not deadlock-free or divergence-free such that their algorithm cannot correctly verify its diagnosability. Because diagnosability is a special case of co-diagnosability, their algorithm cannot correctly verify co-diagnosability either when LFSAs are not deadlock-free or divergence-free. Second, they wrongly claimed that adding at each dead state an unobservable self-loop can help verifying diagnosability for an LFSA that is not deadlock-free or divergence-free, but this is wrong, because such a modification sometimes changes the diagnosability of an LFSA. Third, they wrongly claimed that their algorithm for verifying co-diagnosability ran in polynomial time. A polynomial-time algorithm unlikely exists, because the problem of verifying co-diagnosability of LFSAs is PSPACE-hard.

Correlated longitudinal noise can be partially converted into common-mode fluctuations in an oddparity two-qubit subspace. We analyze an encoded logical qubit formed by the states in two coupled fluxonium qubits. Projecting the exchange-coupled two-qubit Hamiltonian onto this subspace yields an effective logical Hamiltonian in which the exchange interaction drives XL rotations and the qubit detuning drives ZL rotations. We model correlated two-levelsystem (TLS) noise by using longitudinal stochastic processes with finite memory time and evaluate encoded-gate performance through the average gate fidelity. Within the projected model, positive spatial noise correlation suppresses the differential fluctuation and thereby improves the fidelity of encoded logical gates. We further compare Gaussian Ornstein-Uhlenbeck, Markovian, and randomtelegraph noise models and examine the role of logical dynamical decoupling. These results identify a noise-adapted control mechanism for odd-parity encoded operations in coupled fluxonium devices and motivate future multilevel simulations including leakage and pulse-level constraints.

Needle-free jet injection generates transient internal stress fields that can influence tissue deformation, pain-related stimulation, and cellular-level mechanical responses. However, the penetration mechanics have often been inferred from cavity deformation and interpreted mainly as shear-dominated behavior. In this study, high-speed photoelastic measurements were used to visualize and quantify optically integrated stress responses in a 5 wt% gelatin tissue simulant during penetration by two needle-free injectors with different actuation mechanisms: the Actranza Lab, a pyro-drive injector driven by cartridge-based combustion, and the Biojector 2000, a commercially available CO$_2$-driven injector. A polarization camera operated at 60,000 fps was used to obtain the phase difference and principal stress orientation, allowing evaluation of the photoelastic stress-intensity response and its decomposed normal- and shear-stress-related components. Under the same injection volume of 20 $μ$L, the Actranza Lab formed a narrow, depth-oriented cavity, whereas the Biojector 2000 produced a wider, bulged cavity. In both cases, a clear normal-stress-difference component developed around the cavity. This component became comparable to or greater than the shear-stress component for the Actranza Lab and became dominant during the later cavity-bulging stage for the Biojector 2000. These results show that needle-free jet penetration cannot be described solely by shear stress; instead, injector-dependent cavity dynamics generate multi-component tissue loading. The findings provide an engineering basis for evaluating needle-free injector performance and for designing systems that improve delivery while reducing mechanical burden on tissue.

Peer review in computational fields remains centered on author-written manuscripts, even though the decisive evidence for many claims resides in executable code, data, configurations, and experiment pipelines. This manuscript-first workflow gives authors substantial control over narrative framing while leaving reviewers with limited time to inspect implementation details, reproduce results, or detect unsupported claims. This vision and protocol paper proposes code-first peer review: authors submit executable research artifacts and minimal claim manifests; a venue-controlled AI system builds the environment, executes experiments, audits code paths, maps claims to evidence, and generates a standardized Review Package for human reviewers. The goal is not to replace reviewers or to give authors an automatic writing assistant. Instead, AI serves as review infrastructure that shifts the target of peer review from polished narratives to executable evidence. We formalize a claim-evidence contract, define the Generated Review View and Review Package abstractions, give a worked example, outline a system architecture, and analyze evaluation and governance challenges including AI bias, prompt injection, model instability, auditability, and author appeal.

Relational Event Models (REMs) provide a rigorous framework for analyzing dyadic interactions observed in continuous time, capturing history-dependent dynamics such as triadic closure and reciprocity. Framing REMs through the lens of counting processes embeds the model in a rich theoretical foundation, facilitating its mathematical analysis. While Maximum Likelihood Estimation (MLE) is standard practice for estimating these models, the underlying statistical guarantees rely on specific asymptotic regimes, namely, whether the network size (n), the observational period (T), or both approach infinity. We review the theoretical foundations of such counting-process-based models, formalizing the core assumptions required to achieve asymptotic normality across these different limits. With a specific focus on Cox-type multiplicative models, we detail the circumstances under which these assumptions hold. Supported by simulation studies, we illustrate how structural modeling choices, including temporal windowing and logarithmic transformations, affect empirical coverage and estimator convergence. We thereby derive several guiding principles for specifying such models in realistic contexts, bridging theory and practice.

PyCBC Live is a low-latency search pipeline that identifies gravitational waves from compact binary coalescences and provides alerts for electromagnetic follow-up. This paper presents improvements to PyCBC Live that were implemented for the fourth observing run (O4) of the LIGO-Virgo-KAGRA network, which operated from May 2023 to November 2025. The ranking statistic was enhanced to incorporate time-dependent background modeling using data quality streams and daily updates of the noise model. Follow-up capabilities were improved through refined probability of astrophysical origin calculations, optimized SNR recovery with reduced computational cost, and a method to incorporate Virgo as a sky-map-only detector. An Early Warning search was implemented to detect binary neutron star and neutron star-black hole systems before merger, providing pre-merger alerts with a pipeline latency of 2.5-3.5 seconds and warning times up to 60 seconds before coalescence. The autogating procedure was extended to apply to the full strain buffer rather than individual analysis segments, improving rejection of loud and rapidly successive glitches. Performance validation using the Mock Data Challenge showed sensitivity improvements of factors of 1.7 to 2.3 for the coincident search depending on source mass at an inverse false alarm rate of 10 years, and factors of 1.3 to 1.7 for the single-detector search. For injections in two-detector time, the O4 configuration identified 1979 of 2495 injections with a decisive SNR greater than 6 at a false alarm rate below one per year (79.3%), compared to 1262 (50.6%) with the O3 configuration. For injections in single-detector time, the O4 configuration identified 218 of 1174 injections (18.6%), compared to 170 (14.5%) with the O3 configuration. The search maintained a median latency of 15.94 seconds from merger to candidate upload.

Multicomponent colloidal gels can exhibit mechanical responses that depend not only on interaction strengths but also on the temporal pathway by which their networks form. Here, we use particle-based simulations to investigate the steady-shear deformation of binary colloidal gels assembled by sequential gelation with tunable delay time and dominant interspecies attractions. Although varying the gelation delay produces markedly different quiescent morphologies, ranging from well-mixed networks to coarse shell-core structures, steady shear drives the systems toward structurally convergent, mixed states as quantified by cluster, connected-component, and coordination analyses. This structural convergence, however, does not imply rheological equivalence. The transient stress response remains strongly dependent on gelation delay and interspecies attraction strength. For moderate interspecies attractions, increasing delay enhances the stress overshoot, particularly at high shear rates. For stronger interspecies attractions, initially heterogeneous gels exhibit two-step yielding at low shear rates, indicating distinct deformation and restructuring processes. These results show that sequential gelation can imprint a persistent rheological memory in binary colloidal gels, even when shear substantially erases differences in common structural descriptors.

The formation of bound magnetic polarons (BMPs) is traditionally described using a Gaussian approximation for host magnetization fluctuations. While successful for diluted magnetic semiconductors, this approach fails for ferromagnetic semiconductors like GdN near their Curie temperature Tc, where diverging susceptibility yields unphysical instabilities. We extend the BMP theory beyond the Gaussian approximation by rigorously incorporating cubic and quartic fluctuations of the Ginzburg-Landau-Wilson functional. Two consistent extensions of the Dietl-Spalek framework are presented: (i) a non-local treatment valid for finite spin correlation lengths xi (to first order in lambda) and (ii) a non-perturbative resummation of dominant local fluctuations to a closed exponential form in the strict local limit xi to 0. The latter is justified by a novel polaronic Ginzburg criterion showing that constraint-induced non-localities are suppressed by O(1/N_eff) with N_eff >> 1. Crucially, the theory incorporates variational optimization of the donor orbital size, capturing magnetic self-trapping even above Tc. When applied to GdN (Tc = 55 K), the model eliminates the Gaussian divergence and predicts stable, ferromagnetically ordered BMPs with a non-zero spontaneous spin splitting Delta_0 deep into the paramagnetic phase. For a realistic exchange coupling Jc = 400 meV, the effective polaron ordering temperature reaches T* = 155-160 K. The model further suggests an optimal donor-concentration window near the metal-insulator transition where enhanced dielectric screening maximizes T*. These results establish a microscopic mechanism for persistent BMP-mediated ferromagnetism well above Tc.

Data from large physics collider experiments in Quantum Chromodynamics (QCD) research differ fundamentally from the modalities used in modern foundation models. The heterogeneity of detector readouts and their technology dependence require principled curation for cross experiment AI applications. We present a design framework for AI-ready QCD data to define a unified data structure that accommodates heterogeneous detector technologies within a single schema. We apply the design principle to the simulated data of the Barrel Imaging Calorimeter (BIC) in the ePIC detector at the Electron--Ion Collider. The BIC simulation data combines AstroPix silicon pixel imaging layers with Pb/ScFi calorimeter layers across different readout types. We describe the schema specialization, data preparation pipeline, and visualization of the curated AI-ready dataset.

Current observations constrain primordial perturbations to be adiabatic, approximately Gaussian, and nearly-scale invariant. However, a generic mixed state satisfying these constraints has additional unconstrained degrees of freedom, which can be parameterized by the purity of the state and its momentum variance. This allowable parameter space reveals a unified geometric landscape of mixed states, allowing us to map and relate distinct models of decoherence and their respective pointer bases. Crossing the threshold of a regular, positive-definite Glauber-Sudarshan $P$-function requires the environment to actively inject momentum into the system, rather than suppress it. This enhanced momentum variance dynamically sources the decaying mode of the gravitational potential in the radiation era. While the decaying mode vanishes fast enough to preserve the temporal coherence of the Cosmic Microwave Background, its initial amplitude places severe theoretical constraints on decoherence models to avoid gravitational non-linearities. These non-linearity bounds definitively rule out decohered thermal states, while long-wavelength divergences restrict amplitude-diagonal decoherence models to fewer than 70 $e$-folds of inflation. Altogether, we present a unifying framework for evaluating the quantum-to-classical transition of the early universe.

We consider a dynamical bifurcation caused by a slow passage through a static bifurcation point: in a system depending on a parameter, the parameter changes slowly in time and passes through the critical value corresponding to the loss of stability of an equilibrium via a Poincaré--Andronov--Hopf bifurcation in the frozen system. If the system is analytic, then the loss of stability is inevitably delayed: phase points attracted to the equilibrium in the stability region remain near the equilibrium for a long time after entering the instability region, so that the parameter changes by an amount of order ~1 independently of how slow the variation of the parameter is. Remarkably, there exists a {\it maximal delay}: all phase points attracted to the stable equilibrium before a certain threshold value of the parameter leave a neighbourhood of the unstable equilibrium almost simultaneously near another threshold value of the parameter, known as {\it a buffer point}. A delay of stability loss beyond the buffer point is impossible unless the initial data have a very special form. We assume that, although the equilibrium is non-degenerate for real values of the parameter, one of its eigenvalues vanishes generically for some complex value of the parameter (a complex analogue of a saddle-node bifurcation), and that this complex singularity is, in a suitable sense, the closest one to the real Poincaré--Andronov--Hopf bifurcation point. We show that the value of maximal delay is determined by this complex singularity: the threshold values defining the maximal delay are the intersection points of the Stokes lines associated with this singularity and the real axis. We study these phenomena in the framework of slow--fast dynamical systems.

Most high-performance elastic textiles rely on yarns composed of chemically dissimilar polymers, rendering them difficult to recycle. Here, we demonstrate fully thermo-mechanically recyclable stretchable yarns composed of polyethylene (PE) family materials. Inspired by structure-property relationships in natural materials, we engineer a library of melt-spun PE fibers spanning mechanical properties from elastomeric to functional by tuning polymer crystallinity and chain orientation. These fibers are assembled into core-sheath yarns comprising an olefin block copolymer elastic core and a high-strength PE sheath, forming a helical architecture. The resulting yarns exceed mechanical performance of commercial PET-spandex yarns while maintaining full recyclability. We further show that PE homopolymers and copolymers can be jointly melt-processed and recycled without phase separation or loss of performance. This approach enables stretchable recyclable textiles from fibers with previously demonstrated cooling, moisture-wicking and stain-resisting performance and provides a scalable pathway toward circular garments compatible with existing polyethylene recycling streams.

We develop a spectral theory of scale-invariant operators on the multiplicative half-line $(\mathbb{R}_+, dx/x)$. A symmetric kernel $M(x, y)$ satisfying $M(kx, ky) = k^{-a}M(x, y)$ necessarily factorizes as $(xy)^{-a/2}F(x/y)$, where the shape function $F$ depends only on the ratio of its arguments. The Mellin transform diagonalizes such operators: the generalized eigenfunctions are $ψ_ω(x) = x^{-a/2+iω}$, and the eigenvalues are the Mellin multiplier $\tilde{F}(ω)$. This structure reveals a fundamental decoupling of two exponents. The geometric exponent $a$, carried by the power-law envelope $(xy)^{-a/2}$, governs the matrix scaling under dilation. The spectral exponent $b$, measured from the eigenvalue decay of the finite-dimensional truncation, is an effective quantity determined by the shape of $\tilde{F}(ω)$. For the explicit kernel $F(t) = c ρ^{|\ln t|}$, the Mellin multiplier is a Lorentzian of width $σ= -\ln ρ$, not a power law -- so $b$ is generically distinct from $a$. This decoupling provides a precise mathematical characterization of multicriticality: the equality $a = b$ corresponds to a simple critical fixed point of the Renormalization Group, while $a \neq b$ signals the presence of multiple independent scaling dimensions. We prove that the discrete self-similarity condition forces eigenvector collapse on the lattice, motivating the continuum formulation. Finite-size corrections from lattice sampling are quantified numerically.

We argue that an airborne proton accelerator is an interesting tool for weather control. Following the findings of the CLOUD experiment at CERN, one expects that a beam of protons, likewise cosmic rays and other aerosols, can enhance the formation of low-altitude clouds, allow for tailor made cooling of overheated areas and induce the precipitation of high-altitude clouds that trap solar radiation reflected from the ground. The proton accelerator can also be used to mitigate droughts, regularise precipitation and avoid that it takes place through large and harmful storms.

The exact ground state of the two-dimensional Hubbard model is critical for understanding cuprate superconductivity. Previous numerical studies on narrow cylinders found insulating, static stripes that inherently suppress superconductivity. Here, using constrained-path auxiliary-field quantum Monte Carlo on isotropic lattices up to $24 \times 24$ sites, we show static stripes are boundary artifacts. The true 2D thermodynamic limit yields a topologically melted fluid of dynamically fluctuating magnetic pockets. Furthermore, we reveal the microscopic real-space origin of cuprate particle-hole asymmetry. Hole doping actively melts the magnetic background, driving a Lifshitz transition that unleashes macroscopic $d_{x^2-y^2}$ phase coherence at an optimal $x \approx 0.150-0.200$. Conversely, electron doping preserves rigid antiferromagnetic domains, confining carriers to narrow fault lines that optimally saturate early at $x \approx 0.100$. By extracting the macroscopic off-diagonal long-range order across both regimes, we perfectly recover the skewed phenomenological superconducting dome. Our parameter-free theoretical curve aligns with empirical Uemura and Božović scaling relations, capturing the underdoped emergence, distinct optimal peaks, the 1/8 anomaly suppression, and overdoped collapse. These results prove that robust d-wave superconductivity is the intrinsic ground state of the pure Hubbard Hamiltonian.

Understanding the influence of wind direction on building drag is essential for predicting urban climate and assessing wind loads in complex urban environments. This study investigates the wind-directional dependence of building drag over the University of Bristol campus, comprising 110 buildings of diverse shapes and heights, using 24 building-resolved large-eddy simulations under a constant imposed pressure gradient. The overall campus drag coefficient exhibits moderate directional fluctuations, with $20\%$ of buildings contributing approximately $80\%$ of the total drag. In contrast, drag on individual buildings shows substantial variability with wind direction, primarily due to shielding by upstream structures. To quantify this, two dimensionless parameters are introduced: the upstream fetch ratio $L_s/H_s$ and the relative height ratio $H_s/H$. Using thresholds of $L_s/H_s = 5$ and $H_s/H = 1$, buildings are classified into four regimes; those in the near-wake shielded regime experience negligible drag, while those in the far-wake non-shielded regime experience the highest drag. A modified drag coefficient, computed by partially or fully excluding shielded buildings, reduces directional anisotropy and yields an effective frontal area that is more consistent across wind directions.

Geometric frustration in quantum systems can stabilize unconventional phases of matter that avoid traditional magnetic ordering at low temperatures. Here, we observe this phenomenon while mapping out the finite temperature phase diagram of the spin-1/2 Heisenberg antiferromagnet on the ruby lattice with next-nearest-neighbor interactions. Using an infinite tensor network state (iTNS) optimized and measured with belief propagation (BP) and corrections to BP, we observe the low temperature formation of stable magnetic plateaus at various magnetic field strengths. We find these plateaus host a novel `simplex liquid state' -- a disordered phase involving strongly paired spin simplices that retains non-zero residual entropy due to an exponentially large subspace of crystalline configurations. We accurately quantify the energy gap associated with these states and show that, as the temperature of the system is lowered, it does not go through a phase transition to reach them: the heat capacity remains finite and continuous at all observed temperatures. Our work demonstrates how BP-based tensor network techniques provide a powerful route to understanding frustrated quantum magnets at finite temperature.

The stability of complex systems hinges on the tension between individual incentives and collective welfare. Modeling these dynamics through strategic network interactions based on anti-coordination, we formally prove that any globally optimal configuration constitutes a Strong Nash Equilibrium, creating topological barriers against collective deviations. However, in sub-optimal states, strictly individualistic agents remain trapped in stagnant equilibria. We show that coalition formation acts as a vital catalyst for global efficiency. Paralleling Tomasello's evolutionary theory of shared intentionality, the emergence of symbiotic joint agency overcomes selfish stagnation and drives the system toward optimal niche partitioning. We validate our framework through extensive computational simulations and apply it to an empirical pollination network, demonstrating how symbiosis may steer real-world ecosystems toward maximum resilience. We uncover metastable dynamics where coalitions continuously reconfigure, revealing that biological evolution relies on a perpetual, adaptive balance between competition and cooperation.

Solutions to well-posed problems in continuum mechanics are continuously dependent upon prescribed boundary conditions. Because of this, variations in the enforcement of boundary data can impact the reliability of inversion techniques that rely on efficient and accurate forward models. To this end, it is necessary to understand how specific boundary implementation techniques can affect the performance of a given forward model. Our work focuses on the impact that key modeling decisions have on physics-informed neural network (PINN) solutions for initial boundary value problems in continuum mechanics. By interpolating boundary data over implicit boundary representations, we measure the performance of a physics-informed neural network across different configurations of soft and hard boundary enforcement. We target the problem of elastodynamic plane-strain and present a method of hard-enforcement of traction conditions over arbitrary, implicitly-defined, domain boundaries considering both first and second order formulations of the governing equations. We show that PINNs achieve a higher relative accuracy when solving the first-order plane strain problem and we observe a tradeoff between the final relative error and the total run time to complete training. This tradeoff is characterized by the number of hard and soft boundaries where, in the extremes, all soft-enforcement results in greater accuracy with a longer run time, while all hard-enforcement leads to lesser accuracy and a shorter run time.

Timely and comparable indicators of the evolving structure of science are increasingly needed for research policy and strategic planning. We present a reproducible and scalable framework for quantifying the topical prevalence and recent dynamics of scientific activity using open scholarly metadata from OpenAlex. The approach combines a unified topic ontology with simple trend estimators derived from short time series, enabling consistent comparisons across journals, countries, regions, and domain-focused corpora. We illustrate the methodology through representative case studies spanning generalist journals, national output, metropolitan research ecosystems, and structural biology. Across these examples, the framework captures both system-level normalization effects and fine-grained specialization patterns. Because the pipeline is fully general and based on open data, it can be readily extended to continuous, multi-scale monitoring of the scientific landscape. The proposed methodology provides a compact and interpretable quantitative layer that can complement expert assessment in science policy, research evaluation, and strategic decision-making.

Coronal mass ejections (CMEs) are explosive and energetic events consisting of strong magnetic structures erupting from the solar corona. We use superposed epoch analysis to investigate the general properties of CMEs as measured {\it in situ} from 0.2 to 2.2 au based on over 1600 events obtained from the HELIO4CAST catalog. We examine the dependence of the CME global properties on solar cycle phase, and compare the CME parameters derived in the active phase (AP) with the quiet phase (QP). Our findings show that during the AP of the solar cycle, the occurring CMEs are faster and have stronger magnetic field strength than during the QP, which has denser but weaker magnetic strength. These differences in magnetic field strength and density remain even when controlling for the speed. This may indicate that the enhanced profiles observed during the AP are not only a consequence of the CME propagation speed but may also reflect intrinsic differences in the eruption mechanism during different solar cycle phases. We also study how the magnetic field strength and components of the CME magnetic ejecta (ME) structure evolve with heliocentric distance. We find that the toroidal and poloidal ME magnetic field components have a similar power law decrease with distance, indicating a comparable expansion behavior of CMEs in these dimensions. We further quantify the CME magnetic field asymmetry %(often associated with CME aging) using the front-to-rear ratio of the toroidal component across heliocentric distance and find evidence of an increase of this ratio with heliocentric distance.

Retraction is a correction to scientific literature when there is a major flaw, fraud or misuse of ethical practices in the published work. With the increasing growth of research output, number of retracted studies has also increased, which raises concerns about the issue of research ethics and transparency. Moreover, retraction data coming from several platforms or databases limits its scope in tracking the time-to-time retraction trends. To address this, we propose a web-based integrated platform, called RetraLytix, for easy analysis of distributed retraction data. It automatically integrates retraction data from major databases like Crossref, Retraction Watch and Open Alex and visualizes data in a user interactive centralized platform. It offers a real-time dashboard, comparative analysis, and benchmarking of entities such as countries, institutions, authors, journals and main research areas. RetraLytix helps users to detect trends, retraction patterns, and assess research environment to make data-driven decisions. The system has a potential to become a research integrity tracking and governance tool for researchers, administrators and policymakers.

Generative artificial intelligence (GenAI) is increasingly operated by natural language instructions (prompts). Across the pipeline, stakeholders designate various forms, e.g. end-user guidelines, developer specifications, or system prompts, as prompt governance instruments. These textual artifacts are intended to shape model behaviour by specifying constraints, priorities, and compliance rules. Policymakers and regulators have begun to treat system-level instructions as accessible prompt-based GenAI intervention points, assuming they function (directly or indirectly) as behavioural control. Yet whether these instructions operate reliably and predictably enough across contexts to support such governance frameworks remains underexplored. Towards this, we systematically evaluate (i) how researchers discuss and treat system-level instructions in the literature, focusing on large language models (LLMs) as they isolate language effects; (ii) how policymakers position system-level instructions as governance objects, incorporating analysis of two policy frameworks (US Exec. Order on Preventing Woke AI, and EU General-Purpose AI Code of Practice); and (iii) whether misalignments between these perspectives warrant closer inspection of the viability of governing AI through natural language. We identify a fragmented literature advancing varying and contradictory claims about what goals system-level instructions can achieve, which we distil into a typology of claims. Further, we show how divergent claims complicate policy approaches that treat system-level instructions as stable, interpretable control mechanisms. We argue that given such misalignments, careful consideration must be given to prompt governance approaches. Our findings have broad implications, extending from a LLM policy context to the use of natural language as control mechanism in technical systems more generally.

The goal of this paper is to study the so--called Hellus--Lyubeznik--Yildirim (HLY) conjecture, that predicts the following: given a regular local ring $(R,\mathfrak{m})$, and any ideal $I\subset R$, zero is an associated prime ideal of the Matlis dual of any non--zero local cohomology module supported on $I$. Among other results, we give some partial positive answers to this conjecture in the following cases: when $\operatorname{depth} (R/I)=1$, when $\operatorname{depth} (R/I)=2$ under some extra assumptions, when $I$ is a squarefree monomial ideal inside a formal power series ring over a field, and when $R$ is a formal power series over a discrete valuation ring of mixed characteristic.

In recommender systems, generative retrieval typically uses an encoder-decoder setup: an encoder processes a user interaction history, and an autoregressive decoder then generates recommended items. In large-scale streaming services, active users accumulate very long histories over time. As histories grow, the encoder becomes a major latency bottleneck because softmax attention scales quadratically with sequence length. In our experiments, using bidirectional attention in the encoder substantially improves quality. However, most sub-quadratic attention methods focus on causal attention. We propose Gated Bidirectional Linear Attention (GBLA), a linear-time bidirectional attention layer that extends kernelized linear attention with three lightweight components: local causal mixing (Conv1D), sequence-level key gating for soft forgetting, and a gated RMSNorm output. On a large-scale Yandex Music dataset, a hybrid encoder that interleaves self-attention (SA) and GBLA in a 1:2 ratio (one SA block followed by two GBLA blocks) matches bidirectional self-attention quality. On H100 GPUs, GBLA reaches up to an $8.2\times$ single-layer speedup at a history length of 32768, compared to FlashAttention-v3. Finally, we show that the same hybrid design generalizes beyond our proprietary setting, consistently preserving self-attention retrieval quality on public Amazon benchmarks.

Long multimodal document question answering is limited by which evidence reaches the reader, rather than by the quantity retrieved. In lengthy documents, findings often recur across figures, captions, and introductory sentences, causing similarity based retrievers in modern multimodal retrieval-augmented generation (RAG) systems to allocate resources to near-duplicates while overlooking complementary evidence. This work introduces a retriever that selects evidence as a Constrained Dominant Set (CDS) on a query-augmented affinity graph, offering three advantages that similarity ranking does not. First, the query is encoded as a hard structural constraint, ensuring that every selected element is directly connected to the question through the cluster anchor. Second, the relevance-redundancy balance is determined automatically by a spectral bound, eliminating the need for manually tuned trade offs required by diversity-aware selectors. Third, the selection process achieves a global equilibrium via replicator dynamics, thereby avoiding the distortions introduced by greedy heuristics. The method is inherently graph-based and does not require training. Using a Qwen3-VL-32B reader, CDS establishes a new state of the art on VisDoMBench ($66.99$ average) and improves over the no-retrieval baseline by $37.1$ points on VisDoMBench and $4.8$ on MMLongBench-Doc.

In this paper we utilize a convex integration scheme to construct non-trivial weak solutions to the $k$-generalized KdV equation which lie in $$ \bigcap_{ε> 0} C_t^0 L_x^{k-ε}([0,1] \times \mathbb{T}) $$ and, when $k \ge 3$, it may also be chosen in \[ \bigcap_{ε>0} C_t^0 H_x^{\frac{1}{2} - \frac{1}{k} - ε}([0,1] \times \mathbb{T}) \] attaining identically $0$ initial data. Since our solutions do not lie in $C_t^0 L_x^k$, this requires introducing a new notion of weak solution, which is in fact stronger than the classical notion of a weak solution when the nonlinearity is integrable. This result shows that a necessary condition for unconditional uniqueness for $k$-gKdV is that the nonlinearity lies in $C_t^0L^1_x$. In the case of KdV this is in fact also sufficient.

We generalize the Einstein condition for Kropina metrics obtained in the positive definite setting by Zhang, Shen and others to all signatures. As examples of Einstein-Kropina metrics $L=L_{a,b}$, we construct new explicit positive definite ones and the first ones with Lorentzian signature. Next, we classify all Einstein-Kropina solutions to the vacuum equation of Finsler gravity by Pfeifer and Wohlfarth, in arbitrary dimension and including a possible cosmological constant $Λ$. For the Lorentzian and positive definite cases, the local picture is as follows. In dimension 4 or lower, only the trivial solution exists: a Minkowski or Euclidean space, essentially. In dimension 5 and higher, the solutions are those $L_{a,b}$ for which the metric $a$ is a product of the real line with a Ricci-flat metric (Lorentzian or Riemannian) and the vector field $b$ is the unique unit vector on the first factor. As a very surprising rigidity phenomenon, all Einstein-Kropina solutions to the $Λ$-vacuum equation are Berwald and Ricci-flat, and the cosmological constant necessarily vanishes.

We consider two sets of related models: initially, these are $SU(2)$ antiferromagnetic spin chains with $N$ sites of spin $S$, and the $O(3)$ nonlinear sigma model in two dimensions with topological coefficient $Θ$ a multiple of $π$ (and later, the extensions of these with any semisimple Lie group symmetry). It is known that, in a continuum description, the low-energy behavior of the spin chain is given by the sigma model with $Θ=2πS$. We study these models with $N$ odd and with antiperiodic (A) boundary condition (b.c.), respectively, which correspond. The A b.c. in the sigma model involves the $\mathbb{Z}_2$ inversion symmetry $\vec{n}\to-\vec{n}$, and amounts to a flux of a $\mathbb{Z}_2$ gauge field through a spacetime torus; summing over the two b.c.s for each direction would amount to gauging the $\mathbb{Z}_2$ inversion symmetry. We show directly that, if and only if $(-1)^{Θ/π}=-1$, the gauging cannot be carried out; there is an 't Hooft anomaly. The partition function for the A b.c. exists, but is not gauge invariant; consequently, the sum over b.c.s cannot be made modular invariant. The gauged model would be a sigma model with target space $\mathbb{R}\mathbb{P}^2\cong \mathbb{S}^2/\mathbb{Z}_2$, and hence this model does not exist for $Θ=π$ (mod $2π$). A related result is that, using semiclassical quantization, in the spin chain we obtain the known values of the ground-state crystal momentum, which at leading order depend only on $N$ modulo $4$ and $2S$ modulo $2$. For a large class of spin chains and associated sigma models we find similar results, but now $(-1)^{Θ/π}$ is replaced by the value $\pm 1$ of the square of the time-reversal operator acting on a single spin, which is still determined by the coefficients of the topological terms, in a way that depends on the symmetry group.