Recent advances in deep learning have highlighted the phenomenon of benign overfitting in overparameterized statistical models, sparking significant interest in understanding its foundations. Owing to its simplicity and practical relevance, the ordinary least squares (OLS) interpolator has become a key object of study for gaining theoretical insight into this phenomenon. While the properties of OLS are well understood in classical underparameterized settings, its behavior in the overparameterized regime -- unlike that of ridge regression or the lasso -- remains comparatively less explored. We contribute to this growing literature by deriving new algebraic and statistical results for the minimum $\ell_2$-norm OLS interpolator. In contrast to much of the existing work, which focuses on prediction risk, we center our analysis on parameter estimation and inference, which are fundamental for many statistics and causal inference applications. Specifically, we establish overparameterized analogues of (i) the leave-$k$-out formulas, (ii) the omitted variable bias formula, and (iii) the Frisch-Waugh-Lovell theorem. Under the Gauss-Markov model, we further extend the Gauss-Markov theorem and analyze variance estimation under homoskedasticity in the overparameterized setting. Collectively, these results provide a systematic framework for studying parameter estimation and inference in overparameterized linear models, offering a novel perspective on benign overfitting beyond its implications for prediction.

Digital Subtraction Angiography (DSA) is one of the gold standards for vascular disease diagnosis. With the help of a contrast agent, time-resolved 2D DSA images deliver comprehensive blood flow information and can be utilized to reconstruct 3D vessel structures for medical assessment. Current commercial DSA systems typically require hundreds of scanning views to perform reconstruction, resulting in substantial radiation exposure. In this study, we propose a neural rendering-based optimization framework tailored for high-quality sparse-view DSA reconstruction to reduce radiation dosage. Our approach, termed vessel probability guided attenuation learning, represents DSA imaging as a complementary weighted combination of static and dynamic attenuation fields, with the weights derived from the time-independent vessel probability field. Functioning as a foreground mask, vessel probability provides proper gradients for both static and dynamic fields adaptive to different scene types. This mechanism enables self-supervised decomposition between static backgrounds and dynamic contrast agent flow, and significantly improves reconstruction quality. Our model is trained by minimizing the discrepancy between synthesized projections and real captured DSA images. We further employ two training strategies to improve reconstruction quality: (1) coarse-to-fine progressive training for better geometry and (2) temporal perturbed rendering loss for temporal consistency. Experimental results have demonstrated high-quality 3D vessel reconstruction and 2D DSA image synthesis.

Unstructured text provides decision-makers with a rich data source in many domains, ranging from product reviews in retail to nursing notes in healthcare. To leverage this information, words are typically translated into word embeddings -- vectors that encode the semantic relationships between words -- through unsupervised learning algorithms such as matrix factorization. However, learning word embeddings from new domains with limited training data can be challenging, because the meaning/usage may be different in the new domain, e.g., the word ``positive'' typically has positive sentiment, but often has negative sentiment in medical notes since it may imply that a patient tested positive for a disease. In practice, we expect that only a small number of domain-specific words may have new meanings. We propose an intuitive two-stage estimator that exploits this structure via a group-sparse penalty to efficiently transfer learn domain-specific word embeddings by combining large-scale text corpora (such as Wikipedia) with limited domain-specific text data. We bound the generalization error of our transfer learning estimator, proving that it can achieve high accuracy with substantially less domain-specific data when only a small number of embeddings are altered between domains. Furthermore, we prove that all local minima identified by our nonconvex objective function are statistically indistinguishable from the global minimum under standard regularization conditions, implying that our estimator can be computed efficiently. Our results provide the first bounds on group-sparse matrix factorization, which may be of independent interest. We empirically evaluate our approach compared to state-of-the-art fine-tuning heuristics from natural language processing.

Existing agent memory remains predominantly reactive and retrieval-based, lacking the capacity to autonomously organize experience into persistent cognitive structure. Toward genuinely autonomous agents, we introduce CogniFold, a brain-inspired "always-on" agent memory designed for the next generation of proactive assistants. CogniFold continuously folds fragmented event streams into self-emerging cognitive structures, bootstrapping progressively higher-level cognition from incoming events and accumulated knowledge. We ground this by extending Complementary Learning Systems (CLS) theory from two layers (hippocampus, neocortex) to three, adding a prefrontal intent layer. Emulating the prefrontal cortex as the locus of intentional control and decision-making, CogniFold achieves this through graph-topology self-organization: cognitive structures proactively assemble under the stream, merge when semantically similar, decay when stale, relink through associative recall, and surface intents when concept-cluster density crosses a threshold. We evaluate structural formation using CogEval-Bench, demonstrating that CogniFold uniquely produces memory structures that match cognitive expectations and concept emergence. Furthermore, across eight downstream benchmarks -- two probing long-term conversational memory (LoCoMo, LongMemEval) and six spanning other cognitive domains -- we validate that CogniFold simultaneously performs robustly on conventional memory tasks. Our code is available at https://github.com/OpenNorve/CogniFold.

We revisit a classic "chicken-and-egg" problem in reinforcement learning: to safely improve a policy, the value function must be accurate on the state-visitation distribution of the updated policy. That distribution over states is unknown and cannot be sampled for the purposes of training the value function. Conservative updates solve this problem, but at the cost of shrinking the policy update. This paper explores an alternative solution, Approximate Next Policy Sampling (ANPS), which addresses the problem by modifying the training distribution rather than constraining the policy update. ANPS is satisfied if the distribution of the training data approximates that of the next policy. To demonstrate the feasibility and efficacy of ANPS, we introduce Stable Value Approximate Policy Iteration (SV-API). SV-API modifies the standard approximate policy iteration loop to hold the target policy fixed while an iteratively updated behavioral policy gathers relevant experience. It only commits to a new policy once a convergence criterion has been met. If certain stability criteria are met, the update is guaranteed to be safe; otherwise, it remains no less safe than standard approximate policy iteration. Applying SV-API to PPO yields Stable Value PPO (SV-PPO), which matches or improves performance on high-dimensional discrete (Atari) and continuous control benchmarks while executing substantially larger target policy updates. These results demonstrate the viability of ANPS as a new solution to this classic challenge in RL.

Language identification (LID) is an essential step in building high-quality multilingual datasets from web data. Existing LID tools (such as OpenLID or GlotLID) often struggle to identify closely related languages and to distinguish valid natural language from noise, which contaminates language-specific subsets, especially for low-resource languages. In this work we extend the OpenLID classifier by adding more training data, merging problematic language variant clusters, and introducing a special label for marking noise. We call this extended system OpenLID-v3 and evaluate it against GlotLID on multiple benchmarks. During development, we focus on three groups of closely related languages (Bosnian, Croatian, and Serbian; Romance varieties of Northern Italy and Southern France; and Scandinavian languages) and contribute new evaluation datasets where existing ones are inadequate. We find that ensemble approaches improve precision but also substantially reduce coverage for low-resource languages. OpenLID-v3 is available on https://huggingface.co/HPLT/OpenLID-v3.

Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking. However, current retrieval-augmented models often rely on a single perspective, follow inflexible search strategies, and struggle to effectively combine information from multiple sources. We introduce SIGMA (Search-Augmented On-Demand Knowledge Integration for AGentic Mathematical reAsoning), a unified framework that orchestrates specialized agents to independently reason, perform targeted searches, and synthesize findings through a moderator mechanism. Each agent generates hypothetical passages to optimize retrieval for its analytic perspective, ensuring knowledge integration is both context-sensitive and computation-efficient. When evaluated on challenging benchmarks such as MATH500, AIME, and PhD-level science QA GPQA, SIGMA consistently outperforms both open- and closed-source systems, achieving an absolute performance improvement of 7.4%. Our results demonstrate that multi-agent, on-demand knowledge integration significantly enhances both reasoning accuracy and efficiency, offering a scalable approach for complex, knowledge-intensive problem-solving. We will release the code upon publication.

World Model, the algorithmic simulator of the real-world environment which biological agents experience and act upon, has been an emerging topic in recent years due to the rising need to develop virtual agents with artificial (general) intelligence. There has been much discussion on what a world model really is, how to build it, how to use it, and how to evaluate it. In this essay, starting from the imagination in the famed Sci-Fi classic Dune, and drawing inspiration from the concept of ``hypothetical thinking'' in psychology literature, we argue the primary goal of a world model to be {\it simulating all actionable possibilities of the real world for purposeful reasoning and acting}. We examine the key design dimensions of world modeling: data, representation, architecture, learning objective, and usage, surveying existing approaches and analyzing their tradeoffs. Building on this examination, we propose a new Generative Latent Prediction (GLP) architecture for a general-purpose world model, based on stateful, hierarchical, multi-level, and mixed continuous/discrete representations, and a generative and self-supervised learning framework, with an outlook of a Physical, Agentic, and Nested (PAN) AGI system enabled by such a model.

Large-scale expert parallelism (EP) is becoming pivotal for training and serving frontier MoE models, but it also amplifies device-level expert load imbalance into compute stragglers, token all-to-all bottlenecks, and activation-memory spikes. Existing balancers redistribute experts periodically based on historical load, which becomes unreliable for production deployments with non-stationary load patterns. We present UltraEP, the first exact-load, real-time balancer for large-EP MoE training and serving prefill on rack-scale nodes (RSNs). Leveraging the extended scale-up connectivity among dozens of GPUs within RSNs, UltraEP rebalances every microbatch and layer on critical paths, which requires nontrivial co-design of plan solving and expert replication communication to minimize exposed overhead. To this end, UltraEP eagerly reacts to post-gating load with an efficient quota-driven planner, and executes the resulting irregular expert-state transfers with RSN-native persistent tile streaming and relay-based fan-out mitigation. We evaluate UltraEP in a multi-RSN deployment of up to 256 GPUs, using cutting-edge MoE models from 106B to 671B parameters. Averaged across training and serving, UltraEP achieves 94.3% of the force-balanced ideal throughput, delivering 1.49$\times$ improvement over no-balancing, while reducing the final inter-rank imbalance from 1.30$-$4.01 to 1.01$-$1.04.

Social media platforms frequently impose restrictive policies to moderate user content, prompting the emergence of creative evasion language strategies. This paper presents a multi-agent framework based on Large Language Models (LLMs) to simulate the iterative evolution of language strategies under regulatory constraints. In this framework, participant agents, as social media users, continuously evolve their language expression, while supervisory agents emulate platform-level regulation by assessing policy violations. To achieve a more faithful simulation, we employ a dual design of language strategies (constraint and expression) to differentiate conflicting goals and utilize an LLM-driven GA (Genetic Algorithm) for the selection, mutation, and crossover of language strategies. The framework is evaluated using two distinct scenarios: an abstract password game and a realistic simulated illegal pet trade scenario. Experimental results demonstrate that as the number of dialogue rounds increases, both the number of uninterrupted dialogue turns and the accuracy of information transmission improve significantly. Furthermore, a user study with 40 participants validates the real-world relevance of the generated dialogues and strategies. Moreover, ablation studies validate the importance of the GA, emphasizing its contribution to long-term adaptability and improved overall results.

Neural networks are a fundamental aspect of modern artificial intelligence, playing a key role in various important machine learning architectures including transformers and graph neural networks. Recently, logical characterisations have been used to study the expressive power of many machine learning architectures, but logical characterisations of plain neural networks have received less attention. In this paper, we provide fuzzy logic characterisations of rational-weight ReLU-activated neural networks via Rational Pavelka logic ($\mathrm{RPL}$) and an extension of $\mathrm{RPL}$ called $\mathrm{RPL}(\odot)_{\leq 1}$, as well as two fragments of $\mathit{L Π} \frac{1}{2}$ called $\mathit{L Π} \frac{1}{2}(\rightarrow_{P}^-)_{\leq 1}$ and $\mathit{L Π} \frac{1}{2}(\odot^-, \rightarrow_{P}^-)$. The activation values of the neural networks are allowed to be arbitrary real numbers. We also provide fuzzy logic characterisations of a generalised polynomial ring over $\mathbb{Q}$ in countably many variables where the use of the ReLU-function is permitted via the fuzzy logic $\mathrm{RPL}(\odot)$ and a fragment of $\mathit{L Π} \frac{1}{2}$ called $\mathit{L Π} \frac{1}{2}(\rightarrow_{P}^-)$.

This manuscript contains preprint of a chapter under consideration for inclusion in the forthcoming third edition of {\em Cover and Thomas's Elements of Information Theory}, posted with permission from Wiley. The table of contents EIT-3 ToC of the new edition can be found at: https://docs.google.com/document/d/1L-m4oQEJw1PJhoxBeMwrrBD8S_HmvzMEkPbYvS24980/edit?usp=sharing . For feedback, please contact abbas@ee.stanford.edu Learning and information theory intersect in both model training and the characterization of fundamental performance limits. This manuscript provides a concise and accessible treatment of the first intersection, requiring only basic background in information theory and statistics at the senior undergraduate or first-year graduate level. End-of-chapter exercises make the material well suited for classroom use as well as self-study. The chapter focuses on the role of divergence measures in model training, with examples ranging from linear and logistic regression to autoregressive models, variational autoencoders, diffusion models, generative adversarial networks, and score-based models. It introduces the evidence lower bound (ELBO), f-divergences, and the Fisher divergence. In particular, the treatment of the generative diffusion model provides a more systematic and explicit derivation than is typical in the literature.

We present the first implementation of AI agents into the design and optimization of detectors in high-energy physics experiments via a bi-level optimization framework that vertically integrates detector geometry, front-end digitization, and high-level reconstruction algorithm parameters in differentiable full simulations. Using the example of a dual-readout, segmented crystal EM calorimeter with a baseline resolution of $3\%/\sqrt{E}$, we investigate the capabilities and value propositions of AI agents in the identification and reduction of key detector parameters and in the nonlinear traversal of design space. We find that frontier LLM reasoning-models today, without being given additional experiment-specific context, are able to effectively execute complex workflows and proactively suggest generic but relevant avenues for further study or improvement. Here, we demonstrate an AI agent's ability to find an optimal design point amidst three competing performance criteria, showing that effective integration of agents into the complex workflows of frontier research areas can yield higher performance for key physics goals while reducing labor and compute. This study establishes the foundation for a future demonstration of the first fully AI-designed detector for future scientific facilities.

We investigate an integrable boundary quench, in which one integrable boundary condition is suddenly switched to another. We develop a general framework for analyzing the resulting real-time dynamics based on form factors of bulk and boundary-changing operators. We first study the problem at the conformal point of the Lee-Yang model and then extend the analysis to its massive perturbation, where we examine the time evolution of the pre-quench vacuum and compute the vacuum-to-vacuum matrix elements of local operators inserted after the quench. The analytical results are validated by numerical calculations using the truncated conformal space approach adapted to boundary-changing situations.

A growing number of Galactic Wolf-Rayet (WR) stars, in particular WC and transitional WN/C (WNC) objects, have been reported at comparatively low luminosities. If confirmed, these low-luminosity WR stars provide stringent tests of stellar-evolution models, because their HR-diagram locations and surface compositions are highly sensitive to internal mixing and to the adopted WR-phase mass-loss history.We examine whether the HR-diagram positions and wind properties of low-luminosity WC/WNC stars can be reproduced by single-star evolutionary tracks at approximately solar metallicity, and we identify cases where additional channels (e.g. binary stripping) or dominant systematic uncertainties are likely required. Low-luminosity WNC/WC stars offer sensitive leverage on WR mixing and mass-loss prescriptions. A staged model-data comparison shows that revised WR winds can alleviate the luminosity-side tension for faint WCL stars, but the simultaneous requirements of temperature, surface composition, and WR-like wind density remain important. The WNC stars provide the strongest evidence that additional mixing, stripping, or binary-related channels may be required.

Similarity search is a fundamental operation in time series analysis. Most existing techniques, however, require users to supply a precise sequence of values (typically an entire time series object) as the query input. This rigid requirement limits real-world applications, where users instead want to express patterns, trends, or value ranges. Flexible, pattern-based search has been explored in text retrieval and complex event processing, but remains underexplored for large-scale distributed time series. To close this gap, we propose TSseek, a regular-expression-powered search framework for distributed time series datasets. TSseek's query language enables users to compose patterns encompassing trends, value ranges, and wildcard segments. We show that conventional approximation techniques (e.g., PAA and SAX) and their index structures are ill-suited for such queries because they cannot operate on regular-expression query constructs. In TSseek, we map the time series objects and the query constructs into the same space by approximating time series objects as sequences of line segments that retain both trend (slope direction) and value range, and translating query constructs into bounding rectangles. To support efficient processing, we build TSseek-X, a distributed spatial index over the time series segments. TSseek supports two fundamental query types, namely whole-matching queries (over entire series) and subsequence-matching queries (over arbitrary windows within a series). Across benchmark and real-world datasets, full-scan, model-based, and SAX-based baselines all sacrifice either accuracy or speed, whereas TSseek returns exact answers efficiently. Also, for subsequence workloads, it achieves significant speedups over state-of-the-art subsequence matching engines.

We address two mass-dependent properties among early-type galaxies (ETGs): (1) abundance ratios [N/Fe] and [Na/Fe], and (2) the centrally concentrated "UV upturn" at far-UV (FUV) wavelengths, which is likely produced by extreme horizontal branch stars with supersolar helium abundances. Using new HST/WFC3 observations of one FUV-weak and one FUV-bright ETG, we probe the "MP scenario" by Goudfrooij who posited that the UV upturn and the mass-dependent abundance variations of N and Na within and among ETGs are physically connected and produced by dissolution of metal-rich globular clusters, which represent the only galactic environment where mass-dependent enrichment of He, N, and Na is known to occur (i.e., second-generation stars of the "multiple stellar populations" (MPs) phenomenon). We show that passbands F275W and F390W are uniquely sensitive to correlated changes in $Y$ and [N/Fe] in integrated-light photometry when combined with archival data in F475W and F850LP. While F475W-F850LP is found to decrease with increasing radius in both galaxies, consistent with known metallicity gradients, F275W-F390W increases with increasing radius, as expected if the UV upturn is caused by second-generation stars with supersolar $Y$ and [N/Fe]. Furthermore, the radial gradient in F275W-F390W and the implied fractions of He- and N-enhanced stars are found to be significantly larger in the FUV-bright ETG than in the FUV-weak one, consistent with the predictions of the MP scenario.

We introduce the degree filtration on the discrete cubical chain complex of a graph, defined in terms of the maximal injective dimension of the facets of singular $n$-cubes, and study the degree spectral sequence which arises from this filtration. This spectral sequence interpolates between the discrete cubical homology of a graph $H_n(G)$ and the injective homology $H_n^{inj}(G)$, a variant of the discrete cubical homology based on injective singular cubes. Building on the work of Babson et al. we introduce the combinatorial condition of quasimonophobicity on graphs, and show quasimonophobicity implies both the vanishing of the degree spectral sequence in certain bidegrees, and implies $H_n^{inj}(G)$ is isomorphic to the homology of the CW complex obtained by ``filling in'' subcubes of the graph. These results are applied to compute $H_2(G_n^{sph})$ for the Greene sphere graphs $G^{sph}_n$.

Understanding the dynamic evolution of opinions, such as U.S. public attitudes toward China, is essential for assessing geopolitical risks. However, existing LLM-based multiagent simulators predominantly rely on static rules and fixed datasets, limiting their ability to capture the dynamic, event-driven nature of macro-level opinion shifts in real-world settings. To address this limitation, we propose an Event-Steered Multi-Agent Simulator (ES-MAS), in which significant events and daily news continuously drive opinion evolution through dynamic interactions among agents. We first construct the China-U.S. Relation Evolution (CURE) dataset, covering 20 quarters from 2021 to 2025, including 258 major events and over 14,000 daily news articles, and providing a comprehensive temporal foundation for modeling opinion dynamics. Building upon the CURE dataset, we propose a Dual-Stream Data Integration Engine (DSDIE) that aligns simulations with historical timelines via macro-level events while enabling personalized information exposure based on individual agent profiles and contextual signals. Furthermore, we design a News-Driven Dynamic Interaction (NDDI) module, which adaptively groups agents with shared news interests into localized interaction contexts, facilitating bottom-up consensus formation while mitigating the risk of isolated information cocoons. Experimental results on the CURE dataset demonstrate that ES-MAS substantially outperforms existing simulators in reproducing real-world historical trends, offering a scalable and effective framework for modeling dynamic opinion evolution.

The spectrum of vector charmonium(-like) states in the 4.1\dash4.6~GeV energy region exhibits a long-standing tension between inclusive and exclusive measurements. While the inclusive $R$-value indicates only conventional vector charmonia such as $ψ(4160)$ and $ψ(4415)$, exclusive $e^+e^-$ cross sections reveal additional structures whose parameters strongly depend on the observed final states when fitted with Breit--Wigner functions. This puzzling pattern suggests that coupled-channel and threshold effects play an essential role. In this work, we develop a unified coupled-channel framework for the $1^{--}$ resonances in this energy region. The framework incorporates the $S$-wave open-charm channels $D\bar{D}_1$, $D^*\bar{D}_1$, and $D^*\bar{D}_2^*$ constrained by heavy-quark spin symmetry, optional bare poles associated with $ψ(4160)$ and $ψ(4415)$, and final-state interactions in the $Z_c$ channels. We perform simultaneous fits to the BESIII cross sections for $e^+e^-\to J/ψπ^+π^-$, $h_cπ^+π^-$, $D\bar{D}^*π$, $D^*\bar{D}^*π$, $J/ψη$, and $χ_{c0}ω$, together with invariant-mass distributions exhibiting the $Z_c(3900)$ and $Z_c(4020)$ structures. The benchmark models differ in the number of bare seed states and the fitting strategy. We show that even the purely dynamical scheme without bare charmonia captures the gross features of the analyzed distributions. The inclusion of bare compact states improves the fit quality but does not change the conclusion that the measured line shapes can be understood in terms of strong coupled-channel effects with dynamically generated poles. We also discuss possible heavy-quark spin partners of the exotic $1^{--}$ states.

Charge conjugation violation (CCV) is a central concept in particle physics and appears also for quasiparticles in quantum many-body systems, which typically relies on an embedded external symmetry breaking to the underlying system. An open question is how an intrinsic CCV mechanism could emerge and what its macroscopic consequences would be. We establish sublattice kinks in bipartite fermionic lattices as a concrete setup showing intrinsic CCV. The intrinsic CCV of the sublattice kink is based on the graph-topological nature of the underlying Hamiltonian, with no explicit symmetry breaking taking place. It leads to a population asymmetry of different configurations and imprints a hidden leaf-like structure in the eigenenergy spectrum. The population asymmetry also leads to an imbalanced sublattice-kink production triggered by the vacuum-instability in the quench dynamics. Our work demonstrates the graph topology as the microscopic origin of intrinsic CCV, with the population asymmetry as the macroscopic consequence, of which the proposed setup is highly amenable to experimental implementation via cold-atom quantum simulators.

Fluctuational electrodynamics relies on the assumption that thermal fluctuations in distinct bodies are statistically independent. It is shown that this approximation breaks down in the extreme near-field regime, where hybridization of surface phonon-polaritons across nanometric vacuum gaps generates finite fluctuating-current cross correlations between opposite interfaces. Using a microscopic coupled-oscillator model combined with a Green-tensor formulation of the Poynting vector, the resulting correlation-induced correction to radiative heat transfer is derived. For polar materials, these correlations become significant when the hybridization energy approaches the intrinsic damping rate and can substantially modify conventional fluctuational-electrodynamics predictions at subnanometric separations.

The proposal to formulate chiral gauge theories using domain wall fermions on $2n+1$ dimensional Euclidean lattice with a slab geometry involves $2n$ dimensional dynamical gauge fields residing on one of the domain walls. The gauge fields are extended into the extra dimension using gradient flow decoupling the mirror fermions on the anti-wall. We implement this construction on the lattice for $n=1$ in the presence of $2n$ dimensional background gauge fields. We also formulate and implement an additional gauge field flow proposal, where the gauge fields satisfy $2n+1$ dimensional equation of motion away from the domain wall, known as the EOM (equation of motion) flow. In both cases, we couple the gauge fields to fermions and demonstrate how current conservation and anomaly inflow work on the lattice.

A recent non-perturbative formulation of $2n$ dimensional chiral gauge theories relies on realizing chiral fermions on the $2n$ dimensional boundary of a $2n+1$ dimensional disk manifold. It also requires extending boundary gauge configurations into the interior of the disk using some flow prescription that preserves 2n dimensional gauge invariance. In this paper we propose a concrete realization of the equation of motion flow with the disk embedded on a square lattice. In addition, we couple the flow gauge field to fermions and demonstrate the mechanism of anomaly inflow and anmaly cancellation at work on the lattice.

We present a hardware-oriented description of GoldenFloat (GF), a static-split floating-point family generated by a single closed rule, and three concrete artefacts: (i) an open multi-width RTL generator covering GF4-GF256 with a continuous-integration differential sweep against a correctly-rounded reference; (ii) an integer-backed Lucas-exact accumulator path verified at 500-digit precision for n = 1, ..., 256; and (iii) a GF16 FPGA codec passing a 35-of-35 testbench at 323 MHz on Artix-7 (Xilinx XC7A35T). A format-conformance oracle (Corona) ships in the same repository and is used as the blackbox check in our continuous-integration audit. The rule and its scope. For each total width N >= 4, the exponent width is e = round((N-1)/phi^2) with fraction f = N-1-e and phi = (1+sqrt(5))/2. The rule reproduces the realised exponent widths of nine formats GF4, GF8, GF12, GF16, GF20, GF24, GF32, GF64, GF256 (9/9) and extends consistently to GF128, GF512, GF1024. The rule is positioned alongside posit (2022 Posit Standard), takum (Hunhold 2024, 2025), OCP-MX (Rouhani et al. 2023), and the IEEE P3109 multi-width float draft, all of which are width-spanning families under a parameterised rule. We make no per-rung accuracy or superiority claim against any of them. What is open. The breadth/toolchain-coherence framing is recorded as an open conjecture with a pre-registered falsification path: a matched-substrate FPGA experiment and a matched-budget software ablation. A falsification ledger (FL-002) records the open questions and the experiments that would settle them. An RTL-correctness erratum dated 2026-05-31 is reported in Section 5.5; the fabricated TTSKY26b dies carry the defective multiplier portfolio, and the corrected generator is the regeneration baseline.

We propose a bipartite entanglement measure defined as the minimal order-1 quantum Wasserstein distance from a state to the set of separable states. Owing to the universal data-processing inequality of the Wasserstein metric, the measure satisfies all fundamental axioms within a single geometric framework. A Lipschitz dual formulation yields explicit lower bounds for pure and mixed states, a sharp constant for two-qubit systems, and an expected value for Haar-random pure states. We further establish a quantitative connection to entanglement witnesses: any negative witness expectation value certifies a lower bound, and the dual variational bound is exactly the maximal violation achievable by a Lipschitz-1 witness. The approach naturally provides subadditivity, trace-distance estimates, and bounds on local observables, while pointing toward large-deviation conjectures. This work introduces a framework at the interface of entanglement theory, optimal transport, and experimental entanglement detection.

The most compelling evidence for spin-triplet superconductivity has emerged from strongly correlated electron systems, yet whether a substantial spin-triplet component can be realized without strong electronic coupling, by virtue of antisymmetric spin-orbit coupling (ASOC), remains unresolved. We address this question in the weakly-correlated noncentrosymmetric superconductor Nb$_{18}$Re$_{82}$ using low-temperature scanning tunneling spectroscopy on single crystals with different crystallographic orientations. The tunneling spectra exhibit orientation-dependent variations. A symmetry-constrained analysis shows that understanding the complete spectroscopic dataset requires an superconducting order parameter combining a nodal spin-singlet component with a spin-triplet contribution reaching up to half of the singlet amplitude. These results resolve the debated pairing symmetry of Nb$_{18}$Re$_{82}$ and demonstrate that ASOC alone can generate substantial parity mixing, suggesting that triplet superconductivity may be more widespread than previously recognized.

Maintenance organizations in manufacturing try to avoid downtime and unnecessary purchasing by reusing existing assets, but the main obstacle is not a lack of parts but a lack of actionable visibility across sites and partners. Inventories are distributed, described with inconsistent naming conventions, and contain duplicates and partially specified references, so the right part often exists somewhere but remains effectively undiscoverable. The paper proposes PhRAG, a hybrid Retrieval-Augmented Generation for pooling this fragmented landscape into a Virtual Stock Pool (VSPool) that can be structured and searched as a single resource. Heterogeneous spare part descriptions are structured via Named Entity Recognition (NER) into a shared virtual pool dataset and indexed to support robust retrieval even when users express needs in natural language rather than exact technical specifications. The proposed modular pipeline leverages the multitasking nature of generative language models to cover two dimensions that make industrial parts pooling challenging: ($\boldsymbol{i}$) unstructured technical specifications from diverse data sources (e.g. new partners, catalogs, marketplace listings) are handled through an offline extraction and ($\boldsymbol{ii}$) request variability at runtime (references, partial references, specifications, price/condition constraints) is handled through a hybrid RAG-based search engine capable of retrieving relevant components and justifying results. The framework demonstrates the potential of generative approaches compared with traditional NER approaches in the presence of data scarcity for technical specifications extraction and overcomes the opacity of standard information retrieval systems by generating justifications for retrieved components.

The gravitino is a prominent example of a freeze-in dark matter candidate. Its relic abundance depends on the reheating temperature and on supersymmetry-breaking parameters, that is the universal gaugino mass, $M_{1/2}$, and the gravitino mass, $m_{3/2}$. As a consequence, the reheating temperature consistent with the observed dark matter abundance exhibits a maximum value, $T_{\rm reh}^{\rm reak}$, which decreases as $M_{1/2}$ increases. This behavior gives rise to a tension between prospective lower bounds on the gluino mass from future collider searches and the high reheating temperatures required for successful thermal leptogenesis. In this work, we investigate a nonstandard cosmological scenario in which the thermal bath is supplemented by an additional scalar field. We show that, for a matter-like equation of state, this component can induce a substantial dilution of the gravitino abundance, thereby allowing significantly larger values of the reheating temperature. In contrast, for a kination-like equation of state, the gravitino abundance is enhanced rather than diluted, leading to a reduction of the maximum allowed reheating temperature.

We consider a general class of ``inexactly smooth'' convex functions, providing a universal model capturing as special cases $L$-smooth, $M$-Lipschitz, and Hölder smooth functions, and any combination thereof. Such functions possess a calculus closely following that of smooth functions. Our main results provide inexactly smooth functions with interpolation theorems that are necessary and sufficient up to modest universal constants. These enable analysis of first-order methods for any inexactly smooth convex problem class via solving convex Performance Estimation Problems (PEPs). Further, these enable the extension of Drori and Taylor's constructive approach to algorithm design. From this, we derive an exactly minimax optimal method for $(β,0)$-Hölder smooth problems, methods with the best-known convergence guarantees up to constants for any $(β,p)$-Hölder smooth convex minimization, and a new universal fast backtracking method for any inexactly smooth convex problem.