We consider the problem of packing edge-disjoint Steiner forests in a graph. The input consists of a multi-graph $G=(V,E)$ and a collection of $h$ vertex subsets $S = \{S_1,S_2,\ldots,S_h\}$. A Steiner forest for $S$, also called an $S$-forest, is a forest of $G$ in which each $S_i$ is connected. In the case where $h=1$, this is the Steiner Tree packing problem. Kriesell's conjecture postulates that $2k$-edge-connectivity of $S_1$ is sufficient to find $k$ edge-disjoint $S_1$-trees. Lau showed that $24k$-edge-connectivity suffices for the Steiner Tree packing problem, which was improved to $6.5k$ by West and Wu and $5k+4$ by Devos, McDonald and Pivotto. In his thesis, Lau asserts that for the Steiner Forest problem, if each $S_i$ is $30k$-edge-connected in $G$, then there exist $k$ edge-disjoint $S$-forests. However, Lau's proof relies on an intermediate theorem called the Extension Theorem, which in this paper we will demonstrate has a gap by providing a counterexample to Lau's Extension Theorem. Furthermore, we will resolve this gap by correcting Lau's proof to show that $36k$-edge-connectivity of each $S_i$ suffices to pack $k$ $S$-forests. More careful analysis yields that $35k$-edge-connectivity of each $S_i$ is sufficient when $k \geq 8$.

Interest in the topic of geodetic co-location in space and space ties has recently intensified within the geodetic community, particularly following the approval of the European Space Agency's (ESA) Genesis mission. From the perspective of Very Long Baseline Interferometry (VLBI), observations of Earth-orbiting satellites are not standard practice yet. To enable VLBI support for future colocation satellite missions, such observations must be integrated into the VLBI processing chain. In this study, we present comprehensive VLBI observations of Galileo navigation satellites conducted with the Australian AuScope VLBI array. Using the 12-m antennas in Hobart, Katherine and Yarragadee equipped with VLBI Global Observing System (VGOS) instrumentation, Galileo E1 and E6 signals were observed in test experiments and a series of four full-scale 24-hour observing sessions. We present the estimation of VLBI station coordinates from observations to navigation satellites, thereby demonstrating, for the first time, inter-technique ties between the VLBI and Global Navigation Satellite System (GNSS) frame. We describe the processing strategy, including correlation, fringe fitting, precision assessment and satellite tracking approach. Delay observables achieve precisions of a few picoseconds in the E1 band and several tens of picoseconds in the E6 band for 1-s integration times. However, unmodelled signals on the order of several hundred picoseconds are found in the residual delays. Estimated station coordinates agree with a priori values at the metre level, while baseline lengths agree at the sub-metre level. These results demonstrate the feasibility of large-scale VLBI observations to GNSS satellites and provide critical groundwork for future co-location satellite missions such as Genesis.

The so-called Ahmed integral $$ \int_{0}^{1}\frac{\arctan\left(\sqrt{2+x^{2}}\right)}{(1+x^{2})\sqrt{2+x^{2}}}\,\mathrm{d} x=\frac{5π^{2}}{96}, $$ has attracted considerable interest since its appearance in the "American Mathematical Monthly" in 2001. Several proofs and extensions have been proposed, including a probabilistic multivariate approach introduced by Pla based on powers of the Gaussian integral. In this note, we extend Pla's method to the fifth power of the Gaussian integral. By expressing this power as a sequence of iterated integrals and performing successive reductions, we obtain a new integral identity closely related to Ahmed's integral. In particular, we prove that $$ \int_{0}^{1}\frac{\arctan\!\left(\sqrt{\displaystyle\frac{2+x^2}{4+x^2}}\right)}{(1+x^{2})\sqrt{2+x^{2}}}\,\mathrm{d} x=\frac{π^2}{30}. $$ The derivation suggests that Pla's technique can systematically generate a family of Ahmed-type integrals associated with higher powers of the Gaussian integral.

Atolls are traditionally explained as the result of coral reefs accreting around volcanic islands followed by gradual subsidence, yielding a hollow, ring-shaped rim that can extend for kilometres. However, satellite imagery shows that similar annular outlines also appear in much smaller patch reefs, where atoll-forming geological pathways do not apply. In some systems, small annular patches occur within the lagoons of larger atolls, producing nested ring-like patterns. The recurrence of annularity across such contrasting contexts and scales suggests that shared, self-organising processes may also contribute to shaping these reefs. Here, we test whether interactions between reef growth and marine currents can generate annular forms and explain their cross-scale geometric regularities. We develop a numerical model in which coral growth follows simple process-based rules, with local colonisation and mortality depending on resource supply and hydrodynamic stress, and water flow resolved using fluid dynamics. Simulations show that this coupling robustly produces ring-like patch reefs and atoll-like configurations across spatial scales, consistent with observed morphologies. Beyond qualitative agreement, the emergent reefs reproduce key geometric signatures reported in global datasets, including scaling laws and fractal dimensions. Together, these results identify coral-current interactions as a plausible pathway to annular reef formation and a mechanistic explanation for scale-free reef geometry.

Microscale granular sliding within fault gouge is fundamental to earthquake nucleation, yet the mechanism by which temperature affects friction through interfacial water remains poorly understood. Here, large-scale molecular dynamics simulations were conducted on a hydrophilic quartz-water-quartz interface over 300-500 K to quantify temperature-dependent changes in frictional strength, real contact area, and water-layer structure. Results show that both the friction coefficient and friction force decrease monotonically with increasing temperature, following near-linear relationships of $μ\propto T^{-1}$ and $F_t \propto A$, indicating that frictional weakening is primarily governed by temperature-driven contact restructuring. Structural analyses further show that heating progressively disrupts the hydrogen-bond network in the first adsorption layer, reduces adsorption-layer density, and weakens radial distribution peaks, demonstrating a transition of interfacial water from an ordered, strongly adsorbed state to a more diffuse, weakly bound configuration with delayering and quasi-phase-transition behavior. This interfacial reconstruction weakens intergranular bridging and structural cohesion, promoting a shift from structural locking to water-mediated lubrication. These results suggest that frictional stability under coupled temperature-water conditions is strongly controlled by the thermal evolution of interfacial water structure.

Gastric interoception influences eating behavior and emotions, making its modulation valuable for healthcare and human-computer-interaction applications. However, whether gastric interoception can be modulated noninvasively in humans remains unclear. While previous research indicates that abdominal-sound-driven haptic feedback resembles gut sensations, its impact on feelings and gastric interoceptive behavior is unknown. We conducted three experiments totalling 55 participants to investigate how gut-sound-driven audio-haptic feedback applied to the stomach (1) affects user's feelings (2) influences perception of hunger and satiety levels and (3) influences gastric interoceptive behavior, quantified with Water Load Test-II. Results revealed that audio-haptic feedback patterns (a) induced the feelings of hunger, fullness, thirst, stomach upset, (b) increased hunger level, and (c) significantly increased volumes of ingested water. This work provides the first evidence showing that audio-haptic stimulation can alter gastric interoceptive behavior, motivating the use of noninvasive methods to influence users' feelings and behaviors in future applications.

This paper investigates the dynamics of noncooperative interactions between artificial intelligence agents and human decision-makers in strategic environments. In particular, motivated by extensive literature in behavioral Economics, human agents are more faithfully modeled with respect to the state of the art using Prospect Theoretic preferences, while AI agents are modeled with standard expected utility maximization. Prospect Theory incorporates known cognitive heuristics employed by humans, including reference dependence and greater loss aversion relative to utility to relative gains. This paper runs different combinations of expected utility and prospect theoretic agents in a number of classic matrix games as well as examples specialized to tease out distinctions in strategic behavior with respect to preference functions, to explore the emergent behaviors from mixed population (human vs. AI) competition. Extensive numerical simulations are performed across AI, aware humans (those with full knowledge of the game structure and payoffs), and learning Prospect Agents (i.e., for AIs representing humans). A number of interesting observations and patterns show up, spanning barely distinguishable behavior, behavior corroborating Prospect preference anomalies in the theoretical literature, and unexpected surprises. Code can be found at https://github.com/dylanwaldner/noncooperative-human-AI.

Over the last seventy years, many Finsler-type geometric and modified gravity theories have been elaborated. They have been formulated in terms of different classes of Finsler generating functions, metric and nonmetric structures, nonlinear and linear connections, and various sets of postulated fundamental geometric objects with corresponding nonholonomic dynamical or evolution equations. In several approaches, the resulting gravitational and matter field equations were not completely defined geometrically, or were developed only for restricted models. We present a progress report with historical remarks and a summary of new results on Finsler - Lagrange - Hamilton geometric flow and gravity theories. Such theories can be constructed in an axiomatic form on (co) tangent Lorentz bundles as nontrivial modifications of Einstein gravity.

Origami, which transforms flat sheets into three-dimensional shapes through folding patterns, has inspired the emergence of deployable systems in architecture and civil realms. Most existing origami-inspired deployable systems are based on rigid or curved-crease origami types. However, they inherently lack shape stability and require additional supports to maintain their deployed shapes. These lead to a fundamental trade-off between deployability and shape stability, which remains a major challenge for large-scale origami systems. Multistable origami, in contrast, achieves energy stability across multiple configurations during deployment. This unique characteristic enables it to maintain stable shapes even under external loads. These properties allow multistable origami to achieve both shape stability and deployability, offering high potential for self-supporting deployable systems in architectural applications. However, realizing both large-scale and structurally stable systems using a single origami faces many practical constraints. To overcome these limitations, origami block assembly has emerged as an effective approach to form global systems. This approach enables flexibility in global geometry and mechanical behaviors while offering reconfigurability. These indicate that the complementary potential of multistable origami and block assemblies can provide a promising solution. This study aims to address the challenges of applying deployable origami to large-scale architectural systems by leveraging the potential of multistable origami as modular building blocks. From a geometric standpoint, we explore design methods for stable configurations of multistable origami blocks that can align and interlock with each other. From a mechanical standpoint, we explore stiffness-controllable design methods that ensure self-supporting and load-bearing capabilities through geometric parameters.

In the northern hemisphere, river subjects the right bank to the pressure generated by the Coriolis force, which will increase the erosion of the river on the right bank. On the other hand, the Coriolis force also causes the sediments in the water to move to the right bank, which will increase the sediment deposition on the right bank of the river. Therefore, for rivers with low sediment content, Coriolis force will increase the erosion of river water on the right bank; for rivers with high sediment content, Coriolis force will increase the sedimentation of sediment on the right bank. It is noted that the Lanzhou section of the Yellow River has siltation of sands and pebbles to the right (south) bank. It is believed that this is caused by the Coriolis force moving the sands and pebbles to the right bank.

Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator ensembles have led to the development of efficient signal processing frameworks that surpass traditional approaches. However, scaling such systems remains challenging due to the significant increase of computational resources and issues with training convergence. This study advances the state of the art by addressing the problem of data processing with ensembles of nonlinear oscillators that can be scaled up. In our approach, the processing is achieved as an anticipated local resonance or echo in a group of coupled chaotic oscillators, driven by external data input. Local resonance is enabled by tuning the coupling terms between the oscillators, which are approximated using the traditional artificial neural network and adapted to match the input feature distributions. Training the framework entails training this neural network to capture the dynamics of the entire oscillator system. The framework is evaluated using synthetic data and demonstrates an accuracy in machine learning classification task, while patterns recognition and dynamic system identification are also presented here as an extension of the functionality that involves additional modifications. Additionally, the universality of this approach is demonstrated by tests with different connections configurations between the oscillators and their types. The main advantage of the proposed framework is that it avoids hand-crafting explicit coupling terms, which requires expert knowledge and does not scale for large problems. Leveraging standard machine learning components simplifies both training and deployment of oscillator networks, enabling gradient-based optimization.

Structured illumination microscopy (SIM) has emerged as a widely adopted super-resolution fluorescence imaging modality, offering high speed, low phototoxicity, large field-of-view, and compatibility with conventional probes. However, when applied to thick or scattering specimens, conventional two-dimensional SIM (2D-SIM) suffers from the missing cone problem in its optical transfer function, resulting in prominent out-of-focus background and severe reconstruction artifacts that compromise image fidelity. Here, we present four-beam interference structured illumination microscopy (4I-SIM), which introduces additional interference orders to expand lateral frequency support and compensate the axial missing cone simultaneously. This strategy achieves artifact-free super-resolution with intrinsic optical sectioning, effectively overcoming the fundamental limitation of 2D-SIM without additional acquisition overhead. Experimental validation across diverse thick fixed and live specimens demonstrates that 4I-SIM delivers nearly twofold lateral resolution enhancement and substantially improved sectioning compared with its 2D counterpart, achieving lateral and axial resolutions of 103 nm and 336 nm, respectively. In particular, 4I-SIM reveals mitochondrial remodeling and apoptosis under high-glucose stress with millisecond temporal resolution -- features that remain obscured with conventional SIM. With minimal hardware modification, low phototoxicity, and open-source reconstruction tools, 4I-SIM establishes a practical and reproducible platform for simultaneous super-resolution and optical sectioning imaging in complex biological environments.

This supplement documents the intellectual trajectory that led to the Category Mistake framework and the Forward-In-Time-Only (FITO) analysis presented in our recent arXiv papers. The ideas crystallized over fifteen years of research, conversation, and engineering practice -- beginning with a 2014 Stanford EE380 lecture on the physics of time in computing, sharpened through a 2016 email exchange with Leslie Lamport following a Papers We Love presentation of his seminal 1978 paper, and matured through the development of Open Atomic Ethernet (OAE). This document traces the concept development from its origins in the physics of entanglement and background-free time, through the recognition that Lamport's "happened-before" relation embeds a category mistake, to the practical engineering consequences documented in "Why iCloud Fails" and "What Distributed Computing Got Wrong." It is intended as archival supplementary material for future arXiv submission.

For the 34 monitor reactions included in the IAEA Beam Monitor Reactions (BMR) 2017 dataset and the 22 reactions listed in the IAEA BMR 2007 dataset, product radionuclide activities were calculated using the IMRA computational framework developed in this work. The aim of this work is to independently validate radionuclide activity calculations for charged-particle monitor reactions by comparing results obtained with the IMRA computational approach against the reference activity data provided in the IAEA-BMR 2007 and 2017 datasets. The calculated activity values were then compared with the corresponding pre-calculated activity data provided in the IAEA BMR datasets. This comparison demonstrates overall consistency between the present calculations and the IAEA reference data across the evaluated monitor reactions. However, for a limited subset of monitor reactions induced by doubly charged particles (α and 3He), notable differences were observed when the IAEA BMR 2017 activity values were used. These observations emerged during the independent validation of the present computational methodology implemented in the IMRA code and are reported as part of a reliability assessment of the activity calculation procedure.

In two-dimensional Lennard-Jones glasses, mechanical probing reveals that local yield surfaces are dominated by regions with a positive second derivative of the yield stress with respect to the loading angle. Each feature corresponds to a shear transformation zone and a characteristic non-affine displacement field at yield. Most features are well described by a combined Schmid-Mohr-Coulomb criterion parameterized by a weak-plane orientation, a critical stress, and a pressure sensitivity. The resulting parameter statistics clarify how the onset of plastic flow is governed by the population of discrete yielding features encoded in the amorphous structure.

We study the effects of hydrodynamic interactions between a wall and the Purcell three-link swimmer in the two-dimensional case. After deriving the equations of motion in a low Reynolds number regime using Resistive Force Theory with suitably modified drag coefficients, we show, by means of criteria from Geometric Control Theory, that the system is controllable at configurations that are nearly parallel to the wall. Furthermore, we study configurations that are tilted, and we show net displacement with respect to the initial orientation. Some numerical experiments illustrate the analytical results.

On April 27, 1900, William Thomson, better known as Lord Kelvin, delivered a visionary speech before the Royal Institution of Great Britain. In it, he presented two unresolved problems which, to him, appeared fundamental and unavoidable at the turn of the 20th century. He compared them to two clouds obscuring our understanding of physics. Dissipating these two clouds would eventually require the development of special relativity and quantum mechanics. This article revisits the second cloud which, contrary to what is often claimed in the literature, did not concern black-body radiation, but rather the specific heat of polyatomic molecules. To clarify this, the article aims to place Kelvin's speech within the historical context of the time and to situate it within the sequence of developments, from Kirchhoff to the first Solvay Conference in 1911, that marked the path of the extraordinary intellectual adventure that led to the birth of quantum mechanics. It will also be shown that Max Planck's initial motivation was not to solve the problem of the so-called "ultraviolet catastrophe."

This paper introduces Capability-Priced Micro-Markets (CPMM), a micro-economic framework designed to enable robust, scalable, and secure commerce among autonomous AI agents on the agentic web. The framework addresses the fundamental challenge of economic coordination in decentralized agent ecosystems, where entities must transact with minimal human oversight. CPMM synthesizes three key technologies into a unified system: MIT originated, Project NANDA infrastructure for cryptographically verifiable, capability-based security and discovery; the HTTP 402 "Payment Required" status code, with modern X402/H402 extensions for efficient, low-cost micropayments; and the Agent Capability Negotiation and Binding Protocol (ACNBP) for secure, multi-step negotiation and commitment. The paper formalizes agent interactions as a repeated bilateral game with incomplete information, demonstrating theoretically that the CPMM mechanism converges to a constrained Radner equilibrium, ensuring efficient outcomes under information asymmetry. A key theoretical contribution is the concept of "privacy elasticity of demand," which is introduced to quantify the trade-off between an agent's information disclosure and the market price of its services. By integrating secure capabilities, micropayment protocols, and formal negotiation mechanisms, CPMM provides a comprehensive, theoretically-grounded solution for creating functional micro-markets for the emergent agentic web.

In this work, we describe the development and application of a low-cost fluid interface visualizer referred to as the ``Meniscope.'' The device works using a color-based surface gradient detector method that maps the gradient of an air-water interface to a specific color on a target pattern below using a converging lens. Sample experiments are outlined that showcase the working principle and functional versatility of the device. The device and assembly instructions were piloted in a hands-on workshop, with pertinent feedback reviewed herein. The Meniscope is a low-cost device that is capable of producing striking visualizations of static and dynamic free-surface deformations while introducing users to free-surface measurement techniques in an accessible and hands-on manner.

Datasets encountered when examining deeper issues in ecology and evolution are often complex. This calls for careful strategies for both model building, model selection, and model averaging. Our paper aims at motivating, exhibiting, and further developing focused model selection criteria. In contexts involving precisely formulated interest parameters, these versions of FIC, the focused information criterion, typically lead to better final precision for the most salient estimates, confidence intervals, etc. as compared to estimators obtained from other selection methods. Our methods are illustrated with real case studies in ecology; one related to bird species abundance and another to the decline in body condition for the Antarctic minke whale.

This study presents a mathematical model that captures the interactions among tumor cells, healthy cells, and immune cells in a tumor-bearing host, with a specific focus on breast cancer. Incorporating the concept of delay, the model consists of four differential equations to analyze these cellular dynamics. The findings demonstrate the superior efficacy of metronomic chemotherapy compared to the maximum tolerated dose (MTD) method and underscore the necessity of adjunct therapies. Oscillatory tumor cell dynamics revealed by the model highlight the challenges of achieving complete tumor elimination through chemotherapy alone. Sensitivity analysis confirms the robustness of the model, particularly under metronomic treatment protocols, aligning with experimental observations regarding metronomic-to-MTD dosage ratios. Furthermore, the results emphasize the importance of synergistic effects from combination therapies. This biologically consistent framework provides valuable insights into tumor-immune interactions and offers a foundation for optimizing therapeutic strategies in cancer treatment.

In many low-income countries, neighborhood diesel generators are widely used to compensate for unreliable or unavailable national electricity grids. These diesel-based microgrids are typically characterized by market power, significant pollution, and weak regulatory oversight. In parallel, households increasingly deploy off-grid solar photovoltaic (PV) systems to gain control over electricity supply. However, these systems suffer from curtailed excess generation during peak solar hours and unreliable access at other times. While prior studies have optimized microgrids in developing contexts from a techno-economic perspective, they largely neglect the market power exerted by monopolistic private generators. This paper addresses this gap by developing a bi-level game-theoretic model that enables household-generated electricity to be fed into the microgrid while explicitly accounting for the market power of a neighborhood diesel generator company (DGC). The regulator sets price and feed-in-tariff caps to maximize household economic surplus (HES), while the DGC acts as a profit-maximizing agent controlling access and supply. The model is applied to a Lebanese case study using high-resolution empirical data collected via logging devices. Results show that: (i) price and feed-in-tariff caps substantially increase HES and consistently induce significant household PV feed-in to the microgrid; (ii) higher DGC budgets or greater PV-owner penetration lead to pronounced gains in HES; and (iii) the renewable energy share reaches 60% under base conditions and approaches 100% at sufficiently high budgets or PV-owner penetration levels, compared to 0% under the status quo.

Multifunctional wound dressings with antibacterial and antioxidant properties hold significant promise for treating chronic wounds; however, achieving a balance of these characteristics while maintaining biocompatibility is challenging. To enhance this balance, this study focuses on the design and development of 3D-printed chitosan-matrix composite scaffolds, which are incorporated with varying amounts of cerium oxide nanoparticles (0, 1, 3, 5, and 7 wt%) and subsequently coated with a vancomycin-loaded alginate layer. The structure, antibiotic drug delivery kinetics, biodegradation, swelling, biocompatibility, antibacterial, antioxidant, and cell migration behaviors of the fabricated dressings were evaluated in-vitro. The findings reveal that all of the formulations demonstrated a robust antibacterial effect against S. aureus bacterial strains in disk diffusion tests. Furthermore, the dressings containing cerium oxide nanoparticles exhibited proper antioxidant capabilities, with over 78.1% reactive oxygen species (ROS) scavenging efficiency achieved with 7% cerium oxide nanoparticles. The sample containing 5% cerium oxide nanoparticles was identified as the optimal formulation, characterized by the most favorable cell biocompatibility, an ROS scavenging ability of over 73.4%, and the potential to close the wound bed within 24 h. This study highlights that these dressings are promising for managing chronic wounds by preventing infection and oxidative stress in a correct therapeutic sequence.

Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresses this challenge by precomputing optimal solutions offline, enabling real-time control through simple function evaluation. While extensively developed for discrete-time systems, this approach suffers from combinatorial growth in solution complexity as discretization is refined. This paper presents a systematic continuous-time multiparametric framework for linear-quadratic optimal control that directly solves Pontryagin's optimality conditions without discretization artifacts. Through two illustrative examples, we demonstrate that continuous-time formulations yield solutions with substantially fewer critical regions than their discrete-time counterparts. Beyond this reduction in partition complexity, the continuous-time approach provides deeper insight into system dynamics by explicitly identifying switching times and eliminating discretization artifacts that obscure the true structure of optimal control policies. Knowledge of the switching structure also accelerates online optimization methods by providing analytical information about the solution topology. Clear step-by-step algorithms are provided for identifying switching structures, computing parametric switching times, and constructing critical regions, making the continuous-time framework accessible for practical implementation.

This work introduces a framework for reconstructing the interaction graph of neuronal networks modeled as multivariate point processes. The methodology performs bivariate inference, identifying synaptic links exclusively from the spike trains of a pair of neurons, without requiring observations of the remaining network activity. We propose a Macro-Micro Extrapolation algorithm to address data sparsity at the micro-scale, inferring synaptic interactions in the limit $Δ\to 0^+$. A key contribution is the Spike-Triggered Estimator, which leverages the local reset property of Galves-Löcherbach dynamics to decouple local synaptic jumps from higher-order network contributions, significantly reducing estimation variance and eliminating spurious dependencies on baseline firing intensities. By employing an adaptive hybrid logic that switches between sample averaging and our novel Pyramid Extrapolation, we ensure robust classification of excitatory, inhibitory, and null connections even in low signal-to-noise regimes. The framework's scalability and precision are validated by numerical results on dense cliques and structured layered networks, achieving perfect classification accuracy across diverse topological motifs.

We analytically investigate a quantum estimation method for a mechanical oscillator in a detuned cavity system based solely on homodyne measurement records, building on the framework developed by C.Meng et al. (Science Advances 8, 7585 (2022)). Estimation based only on measurement records is important because it enables state verification without assuming knowledge of the true system state. We construct a relative estimate operator from causal and anti-causal quantum Wiener filters and calculate its variance. The deviation from the causal conditional variance is defined as a reconstruction bias, whose magnitude is evaluated analytically. We show that, within experimentally relevant parameter regimes for typical quantum-state preparation, the reconstruction bias is sufficiently small to be neglected. As applications to state verification, we apply the method to proposals for macroscopic quantum entanglement mediated by electromagnetic interactions and for conditional momentum-squeezed states generated by homodyne detection, and clarify the conditions under which the bias remains negligible and when the reconstruction bias becomes significant.

Quantum digital signatures (QDS) offer information-theoretic security for message integrity, authenticity, and non-repudiation, and constitute a fundamental cryptographic primitive for future quantum networks. Despite significant progress, the practical deployment of QDS has been severely constrained by limited signature rates and poor tolerance to channel loss, particularly in long-distance and metropolitan-scale networks. Here, we report a high-rate, loss-resilient QDS system that overcomes these two key bottlenecks simultaneously. Our implementation combines intrinsically phase-stable polarization modulation based on a Sagnac interferometer with gigahertz-rate quantum state encoding and low-timing-jitter superconducting nanowire single-photon detectors, enabling robust and continuous operation at high repetition frequencies. By integrating this hardware platform with a one-time universal hashing-based QDS protocol, we achieve a signature rate improvement of more than two orders of magnitude compared with existing QDS implementations under comparable channel-loss conditions. Notably, the system maintains a non-zero effective signature rate of approximately 1.25 times per second at a total channel loss of up to 49.05 dB, representing the highest loss tolerance reported for QDS to date. These results establish a practical and scalable technological pathway for deploying QDS in real-world quantum communication networks.

Quantum entanglement provides a quantitative probe of the internal structure of hadrons and offers a sensitive means to study the quantum correlation in the hadron wave functions. For baryons, the spin state of the three valence quarks forms a tripartite qubit system, whose entanglement structure can be characterized by the four classes of three-qubit states. In this work, we compare the proton spin entanglement obtained from Basis Light-Front Quantization (BLFQ) with that from a quark-diquark model. By analyzing both bipartite and tripartite entanglement, we find that the quark-diquark model yields a substantially more entangled spin state than the BLFQ wave function in the valence Fock sector. This difference mainly originates from the larger W-type and Bell-type entanglement in the quark-diquark model. Within BLFQ, larger stronger coupling constant and smaller quark mass drive the spin correlation among the valence quarks towards an effective quark-diquark configuration with an active $d$ quark and a correlated $uu$ pair.

Solving the classical equations of motion in general relativity recursively, we consider the metric of a spatially localized and stationary source of matter. Having in mind a star of general composition, we characterize it by means of its infinite set of mass and current multipoles. Specializing to de Donder gauge we set up the recursive equations that produce the metric outside the star to any desired order in perturbation theory, expanded both in Newton's constant and in the order of multipoles. Up to second post-Minkowskian order we express the result to any order in the multipole expansion in terms of generalized (tensor) bubble integrals in momentum space and a corresponding simple expansion in inverse distances. In a special corner of the space of multipoles we recover the Kerr black hole solution to the given order. By tweaking just slightly the multipoles away from the Kerr limit the metric will describe stars that are Kerr-like and yet are not black holes. A subtlety with respect to the gauge ambiguity of de Donder gauge is also pointed out.

We report evidence for the resonant scattering effect at the center of the galaxy cluster PKS 0745-191 with XRISM. We analyzed XRISM/Resolve commissioning-phase observations of the distant cluster PKS 0745-191 (z = 0.103) with a 54 ks exposure. The gain drift was corrected using the onboard modulated X-ray source (MXS), and spectra were extracted from all pixels well illuminated by MXS, the core region (four central pixels, about 100 kpc), and the surrounding region. A single-temperature collisional ionization equilibrium (CIE) model fits the full field-of-view spectrum with kT about 6 keV and a turbulent velocity of about 120 km/s. From the core (r < 50 kpc) spectrum, we detect about 22 percent suppression of the Fe XXV He-alpha resonance (w) line relative to the CIE prediction. We performed Monte Carlo simulations to calculate the resonant scattering (RS) effect using radial profiles from Chandra data. The RS-inferred turbulence agrees with that inferred from Resolve line broadening, demonstrating that RS provides an independent and consistent constraint on ICM turbulence. These results highlight the potential of XRISM/Resolve for turbulence studies in galaxy clusters.