Papers

Quantum imaginarity is a fundamental quantum resource essential for quantum information processing. In this paper, we investigate the dynamical evolution behavior of quantum imaginarity for tripartite quantum mixed states in Schwarzschild spacetime. We find that Hawking radiation degrades the quantum resource of imaginarity, consistent with the behavior of entanglement and coherence under the Hawking effect. Interestingly, imaginarity exhibits a sharp change in the early stage of Hawking radiation, after which it varies slowly and asymptotically approaches a steady value. We further derive several trade-off relations that characterize the nonlocal redistribution of imaginarity across Rindler horizons. The findings of this study contribute to a deeper understanding of quantum resource behaviors in black hole spacetimes.

At the water-land interface, amphibious fishes encounter wet flowable substrates made of granular solid-water mixtures, which can stay solid or flow like a fluid. As these substrates become wetter or drier, their yield strength (at which solid-fluid transition occurs) and cohesion (how sticky they are) both change, challenging locomotion. Despite substantial understanding of tetrapod locomotion on flowable substrates (mostly dry sand), we know little about how amphibious fishes cope with wet flowable substrates of various wetness. Here, we studied mudskippers on clay mud of controlled, variable wetness over the range where solid-fluid transition occurs. As mud became wetter, its strength decreased by 100-fold, leading the animal to sink deeper, with larger areas of body and fins contacting mud. By contrast, mud stuck most easily at intermediate wetness. The increased sinkage and contact and stickiness change caused more mud to stick to and pull against the animal on wetter mud. We also tested dry mud, which stuck to animal fins as its mucus dried. Despite these challenges, the mudskipper predominately used a conserved crutching gait on all except the wettest mud tested, with a modest performance reduction. When normal crutching became less effective, the animal assisted it with tail thrusting, by bending and straightening it to push downward and backward to generate additional thrust and lift, or even thrusting the tail to jump. These observations suggest that mudskipper's crutching motor program is well adapted to its native muddy substrates but inflexible, with most novelty in tail use.

Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are within the solid. Despite understanding of locomotion on/within dry sand dominated by coarse grains with repulsive normal forces and friction, little is known for mud dominated by fine clay with strong cohesion. Here, we developed methods to prepare uniform mud of controlled, variable yield strength and characterize and track its drift from water evaporation. Compared to other flowable substrates, mud strength measured by upward force during penetration is weaker and can vary more, and mud sticks more during extraction to pull downward, making it more challenging for locomotion.

Numerical evidence has shown that a period of vanishing entropy production during far-from-equilibrium stages induces subsequent violations of the dominant energy condition in strongly coupled plasmas. This behavior also appears to hold for a Bjorken-expanding, hot and dense strongly coupled quantum fluid. In this context, it has been established that the chemical potential-to-temperature ratio ($\mu/T$) in the medium increases with higher initial charge density, $\rho_0$, and/or lower initial energy density, $\varepsilon_0$. Here, we present a numerical method to evolve Bjorken R-charged plasmas by varying $(\varepsilon_0,\rho_0)$ in order to generate a curve that preserves a constant $\mu/T$. This allows us to address the case in which all Bekenstein-Hawking entropy densities evolve towards configurations with the same $\mu/T$. This approach enables a more direct comparison with the $\mathcal{N}=4$ SYM plasma case ($\mu/T=0$) and, consequently, provides clearer evidence of the correlation between entropy production and violations of the dominant energy condition. Moreover, this procedure offers a characterization (albeit numerical and partial) of the iso$-\mu/T$ entropy density hydrodynamic attractor for hot and dense strongly coupled quantum fluids.

We introduce an operator-valued maximal f-divergence for completely positive (CP) maps between von Neumann algebras, associated with an operator convex function f on (0,+infinity). The construction takes values in the extended lower-semibounded self-adjoint part of the codomain von Neumann algebra. We prove independence of the common CP upper bound used in its computation, joint subadditivity, monotonicity under unital precomposition and normal postcomposition, a martingale convergence theorem for normal CP maps, and joint lower semicontinuity in the point-sigma-weak topology. For normal positive functionals, our construction recovers Hiai's maximal f-divergence. As a consequence, we establish its joint weak lower semicontinuity for arbitrary von Neumann algebras, answering a question left open by Hiai. For eta(t)=t log t, we obtain an operator-valued Belavkin–Staszewski (BS) relative entropy. Moreover, for normal channels with sigma-finite codomain, we prove that the BS channel divergence of Hollands and Ranallo coincides with the extended norm of our operator-valued divergence. Finally, we give finite-dimensional examples and obtain an explicit formula for a finite-index conditional expectation. In the BS case, this formula reduces to the logarithm of the Jones–Kosaki index.

We show that for any potential with a discrete energy spectrum, the well-known interpolation between ideal boson and fermion partition functions at discrete values of $\xi=-1/m$ yielded zero temperature ground state energies corresponding to $m$ fermions occupying a single quantum state. The grand canonical partition function in this case can be a result from genuine parastatistics.

High-resolution precipitation nowcasting is critical for reducing the impacts of severe weather but remains difficult because of rapid storm evolution. Deep learning models have shown great promise for this task, but their predictive skill often deteriorates over longer forecast horizons. This leads to increasingly blurry forecasts that fail to capture the complex, non-linear evolution of storm systems. In order to address these limitations, we introduce Spatio-Temporal U-DeepONet (GenONet), a novel architecture for long-range precipitation forecasting up to 3 hours, specifically designed to produce sharp and physically consistent results. GenONet's architecture pioneers the use of a Deep Operator Network (DeepONet) as a generator within a Generative Adversarial Network (GAN) framework for this task. The DeepONet learns the continuous-time dynamics of precipitation, ensuring stability over long forecast horizons. Adversial training against a spatio-temporal discriminator compels the model to produce sharp, coherent forecasts, while a physics-informed loss regularizer, derived from the Moisture Conservation Equation, improves physical plausibility in our ablation setting. Quantitative evaluations show that our model achieves consistently higher scores on most of the metrics, especially for highintensity events and at longer lead times. Qualitatively, GenONet produces structurally coherent forecasts that maintain their integrity, whereas baseline models degrade into indistinct patterns. Finally, an ablation study confirms the benefit of this physics-informed loss, highlighting the strength of combining operator learning with adversarial training.

High-temperature superconductivity has been found in bilayer Ruddlesden-Popper (RP) nickelates in bulk samples under high pressure, or in thin films via compressive strain. In the superconducting state, a tetragonal structure with a straight Ni-O-Ni bond along c-axis has been commonly observed, together with the suppression or diminishing of the density-wave orders. Therefore, it remains an open question whether these factors are sufficient for achieving superconductivity at ambient pressure. Here we report the first successful synthesis of heavily Sr-doped La$_{2}$SrNi$_{2}$O$_{7-{\delta}}$ under high-pressure and high-temperature (HPHT) conditions with a flux method. X-ray diffraction and scanning transmission electron microscopy (STEM) confirm that the material adopts a tetragonal (I4/mmm) structure with an 180$^{\circ}$ Ni-O-Ni bond angle along c-axis. Resistance measurements reveal metallic behavior with a low-temperature upturn and no density-wave features are observed. However, neither pressure nor oxygen variation induces superconductivity. Density functional theory calculations indicate that the holes introduced by Sr doping are predominantly doped into the Ni-3d$_{z^2}$ orbital, leading to the appearance of a very large ${\gamma}$ pocket on the Fermi surface at ambient pressure and significantly reducing the occupation of the Ni-3d$_{z^2 }$ orbital. Combining the experimental observations with theoretical calculations, we attribute the absence of superconductivity to the serious deviation from the half-filling state of the Ni-3d$_{z^2 }$ band, which is crucial for the interlayer antiferromagnetic interaction and thus for pairing. Our work unravels important issues for achieving superconductivity in bilayer nickelate system.

The Sun's faintness at Mars' orbit makes producing energy, melting ice, and staying warm more difficult. Orbiting solar reflectors (OSRs) can augment sunlight at Mars, but the area of OSRs needed to double sunlight at a Mars base is not known. Here, we analyze Sun-synchronous Mars orbits to find the OSR area that doubles insolation to a Mars base. We show that the reflectors can deliver sunlight and maintain a stable orbit via attitude control and solar-sail propulsion, with no propellant. We also show that these Mars orbits can be reached via solar sailing from low Earth orbit, reducing delivery cost. Doubling sunlight is viable with an orbiting solar reflector areal density of $20 {\rm g/m^2}$, a 7-fold improvement over flight-proven solar sails. However, designing a spacecraft with low areal density, agile maneuverability (for accurate pointing), high tension in the sail membrane (to smooth wrinkles), and mass-manufacturability (to enable a constellation of reflectors) would be challenging. Still lower areal density of $<5 {\rm g/m^2}$ would be needed for more ambitious applications, such as sublimating the CO$_2$ ice at Mars' south pole to aid in terraforming.

We present a spectral element lattice Boltzmann method (LBM) for partial wetting on curved geometries. A non-ideal gas phase-field model is incorporated into the LBM framework to enable phase separation with a constant interface thickness and the potential form of surface tension force is used. We adopt the force-splitting approach, yielding significantly improved stability and accuracy. Complex boundaries are naturally handled using a flux bounce-back scheme, which resolves inconsistencies in normal vectors across adjacent elements. Additionally, a general wetting boundary condition is implemented to capture static contact line in a thermodynamically consistent manner. The method is validated through simulations of droplets on flat surfaces, 2/3-dimensional curved surfaces, and equilibrium droplets without boundaries. Results demonstrate that parasitic currents are significantly reduced on unstructured meshes with complex geometries, reaching residual kinetic energy levels on the order of $10^{-24}$ for wetting configurations and $10^{-30}$ for isolated droplets.

Quantum imaginarity is an essential physical resource that underpins key functionalities of modern quantum technologies. We improve imaginarity witnessing via the prior knowledge of imaginarity-witness operators. To this end, we derive a rigorous upper bound on the maximum expectation value of an imaginarity witness operator over the set of all free (real) quantum states, which is given by the spectral norm of the real component of the corresponding witness operator. We demonstrate via detailed examples that this bound substantially improves imaginarity detection. We further classify all imaginarity-witness operators into four distinct families based on this bound. For these four witness classes, we perform a comprehensive analysis of their completeness and finite completeness, the joint detection of shared imaginary quantum states by different witnesses, and the conditions for distinct witnesses to identify identical imaginary states. Our results advance the fundamental understanding of imaginarity detection and offer useful insights for both theoretical studies and experimental implementations of quantum imaginarity.

It is traditionally believed that the no-slip boundary condition is necessary for vorticity generation, as might be implied by the Lighthill vorticity generation mechanism. However, the investigations of Morton (1984) and Terrington et al. (2020) assert that the vorticity-generation mechanism is independent of the no-slip boundary condition. To investigate this hypothesis, we simulate viscous flow over a circular cylinder in the laminar periodic von Kármán vortex-shedding regime at Re = 170, without enforcing the no-slip condition at the wall. Instead, we close the wall tangential velocity and its normal derivative using one-sided finite-difference approximations. Accordingly, the wall tangential velocity is dynamically determined from the evolving interior solution rather than prescribed. The resulting flows exhibit qualitatively similar patterns of periodic vortex shedding across all three wall treatments (no-slip, second- and third-order one-sided approximations), although the mean drag coefficient, r.m.s. lift coefficient, and Strouhal number differ from those of the standard no-slip simulation. More significantly, the velocity distributions just outside the boundary layer closely match those of the standard no-slip simulation, regardless of the approximation order. In particular, the circulation evaluated along a contour at the edge of the boundary layer, which corresponds to the total vorticity contained within the layer in the no-slip case, is found to be remarkably insensitive to the wall treatment. These results suggest that the no-slip condition is not necessary for vorticity generation or periodic shedding. However, it may still be required for accurate quantitative prediction of the integral flow quantities and shedding dynamics.

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

Upcoming and ongoing surveys will detect thousands of stellar streams around galaxies other than the Milky Way. Studies from the Milky Way have shown that time-dependent evolution of the Galactic halo plays a key role in shaping stellar streams, but remains unexplored for extragalactic stellar streams. We use the FIRE-2 m12m cosmological zoom-in simulation, mock observed as an extragalactic system including three stellar streams, to examine how halo time-dependence affects progenitor and host halo inference from extragalactic systems. We show that two of the three m12m streams are well reproduced in a static halo if we only allow for tidal stripping near pericenter. We apply the extragalactic stream fitting code X-Stream to each mock observed stream, and obtain constraints on the host dark matter halo and stream properties. Using on-sky morphology alone and then fixing the progenitor radial velocities, we compare recovered orbits and halo parameters to the FIRE-2 m12m ground truth. For the longest stream with a looped segment, we find unbiased strong constraints on progenitor and halo properties. For the shortest stream, we find limits on orbital parameters, but no constraints on progenitor and halo mass unless we include fainter, more extended debris. For the most massive stream, which was not well produced in a static halo, the recovered orbital parameters are biased, reflecting unmodeled time-dependence. We conclude that imaging of stream debris from extragalactic dwarf galaxies can, in some cases, be used to infer present-day dark matter halo properties, even in a cosmological environment.

Recently in the physics literature there have been a small, but growing, number of papers that have applied the Eynard-Orantin topological recursion procedure to spectral curves with ramification loci of infinite cardinality. However, there is a corresponding gap in the mathematics literature; indeed, it has not been checked rigorously whether the resulting infinite sums converge, or whether the resulting correlators have all the desired properties of the topological recursion. The present work aims to bridge this gap by defining topological recursion on a suitably broad class of spectral curves to cover the aforementioned physics applications and to rigorously prove that this definition has the properties one would intuitively expect. As a by-product, some interesting coincidences involving quantum curves are discovered, where two different spectral curves yield the same quantum curve, a situation that has, hitherto, not appeared in the literature.

Materials exhibiting strongly anisotropic lattice thermal conductivity are desirable for thermal-management applications, yet such behavior is commonly associated with layered or quasi-one-dimensional van der Waals crystals and highly anisotropic elastic properties. Here, we investigate lattice thermal transport in the hexagonal perovskites Cs$BX_3$ ($B=$ Mg, Cd; $X=$ Cl, Br, I) using first-principles calculations. At 300~K, the calculated in-plane and out-of-plane lattice thermal conductivities range from 0.13–0.83 and 0.34–6.26~Wm$^{-1}$K$^{-1}$, respectively, corresponding to anisotropy ratios of 2.6–7.5. This pronounced anisotropy is remarkable given the relatively modest elastic anisotropy, characterized by $C_{33}/C_{11}$ = 0.994–1.842. Our analysis reveals that medium-frequency optical phonons provide an efficient out-of-plane heat-transport channel, contrary to the conventional picture in which heat transport is dominated by acoustic phonons. These findings identify face-sharing octahedral frameworks as a promising platform for engineering strong thermal-conductivity anisotropy in mechanically near-isotropic, non–van der Waals crystals.

High-harmonic generation (HHG) provides a coherent ultrashort-pulse light source in the extreme- ultraviolet (XUV) region and has potential applications in time-resolved spectroscopy and materials characterization. In this study, we constructed an HHG system using a Yb:KGW laser system (PHAROS, Light Conversion) as the driving source and Ar gas as the nonlinear medium. High-order harmonics were observed up to a photon energy of 70.6 eV, corresponding to the 59th harmonic order. As an application of the developed XUV source, we measured the transmission of a Mg thin film and a Si3N4 membrane. In addition, the surface chemical state of the Mg thin film was characterized by X-ray photoelectron spectroscopy (XPS), and the results were compared with the transmission measured using the HHG source. This comparison was used to examine the relationship between the surface condition, including surface oxidation, and the XUV transmission of the Mg thin film. These results demonstrate the applicability of the developed Ar-based HHG source to the characterization of thin-film transmission in the XUV spectral region.

The classical problem of a rigid body in an ideal fluid is a six-dimensional dynamical system with three conserved quantities. Despite its long history and its importance as a reduced model of many fluid-structure problems, basic questions remain, including the shapes and connectivities of the three-dimensional submanifolds of solutions, and the nature of chaotic motions on these. We explore the problem with a particular ellipsoidal body, beginning with integrable motions— steady linear translation and rotation and periodic planar tumbling and fluttering. The stability of these states depends on the relative magnitudes of linear and angular momentum or energy. Linear stability, including Floquet, analysis of lower-dimensional perturbed systems is consistent with direct integration of the full system. We document instabilities leading to a variety of regular and chaotic motions, including flipping and twirling, whose trajectories appear to follow paths near connections between the integrable states. Such indirect observation of these connections provides insight into the structure underlying the rich dynamics of this simple system. For the submanifold where linear and angular momentum are perpendicular, we further examine how solutions fit together to fill momentum space in different zones of stability of the integrable states, and thereby uncover additional bifurcations in connectivity and what appear to be new integrable solutions.

Combining attosecond science with semiconductor physics provides a promising interdisciplinary platform for the attosecond control of semiconducting properties. In each field, the reconstruction of attosecond beating by interference of two-photon transitions (RABBIT) and the time-resolved and angle-resolved photoemission spectroscopy (tr-ARPES) have been central experimental techniques for probing microscopic dynamics of electrons. However, the integration of the two techniques, bridging the two fields, has been missing so far although they have many technical similarities. Here, we develop a theoretical framework that integrates the two techniques based on the second-order time-dependent perturbation theory. Within this framework, we investigate the RABBIT spectroscopy in semiconductors focusing on the recent hallmark of tr-ARPES, namely quantum path interference between Floquet and Volkov states. Moreover, we theoretically identify a novel quantum path incorporating the virtual excitation, which substantially interferes with the Floquet and Volkov states in both the RABBIT spectroscopy and tr-ARPES of semiconductors. Importantly, we find that such virtual excitation channel induces an attosecond topological interference with the Floquet-Volkov paths, encoding topological quantities such as the local Berry curvature into the time shift of RABBIT sidebands, which is directly related to the photoelectron emission delay. Our findings establish a theoretical framework connecting attosecond spectroscopy to tr-ARPES, paving the way for future applications of attosecond science in semiconductors.

We study the phase boundary of the finite-lifespan frog model. For rate-one continuous-time simple random walk on an infinite, connected, locally finite transitive graph of superlinear growth, we prove that the critical-density curve is continuous and strictly decreasing, with $-\log\lambda_c$ locally bi-Lipschitz. The inverse critical-lifespan curve has the corresponding regularity wherever it is finite. Thus the critical-curve conjecture of Angel, de la Riva, Hermon, and Shi reduces to finiteness of the critical lifespan at every positive density. We identify the exact short-lifespan limit $t\lambda_c(t)\to\Delta\log(1/(1-p_c(G)))$, where $\Delta$ is the degree and $p_c(G)$ is the bond-percolation threshold, and extend critical-curve regularity and sharpness to a class of long-range frog models. The main tool is a local-to-global principle for activation processes generated by independent finite rooted ranges: local one-hit comparison implies comparison of global reachability and survival. The comparison allows disconnected ranges and source-dependent laws, and therefore also applies to activation models beyond random walks on a fixed graph.

We determine the quantum value of the three-setting, two-outcome Bell functional I3322. The value is the unique intersection \(q_\dagger\) of an analytic A-high stable curve of the exact Jacobi characteristic map with a central reverser curve. A computer-assisted proof isolates this intersection in a rational interval of width \(10^{-55}\), beginning 0.2508753845139765356173366109459512989013219739714764755. We prove that the supremum over finite-dimensional tensor-product strategies, the unrestricted spatial value and the commuting-operator value all equal \(q_\dagger\). No finite-dimensional strategy attains the value, whereas a normal infinite-dimensional spatial strategy and a commuting GNS strategy do. The proof combines an exact Bellman/path variational reduction, extraction of a positive bilateral calibrated Jacobi fibre from a maximizing weak-star state, a reflected-fibre central-incidence theorem and interval certificates for the unique stable/central intersection. A separate operator-positive three-remainder decomposition gives the commuting upper bound. The complete verification record is archived at DOI 10.5281/zenodo.22160086.

Quantifying mitral regurgitation severity remains limited by the assumptions of clinical flow convergence methods, while high-fidelity simulation and volumetric velocimetry are too slow for routine use. We investigate whether a learned solution operator can reconstruct transient three-dimensional transvalvular hemodynamics from the sparse observation an in-vitro experiment actually provides: a single planar velocity slice and two boundary pressure traces. A Deep Operator Network is pretrained on an experimentally benchmarked URANS database spanning eleven mitral regurgitation orifice phantoms, learning a mapping from a masked two-component planar velocity snapshot to the surrounding volumetric field, and is subsequently adapted to unseen target cases by fine-tuning on their sparse measurements. Adaptation reliably corrects the flow topology within the supervised plane, reorienting a strongly eccentric jet that the pretrained operator predicts as straight, and yields full-field predictions in minutes rather than the days required by the underlying simulations. Its influence decays sharply with distance from that plane, however: measured against phase-resolved particle image velocimetry, the reconstruction error rises from 24.6% at 2mm to 52.6% at 6mm, and the resulting mismatch between corrected and uncorrected layers degrades physical consistency. Single-plane supervision thus constrains the observed plane far more effectively than the surrounding volume, which we identify as the principal obstacle to coherent 4D reconstruction from sparse planar data.

Prosthetic mechanical heart valves (MHVs), particularly the bileaflet types, have been one of the most advanced and commonly implanted heart valves for more than four decades. These bileaflet mechanical heart valves (BMHVs) offer superior durability and improved hemodynamics; however, they have certain drawbacks, including the need for lifelong anticoagulation to prevent blood clot formation and the associated risks of thromboembolism. To overcome these limitations, comprehensive research studies are deployed, among which controlling the overall hemodynamics by means of passive interventions, such as placing (multiple) vortex generators (VGs) on the heart valve leaflets, is one possibility. These VGs, in particular, are known to delay the separation of boundary layers formed around the leaflet surfaces, provided they are precisely positioned and have their chosen design features. Limited research has shown that VGs improve hemodynamics beyond a BHMV when rectangular-type VGs (RVGs) are considered. Specifically, configurations such as co-rotating and counter-rotating are investigated at an incidence angle of $23^{\circ}$; however, their location on the heart valve leaflets and their shape can prove vital, an aspect that has not been explored so far. Suffice it to add, the alteration in hemodynamic performance due to these VGs may often lead to an impact on several critical clinical indices such as the pressure gradients, turbulent intensity, wall shear stress (WSS), blood damage (BD), etc., which typically establish the overall functional efficiency of an MHV.

Human blood is a complex biological suspension whose macroscopic flow behaviour arises from the coupled microscopic dynamics of deformable blood cells, plasma proteins, and evolving cellular microstructures. As a result, blood exhibits a range of nonlinear rheological behaviours, including shear-thinning, viscoplasticity, viscoelasticity, and thixotropy, which strongly influence its physiological and clinical hemodynamics. This review provides a comprehensive assessment of the role of blood rheology in arterial and blood-contacting cardiovascular device flows, with particular emphasis on the extent to which different rheological characteristics alter clinically relevant flow quantities and on whether the conventional Newtonian approximation remains adequate for the analysis. The underlying physical mechanisms responsible for the major rheological behaviours of blood are first discussed, followed by a critical review of the constitutive models commonly employed in hemodynamic analysis, including generalised Newtonian, viscoelastic, and thixo-elasto-viscoplastic (TEVP) ones. The effects of blood rheology on arterial flows involving stenosis, bifurcation, and aneurysm under both steady and pulsatile flow conditions are subsequently reviewed and discussed in terms of several physiologically important parameters, such as pressure drop, flow resistance, wall shear stress, flow separation, and recirculation zone. The influence of blood rheology on cardiovascular devices, including prosthetic heart valves and stents, is also reviewed, particularly regarding flow stagnation, residence time, hemolysis, and thrombosis.

We comment on the recent proposal (arXiv:2608.21211v1 (2026)) of a new transverse Hamiltonian for electromagnetic interacting charged particles that ignores both the classical and quantum-mechanical versions of the already known one. 1 Introduction

In this paper, we establish a rigorous geometric framework that applies the formal architecture of finite-dimensional bi-Hamiltonian structures and Nambu-Poisson mechanics to macroeconomic growth theory. Moving beyond static empirical correlations, we deploy Ryuzo Sato's principle of simultaneous holotheticity to demonstrate that economic production functions emerge natively as stable, time-independent geometric leaves of integrable flows. We construct a unified, hierarchical taxonomy of three fundamental economic growth regimes that sequentially generalize one another: the classical, unconstrained Cobb-Douglas mode; the resource-limited S-shaped econsystem response; and the capacity-bounded "overshoot-and-collapse" regime. Furthermore, we push this paradigm into non-smooth territory by investigating the structural boundary crises that occur when aggregate economic trajectories encounter definitive resource carrying capacity ceilings. We show that these capacity limits induce a catastrophic rank-collapse of the compatible contravariant Poisson pencil.

Production deployments of large language model (LLM) agents remain unreliable on long, multi-step workflows even as benchmark success rates climb steadily. We argue this gap is largely an artifact of task horizon: benchmarks are dominated by short-to-medium horizons where success remains high, while production workloads demand an order of magnitude more dependent steps. We measure the effect directly, characterizing the shape of agent degradation and disentangling its cause across a large controlled study spanning nine models, six open models from 1.2B to 671B parameters, and three deployed proprietary systems; four task families, including a genuinely agentic tool-use loop; five horizons; and three context regimes. Task success follows a geometric law governed by a single per-step reliability parameter, which rises with model scale but saturates well below 1 even for the strongest models, guaranteeing eventual collapse at sufficiently long horizons. The effect is sharpest on the agentic task, where every model tested, including widely deployed systems, falls from near-perfect success to near zero within sixteen steps of (n=10,664 analyzed trajectories. Degradation is driven by step count rather than context length: bounding the context window steepens decay rather than easing it (logit slope -0.69 vs. -0.44), p=3x10-6), contradicting a lost-in-the-middle explanation and warning against a common production shortcut. Projecting measured reliability onto representative benchmark horizons quantifies a substantial gap between benchmark and production conditions, from 0.42 at GAIA-length horizons to 0.24 at hundred-step production horizons. For teams responsible for agent orchestration and reliability at scale, these results argue for horizon-aware evaluation and reliability budgeting in place of aggregate pass-rate metrics. Code, prompts, seeds, and raw trajectories are released.

Non-stationary phenomena are ubiquitous, with examples to be found in climatological measurements, brain activity, and the behavior of financial markets. Starting with a time series from a non-stationary process, a key challenge is to infer the time-varying parameters that underlie the non-stationarity in these systems, without requiring a generative model of the dynamics to be learned. This problem is referred to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Here we introduce a PINUP method called feature-based Slow Feature Analysis (f -SFA) comprising the computation of time-series features across sliding windows, followed by dimension reduction using slow feature analysis (SFA). This allows us to detect slow variation in a potentially wide range of statistical properties of the measured dynamics on a timescale determined by the window length. Crucially, using a comprehensive time-series feature set avoids the subjectivity of feature selection, while the SFA slowness constraint overcomes the bias towards irrelevant correlated features seen with variance-based dimension reduction. The performance of f -SFA surpasses that of four benchmark PINUP methods across a diverse range of non-stationary chaotic processes, and we explore the impact of various parameters on performance, including observation noise, parameter timescales, parameter amplitudes, and unseen parameter values. Further, applying f -SFA to sleep polysomnography data, we show that it is able to infer a time-varying parameter underlying the non-stationary sleep recordings that closely tracks depth of sleep. To our knowledge, this work presents the first comparative study of PINUP methods, and we demonstrate that f -SFA is a simple, effective, and noise-robust approach for quantifying non-stationarity from time series, that can be applied in a range of fields.

Atom interferometers (AIFs) are highly precise inertial sensors and are considered promising instruments for the detection of gravitational waves (GWs) and certain dark matter (DM) candidates in the mid-frequency band. While GW detection with AIFs was initially proposed for space-based experiments with baselines spanning thousands of kilometers, recent developments suggest that terrestrial setups with baselines of at least 100 meters may also be capable of detecting GWs. In this work, we analytically derive the GW phase response formula of a ground detector, find an additional term compared to the existing literature and check it our findings numerically. Based on this treatment, we analyze the optimal geometric parameters for earth-bound AIF experiments. Subsequently, we numerically simulate GW detection schemes for these optimized interferometers using an open-source Python algorithm. Numerical simulations of these schemes have are not available to the community, yet crucial for the accurate modeling of noise and non-trivial gravitational backgrounds.

We report adaptive-optics Ks-band imaging of the composite Seyfert 2 and Wolf-Rayet galaxy NGC 6764 (D = 32 Mpc), obtained with LUCI/SOUL at the Large Binocular Telescope. The nucleus resolves into three compact sources with pairwise projected separations of 0.07-0.20 arcsec, corresponding to 11.0-30.9 pc. All three have indistinguishable H, Ks, H2, and Br-gamma colours, so photometry alone cannot separate accretion from star formation. The system is consistent with a Seyfert nucleus and two star-forming regions, but a dual or triple AGN cannot be excluded. In the latter case, the separations would be two orders of magnitude smaller than in any confirmed or candidate AGN triplet reported to date. Diffraction-limited near-infrared integral-field spectroscopy is required to establish the nature of each component.