For a surface group $π_1(Σ_g)=\langle c_1,\dots , c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2g}^{-1}\rangle$ with genus $g\geq 2$, we provide an explicit bound $n-1\leq \mathrm{CL}(2n)=\mathrm{CL}(2n+1)\leq n+8g-1$ for the conjugator length function $\mathrm{CL}:\mathbb N\to\mathbb N$ of $π_1(Σ_g)$ via a detailed analysis of conjugation reductions.

We experimentally and theoretically study the thermodynamically optimal control of interacting multiple-particle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that transport the system between prescribed trap configurations within a fixed time in the most energy efficient way. For Markovian systems with conservative pairwise interactions, we establish a general result in the low-noise limit: optimal particle trajectories are linear in space and time, corresponding to steady straight-line motion, irrespective of the specific interaction potential, even for nonlinear forces. Thus, conservative interactions do not modify the geometry of the optimal paths. This property breaks down in the presence of strong noise or nonconservative interactions. For the paradigmatic case of hydrodynamic coupling, we demonstrate experimentally that optimal control can involve curved trajectories that significantly reduce the energetic cost by exploiting collectively generated fluid flows. The emergence of curved paths as optimal solutions highlights a fundamental distinction between non-interacting and interacting systems and reveals a cooperative mechanism for energy-efficient control.

We develop a continuous-time general equilibrium framework for economies with a heterogeneous population -- modeled as a continuum -- that repeatedly optimizes over short horizons under relative-income (Duesenberry-type) criteria. The cross-section evolves through a Brownian flow on a type space, transporting an effective impatience field that captures time variation in preferences induced by demographic changes, aging, and broader social shifts. We establish three main results. First, we prove an optimal consumption--investment theorem for infinite heterogeneous populations in this Brownian-flow setting. Second, we define a \emph{short-horizon Duesenberry equilibrium} -- a sequential-trading (Radner-type) equilibrium in which agents repeatedly solve vanishing-horizon problems under a relative-income criterion -- and provide a complete characterization and existence proof under mild regularity conditions; notably, market completeness and absence of (state-tame) arbitrage emerge endogenously from the market clearing, rather than being imposed as hypotheses. Third, we derive sharp asset-pricing implications: in equilibrium, the market price of risk is pinned down by the volatility of aggregate \emph{total wealth} (financial plus human capital), implying that the equity premium is governed by the magnitudes and correlations of wealth and equity volatilities rather than by consumption volatility alone. This shifts the equity premium puzzle from an implausibly low consumption volatility to a question about the volatility of aggregate total wealth. The framework delivers explicit decompositions of the risk-free rate that are consistent with macro-finance stylized facts. All equilibrium quantities are expressed in terms of market primitives.

We study the Cauchy problem for generalized electron magnetohydrodynamics (EMHD). We establish the local existence and uniqueness of solutions in critical Sobolev spaces, as well as global existence and uniqueness for small initial data. In addition, we prove an instantaneous smoothing effect for the corresponding solutions. Finally, we derive time decay rates for the global solutions.

We give a mathematical interpretation of the dualities between type $A$ Argyres-Douglas theories recently obtained by Beem, Martone, Sacchi, Singh and Stedman, building on work of Xie. Using the fact that, via the wild nonabelian Hodge correspondence, the data defining such a theory amount to singularity data for irregular connections on $\mathbb P^1$ of a specific form, we show that these dualities can all be realized as compositions of two types of more basic operations acting on such irregular connections: the Fourier transform and a Möbius transformation exchanging zero and infinity. The proof relies on the stationary phase formula giving explicit expressions for the singularity data of the Fourier transform. We also clarify the relation between the quivers describing the 3d mirrors of type $A$ Argyres-Douglas theories and the nonabelian Hodge diagrams defined in work of Boalch-Yamakawa and of the author: the 3d mirror corresponds to the unique nonabelian Hodge diagram with no negative edges/loops among those of singularity data in the corresponding orbit under basic operations.

Context. Galaxies discovered by JWST at z > 10 are predominantly characterized by extremely blue rest-frame UV slopes. Conversely, the existence of dust-reddened systems at such early epochs has remained largely unconfirmed spectroscopically. Aims. We present the spectroscopic confirmation of EGS-z11-R0 at z = 11.45, the most distant red galaxy identified to date, discovered serendipitously through inspection of publicly available JWST/NIRSpec data. Methods. We analyze JWST/NIRSpec PRISM and G395M spectroscopy together with multiwavelength HST, NIRCam, and MIRI photometry. We identify significant detections of the C IV 1548,1551 and C III] 1908 transitions, yielding a redshift of zspec = 11.452 +/- 0.021. We measure rest-frame UV emission-line fluxes and equivalent widths and use these diagnostics to constrain the nature of the ionizing radiation field. Finally, we perform spectral energy distribution modeling with CIGALE, combining spectroscopy with photometry and including stellar, nebular, dust, and active galactic nuclei (AGN) components. Results. EGS-z11-R0 exhibits a red UV continuum slope (betaUV approximately -1.0), placing it well above the canonical MUV-betaUV relation at z~10-12 and making it the highest-z spectroscopically confirmed member of the emerging "red monster" population. Emission-line diagnostics reveal a hard ionizing spectrum consistent with extreme star formation and compatible with a composite stellar plus AGN scenario. The best-fit SED solution favors a stellar mass of log(M*/Msun) ~ 9.2-9.6, a SFR of 10-40 Msun yr^-1, and substantial dust attenuation (AV~1.2 mag). Conclusions. The confirmation of EGS-z11-R0 establishes that chemically evolved, dust-enriched galaxies were already in place at z approximately 11.5. [abridged]

We develop an unsupervised physics-informed neural network to solve saddle-point equations (SPEs) governing direct above-threshold ionization (ATI) within the strong-field approximation. This setting provides a well-understood testbed in which the saddle-point structure is known for tailored driving fields, enabling systematic validation of the proposed solver. The network is trained by minimizing the residual of the SPEs and requires only the definition of the driving-field shape and its parameters, such as intensity, carrier-envelope phase, ellipticity, and relative phase. We introduce a window parametrization strategy that maps network outputs to prescribed regions of the complex-time plane, guiding the optimization toward physically relevant solutions and improving convergence stability. We benchmark the PINN against a conventional solver for a range of fields, demonstrating robust recovery of the dominant complex ionization times over wide parameter ranges. The network tracks changes in ionization event dominance as laser parameters are varied, enabling exploration of regimes where conventional solvers require repeated manual initialization. Using the PINN-derived solutions, we compute coherent ATI photoelectron momentum distributions and show the symmetries of the driving fields are reflected in both the saddle-point structure and the resulting spectra. These results establish PINNs as a promising framework for semiclassical strong-field calculations and provide a foundation for extending machine-learning solvers to Coulomb-corrected models or to more complex processes, such as rescattered ATI for which the SPEs are highly nonlinear and the presence of multiple closely-spaced solutions makes conventional Newton-type root-finding highly sensitive to initial guesses, which hinders systematic investigations across laser-parameter spaces, particularly for tailored fields.

We present \texttt{py5vec}, a Python package for implementing and extending the 5-vector method, used to search for continuous gravitational wave (CW) signals. We also provide a comprehensive theoretical review of the 5-vector method and extend the relative likelihood formalism by marginalizing over the noise variance, resulting in a more robust Student's t-likelihood, and over the initial phase to account for pulsar glitches. \texttt{py5vec} provides a modular architecture that separates data representation, signal demodulation, and statistical inference into independent abstract stages. It supports multiple input data formats and interoperates with existing Python software, providing a bridge between different approaches. For example, using a \texttt{bilby}-based interface, \texttt{py5vec} implements Bayesian parameter estimation within the 5-vector formalism for the first time. The modular design also allows for making exact multi-level and direct comparisons between other software, such as \texttt{cwinpy} and \texttt{SNAG} in MATLAB. In \texttt{py5vec}, we implement a multidetector targeted search for known pulsars, validated using LIGO data from the O4a run and hardware injections, demonstrating consistent reconstruction of signal parameters. This package therefore provides a flexible platform for current targeted searches and for future extensions to other CW search strategies.

We study the properties of plasma sheath containing the cold positive ions, the secondary electrons, and the primary electrons with a Cairns-distribution (a non-thermal velocity-distribution). We derive the generalized Bohm criterion and Bohm speed, the new floating potential at the wall, and the new critical secondary electron emission coefficient. We show that these properties of the plasma sheath depend significantly on the a-parameter in the non-thermal a-distribution, and so they are generally different from those of the plasma sheath if the primary electrons were assumed to be a Maxwellian distribution.

Among various applications of the AdS/CFT correspondence in condensed matter physics of particular importance is the realization of the phase transition between the normal and superconducting phase in a holographic QFT. After seminal papers on holographic superconductors that introduced the basic setup, one of the main lines of development focused on capturing the Meissner effect with all the relevant parameters, which requires inclusion of an external magnetic field. Although a complete holographic description of a superconductor is still lacking, the basic elements of the gravitational systems dual to what can be most accurately characterized as a charged superfluid have been established. Using holographic setups for describing three- and four-dimensional superconductors, we investigate the effect of noncommutative twist deformation of bulk fields on the phase transition parameters, such as the critical magnetic field and condensate. In a wider context, our results represent a first systematic attempt to elucidate the role of noncommutative gauge field theory as part of the bulk description of condensed matter systems.

The ultimate non-classic light sources for modern photonic quantum technology require on-demand generation of indistinguishable quantum light with high brightness and flexible engineering of quantum emission in multiple degrees of freedom. In this work, we present monolithic microcavity-metalens interfaces consisting of quantum-dot-micropillar single-photon sources and ultra-thin metalenses accurately aligned on opposite sides of an III-V compound semiconductor chip. The pronounced cavity quantum electrodynamics effect enabled by the micropillar cavity facilitates single-photon emission from quantum dots with simultaneous high degrees of single-photon purity, source brightness and photon indistinguishability while the multi-functional metalenses concurrently tailor quantum emission in multiple physical degrees of freedom including radiation divergence, emission directionality, polarization state and orbital angular momentum (OAM). Furthermore, high-fidelity polarization-OAM entanglement and single photons with local spin topologies are successfully generated in our integrated device. In particular, we demonstrate stable propagations of single-photon skrymions in atmospheric turbulence and reveal their topological advantages over the conventional structured quantum light. Our work advances the research fields of integrated quantum photonics and meta-optics, providing integrated high-dimensional quantum light sources for advanced photonic quantum science and technology.

This paper presents a new data-driven robust predictive control law, for linear systems affected by unknown-but-bounded process disturbances. A sequence of input-state data is used to construct a suitable uncertainty representation based on interval matrices. Then, the effect of uncertainty along the prediction horizon is bounded through an operator leveraging matrix zonotopes. This yields a tube that is exploited within a variable-horizon optimal control problem, to guarantee robust satisfaction of state and input constraints. The resulting data-driven predictive control scheme is proven to be recursively feasible and practically stable. A numerical example shows that the proposed approach compares favorably to existing methods based on zonotopic tubes.

This survey is intended as an invitation to the theory of stable $\infty$-categories, addressed primarily to mathematicians working in the representation theory of algebras and related subjects.

Many statistical problems involve optimization over a discrete parameter space having an unknown dimension. In such settings, gradient-based methods often fail due to the non-differentiability of the objective function or a non-convex or massive search space with an objective function having many local maxima/minima. This paper presents GAReg, a unified genetic algorithm package that handles discrete optimization regression problems, which works well when standard algorithms are unjustified. GAReg provides a compact chromosome representation supporting optimal knot placement for regression splines, best-subset regression variable selection, and related problems. The package allows for uniform initialization, constraint-preserving crossover and mutation, steady-state replacement, and an optional island-model parallelization. GAReg efficiently searches high-dimensional model spaces, providing near-optimal solutions in settings where exhaustive enumeration or integer or dynamic programming approaches are infeasible.

A dissociation set in a graph is a subset of vertices which induces a subgraph with maximum degree at most one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we consider the $n$-vertex connected graphs with a given dissociation number that attain the minimum spectral radius. By using structure analysis and constructing difference equations, we characterize the extremal graphs with dissociation number $n-3$.

In this paper, we study a family of symplectic manifolds introduced by Woodward. These manifolds belong to the broader class of \emph{multiplicity-free} Hamiltonian $G$-manifolds, a generalization of toric manifolds for non-abelian Hamiltonian group actions. Prominent examples of multiplicity-free spaces include coadjoint orbits of $U(n)$ and $SO(n)$ equipped with multiplicity-free $U(n-1)$- and $SO(n-1)$-actions, respectively. Although these multiplicity-free $U(2)$-manifolds are not toric, we may study a family of Lagrangian tori by performing a symplectic cut that allows us to apply the toric Lagrangian Floer theory. In particular, we employ Venugopalan--Woodward's study of pseudoholomorphic curves under symplectic cuts to obtain the leading order potential. This allows us to identify a number of critical points of the potential function which correspond to a non-displaceable Lagrangian submanifold. Moreover, we adapt McDuff's probe method to show that the majority of the other Lagrangian submanifolds in these spaces are displaceable. Finally, we prove that the open-closed map for the Fukaya subcategory generated by these branes is an isomorphism. It follows that they satisfy Abouzaid--Fukaya--Oh--Ohta--Ono's generation criterion.

Charge density waves (CDWs) with multi-component order parameters can break unexpected symmetries through the interplay of nearly degenerate instabilities. In the widely investigated material 1T-TiSe$_2$, a central question is whether the observed CDW has a chiral character, which would manifest as the spontaneous breaking of mirror and inversion symmetries. Previous experiments have reported conflicting results about the broken symmetries in the CDW phase of 1T-TiSe$_2$. Here, we resolve this controversy by identifying the bulk broken symmetry as ferroaxial, corresponding to the breaking of vertical mirrors while preserving inversion symmetry. Using symmetry-resolved elastoresistivity, we detect the spontaneous emergence of intrinsic off-diagonal elastoresistivity coefficients that satisfy an antisymmetric relation ($m_{xx-yy,xy} \approx -m_{xy,xx-yy}$), providing an unambiguous bulk transport signature of a macroscopic electric toroidal moment. Simultaneous elastocaloric measurements reveal that the onset of ferroaxial order occurs just below the CDW transition. As the temperature is lowered further, a diverging nematic susceptibility signals a distinct rotational symmetry-breaking instability inside the ferroaxial CDW state. Our findings demonstrate that the proposed ``chiral'' CDW in 1T-TiSe$_2$ is actually a centrosymmetric ferroaxial state, reconciling previous surface-sensitive observations with bulk symmetry constraints.

Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges while preserving desired network properties. Distance backbones of weighted graphs, which remove edges that break a generalized triangle inequality for any given path-length measure, preserve all shortest paths of weighted graphs. They have been shown to typically sparsify graphs more, as well as preserve community structure and spreading dynamics better than alternative state-of-the-art methods. Here, We show that they significantly best preserve node centrality ranks, as well as local and global dynamics in spreading phenomena. This is done by introducing the distance backbone synthesis (DBS) to progressively sparsify weighted graphs according to a general family of nested distance backbones, whereby each edge is associated with the smallest distance backbone in which it appears. DBS provides a principled and natural method to sweep all degrees of sparsification possible while preserving connectivity, allowing us to precisely study (directed and undirected) weighted graph sparsification under multi-objective criteria. It provides an algebraically-principled explanation of edge importance by revealing the precise topological space associated with each edge. The theory is demonstrated with a battery of social contact networks obtained from real-world social activity in different scenarios. Our study also shows that the optimal preservation of node centrality and spreading dynamics happens for the distance backbone obeying the generalized triangle inequality for the path-length measure $g(x, y) = (\sqrt[3]{x}+\sqrt[3]{y})^3$, which removes more than half of the edges from the empirical networks studied.

We study the Borwein--Bailey--Girgensohn sinusoidal series S_BBG = sum_{n=1}^\infty (1/n) * ((2+sin n)/3)^n, originally posed as an open problem by Borwein, Bailey, and Girgensohn, whose convergence was established by Boppana using the irrationality measure of pi. We present three unconditional results. First, applying the Weyl equidistribution theorem with a quantitative Erdos--Turan bound, we split S_BBG = M + R, where M = sum_{n=1}^\infty I_n/n is a Bessel averaging series and |R| < infinity. Second, we evaluate M exactly via Fubini's theorem and the Fourier series of log(1-cos t): M = sum_{n=1}^\infty I_n/n = log 6. Third, we decompose the remainder R into a convergent series of Fourier harmonics: R = sum_{k=1}^\infty 2*Re[G_k((2/3)e^{ik})], where each G_k(z) = sum_{n=1}^\infty c_k(n) z^n/n is a Dirichlet-type generating function built from the k-th Fourier coefficients of (theta -> (1 + (sin theta)/2)^n). The series converges absolutely because |(2e^{ik})/3| = 2/3 < 1. Numerical computation strongly suggests S_BBG = Ei(log 3) = li(3) approx 2.16358...; we reduce this conjecture to a single Diophantine identity for R and indicate the Mellin-transform approach most likely to settle it.

In this paper, we precisely describe the spectrum of closed invariant $(1,1)$-forms viewed as an operator acting on complex spinor bundles over rational homogeneous varieties. Using this result, we describe the spectrum of the Weitzenböck remainder of ${\rm{Spin}}^{c}$ Dirac operators on rational homogeneous varieties. In particular, we present an explicit formula for their smallest eigenvalue. As a byproduct, we obtain a new lower bound for the eigenvalues of the ${\rm{Spin}}^{c}$ Dirac operator, expressed in terms of Lie-theoretic data. Additionally, combining the Atiyah-Singer index theorem with the Borel-Weil-Bott theorem, we provide a complete classification of ${\rm{Spin}}^{c}$ structures on rational homogeneous varieties which admit harmonic spinors. In this last setting, we present an explicit formula for the index of the associated ${\rm{Spin}}^{c}$ Dirac operator in terms of Lie theory.

The system frequency is a critical measure of power system stability and understanding, and modeling it are key to ensure reliable power system operations. Koopman-based autoencoders are effective at approximating complex nonlinear data patterns, with potential applications in the frequency dynamics of power systems. However, their non-invertibility can result in a distorted latent representation, leading to significant prediction errors. Invertible neural networks (INNs) in combination with the Koopman operator framework provide a promising approach to address these limitations. In this study, we analyze different INN architectures and train them on simulation datasets. We further apply extensions to the networks to address inherent limitations of INNs and evaluate their impact. We find that coupling-layer INNs achieve the best performance when used in isolation. In addition, we demonstrate that hybrid approaches can improve the performance when combined with suitable INNs, while reducing the generalization capabilities in combination with disadvantageous architectures. Overall, our results provide a clearer overview of how architectural choices influence INN performance, offering guidance for selecting and designing INNs for modeling power system frequency dynamics.

We prove that there exists a weak truth-table introimmune set in the class $Π^0_1$, settling the question left open in previous work of whether the known $Δ^0_2$ existence result can be improved to $Π^0_1$. Since $Σ^0_1$ sets cannot be immune, this is best possible for weak truth-table introimmunity. We also study introimmunity for Jockusch's bounded-search reducibility $\le_{bs}$ and Andersen's Dartmouth reducibility $\le_D$, proving the existence of $Δ^0_2$ sets that are $bs$-introimmune and $D$-introimmune; hence there also exists a $Δ^0_2$ $D^+$-introimmune set. We next consider the classical reducibility $\le_Q$, which is not contained in $\le_T$ on all subsets of $ω$. We show that no infinite $Π^0_1$ set is $Q$-introimmune, while a $Δ^0_2$ $Q$-introimmune set does exist. Thus the existence of $Δ^0_2$ $Q$-introimmune sets is best possible within the arithmetical hierarchy. Finally, for enumeration reducibility $\le_e$, we show that no infinite $Π^1_1$ set is $e$-introimmune, although $e$-introimmune sets do exist in the unrestricted sense. The proofs combine finite-injury priority arguments with dynamic spacing methods for $\le_{wtt}$, $\le_{bs}$, and $\le_D$, a bit-by-bit finite-extension construction for $\le_Q$, and an application of Soare's abstract existence theorem in the enumeration case.

Rare nonadiabatic reactions are a key component of many important molecular processes but are challenging to capture with direct dynamical simulations. In this paper, we combine our recently developed mapping approach to surface hopping (MASH) with transition-path sampling to create a framework to efficiently simulate these rare events. This is possible because MASH trajectories are Markovian, time-reversible and obey Liouville's theorem. The combined approach generates nonadiabatic reactive pathways without biasing the underlying dynamics. The resulting ensemble allows for a detailed analysis of reaction mechanisms and the unraveling of statistical and dynamical properties, including rate constants. We apply the method to study a spin-boson model in thermal equilibrium over a wide range of diabatic coupling strengths. Our results demonstrate how this approach provides a practical and systematic tool for investigating rare nonadiabatic processes, potentially beyond the reach of brute-force simulations.

Structural assumptions are central to the causal inference literature. In practice, it is often crucial to assess their validity or to test implications that follow from them. In many settings, such tests can be framed as evaluating whether a function-valued parameter equals zero. In this paper, we propose a class of generalized projection tests based on series estimators for function-valued parameters. We establish conditions under which the proposed tests are valid and illustrate their applicability through examples from the data fusion and instrumental variables literature. Our approach accommodates flexible machine learning methods for estimating nuisance parameters. In contrast to many existing approaches, the limiting distribution of the proposed test statistics is straightforward to compute under the null hypothesis. We apply our method to test the equality of conditional COVID-19 risk across vaccine arms in the COVID-19 Variant Immunologic Landscape (COVAIL) trial.

We investigated a two-dimensional superfluid model immersed in a black hole spacetime and hypothesize that if a black hole collides with a thin superfluid film, it will trigger a topological phase transition within the superfluid, characterized by the production of vortex--antivortex pairs. We adapted the 2D XY model to a curved spacetime and elucidated the topological phase transition in response to variations in the black hole's temperature. Specializing the model to a Schwarzschild--de Sitter black hole, we found a proliferation of vortex--antivortex pairs close to the event and cosmological horizons.

Observations show that multiple stellar populations (MPs) are ubiquitous in globular clusters. The Hubble Space Telescope (HST) has been a pivotal tool for previous photometric studies of MPs. The Chinese Space Station Survey Telescope (CSST) is a two-meter telescope scheduled for launch. One of its imaging instruments, the Survey Camera (SC), combines ultraviolet sensitivity comparable to that of HST with a significantly larger field of view, making it well-suited for conducting large-scale photometric surveys of MPs within extensive stellar stream structures. In this work, we perform mock observations of the stellar stream Palomar 5 to assess the feasibility of detecting MPs with the CSST/SC. The results indicate that the CSST/SC cannot resolve MPs in stellar streams at distances comparable to Palomar 5 ($\gtrsim 20$ kpc) with one or ten 150 s exposures. This fundamental limitation arises from the absence of the precise proper motions required to disentangle stream members. We estimate that successful resolution would require the target stream to be $\lesssim$ 8 kpc under a 150 s exposure. Furthermore, using theoretical color-magnitude diagrams, we find that the CSST/SC $g$-band provides an optimal balance between contamination rate and completeness rate for member identification in the cluster's core. However, this approach fails in the stream due to severe field star contamination. Therefore, future CSST observations of Palomar 5 and its tidal tails will employ multiple epochs across several bands to obtain the deep photometry and proper motion data for a definitive MP analysis.

The Le Roy function has been the focus of intensive research in recent years, owing both to its relevance in analysis and its versatility in applications involving fractional differential operators. Other special functions - such as the Lerch transcendent and the Legendre chi function - have found applications ranging from Bose-Einstein and Fermi-Dirac statistics in physics to pure mathematical investigations involving polylogarithms and Dirichlet L-series. In this article, we present a unified framework based on a recent reformulation of Indicial Umbral Theory (IUT) grounded in the formal theory of power series. Within this setting, we study the properties and generalisations of these special functions. In particular, we build upon the revised formulation of IUT to incorporate the role of the Borel-Le Roy transform, and to explore the extension of the formalism to divergent series via appropriate resummation techniques.

In this expository paper, we discuss a unified framework for proving various geometric inequalities, based on the so-called Alexandrov-Bakelman-Pucci technique. Examples include Cabré's proof of the classical isoperimetric inequality in Euclidean space; the Fenchel-Willmore-Chen inequality for the mean curvature of a submanifold; the sharp version of the Michael-Simon Sobolev inequality for submanifolds; the sharp version of Ecker's logarithmic Sobolev inequality for submanifolds; and the Sobolev inequality for complete manifolds with nonnegative Ricci curvature and Euclidean volume growth. Finally, we discuss a connection to the work of Heintze and Karcher on the volume of a tubular neighborhood of a hypersurface in a manifold with nonnegative Ricci curvature.

Universal Machine Learning Interatomic Potentials (uMLIPs) enable atomistic simulations and high-throughput screening at scales far beyond those accessible with density functional theory (DFT). However, most existing uMLIPs are trained on Perdew--Burke--Ernzerhof (PBE) generalized gradient approximation (GGA) data and are therefore fundamentally limited by PBE-level accuracy. In this paper, we argue that better zero-shot predictions versus experiments must be an explicit design target for uMLIPs and present PFP v8, a uMLIP available on the Matlantis service that overcomes the inherent limitations of the PBE functional by being trained to reproduce the regularized-restored strongly constrained and appropriately normed (r2SCAN) meta-GGA potential-energy surface across a wide range of chemical domains. Without requiring domain-specific fine-tuning, PFP v8 delivers systematically improved agreement with experimental data or high-accuracy references for crystals, molecules, and surfaces, outperforming PBE-based DFT calculations. Crucially, in long-time molecular dynamics simulations that are computationally impractical with DFT, PFP v8 predicts melting points with an average error of approximately 130 K, halving the error relative to PBE-trained models. These results establish that uMLIPs can move beyond the limitations of their training approximations and achieve substantially improved agreement with experiment across diverse chemical domains, further narrowing the gap between simulation and reality.

A measurement of the flavour-untagged decay-time-integrated ${C\!P}$ asymmetry in the flavour-specific decay ${B_s^0 \to D_s^-π^+}$, ${\langle A^s_{\rm untagged}\rangle}$, is performed using proton-proton collision data collected by the LHCb experiment between 2016 and 2018 at a center-of-mass energy of ${13\,{\rm TeV}}$, corresponding to a total integrated luminosity of ${5.4\,{\rm fb}^{-1}}$. The ${C\!P}$ asymmetry is measured in two $D_s^-$ meson decay modes, ${D_s^- \to K^-K^+π^-}$ and ${D_s^- \to π^-π^+π^-}$. The combined result, $\langle A^s_{\rm untagged}\rangle = ( -1.4 \pm 5.9\,\rm{(stat)} \pm 1.1\,\rm{(syst)}) \times 10^{-3}$, is consistent with the Standard Model expectation and provides a direct constraint on new physics in tree-level $b$-hadron decays.