In this work, we investigate the valence quark parton distribution functions (PDFs) of the pion within the light-cone quark model. The initial quark PDFs are calculated by solving the quark-quark correlation function for the pseudoscalar mesons. The initial quark PDFs have been evolved to higher energy scales through the Dokshitzer,Gribov,Lipatov,Altarelli,Parisi (DGLAP) evolution equations. We also find that our calculated evolved PDFs match experimental and available theoretical extraction data. For the first time, we have also predicted the $F_2$ structure function at next-to-leading (NLO) order accuracy. The calculated $F_2$ structure function has been compared with the available ZEUS and H1 experimental data at DESY-HERA over a wide range of energy scales. Additionally, we display the forward pion production cross-section for the Drell-Yan process caused by pions using the pion PDFs that were calculated and the target nucleon PDFs from the LHAPDF nucleus datasets. The evolved $F_2$ structure function of the pion have been studied at the upcoming electron-ion collider energy kinematics. Overall, it was observed that the quark PDFs of pions computed using the light-cone quark model consistent with the experimental results.

We investigate the second volume moment of the zero cell $Z_o$ of a Poisson hyperplane tessellation with intensity $γ$ in the $d$-dimensional hyperbolic space. We focus on the phase transition at the critical intensity $γ_c^{(d)}$, the minimum value for which $Z_o$ is almost surely bounded. In the critical regime $γ=γ_c^{(d)}$, we show that the second volume moment of the restricted zero cell $Z_o \cap B_R$, where $B_R$ is a hyperbolic ball of radius $R$ centred at $o$, diverges in any dimension at the universal rate $R^3$ as $R \to \infty$. In the supercritical case $γ> γ_c^{(d)}$, we prove that the full second volume moment is finite. Using tools from harmonic analysis in hyperbolic space, we derive an exact expression for this moment in terms of the Meijer $G$-function. Furthermore, we determine the asymptotic behaviour of the second moment as $γ\to \infty$ and as $γ\downarrow γ_c^{(d)}$, facilitating a direct comparison with the corresponding Euclidean values as well as the mean-field universality class of percolation theory.

Reliability-based design optimization (RBDO) is traditionally formulated as a nested optimization and reliability problem. Although surrogate models are generally employed to improve efficiency, the approach remains computationally prohibitive in high-dimensional settings. This paper proposes a novel RBDO framework based on a stochastic simulator viewpoint, in which the deterministic limit-state function and the uncertainty in the model inputs are combined into a unified stochastic representation. Under this formulation, the system response conditioned on a given design is modeled directly through its output distribution, rather than through an explicit limit-state function. Stochastic emulators are constructed in the design space to approximate the conditional response distribution, enabling the semi-analytical evaluation of failure probabilities or associated quantiles without resorting to Monte Carlo simulation. Two classes of stochastic emulators are investigated, namely generalized lambda models and stochastic polynomial chaos expansions. Both approaches provide a deterministic mapping between design variables and reliability constraints, which breaks the classical double-loop structure of RBDO and allows the use of standard deterministic optimization algorithms. The performance of the proposed approach is evaluated on a set of benchmark problems with dimensionality ranging from low to very high, including a case with stochastic excitation. The results are compared against a Kriging-based approach formulated in the full input space. The proposed method yields substantial computational gains, particularly in high-dimensional settings. While its efficiency is comparable to Kriging for low-dimensional problems, it significantly outperforms Kriging as the dimensionality increases.

In a binary groupoid $(G, *)$, a Fibonacci sequence is a recurrent sequence defined by $f_1 = a, f_2 = b, \ldots, f_n = f_{n - 2} * f_{n - 1}$. A universal Fibonacci sequence (UFS) is a singly or doubly infinite sequence whose set of suffixes coincides precisely with the set of all Fibonacci sequences in the groupoid. This paper studies UFS-groupoids, i.e., groupoids that admit a universal Fibonacci sequence (UFS). It is shown that every nontrivial UFS-groupoid is at most countable, locally cyclic, and non-power-associative; that the right-cancellative law holds for all but possibly one pair of elements; that no neutral element or zero element exists; and that there is at most one idempotent element. It has been proved that the class of UFS-groupoids is closed under taking subgroupoids and homomorphic images, but is not closed under finite direct products. A complete classification of UFS-groupoids is given in terms of the cardinality of $G$ and the periodicity of the UFS. Finite UFS-groupoids are described combinatorially via de Bruijn sequences. The number of distinct UFS-groupoids on a finite set is determined, and explicit constructions are provided for both finite and infinite cases across all periodicity classes.

With the rise of multi-core processors and distributed systems, concurrent programming has become essential yet challenging, primarily due to the non-deterministic nature of thread execution. Manually addressing concurrency bugs is time-consuming and error-prone. Automated Program Repair techniques provide a promising solution. However, developing an end-to-end concurrency bug repair tool is particularly challenging. Most existing tools rely on the assumption that bug-related information is readily available or that concurrency bug contexts are ideally extracted, which is often impractical in real-world scenarios. This paper introduces ConFixAgent, an LLM-driven agent capable of fixing various types of concurrency bugs in an end-to-end manner, eliminating the need for any prior bug-related information. Specifically, we propose a novel context extraction approach designed for concurrency bug repair, utilizing Static Happens-Before Graphs to identify bug-relevant sections.We implemented ConFixAgent and evaluated it across multiple benchmark sets. Our extensive experiments demonstrate that ConFixAgent significantly outperforms state-of-the-art tools in addressing diverse types of concurrency bugs, with its context extraction method markedly enhancing the accuracy of LLM-generated repair solutions.

We study first-order ordinary differential equations such that the intrinsic Gauss curvature of the associated surface depends only on the independent variable: $\mathcal{K}(x,u)=κ(x)$, showing that this geometrically motivated class of equations admits a threefold connection to the second-order linear operator $L=d^2/dx^2+κ(x)$: the divergence along every solution satisfies a Riccati equation that linearizes to $L(y)=0$; every solution of the first-order equation satisfies the non-homogeneous equation $L(u)=c(x)$; and solutions of $L(y)=0$ give rise to integrating factors for the original nonlinear equation. By means of differential Galois theory, we prove that the nonlinear equation is integrable by quadratures if and only if $L$ admits a non-zero Liouvillian solution; when $κ$ is rational, Kovacic's algorithm provides a complete decision procedure.

We present analytic exact solutions to the nonlinear Dirac equation: they display a ring singularity for the Nambu--Jona-Lasinio nonlinearity and a shell singularity for the Soler nonlinearity. For both cases the size of the singular region is of the order of the Compton length.

Attaining the ultimate precision remains a central objective in the engineering of nanoscale systems and the investigation of nonequilibrium processes. While thermodynamic and kinetic uncertainty relations establish fundamental precision bounds, prior derivations in the quantum regime have remained confined to single-body systems. Consequently, the ultimate precision limits for interacting many-body systems have been unknown. In this Letter, we analytically formulate a kinetic uncertainty relation for a many-body system undergoing collective dissipation, a paradigmatic model of boundary time crystals. By applying a mean-field approximation, we derive lower bounds for relative fluctuations expressed in terms of clear physical quantities. Our analysis identifies a cooperative enhancement mechanism, demonstrating that collective interactions allow the precision to scale with the number of particles. We validate these findings through numerical simulations across the stationary, critical, and boundary time crystal phases. Our work presents the first theoretical description of precision bounds in collective dissipative quantum many-body systems for an arbitrary particle number $N$, providing a solid foundation for designing future quantum technologies that exploit many-body phenomena.

SNO+ is a multipurpose liquid-scintillator neutrino detector located 2 km underground at SNOLAB, Canada. Three large nuclear reactors at baselines of 240-350 km allow a precise measurement of the neutrino oscillation parameter $Δm^2_{21}$ and, to a lesser extent, $θ_{12}$. A spectral analysis is performed, simultaneously fitting $Δm^2_{21}$, $θ_{12}$, the reactor antineutrino flux, background rates, and associated systematics. Using data collected between May 2022 and July 2025, corresponding to a livetime of 685 days, a value of $Δm^2_{21} = (7.93^{+0.21}_{-0.24}) \times 10^{-5}$ eV$^2$ is obtained. This result is compatible with other long-baseline reactor antineutrino measurements by KamLAND and JUNO. SNO+ has also made the first measurement of the geoneutrino flux in the Western Hemisphere, measuring $49^{+13}_{-12}$ TNU, in agreement with predictions from geological models.

The modeling and reconstruction of economic networks from aggregate information has important implications for counterfactual analysis and policymaking. The traditional Fitness Model (FM) achieves good performance by using node-specific variables that are easily accessible (e.g., GDP for countries or total assets for banks or firms) and the overall link density as the only sufficient statistic. However, it often ignores additional contextual or mesoscopic features which may be more difficult to observe. In this paper, we extend the framework by incorporating block structure as in the Fitness-Corrected Block Model (FCBM), which allows for heterogeneous densities within and across blocks, but in the more challenging setting where such block-specific densities are not empirically available. Our method compensates for the absence of empirical information about the sufficient statistics by using a Jeffreys prior to average, in the most unbiased way, over all compatible solutions that are otherwise left unidentified. We evaluate the method on three international trade datasets across different product classes, including fresh products, common products, geographically specific products, and high-technology products. The underlying block structure is represented by economic regions as defined by the World Bank, and we only assume empirical knowledge of the total GDPs and the overall link density. The new method systematically outperforms the baseline Block-Agnostic FM (which uses the same input information) and sometimes even the FCBM (despite the latter uses more information), thereby suggesting reduced overfitting risk.

Strong epimorphisms and regular epimorphisms are two important classes of morphisms, and they do not coincide in general. Yet, in a locally presentable category, it is known that any strong epimorphism can be decomposed into a transfinite composite of regular epimorphisms. In this paper, we provide two syntactic methods to determine how many regular epimorphisms are needed in such a decomposition, using partial Horn theory and generalized algebraic theory. We start by discussing a general problem of decomposing a morphism into a transfinite composite of morphisms in a given class, which also covers the decomposition of an adjoint functor into monadic functors.

The quantum Rabi model has been a useful and pedagogical quantum model in the past decades, sufficiently simple to be solved analytically and intuitively understood, while sufficiently complex as to provide highly non-trivial eigenstates and a practical description of quantum optical platforms for quantum technologies. The Dirac equation, especially when restricted to 1+1 dimensions, is a simple toy model as well, but its easy diagonalization enabled historically to connect the electron spin to the fermionic statistics, among others. Both models share a symmetry at the purely mathematical level, namely, the spectra of each one has a dual equivalent under energy sign change, that I name a mirror dual symmetry. Usually, one quantizes these equations by assuming a ground state energy for the bosonic mode. But there is another option for the interpretation of the Hamiltonian, as I will argue, that is to assume a total symmetry principle, namely, that the total energy is zero at all times, for either the quantum Rabi model or the Dirac equation, and impose the constraint that every positive energy excitation has a mirror excitation of negative energy. This possibility, which was, apparently, ignored in the times when Paul Dirac was studying the implications of his equation, would avoid the worries in the scientific community that the negative energy solutions would decay until minus infinity, thus obviating the necessity to build a highly artificial Dirac sea, and instead impose what has always been successful in Physics, which is the enforcement of symmetry principles. Assuming a total symmetry principle, many of the problems of current Physics, such as renormalization of quantum gravity, dark matter, and dark energy, may possibly be automatically solved. One obvious result would be the automatic cancellation of the zero point energy.

Let X be either a smooth K3 surface or a smooth Fano variety (i.e. $-K_X$ is ample) of dimension $n$ and index $i_X> n-3$ and let E be an initialized Ulrich bundle on X. In this paper, we show that the syzygy bundle $S(E)$, defined as the kernel of the evaluation map $H^0(X,E)\otimes O_{X}\rightarrow E$, is semistable.

We present certain results on the Iwasawa theory of an abelian variety with potentially good ordinary reduction at all primes above $p$. These are then applied to study Diophantine stability and integally Diophantine extensions. Along the way, we also obtain some results pertaining to Mazur growth conjecture which refine previous results of Gajek-Leonard, Hatley, Kundu and Lei. Finally, we extend our investigation to the case of an elliptic curve with good supersingular reduction at the prime $p$ and make a similar analysis.

This volume contains the proceedings of PLACES 2026, the 17th edition of the Workshop on Programming Language Approaches to Concurrency and Communication-cEntric Software. The workshop is scheduled to take place in Turin, Italy, on April 11, 2026, as a satellite event of ETAPS, the European Joint Conferences on Theory and Practice of Software. PLACES offers a forum for exchanging new ideas on how to address the challenges of concurrent and distributed programming and how to improve the foundations of modern and future computer applications. PLACES welcomes researchers from various fields, and its topics include the design of new programming languages, models for concurrent and distributed systems, type systems, program verification, and applications in various areas (e.g., microservices, sensor networks, blockchains, event processing, business process management).

The present article concerns the stochastic modeling of the turbulent dissipation field and in particular its temporal evolution. To do so, we will be calling for a random distribution, ubiquitous in several aspects of physics and probability theory, known as the Gaussian Multiplicative Chaos (GMC), that takes its roots in the phenomenology of fluid turbulence. Firstly introduced by Mandelbrot, shortly after Yaglom's discrete multiplicative cascade models, and rigorously studied by Kahane, the GMC appears as an appropriate statistically homogeneous model of the turbulent dissipation field. In this article, we will be recalling several ingredients of the associated turbulent phenomenology and its stochastic representation as a GMC, and propose a generalization to a spatio-temporal framework. All along the presentation of known properties in space, and in order to support new propositions concerning the temporal evolution, we will be calling for a comparison against Direct Numerical Simulations of the Navier-Stokes equations extracted from a publicly accessible database.

The $Δ$-Self-Consistent-Field ($Δ$SCF) method permits calculations of core electron binding energies in materials and molecules at a modest computational cost. However, it has been reported that whilst this method works well for small molecules, its accuracy drops off dramatically when larger systems are considered. Particularly large errors have been reported for the anthrone molecule, which consists of 25 atoms. In this work, the gas-phase photoelectron spectrum of anthrone is revisited both computationally and experimentally. The measured C 1s binding energies in anthrone differ markedly from previously published values, and the new experimental results are in good agreement with $Δ$SCF calculations based on the SCAN functional. In addition, the performance of the $Δ$SCF method is evaluated for a dataset of 44 core electron binding energies from medium sized molecules containing between 10 and 40 atoms. The mean absolute error for this dataset - 0.19 eV - is comparable to the results of previous computational benchmarks. Overall, these results and general theoretical considerations indicate that the $Δ$SCF method is suitable for modelling localized excitations in both small and large molecules, and applications to other extended systems are also promising.

In this work, we access the performance of RI-CC2 for ultrafast internal conversion using pyrazine as a benchmark system. We implement analytical gradients and nonadiabatic coupling vectors for RI-CC2 in the Q-Chem package and employ them in two complementary approaches: a reduced-dimensionality vibronic coupling (VC) model and full-dimensional ab initio on-the-fly trajectory surface hopping simulations. To accelerate the on-the-fly dynamics, we employ a diabatic artificial neural network model trained on RI-CC2 data. Both the VC model and the full-dimensional dynamics reveal that the dark $A_\text{1u}$ state actively participates in the internal conversion process. RI-CC2 identifies the $Q_\text{9a}$ and $Q_\text{8a}$ vibrational modes as key drivers of the coherent population transfer between the $A_\text{1u}$ and $B_\text{3u}$. The on-the-fly dynamics reproduce the experimental $B_\text{2u}$ population decay time of 26 fs, consistent with the measured value of $22\pm3$ fs. The high-quality dataset of energies, forces, and nonadiabatic couplings generated here provides a valuable resource for future machine-learning developments, while the stochastic variant sRI-CC2 promises to extend such dynamics to larger molecular systems.

In this paper, we introduce the resonance-correlation method to study small gaps between consecutive zeros of the Riemann zeta-function. Our method is based on a synthesis of Montgomery's pair correlation approach and the Montgomery-Odlyzko method. As an application, we break the persistent practical barrier around $0.515$ and prove $μ< 0.50895$ under the Riemann Hypothesis.

Despite the fact that electrons observed in situ in space plasmas have three major components-the quasi-thermal core, suprathermal halo, and strahl-the analysis of instabilities triggered by kinetic, velocity-space anisotropies (such as relative drifts and temperature anisotropy) generally considers only two. We demonstrate that realistic modeling with all three components is achievable in the present analysis focusing on heat-flux instabilities. In the absence of particle collisions, these instabilities regulate the heat flux carried mainly by suprathermal electrons. The velocity distributions were modeled according to in situ observations, with a Maxwellian core and Kappa-distributed halo and strahl. We exploited advanced numerical codes capable of solving the linear dispersion and stability properties of plasma systems with Maxwellian and Kappa distributions. The unstable solutions differ significantly from those obtained with simplified two-component models (such as core-strahl or core-beam). The growth rates predict the excitation and interplay of two unstable modes, whistler and/or firehose heat-flux instabilities. The numerical solver 'ALPS' was successfully applied to systems with regularized Kappa distributions, for which analytical derivation of dispersion relations is not straightforward. The two instabilities are triggered by the relative drifts, core-strahl and halo-strahl, and may have new consequences for heat-flux regulation. Particularly important are cases when the core-strahl instability is in competition with the instability driven by the halo-strahl drift, as well as when the two instabilities have the same nature and accumulate. Future studies are motivated to confirm these predictions in quasilinear theories and numerical simulations.

In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. A feasible range for the momentum parameters is determined. Numerical experiments demonstrate that the proposed methods are much more effective than the existing ones, especially the method with momentum.

This study examines the influence of niobium and oxygen on phase stability, crystal structure, and martensitic transformation pathways in Ti-Nb-O alloys. A series of Ti-(8-28)Nb-(0-3)O (at.%) alloys were prepared and solution-treated in the $β$-phase field. Microstructure and crystallography were characterized by X-ray diffraction, electron microscopy, and reciprocal-space mapping. A 2D-XRD orientation simulation approach was applied to distinguish all 12 crystallographically equivalent $α"$ martensitic variants originating from a single prior $β$ grain, enabling detailed diffraction analysis. This method further allowed quantitative evaluation of the atomic shuffle parameter y, describing the $β\rightarrowα"$ transformation. The results demonstrate that Nb primarily governs $α"$ martensite evolution. Increasing Nb stabilizes the $β$ phase and shifts the $α"$ structure toward higher symmetry, as reflected by systematic changes in lattice parameters and increasing shuffle parameter y, indicating suppression of transformation toward the hexagonal $α'$ phase. Oxygen, in contrast, modifies transformation pathways. At lower Nb contents, it suppresses the $ω$ phase formation and promotes $β\rightarrowα"$ transformation, while at higher Nb levels it inhibits long-range martensitic transformation, resulting in retained $β$ or competing $ω$ phase. These effects are attributed to local lattice distortions induced by interstitial oxygen.

Macroscopic active matter systems, such as bristle bots, provide a compelling platform for investigating nonequilibrium dynamics at highly visible scales. To fully leverage their accessibility, accurate mathematical models are needed to corroborate experiments. In this work, we study the motion of a free chiral hexbug (Nano-Newton Series) via video tracking and compare the results to theoretical predictions from overdamped Langevin equations for active Brownian circle swimmers (ABCs). We find good agreement between the hexbug's dynamics and ABC model predictions, particularly for the mean-squared displacement and the intermediate scattering function (ISF). Deviations between the hexbug data and the ABC model arise primarily in the short-time behavior of the real-space propagator, where translational noise is most evident. Our results generally support the use of models based on overdamped Langevin equations as a robust framework for describing hexbug motion when the influence of translational noise is negligible. Moreover, they demonstrate the sensitivity of ISF- and propagator-based analyses in characterizing active systems. Our approach opens new avenues toward refining coarse-grained models and advancing the theoretical understanding of macroscopic active systems.

We investigate the dynamics of an inertial chiral active Brownian particle in the presence of a harmonic confinement. Through numerical simulation, we observe that when the harmonic frequency becomes comparable to the chiral frequency, the position distribution transitions from a Gaussian to a platykurtic distribution, corresponding to short tails with a nearly uniform probability near the minimum of the potential. This result is further confirmed by analyzing the kurtosis of the position of the particle as a function of harmonic frequency, which exhibits a dip when the harmonic frequency matches the chiral frequency. At the same time, the steady state mean square displacement (MSD) shows a non-monotonic feature with the harmonic frequency and shows a maximum only when the harmonic frequency is of the same order as the chiral frequency. In the rotational overdamped limit of the same model, we have calculated the exact expression for kurtosis, steady state MSD and find that the qualitative behavior remains the same. Kurtosis still exhibits a dip in the matching of chiral and harmonic frequencies, but the feature is less pronounced with a higher minimum. These findings might be relevant for controlling the transport and spatial distribution of chiral microswimmers in optical or acoustic traps, where confinement can be tuned to optimize particle distribution.

This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of generalised Darwinism -- that is, for any system in which heredity, variability, and selection can be meaningfully defined, regardless of the specific biological substrate. Starting from the Kolmogorov equations for interacting populations, we derive the replicator equation and examine three canonical regimes: independent, autocatalytic, and hypercyclic replication. The hypercycle is shown to be permanent and to carry evolutionary variability intrinsically. We then survey the quasispecies framework -- the Eigen and Crow--Kimura models -- covering global stability of equilibria, sequence space structure, and the error-threshold phenomenon. Throughout, the emphasis is on the mathematical structures that underlie these models rather than on biological detail, with the goal of making the framework applicable to abstract evolutionary dynamics beyond its original molecular biology context.

We propose and analyze a class of finite element methods for the time-dependent incompressible magnetohydrodynamics system based on $H(\mathrm{curl})$-conforming discretizations for both the velocity and the magnetic field. This choice is guided by the aim of developing methods that are also suitable for the types of solutions arising in problems posed on nonconvex domains. Within this framework, we introduce three stabilized formulations, and study how the stabilization mechanisms employed influence their structural properties. In particular, we focus on suitability for nonconvex polyhedral domains, the need for Lagrange multipliers for the magnetic field, pressure-robustness, and quasi-robustness with respect to both the fluid and magnetic Reynolds numbers. The proposed formulations are further assessed through numerical experiments, highlighting their practical performance.

Artificial intelligence tools are accelerating manuscript production far faster than peer review capacity can expand. Applying the theory of constraints from manufacturing science, we formalize this asymmetry through a minimal two-variable ordinary differential equation model coupling review queue evolution and verification quality degradation via an endogenous, queue-pressure-driven review AI adoption mechanism. The causal chain is: writing AI adoption increases submissions, growing the review queue, which drives reviewer AI adoption under pressure, degrading verification quality and reducing net knowledge output. Under empirically informed parameters (writing acceleration γ = 2.0, review acceleration δ = 0.5), the model predicts a deceptive honeymoon where knowledge output peaks at 1.10K0 (circa 2026), followed by paradox onset at t = 6 years (2028) and long-term degradation to 0.68K0 (32% loss), approaching a steady state of 0.60K0 (40% loss). The critical condition for net benefit is δ > γ; the current operating point lies deep in the paradox regime. Empirical validation against NeurIPS, ICLR, arXiv, and bioRxiv submission data shows qualitative consistency with observed post-ChatGPT acceleration patterns. Policy analysis reveals that only combined interventions such as review infrastructure investment paired with institutional quality standards can restore positive knowledge production.

Bohr chaoticity is a topological notion of dynamical complexity defined through non-orthogonality to all non-trivial weights. It is strictly stronger than positivity of topological entropy and also has strong consequences for the invariant-measure structure. In this paper, we show that every dynamical system having a semi-horseshoe, including every positive-entropy graph map and every $C^1$ partially hyperbolic diffeomorphism, is Bohr chaotic; furthermore, the set of points correlated with any given non-trivial weight has positive topological entropy. Moreover, for positive-entropy dynamical systems with either the shadowing property or the modified almost specification property, such set can has full topological entropy. Our results also yield applications in several classical algebraic and smooth settings, as well as in the $C^0$-generic setting of topological dynamics.

A measurement of the CKM angle $γ$ is performed by applying a novel, unbinned, model-independent approach to datasets of electron-positron collisions collected by the BESIII experiment and proton-proton collisions by the LHCb experiment, corresponding to integrated luminosities of 8 fb$^{-1}$ and 9 fb$^{-1}$, respectively. The $C\!P$-violating phase $γ$ is determined from ${B^{\pm}\rightarrow D(\rightarrow K_{\rm S}^{0} h^{\prime+}h^{\prime-}) h^{\pm}}$ decays in LHCb data, where $h^{(\prime)}$ is either a pion or kaon, while the corresponding strong-phase parameters are measured using doubly tagged ${D\rightarrow K_{\rm S/L}^0 h^{\prime+} h^{\prime-}}$ decays in the quantum-correlated $D\overline{D}$ system present in BESIII data. A joint fit to both datasets, which allows for a simultaneous determination of the associated $C\!P$-violating observables and strong-phase parameters, yields ${γ= (71.3\pm 5.0)^{\circ}}$. The result is the most precise to date and consistent with previous measurements and world averages.

Second-harmonic generation (SHG) is a quintessential probe of inversion symmetry breaking in condensed matter. While perturbative $χ^{(2)}$ processes are well-documented, the nonperturbative regime under intense driving remains largely unexplored. In this Letter, we develop a nonperturbative Floquet-Keldysh theory to describe SHG in two-band systems. Our analysis reveals the emergence of two distinct types of nonperturbative saturation: a transition from the conventional $E^2$ scaling to a linear $E$ dependence, and a stronger saturation regime where the SHG response becomes independent of the field amplitude. These behaviors are analytically shown to be governed by one-photon and two-photon resonance processes, respectively. By applying our formalism to a tight-binding model of monolayer GeS, we demonstrate that these specific scaling behaviors are observable in realistic materials and are fully consistent with large-scale numerical Floquet-matrix calculations.