Using divisibility relations between the generators of a square-free monomial ideal $I$, we describe divisibility relations between the generators of the second power $I^2$. We then employ discrete Morse theory to produce a cellular free resolution of $I^2$ which is minimal for specific ideals that are extremal with respect to a given divisibility relation. In particular, we provide sharp bounds on the projective dimension of $I^2$ when the generators of $I$ satisfy at least one divisibility relation.

For the solid state physics, recent interest to topological systems is mostly connected with topological semimetals, in particular, to Weyl ones as the most representative semimetal type. Like other topological materials, e.g. topological and Chern insulators, topological semimetals acquire topologically protected surface states with linear dispersion. In contrast to helical surface states in topological insulators, the surface states are chiral for Weyl semimetals, similarly to Chern insulators, which allows to consider Weyl semimetals as the three-dimensional analog of the quantum Hall effect regime. Weyl semimetals are also interesting for spin-dependent effects, due to the spin-momentum locking in the topological surface states. For topological semimetals, the main problem of transport investigations is to reveal the surface states contribution in the material with gapless bulk spectrum. Here, we present review of experimental results on charge and spin transport in topological semimetals: charge transport in different superconducting proximity devices; spin-dependent transport; magnetic response of the topological surface states; non-linear anomalous Hall effect as the direct manifestation of the non-zero Berry curvature in topological semimetals. Possible applications are also considered for this new class of topological materials.

Artificial Intelligence Generated Content (AIGC) powered by Generative Diffusion Models (GDMs) has emerged as a transformative paradigm for automated content creation. To satisfy the stringent latency requirements of AIGC services in many edge intelligence scenarios (e.g., smart cities), Mobile Edge Computing (MEC) provides critical computational support by deploying GDMs at edge servers (ES) close to end users. This paper investigates an MEC-enabled AIGC network comprising multiple ES, wireless access points (APs), and mobile users (UEs) with heterogeneous latency and accuracy demands. We formulate a Joint Communication Association and Computation Offloading (JCACO) game, where each UE strategically selects its serving AP, ES, and inference steps to minimize the overall service completion time while meeting accuracy constraints. The problem is challenging due to the network dynamics and the incomplete information. We prove that the JCACO game is a potential game under both complete and stochastic information settings, ensuring the existence of Nash Equilibrium (NE) in both cases. To derive the NE efficiently, we develop a distributed Multi-Agent Stochastic Learning (MASL) algorithm that provably converges to the NE with strict performance guarantees. Unlike conventional best-response schemes, MASL requires neither the knowledge of other players' strategies nor global network information, making it fully distributed and adaptive to dynamic environments. We further provide a strict theoretical convergence analysis for MASL by using Ordinary Differential Equations (ODEs). Simulation results demonstrate that MASL significantly reduces service completion time compared with benchmark methods while satisfying accuracy constraints, confirming its effectiveness and practicality for real-world MEC-enabled AIGC networks.

This paper presents a unified gas-kinetic wave-particle (UGKWP) method for simulating multiscale binary-species gas mixtures. Benefiting from direct modeling in a discretized space, the UGKWP method enables the automatic decomposition of the gas distribution function into analytical hydrodynamic waves and discrete particles, which respectively describe its near-equilibrium and non-equilibrium parts. This approach offers significant advantages for simulating various multiscale physical phenomena, such as hypersonic flows, plasma transport, and radiation transport. In this study, we employ the model proposed by Groppi et al. [EPL, 96 (2011) 64002] to calculate the macroscopic velocity and temperature of the local target equilibrium distribution function, thereby recovering the correct viscosity and diffusion coefficients in the continuum flow regime. To address the heat conduction coefficient, the Shakhov model is incorporated to correct the Prandtl number. Diffusion effects are accounted for not only in the source term via an operator-splitting method, but also in the flux evolution through the characteristic integral solution, while strictly maintaining consistency between the wave and particle descriptions. Furthermore, the microscopic model for high-speed particles is improved by utilizing a physically corrected collision time to determine their free-transport time. Through a series of numerical tests spanning the continuum to rarefied regimes, the proposed UGKWP method is shown to accurately capture the differences in velocity and temperature between different species. Notably, for hypersonic flows, the predicted wall pressure, shear stress, and heat flux coefficients agree well with DSMC results.

The advent of additive manufacturing has opened opportunities to rapidly prototype devices and products ranging from automotive and aerospace applications to micro/nanoscale metastructures, as examples). Three-dimensional (3D) printing has become relevant for electromagnetic structures, integrated optics and photonics systems, however, the optical properties of commercially available 3D printed polymers at telecommunication wavelengths (wavelength 1550nm) is not always available. Provided the importance of 3D printing technologies, in this work, we evaluate both theoretically and experimentally the complex refractive index of four polymers including some recycled versions (namely Butenediol Vinyl Alcohol (BVOH), Polylactic Acid (PLA), Recycled Polyethylene Terephthalate (rPET), and recycled Polylactic Acid (rPLA)) as potential candidates for photonics applications. The 3D printed samples have thicknesses from ~100 to 400 nm (~64wavelengths to ~258wavelengths, respectively). The experimental reflectance and transmittance spectra are extracted and used to retrieve the complex refractive index of each printed material demonstrating extinction coefficients in the order of 10^-4 at wavelength=1550nm. The experimental results are validated using numerical simulations. Finally, as a proof-of-concept, a convex-planar lens and a Bragg mirror are designed and numerically evaluated, showing the potential of the proposed polymers for 3D printing photonic structures at telecommunication wavelengths.

We emulate optically interconnected quantum processors in ring, star, and line topologies using a quantum computer. GHZ benchmarks show that the star provides the best trade-off between cost and fidelity under transduction and fiber noise.

This work develops a conceptual framework for the foundations of quantum physics, linking two main approaches: the algebraic formulation and quantum probability. Rather than proposing new axioms or theories, the text reorganizes and synthesizes existing models, highlighting their assumptions, conceptual structures, and operational significance. The analysis begins with von Neumann's measurement theory and its subsequent developments by Mackey, emphasizing the role of experimentally feasible procedures and the need for a statistical model grounded in laboratory practice. The work adopts an operational perspective, according to which physical quantities are defined solely through experimental measurement methods, and the corresponding probabilistic measures are derived from measurement outcomes. The introduction critically examines the limitations of purely mathematical formulations - such as the algebraic method - when separated from experimental interpretation. The text argues for a clear distinction between axioms, postulates, and presuppositions, and for a reconstruction of quantum theory that respects both empirical constraints and conceptual clarity. Overall, the goal is to provide a coherent path from operational principles to algebraic structures, offering a basis for an axiomatic reformulation of quantum mechanics that remains faithful to physical practice.

This paper investigates the fundamental limits of information-theoretic decentralized secure aggregation (DSA) with user dropouts. We consider a fully decentralized network where $K$ users communicate over broadcast channels without a trusted aggregation server. Each user holds a private input and aims to recover the sum of the surviving users' inputs (users may drop) while ensuring that no additional information about individual inputs is revealed to that user, even if it can collude with other users. A two-round communication protocol is considered, where we assume at least $U$ users survive and each user can collude with at most $T$ other users. For this setting, the optimal communication rate region is fully characterized: we show that DSA is infeasible if $U\le T+1$; otherwise, the optimal rate region is given by $R_1\geq 1$ and $R_2\geq \frac{1}{U-T-1}$, where $R_1$ and $R_2$ denote the first- and second-round communication rates, respectively. The proposed aggregation scheme is based on correlated secret keys constructed from $(T+1)$-private maximum distance separable (MDS) matrices, which simultaneously provide robustness against user dropouts and security against collusion. We also derive tight converse bounds that establish the optimality of the proposed scheme. Our result shows that the optimal second-round communication rate depends only on the effective redundancy level $U-T-1$ regardless the total number of users.

The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with this symmetry and building quantum versions of them. In this article I distinguish between two senses of gauge transformation: local and global, and I argue that the notion of observable appears more naturally in the local sense of gauge transformation. Then, I argue that diffeomorphism invariance can be understood as a gauge symmetry only from a global point of view, and hence, that the concept of observable applies only in a restricted manner. This has the consequence that some popular claims in the literature, such as the claim that the physical content of diffeomorphism-invariant models is encoded in correlations, are unfounded.

This extended preface [to the Book `Bayesian Nonparametrics', Cambridge University Press, 2010, by NL Hjort, CC Holmes, P Mueller, SG Walker] is meant to explain why you are right to be curious about Bayesian nonparametrics -- why you may actually need it and how you can manage to understand it and use it. The preface also serves as an introductory chapter, giving an overview of the aims and contents of the book. We also explain the background for how the book came into existence, delve briefly on the history of the still relatively young field of Bayesian nonparametrics, and offer some concluding remarks, pertaining to various challenges and likely future developments of the area.

We study online optimization problems in which the cost function depends on latent, time-varying parameters that are unmeasurable and governed by unknown dynamics. Specifically, we consider a strongly convex cost function whose linear term evolves according to unknown linear stochastic dynamics, while the algorithm has access only to finite noisy gradient measurements. We propose a solution that uses control theoretic tools to reconstruct the latent parameters from gradient observations using a Gauss-Markov estimator, then identifies the parameter dynamics using an instrumental-variable estimator, and finally forecasts the parameters to compute the future minimizer. We provide a bound on the expected tracking error. We illustrate the effectiveness of our algorithm on a series of numerical examples.

We prove that being of klt type is not an open condition in flat families of varieties. This answers a question of Han and Jiang. The construction in this paper substantially uses generative AI: the general idea for the counterexample was suggested by ChatGPT Pro 5.5, and the explicit example was found and proved by the Rethlas system.

Low-index transparent conducting oxides have attracted significant attention because ultrafast optical excitation in these materials can induce exceptionally large temporal index gradients. Due to this remarkable nonlinear optical behaviour, this material platform enables sub-picosecond, all-optical control of photon energy and momentum, with growing relevance for integrated photonics, quantum optics, and optical computation. Owing to their hybrid electronic structure, transparent conductors exhibit both intraband and interband nonlinearities, previously accessed using dual-colour excitation with near-infrared and ultraviolet pumps. Here, we show that both excitation regimes can be activated using a single, intense near-infrared pump. Above a threshold intensity, the pump drives hot-electron intraband dynamics while simultaneously generating higher harmonics that trigger interband excitation. The interplay of these two effects sharpens the temporal features of the recorded transmissivity which in turn substantially broadens the effective material bandwidth. Finally, by comparing linear and circular pumping conditions, we further demonstrate that the observed interband nonlinearities originate from harmonic generation rather than from direct multiphoton absorption. Our results provide key insights into the strong-field optical response in these time-varying photonic materials, opening new frontiers for the ultra-fast manipulation of photons in both classic and quantum regimes.

Neutron star (NS) is one of the most promising astrophysical targets to probe non-gravitational interaction of dark matter (DM) with visible matter. Their compactness makes them an ideal object which can capture particle DM efficiently over its lifetime using the DM-nucleon scattering cross-section. If DM particles are bosonic, then the captured DM population may form a Bose-Einstein condensate at the center of the NS, increasing the DM density significantly. In this work, we study the phenomenology of such scenario with enhanced DM annihilation rate due to the increased density in a condensate. The enhanced DM annihilation makes the NS surface `hotter' than in the standard cooling scenario. We show that the annihilation rate is enhanced by a factor of $\mathcal{O}(10^{15}-10^{20})$ if DM forms a condensate, and DM with freeze-in value annihilation cross-section can heat up the NS to higher temperatures, bringing it within the reach of James Webb Space Telescope. It also allows us to probe DM-nucleon scattering cross section within the neutrino fog regime which will complement the terrestrial direct detection searches. Moreover, the enhanced annihilation from the condensate changes the lower limits on s-wave DM annihilation cross-section for capture-annihilation equilibrium and the formation of a black hole inside the NS. Finally, we show an example of a scalar DM model where such small annihilation and DM-nucleon scattering cross sections can generically arise.

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$, where $g$ is of the form $af^p + b$ with $a,b \in \C$, $p \in \N$, and $a \neq 0,1$. We establish that the escaping sets, filled Julia sets, and bungee sets of $f$ and $g$ all coincide. As an immediate consequence, we obtain in particular that the Julia sets of $f$ and $g$ are identical. Our theorem extends the 1998 result of Poon and Yang. Furthermore, following Wang and Yang, we consider a non-constant polynomial $Q$ and permutable entire functions $f$ and $g$ satisfying the relation $Q(g)=aQ(f)+b$, where $a(\neq 0,1), b \in \C$. In this more general setting, we also prove that the escaping sets, filled Julia sets, and bungee sets of $f$ and $g$ are equal.

We provide a complete combinatorial and asymptotic analysis of positive linear systems of equations in one catalytic variable that appear in several combinatorial problems such as in lattice path counting or stack-sortable permutation counting. We show that the corresponding generating functions satisfy a positive polynomial system of equations (which is associated to a context-free grammar). Furthermore we prove a universal asymptotic behaviour.

Blockchains and distributed ledger technologies allow the operation of manifold decentralised applications (dApps). Such applications are based on smart contracts, a programmable abstraction that is executed in a decentralised manner. To ensure the correctness of smart contracts, blockchain application developers rely on DevOps practices such as automated testing and continuous integration and deployment. However, such infrastructure is often controlled by single entities. For larger blockchain applications, this issue is resolved by relying on concepts of Decentralised Autonomous Organisations (DAOs), which allow proposals to be autonomously executed once they reach a pre-defined quorum. Such a governance architecture is complex and requires integration with existing patterns for contract discovery and upgradeability. In this paper we integrate these concepts considering DevOps best-practices into a novel architecture that remains agnostic to different governance and upgrade implementations. We extend the known registry pattern to support deterministic deployments and present a decentralised deployment framework, including integration and deployment pipelines, user-interfaces, and version control integration. In our approach, each party implements and verifies their own tests before engaging in the use of a (newly deployed) smart contract. We provide a reference implementation, available as open-source, and evaluate the proposal thoroughly. Our architecture can serve as a reference for future integrations, while our open-source framework is aimed at reducing the complexity of adopting such a process in practice.

Among metallic alloys, ceramics, and even common compounds such as water ice, it is usual to find materials in which crystalline order is expressed as a probability. In such cases, one or more sites within a crystal can be occupied by multiple elements or vacancies, according to a set of probabilities. These crystal structures remain inaccessible to common first-principles materials simulation methodologies, which assumes perfect crystal order. Workaround strategies to this limitation include quasirandom structures and cluster expansion. These methods are system-specific and computationally expensive as they rely on large scale Monte Carlo simulations of enlarged unit cells. To address these limitations, we propose a pipeline combining a permutation-based virtual cell generation algorithm, sampling regime, and thermodynamic post-processing which greatly improves the feasibility of computation analyses for site-disordered materials. We demonstrate that the massive configurational space can be adequately sampled with 400 virtual cells, as long as the supercell definition is sufficiently large.

Solar prominences are dynamic structures suspended within the solar corona and are manifestation of solar activity. Their evolution includes eruptions linked to coronal mass ejections, making their detection critical for space weather monitoring and forecasting. The vast amounts of high-cadence data provided by missions such as SDO/AIA motivate the application of deep learning frameworks capable of assimilating large-scale datasets. However, previous studies have reported poor model performance caused by contamination from hot coronal emission from the EUV HeII 304 Å channel. Using an existing labeled prominence dataset, we find that trained YOLOv5 object detection models exhibit a strong bias towards the 304 Å colormap, rather than physically meaningful prominence features. We develop a further two models comprising three-channel images constructed through an original dataset preprocessing pipeline: (i) full-disk grayscale, full-disk enhanced corona, and disk-removed, (ii) same as (i) with all disk-removed images. Our pipeline corrects instrument degradation to maintain more consistent feature representations across the solar cycle. The composite model (i) achieves a mAP@50 of 0.749 and a recall of $78\%$ on the test set, outperforming previous bounding box methods. Visual analysis of the composite models reveals that many apparent false positives are valid unlabeled prominences. We additionally demonstrate cross-instrument generalization by testing the composite model on SUVI image data. By examining dataset biases that propagate into model predictions, we provide recommendations for robust dataset construction. We present a reliable, physically-motivated, and versatile deep learning model to automatically detect prominences in EUV images, providing a framework beneficial for space weather applications.

A problem of Erdős asks for extremal conditions forcing edge-disjoint cycles with a prescribed nested structure. In the geometric version, the nesting is required to be noncrossing with respect to the cyclic orders. Fernández, Kim, Kim and Liu proved that constant average degree forces two such cycles. We prove a polylogarithmic bound for the natural multi-layer version: for every fixed $k\ge 3$, every sufficiently large $n$-vertex graph with at least \[ C_k n(\log n)^{k-1}(\log\log n)^{k-3} \] edges contains $k$ pairwise edge-disjoint nested cycles without geometric crossings. The proof combines the robust sublinear expander framework of Alon, Bucić, Sauermann, Zakharov and Zamir with a controlled wrapping lemma that permits the layers to be built successively with controlled length.

Alpha emission from actinide impurities in Al is a source of background counting rate in Multi-Grid type detectors of thermal neutrons. The alpha emission rates from samples of radio-purity Al and \mathrm{Al/B_{4}C} composite, used in grid construction, were measured on a large-area, low background spectrometer. Although the alpha emission rate from the composite was a factor \sim280 higher than radio-pure Al, \mathrm{25\:μm} Ni plating of the composite reduced the rate by a factor \sim1170. Background counting rates in two Multi-Grid prototypes were compared. They used identical configurations of \mathrm{B_{4}C}-coated, radio-pure Al normal blades for the grids, but the first employed radio-purity Al for the radial blades, while the second used Ni-plated \mathrm{Al/B_{4}C} on the radial blades. The background rate from the second prototype was around 20% of that from the first.

Advanced nanodevices require high-precision machining of thin films using ultrafast lasers. However, thin-film fabrications cause variations in microstructure, crystallographic orientation, and residual stresses owing to coating conditions and substrate choice. This work investigates the complex interplay between these factors in ultrafast laser-irradiated gold (Au) thin films using a hybrid Two Temperature Model-Molecular Dynamics simulations. We realized microstructure-informed atomistic models with varying grain topologies (randomized vs. equiaxed), grain sizes, and residual tensile/compressive stress configurations. Our results reveal a clear hierarchy of influence on laser-metal interaction: 1.) Microstructure configuration 2.) Topology 3.) Grain Size 4.) Crystallographic orientations. In fine-grained thin films, grain boundaries act as primary melting precursors, while local crystallographic orientation determines the melting extent in coarser grains. Residual tensile stresses contribute to higher melting and greater laser-induced expansion than unstrained films. Conversely, residual compressive stresses resist deformation, as deposited thermal energy is utilized to overcome lattice compression, leading to reduced expansion. We found that microstructure grain topology and size exert a stronger fingerprint on film expansion than the initial defect density.

Geometric analogs of Bloch oscillations studied so far have relied on Berry curvature. We show that a weakly inhomogeneous electric field adds a distinct quantum-metric term to semiclassical wavepacket dynamics, generating an oscillatory real-space contribution even when the Berry curvature vanishes. The associated transport response comprises an intrinsic and a scattering-time-dependent part. In the regime studied, the latter can dominate and approach finite saturation at high field when the relative field inhomogeneity is held fixed. A tilted Dirac model illustrates the mechanism. Realistic platforms will likely require synthetically engineered superlattices, with a finite quantum metric and an adequate band gap.

Not all entangled states are useful for quantum teleportation. We present a geometric method to construct optimal teleportation witnesses, which provide operational necessary and sufficient criteria for identifying the teleportation usefulness of arbitrary two-qudit entangled states. Specifically, by developing a two-layer iterative cutting-plane algorithm to solve the shortest distance problem from the target state $ρ$ to the convex set $S$ of useless states, we obtain the projection point $σ^* \in S$ and then construct the optimal teleportation witness from the projection geometry. Moreover, the shortest distance $D(ρ)$ obtained during this construction also serves as a necessary and sufficient criterion for usefulness. We apply our method to identify the teleportation usefulness of three classes of entangled states.

Orbital Angular Momentum (OAM) of light is a promising degree of freedom for next-generation communication. By exploiting the orthogonality of OAM modes, multi-channel division enables a linearly increase in communication performance proportional to the number of available modes. However, the multiplexing and demultiplexing of each superposition state remain essential yet complex processes. Demultiplexing has been established through spatial-domain methods that require additional optical elements such as gratings and apertures, which can decrease communication efficiency and accuracy under various conditions. In this paper, we propose a demultiplexing method under a single intensity profile by orthogonality renormalization of OAM pair states. This method can be applied directly to an OAM multichannel communication system without additional receiver-side optical structure. We present simulation results of our method under various conditions.

I point out three ways in which the perspective of quantum information may lead to distorted claims about physics: forgetting that light does not need to be quantised to show coherence; ignoring the generators of unitary evolutions; and approaching the discovery of nature as a fight against an adversary.

Generating synthetic data for financial time series poses challenges, especially considering their non-stationary nature. Traditional statistical time series models normally assume weak stationarity. However, this assumption can constrain their effectiveness. Deep learning models, particularly Generative Adversarial Networks (GANs), have exhibited considerable potential in emulating complex probability distributions. GANs employ a generator-discriminator framework, where the generator creates data samples, while the discriminator distinguishes real from generated data. In this research, we introduce the Sig-Graph GAN model, which integrates the time-series signature, offering a structured summary of its temporal evolution; the Long Short-Term Memory network, capturing its inherent autoregressive structure; and Graph Neural Networks (GNNs), leveraging geometric patterns within the time-series data. To employ GNNs optimally, we use the visibility graph algorithm to derive a graph-based representation of the underlying time series. Numerical evaluations demonstrate that the Sig-Graph GAN model outperforms baseline methods in replicating the distribution of logarithmic returns across different stock exchanges. The integration of the graph structure with the autoregressive component effectively captures both geometric and temporal patterns embedded in time-series data. This research advances the field of GAN models for time series by introducing a model capable of leveraging both autoregressive properties and geometric structures for synthetic data generation.

We present a free energy lattice Boltzmann model capable of simulating fluid systems with an arbitrary number of immiscible components in principle. Our method is strictly reduction consistent, ensuring that absent fluid components do not spontaneously nucleate. We introduce a novel discretization of the surface tension force that globally conserves momentum to machine precision, and we enforce reduction consistency through a flux correction that is independent of the mobility. The method is benchmarked with a range of static and dynamic problems, including: liquid lenses, Janus droplets, quaternary phase separation, and six-component layered Poiseuille flow, and we obtain excellent agreement with theoretical predictions throughout. Finally, we demonstrate the applicability of the proposed method through patterned liquid surfaces and microfluidic emulsion droplet generation.

The distribution of dark matter (DM) halo around supermassive black holes (BHs) may leave observable imprints on stellar dynamics near galactic centers. Motivated by this, we investigate the orbital motion of the S2 star in the spacetime of a recently derived generalized Schwarzschild BH solution embedded in a Dehnen-type $(1,4,γ)$ DM halo, considering it as a possible model for Sgr A$^{\star}$ at the center of the Milky Way. Unlike previous studies restricted to specific values of the halo parameter $γ$, the present solution describes the fully generalized case with arbitrary $γ$. We derive the corresponding equations of motion and obtain the associated perihelion shift over one orbital period. Using observational data of the S2 star, we constrain the parameters of the Schwarzschild--Dehnen BH-DM system through a Markov Chain Monte Carlo (MCMC) analysis. Our results yield the best-fit values $γ= 1.18^{+1.03}_{-0.81}$ $(1.23^{+1.01}_{-0.85})$, $ρ_s = 0.37^{+0.42}_{-0.29}$ $(0.31^{+0.44}_{-0.26})$, and $r_s = 0.05^{+0.05}_{-0.03}$ $(0.14^{+0.18}_{-0.10})$ for observational data of Do et al.~\cite{Do19} and Gillessen et al.~\cite{Gillessen17ApJ}, respectively. We further obtain the corresponding 95\% confidence upper bounds: $γ< 2.66$ $(2.67)$, $ρ_s < 0.93$ $(0.92)$, and $r_s < 0.16$ $(0.52)$. These results demonstrate that precise stellar orbit measurements can provide meaningful constraints on the DM halo distributions surrounding supermassive BHs and may offer insights into the DM environment of Sgr A$^{\star}$ at the center of the Milky Way.

We present a four-dimensional equation of state for strongly interacting matter at finite temperature and conserved charge densities, constructed using a deep neural network. It is designed for direct use in hybrid models of relativistic heavy-ion collisions: it reproduces hadron resonance gas thermodynamics at typical particlization scales, is consistent with lattice QCD at low baryon chemical potential, and extrapolates into the high-density region inaccessible to either approach, which is precisely the regime targeted by RHIC BES, FAIR, HADES, and CBM. Thermodynamic consistency throughout the full phase space is enforced via a physics-informed loss function. We demonstrate the developed equation of state by implementing it at zero net strangeness and fixed electric-to-baryon charge ratio within the integrated hydrokinetic model.