We investigate the geometry of mixed quantum states near rank-changing points, showing that these singularities function as effective geometric defects. The Uhlmann connection is well-defined on the full-rank sector of the density-matrix manifold, while rank-deficient states form singular boundary strata where the bundle structure degenerates. By restricting to a punctured state manifold that excludes the singular set, we obtain a well-defined gauge structure and identify an asymptotically robust invariant: the Uhlmann holonomy around noncontractible loops encircling the defect on a restricted two-dimensional punctured submanifold. In an exactly solvable qutrit model, a restricted submanifold emerges on which the connection is locally flat yet carries nontrivial monodromy, analogous to flat connections with Aharonov--Bohm-type transport. The holonomy depends only on the ratios of the vanishing eigenvalues under frozen radial dependence of the eigenbasis geometry and a fixed angular loop. In contrast, the Uhlmann curvature may diverge path-dependently when eigenvalues shrink with distinct powers, with a leading spectral-prefactor scaling law, establishing that the holonomy survives as a universal asymptotic invariant while the curvature remains non-universal. Within the effective SU(2) defect sector, the conjugacy class of the holonomy, equivalently the Wilson loop variable, provides a continuous, non-quantized classification of the asymptotic monodromy surrounding the rank-deficient defect. This non-quantization does not imply a lack of robustness: the asymptotic holonomy is an invariant of the restricted punctured submanifold and is insensitive to smooth deformations of the loop or the radial profile within the fixed spectral-ratio sector.

Let $E$ be an elliptic curve over $\mathbb{Q}$ having split multiplicative reduction at a prime number $p$. We describe the tame part of the $\mathcal{L}$-invariant of $E$ at $p$ in terms of automorphic $p$-adic periods introduced in the work of Darmon. More precisely, we prove an equality of refined $\mathcal{L}$-invariants using twisted versions of refined exceptional zero conjectures. When the conductor of the elliptic curve is exactly $p$ and the automorphic period is attached to an optimal embedding of conductor $1$ then we prove this equality unconditionally by using the work of de-Shalit.

In magnetic confinement fusion reactors, hydrogen plasma irradiation causes material saturation and recycling, where hydrogen released from the tungsten wall significantly impacts the peripheral plasma. Kinetic Monte Carlo (kMC) simulations are essential for investigating the dynamic balance between incident and emitted fluxes at the atomic scale. However, standard kMC frameworks are inadequate for handling realistic material complexities, such as polycrystalline structures and dynamic evolution under irradiation, being computationally bottlenecked by continuous transition parameter updates. Conventionally, evaluating migration barriers in disordered systems (e.g., grain boundaries) relies on computationally prohibitive on-the-fly atomistic calculations like the Nudged Elastic Band (NEB) method. Here, we present a deep learning-accelerated Dynamic kMC framework that eliminates this reliance. Our approach integrates a three-stage deep learning pipeline: a pix2pix model for predicting local 3D potential energy distributions, a U-Net for extracting hydrogen trapping sites, and a 3D-CNN for directly evaluating migration barriers. To achieve macroscopic timescales, we implemented a hierarchical spatial index combined with a differential local-update algorithm operating in O(1) complexity. This architecture restricts recalculations to the immediate vicinity of moving atoms, accelerating updates. Demonstrated on a large-scale realistic polycrystalline tungsten model, the framework successfully reproduces preferential hydrogen trapping along grain boundaries, bridging the gap between atomic-scale accuracy and macroscopic timescales for full-scale plasma-wall interaction simulations.

In this paper, a cooperative passive sensing system in millimeter-wave (mmWave) band for simultaneous device localization and target tracking, namely mmAlert, is proposed. Specifically, in uplink communication with at least two transmitters, the receiver receives the line-of-sight (LoS) signals and the scattered signals off a moving target, respectively. Based on the received signals of the sensing time intervals, when a passive target moves along one or multiple unknown trajectories, mmAlert could measure the angles-of-arrival (AoAs) and bistatic Doppler frequencies of the echoes from the sensing target, and then jointly estimate the locations of the transmitters and the trajectories of the target. Specifically, the transmitters' locations and the moving target's trajectories can be searched by minimizing the weighted mean squared error of the AoA and Doppler measurements. The optimal solution of the minimization problem is prohibitive due to the large number of variables. Hence, a low-complexity algorithm based on the alternating optimization is proposed, where the extended Kalman filter (EKF) is introduced to quickly shape the trajectories. The mmAlert is implemented in a 60GHz communication testbed. The experiment shows with the received signal spanning a single trajectory, the average localization error of the transmitters and average trajectory reconstruction error are 0.76 m and 0.29 m, respectively. The average errors are suppressed to 0.07 m and 0.2 m respectively, if the received signal spanning 50 trajectories is used. This justifies the benefit of trajectory diversity in localization and tracking.

In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.

If $f$ is a continuous selection for the Vietoris hyperspace $\mathcal{F}(X)$ of the nonempty closed subsets of a space $X$, then the point $p=f(X)\in X$ is not as arbitrary as it might seem at first glance. In fact, the set $\mathcal{O}_{cs}(X)$ of all these points reveals certain information about the variety of Vietoris continuous selections for $\mathcal{F}(X)$. Thus, for a connected space $X$, we will show that every point $p\in \mathcal{O}_{cs}(X)$ is not only noncut, but also an endpoint of $X$. Another result of this paper is that in an arbitrary topological space $X$, the closure of the set $\mathcal{O}_{cs}(X)$ is always a totally disconnected subset. Furthermore, we will also show that $\mathcal{O}_{cs}(X)$ is a closed subset of every first countable totally disconnected space $X$.

This study examines the role of self-duality in the axiomatization of the Shapley-Shubik power index. We show that, when self-duality is imposed, the transfer axiom can be weakened to a restricted version requiring transfer only among voting games with no veto player. This result shows that self-duality can partially substitute for the transfer axiom.

The STAR experiment at RHIC reports measurements of the semi-inclusive yield of charged-particle jets recoiling from high transverse momentum charged-hadron triggers in centrality-selected Ru+Ru and Zr+Zr collisions at the nucleon-nucleon center-of-mass energy of 200 GeV. The effects of jet quenching, arising from the interaction of jets with the quark-gluon plasma, are quantified by comparing trigger-normalized recoil yields in central and peripheral collisions. Such measurements with intermediate-mass beams provide unique insight into spatial and temporal aspects of jet quenching. Suppression of the recoil yield in central collisions is observed, indicating medium-induced partonic energy loss due to quenching. The ratio of recoil jet yields for small and large resolution parameter is found to be suppressed in central relative to peripheral collisions, characteristic of medium-induced intra-jet broadening. The results are compared to similar measurements in smaller and larger collision systems.

We study the band structure and topology of magnons for a Heisenberg model with DM interaction on a deformed Kagome lattice. For simplicity, we focus on a periodically deformed lattice with hexagonal symmetry and an enlarged unit cell. This enlarged unit cell gives rise to a richer band structure than in the undeformed case. Analyzing band topology, there is a distinction between the topologically trivial case with anti-ferromagnetic coupling and the topologically rich case with ferromagnetic coupling. In the anti-ferromagnetic case, a spin-space symmetry, also present in the classical ground state, enforces these topologically trivial states. In the ferromagnetic case, this symmetry is spontaneously broken by the classical ground state. Consequently, the band structure also hosts rich topological features. Specifically, we observe many topological transitions and bands with Chern numbers ranging from $+2$ to $-2$, which makes the system richer than in the undeformed case. This emergent rich topological structure demonstrates that deformed magnets can host new and exciting physics.

LLM agents are increasingly used in moderation-relevant public forum workflows, where their choices to answer, acknowledge, repair, or decline are routinely challenged by users, platforms, and regulators. The same agent often returns different responses on identical content, so any defense based on the agent's behavior cannot be reliably reproduced. The variation is structural. Four deployment choices typically invisible to the operator each shift the agent's response rate, and their combinations can produce substantially different interventions on the same forum posts. The four choices are (1) which model version is currently served, which can change between calls without notice; (2) the model's weight-release status (open-weight, with weights publicly downloadable, vs. closed-weight, with weights held by the provider); (3) which provider serves the request; and (4) which system-prompt policy is in force. Across LLMs spanning both open-weight and closed-weight families, we find that the previously reported tendency to decline more on visible than hidden challenges aligns with the open/closed weight boundary in our panel more than with access surface. Every closed-weight cell declines more on visible challenges; every open-weight cell reverses this or shows no gap. Auditable forum-agent governance requires awareness of all four choices, not just the model name, since each independently shifts behavior.

We study the minimax risk for detecting a sparse elevated-mean Gaussian submatrix inside a larger noisy matrix. When the planted submatrix has size $n\times n$ and the ambient matrix has size $N\times N$ with $N = n^{1+α}$, the classical work of \cite{butuceasubmatrix2013} identifies the sharp detection boundary around which the minimax risk converges to $0$ or $1$. This paper extends that zero-one theory by determining the precise asymptotic rate of the minimax risk throughout a two-variable phase diagram. Above the detection boundary, we determine the precise exponent for the stretched or super-exponential decay of the risk. Below the boundary, where the risk tends to 1, we identify the exact polynomial order of the rate of convergence up to absolute multiplicative constants. In both of these regimes, the form of the sharp asymptotics changes around the line $α+ δ= 1/2$ where $δ$ indicates the signed distance from the boundary. Finally, on the detection boundary, we show that the minimax risk converges to the non-degenerate constant $\frac12$ in the very sparse case where $n$ remains fixed and $N \to \infty$. Each of these rates corresponds to the risk of a suitably calibrated scan or sum test, whence follow the upper bounds. To show the sharpness of these bounds, we rely on refined second-moment methods applied to random variables chosen carefully according to the particular regime. Our results also extend to the tensor setting.

TREE CONTAINMENT is a central decision problem in mathematical phylogenetics, asking whether a given rooted phylogenetic tree is embeddable in ("displayed by") a given rooted phylogenetic network. While the problem is NP-complete for general networks, many algorithmic advances have relied on structural parameters that capture how "tree-like" a network is. In this paper we investigate TREE CONTAINMENT under the structural parameter scanwidth, a directed width measure generalizing popular parameters measuring tree-likeness of phylogenetic networks. We first present a parameterized algorithm that solves the problem in $O(4^{k + k\log{k}} n + nm^2)$ time, where $n$ and $m$ are the numbers of nodes and arcs in the network and $k$ is the width of a given tree-extension. Complementing this upper bound, we prove a matching lower bound under the Exponential-Time Hypothesis (ETH), showing that there is no algorithm for TREE CONTAINMENT that runs in $2^{o(c\log{c})} n^{O(1)}$ time, even on binary inputs, where $c$ is the directed cutwidth of the input network, which upper-bounds the scanwidth $k$.

Under what conditions does the sign of the Ollivier Ricci curvature on a graph of a certain order change? In this paper, we discuss the curvature of graphs obtained by removing edges from complete graphs, as complete graphs have a stable positive curvature. We defined graphs obtained by removing matching edges, the set of edges incident with the vertex, and cycle edges from complete graphs, and then analyzed the Ollivier Ricci curvature of those graphs. The results show that the curvature of the graphs in the above three patterns is equal to the value obtained by dividing the number of triangles, including two vertices, by the maximum degree of the two vertices. This result also indicates that the curvature of the above graphs is zero or positive. This study concludes that the Ollivier Ricci curvature is predicted to be positive even if some edges are removed from a complete graph, and we suggest that these discussions are suitable for investigating the conditions under which the sign of the Ollivier Ricci curvature on a graph.

We develop a geometric formulation of vertex operators in superstring theory based on integral forms on super Riemann surfaces. Starting from the integrated NS-NS vertex operator, we derive descent equations that relate operators with different ghost and picture numbers. A key result is a correspondence between supergeometric objects and ghost superfields, in which the one-form $dz-θdθ$ and the even differential $dθ$ are identified with the ghost superfield and its superderivative. This provides a geometric realization of the superghost structure. We further extend the construction by incorporating inverse picture-changing operators, which generate new descent sequences across different picture sectors. We also introduce a superfield construction of higher-ghost-number operators, for which additional terms are required compared to the bosonic case. All operators are organized into a universal descent structure and are well-defined in BRST cohomology.

In this paper we provide a constructive way for researchers to salvage the classic De Loecker and Warzynski (2012) markup recovery procedure when falsified. To do this, we consider continuous relaxations of the standard assumptions behind markup estimation. By computing the values of the markup as a function of the relaxations across the set of non-falsified models, we obtain an identified set for the markup which generalizes the standard baseline markup estimand to account for possible falsification without the need to impose additional assumptions. We illustrate our results using Chilean data from Raval (2023).

In multimodal multi-hop question answering, we focus on the initial retrieval stage via two distinct tasks: (1) evidence set completion, retrieving missing evidence given context, and (2) sequential pool construction, iteratively building the top-$K$ pool from the scratch. Under these settings, we point out that conventional iterative retrieval frameworks often suffer from Semantic Anchoring, where previously fetched evidence traps the retriever and yields entity-centric redundancy. To break this trap, we propose GRAIL (Gap-aware Retrieval via Adaptive Implicit Localization), a paradigm that performs implicit query rewriting directly at the embedding level. By context-subtractive query steering, GRAIL excels at compositional cross-modal reasoning, while additive embedding updates show strength on localized information aggregation. By dynamically routing queries based on task type, our Hybrid Framework achieves a 40.3% macro-averaged performance gain on MultimodalQA. Extensive evaluations demonstrate that sequential GRAIL retrieves in a superior, noise-resilient manner, significantly expanding the search horizon through iterative gap-aware optimization.

We train an instantaneous quantum polynomial-time (IQP) Born machine on real high-energy-physics calorimeter shower images at 64 qubits and compile the trained model into a single sampling-hard IQP circuit for quantum deployment. The pipeline has three components. The first is a Mixture-of-IQP (MoIQP) architecture, whose Walsh-diagonal MMD$^2$ loss is classically trainable by Van den Nest Fourier Monte Carlo. The second is the Pearson-Stabilized Correlation Kernel (PSCK), a positive-definite MMD kernel that biases descent toward correlation-sensitive directions through a data-evaluated Jacobian of the empirical Pearson matrix. The third is an exact deferred-measurement compilation of MoIQP into a single IQP circuit on n + $log_2 L$ qubits (cIQP). Across five seeds at L = 8, 1500 epochs, the model reaches $\mathrm{MAE}_ρ$ = $0.069 \pm 0.008$ against a 0.052 encoding-fidelity floor on the training split and $0.071 \pm 0.008$ on a held-out test split, versus a Liu-Wang baseline at $\mathrm{MAE}_ρ$ = 0.100. The compiled cIQP reproduces the MoIQP marginal to $0.591 \pm 0.012$ times the Monte Carlo noise floor.

We construct the exact Robin bulk-to-boundary propagator for a Breitenlöhner--Freedman scalar on AdS$_{d+1}$ and the BTZ black hole, realizing the double-trace RG flow between standard and alternate quantization geometrically as a one-parameter family of bulk boundary conditions. We derive the UV and IR chain expansions of the kernel intrinsically from the boundary-value problem, without an auxiliary-field decoupling, and identify a branch split at each order that separates the local data the boundary CFT observes from finite-bulk-depth structure visible only to bulk probes -- the part of $K_f$ that distinguishes holographic reconstruction from boundary calculation. On BTZ we obtain the closed-form Robin kernel and the corresponding family of quasinormal-mode trajectories, each connecting an alternate-quantization pole at $g=0$ to a standard one at $g\to\infty$. We locate an exceptional-point locus along this family at which two trajectories coalesce into a Jordan block, and show it acts as a non-Hermitian phase boundary for the double-trace flow itself: crossing it reorganizes the global pole-pairing topology of the spectrum. Unlike holographic EPs reached by analytic continuation in momentum or frequency, this transition lives on the interpolation between quantizations and is reachable at finite real momentum and temperature by tuning the physical Robin coupling.

We explore Seshadri constants associated to weighted blow-ups of complex projective varieties and demonstrate how to use this notion to construct symplectic embeddings of ellipsoids. We illustrate the utility of this point of view by providing constructions of full fillings of $\mathbb{CP}^2$ by ellipsoids corresponding to all of the exceptional (post-Fibonacci) steps of the McDuff--Schlenk staircase and some non-obvious embeddings of ellipsoids in ellipsoids.

In this work, we develop a new theory of multivariate V-filtration on D-modules along a simple normal crossing divisor and relate it with Sabbah's multi-filtration. We establish several new structural results and relate them with the Hodge filtration on free-monodromic local systems from geometric representation theory. As an illustrative application, we give a conceptual and very quick proof of the Strong Monodromy Conjecture and its multivariate generalisation for hyperplane arrangements. Along the way, we confirm both the n/d-conjecture of Budur--Mustaţă--Teitler and its multivariate form due to Budur.

For graph $G$, a connected graph $H$ of order $n$ is $G$-good if $r(G,H)=(χ(G)-1)(n-1)+s(G)$, where $χ(G)$ is the chromatic number of $G$ and $s(G)$ is the minimum size of a color class in a $χ(G)$-coloring of $G$. Let $K_{α_{1},\ldots ,α_{p},n}$ be the complete $(p+1)$-partite graph with partite sets of sizes $α_1,\ldots,α_p,n$. Burr, Faudree, Rousseau and Schelp (1983) showed that $K_{α_1,\ldots,α_p,n}$ are $(K_2+mK_1)$-good for large $n$. We determine graphs $G$ such that $K_{α_{1},\ldots ,α_{p},n}$ are $G$-good for large $n$. The characterization depends on $\mathrm{snd}(α_i)$, the smallest non-divisor of $α_i$, where $1\le i\le p$.

We investigate the dynamical mechanisms underlying the contrasting Floquet spectral evolutions observed in viscously damped and in nonlinear mean-flow damped higher-order nonlinear Schrödinger models. Motivated by the persistent organized Floquet-band structure under nonlinear mean-flow damping and the repeated Floquet band reconnection observed under viscous damping, we derive a reduced five-mode carrier-sideband truncation and reformulate the dynamics in amplitude-phase variables to isolate the dominant interaction phases associated with the principal four-wave interaction products. Within this framework, viscous damping acts primarily modewise and does not directly modify the leading interaction-phase dynamics. By contrast, nonlinear mean-flow damping contributes directly to the interaction-phase evolution through interaction-dependent dissipative corrections. In the carrier-sideband regime, these corrections generate terms of the form $-κ_j \sin(ψ_j)$, introducing dissipative feedback into the dominant carrier-sideband interaction dynamics. To interpret the resulting interaction-phase evolution, we examine recurrent finite-gap NLS benchmark solutions whose modulation dynamics are independently understood. These benchmarks show that substantial interaction-phase evolution and localized restructuring may occur even within organized quasiperiodic dynamics possessing invariant Floquet spectral structure. Numerical diagnostics show that the nonlinear mean-flow damped system exhibits persistent recurrent carrier-sideband focusing dynamics together with organized Floquet evolution despite substantial interaction-phase restructuring, whereas the viscous system exhibits progressively diffuse modulation dynamics together with repeated Floquet reconfiguration and weakening persistence of the recurrent carrier-sideband interaction structure.

Harnessing active matter calls for strategies that break the directional symmetry of self-propelled motion without altering the propulsion mechanism itself. Here, we show that magnetically inert spherical active colloids can be steered through the anisotropic viscous response of a ferrofluid under a uniform magnetic field. Self-propelled Janus colloids exhibit robust cross-field motion transverse to the magnetic field, although the applied magnetic field directly controls neither the particles nor their propulsion speed. Quantitative measurements reveal an emergent reorientation torque that grows with both propulsion speed and magnetic field strength. A squirmer model in a magnetoviscous medium captures these observations and shows that the torque arises from the coupling between swimmer-generated flow and anisotropic rotational viscosity. Our findings establish a hydrodynamic basis for converting viscous dissipation into directional symmetry breaking through anisotropic rheology, providing a route to field-controlled material transport by active matter.

Motivated by the emergence of local groundwater exchanges, we construct and analyze stochastic models of dynamic groundwater markets. Our primary focus is endogenizing the price formation and groundwater pumping strategies in a closed market with stochastic groundwater allocations and opportunities for intertemporal transfer through rights banking. In our model, several agents, interpreted as farmers or agricultural districts, make competitive decisions on water consumption to produce a basket of goods, as well as on trading allocations among themselves, or banking them for future periods. We define the respective discrete-time non-zero-sum non-cooperative game and construct its sub-game perfect Nash equilibria characterized by the groundwater price process $\{p^\circ(t)\}$. We furthermore construct an algorithm to determine equilibrium strategies and prices through a machine learning approach on top of best-response iterations. Extensive numerical experiments illustrate dynamic phenomena, including the role of groundwater recharge dynamics, agents' risk aversion and groundwater allocations. Our model provides insights into competitive effects in environmental markets with banking features.

In this paper, we prove that every prime $p$ which is congruent to $4,7$ modulo $9$ is the sum of two rational cubes. This is $2/3$ of Sylvester's conjecture which has a history of nearly 150 years since 1879. In the proof, we use recent progress on Full BSD conjecture of rank $0$ elliptic curves in \cite{BF} to deduce that the Manin-Stevens constants of some families of elliptic curves are units. We also use recent solutions of Unbounded Denominators Conjecture in \cite{CDT} to prove that some cubic roots of modular functions are invariant under some congruence subgroups. Instead of using the Unbounded Denominators Conjecuture, we also give another conditional proof assuming the GRH for number fields or Artin's primitive root conjecture for arithmetic progressions.

It is well known from classical physics that weakly coupled self-sustained oscillators may spontaneously lock their phases. Just like classical synchronization is known to break down due to noise induced phase slips, we show here how the synchronization of continuous variable quantum systems breaks down by proliferation of quantum phase slips. Within a Keldysh path integral formulation of limit cycles, we analyze the phase dynamics and show how, in spite of strong phase correlations, quantum phase slips degrade the actual phase locking. This approach also allows us to address non-Markovian effects on the synchronization of limit cycles, which we illustrate explicitly for superconducting resonators coupled via a voltage biased double quantum dot.

[Note added after submission. After posting the first version of this preprint and corresponding with Ved Kunte and Kuntal Sengupta, we identified an issue with the claimed separation between real quantum theory and ordinary complex quantum theory in the process-matrix framework. This version imposes normalization only for local CPTP maps acting on the parties' process input-output systems, which we call N1. A stronger compositional requirement is to impose normalization also after arbitrary shared ancillary systems are introduced and each party acts jointly on its process system and local share of the ancilla, which we call N2. Under N2, the process matrix used in this version to separate RQT from QT is not valid, and the claimed RQT/QT separation is therefore not established. We are preparing a revised version that clarifies this distinction and revises the affected claims. This temporary update is intended to alert readers to this issue while we work on revising the manuscript.]

Perovskite-based solar cells have undergone rapid improvements over the last decade enabling highest power conversion efficiencies of single-junction and multi-junction devices. The implementation of nano- or micro-textures has played a major role in this development due to their ability to minimize reflection losses, maximize light trapping, and hence increase light harvesting in the active layer. In the slipstream of these advances, it has become apparent that nano- and micro-textures can also have many other collateral benefits beyond light management. In this article, very recently reported texture-related benefits for perovskite-based solar cells different from light management are reviewed. These are namely (1) improved film wetting from perovskite-solution, (2) enhanced perovskite crystallinity in terms of grain size, crystal orientation and phase homogeneity, (3) enhanced carrier extraction leading to higher open-circuit voltages, and potentially (4) increased mechanical stability upon bending in flexible devices and reduced residual stress. This survey helps to understand textures as a holistic concept to further improve perovskite-based solar cells, photodetectors and light emitting diodes.

We present MARUT, a scalable multi-GPU computational fluid dynamics (CFD) framework designed for high-fidelity simulations of compressible flows spanning subsonic to hypersonic regimes, including chemically reacting nonequilibrium flows with finite-rate chemistry and adaptive mesh refinement (AMR). The framework addresses a central challenge in contemporary scientific computing: the development of numerically accurate and computationally scalable algorithms capable of resolving strongly nonlinear, multiscale flow physics on emerging heterogeneous supercomputing architectures. Built around a distributed-memory MPI-parallel infrastructure and implemented natively on NVIDIA GPUs, MARUT combines high-order spectral discontinuous Galerkin discretisations with strong-stability-preserving Runge--Kutta time integration to achieve low-dissipation and high-resolution representation of shocks, vortical structures and reactive interfaces. Dynamic AMR further enables efficient concentration of computational resources in localized regions of physical complexity, thereby substantially reducing computational cost while preserving solution fidelity. MARUT is designed to maintain strong parallel efficiency through GPU-resident computations and scalable MPI communication strategies, achieving near-linear strong scaling across multiple GPUs. The solver is validated against a broad suite of canonical benchmark problems involving inviscid, viscous, and reactive compressible flows, including subsonic, transonic, supersonic, and hypersonic configurations with multi-species nonequilibrium chemistry. The numerical predictions show close agreement with established reference solutions. Beyond its immediate performance characteristics, the framework reflects the broader transition of computational science towards modular, adaptive and AI-compatible simulation ecosystems.

In this work, first, we discuss the connections between various low-dimensional quantum gravity models, including 3d Chern-Simons, 2d JT, 2d BF theory, 2d Liouville, 2d WZW, and 1d Schwarzian, which are related through holography and dimension reduction, and discuss some universalities in their partition functions. Then, we specifically examine the JT partition function and the partition function of $\mathcal{N}=(2,2)$ on $S^2$ and $\text{AdS}_2$ and discuss their similarities and therefore examine our proposed universalities. We change the parameters in each model and based on the change in the structure of the partition functions, strengthen our conjectures. We also use eigenfunctions, spectra and the behaviors of Wheeler-DeWitt wavefunctions to generate more universalities between these low-dimensional quantum gravity models, specifically in their partition functions. Then, we use entanglement entropy, complexity and RG flows, particularly in the context of wormholes, to find more universalities in quantum gravity models. Finally, we use the new results about the connections between wormholes and defects to discuss our universalities further.