Papers

Ringdown gravitational waves from binary black hole mergers can be modeled as superpositions of quasinormal modes (QNMs), whose frequencies and excitation factors encode properties of the remnant Kerr black hole. Reliable extraction of multiple QNM components is challenging because of mode overlap and noise. We develop an autoencoder-based framework for multi-component QNM analysis, in which the latent space is trained to represent the physical parameters of individual modes, enabling waveform denoising and parameter estimation within a common framework. Using controlled model waveforms constructed as finite sums of Kerr QNMs with recently established high-precision frequencies and excitation factors, including their nontrivial spin dependence near resonant excitation, we assess the method across partitioned spin intervals. The model achieves good in-domain waveform reconstruction and parameter recovery for the two longest-lived components of eight-component input waveforms, while its performance degrades when the validation spins lie far outside the training range. In a selected spin interval, the framework also recovers the 32 parameters of an eight-component waveform with good overall agreement. These results demonstrate the feasibility of physics-informed autoencoder-based inference for a prescribed multi-component ringdown waveform family and motivate further tests with progressively more realistic signals.

We give a quantitative disorder comparison for the zero-field Sherrington–Kirkpatrick model at inverse temperature one. For any fixed number of replicas, replacing Gaussian couplings by independent couplings from a bounded symmetric variance-one law changes a bounded replica expectation by at most a constant times the Gaussian overlap second moment plus $N^{-1}$. A multiplicative comparison for nonnegative observables controls the tails. The proof uses Talagrand's positive-observable estimates and Yu-Ting Chen's fourth-order replica cancellation. Assuming the Gaussian critical overlap limit stated by Du and Huang, we obtain the same limit for the random quenched overlap measure in the iterated Wasserstein-2 topology. No separate moment assumption is needed for this transfer. Their additional exponential moment bound gives convergence of the rescaled spin-glass susceptibility in every finite Wasserstein distance. The coupling class includes fair signs, uniform disorder, and signs thinned at any fixed positive density.

A quantum ensemble contains preparation weights that are lost in its average density operator. We show how optimal decisions read these weights as a wave on projective state space. Varying the input prior sweeps a surface of fixed Born overlap through the ensemble; the resulting response propagates according to the geometry of pure states and reconstructs their distribution in every finite dimension. Conditional preparations can fix this wave through contact, selecting the ensemble at a steering boundary. Positive propagation gives exact biased-qubit solutions and explicit parent measurements for noisy channels. When measurement records are combined, their state directions are averaged and the wave acquires a source whose growth measures the lost discrimination advantage. Preparation, inference and noise can thus be understood as operations on the same recoverable distribution, linking quantum correlations to measurement resolution.

The intracluster medium (ICM) in merging galaxy clusters exhibits turbulence and bulk flows. Unraveling these components is crucial not only for elucidating the geometry of the cluster mergers, but also for understanding the physics of magnetic field amplification and relativistic particle acceleration. XRISM/Resolve data for two $3'\times3'$ fields in the core of the Coma cluster reveales that the ICM in the central field moves with $\Delta cz = -430$~km~s$^{-1}$ relative to the cluster galaxy average, while that in the southern field moves with $\Delta cz = -730$~km~s$^{-1}$ (see \cite{2025ApJ...985L..20X}, hereinafter “Paper I”). In this paper, we perform a more detailed analysis of these data sets to search for non-Gaussian features in the Fe-K line complex profiles. In the spectra from the northwest (NW) quadrant of the central field, in addition to the main and redshifted ICM components ($\Delta cz = -40$ km s$^{-1}$) reported in Paper I, we find evidence of another, blueshifted component, moving with $\Delta cz = -1250$ km s$^{-1}$. For a systematic search for other significant velocity components, we perform a bias-free 3 eV step multi-component fit to the Resolve full-array spectra from the central and southern fields. This search uncovers another redshifted component in the southern field, moving with $\Delta cz \sim +1230$ km s$^{-1}$. We estimate the energy densities of the ICM turbulence and bulk motion to be similar to each other and several times greater than the energy density of the cluster's $B\sim 5~\mu$G magnetic field.

We present PepC-Global, a global version of the Princeton environment-dependent probabilistic tropical cyclone (PepC) framework that uniquely implements basin-wise tuning within a single unified tropical cyclone climatology model. PepC-Global represents tropical cyclone climatology as a coupled stochastic process linking genesis, track, and intensity conditioned on large-scale environmental predictors. Each of the genesis, track, and intensity modules outperforms widely used linear models in out-of-sample tests. The intensity module also incorporates an environment-dependent over-land decay model, offering greater sensitivity to climate change signals than conventional fixed decay rate approaches. Systematic evaluation against observations demonstrates that PepC-Global closely reproduces genesis basin-wise frequency, seasonal cycles, interannual variability, and spatial distributions. The model also accurately captures basin-wise track patterns, along-coastline landfall frequency, and intensity statistics including lifetime maximum intensity and landfall intensity distributions. PepC-Global provides a versatile tool for probabilistic tropical cyclone hazard and risk assessment and a practical framework for investigating changes in tropical cyclone activity across future climate scenarios.

Biological swimmers and flyers exploit unsteady vortices for propulsion, whereas engineered vehicles usually suppress them as disturbances. Learning such flow exploitation in machines is difficult because real-fluid interaction data are scarce and unstructured exploration is unstable in high-dimensional, history-dependent flows. Here we present REEF, a co-designed physical-learning framework that integrates SHOAL, an eight-channel high-throughput array for real fluid–structure interaction, with V-STAR, a staged algorithm that converts these interactions into policies through imitation, offline internalization, and online adaptation. Across lift-based, drag-based, and momentum-jet propulsors, REEF expands the attainable force envelope to more than twice that of parameterized search. Particle image velocimetry shows that these gains arise from coordinated vortex formation, growth, and force projection, rather than refinement of a fixed motion-to-force mapping. Force-trained policies transfer zero-shot to free-moving robots whose body motion changes the surrounding flow, suggesting that REEF learns transferable wake-coupling principles for embodied propulsion in unsteady fluids.

Classical simulability of quantum circuits plays a central role in characterizing and quantifying quantum computational advantage. Typically, the presence of non-Clifford gates introduces an exponential runtime overhead for classically estimating expectation values of observables. In this work, we introduce an efficient simulation framework that integrates the sum-over-Clifford method with quasi-probability-based stabilizer simulation to directly estimate expectation values. To optimize efficiency, we incorporate a circuit-adaptive reduction via variance estimation protocol, which terminates simulations once an empirical confidence bound is sufficient to guarantee the prescribed error tolerance. Our method circumvents overly conservative Hoeffding's inequality, thereby reducing the dependence on the gate-wise stabilizer extent from quadratic to linear in the low-variance regime, while maintaining the same space complexity as previous approaches. We explicitly prove the sample-complexity reduction for random quantum circuits and T-doped Clifford circuits and also empirically validate these advantages in the quantum approximate optimization algorithm and quantum kernel method.

Classical theories of random neural networks typically assume independent connectivity, overlooking the local motif structures prevalent in biological circuits. Here, we investigate how four second-order synaptic motifs (chain, reciprocal, convergent, and divergent) shape the dynamics of nonlinear firing-rate networks. While previous studies have established that chain correlations generate outlier eigenvalues, we demonstrate that these motifs also jointly reshape the Jacobian eigenvalue bulk. Using the path-integral formalism, we derive a dynamic mean-field theory which reveals that the chain motif acts as a retarded feedback of the ensemble-mean activity through the response kernel, producing a rich repertoire of dynamical regimes, including ferromagnetic states and limit cycles. At sufficiently large magnitude, negative chain correlations produce a glassy, multistable regime that was previously mainly associated with partially symmetric networks. Our theory also distinguishes convergent from divergent motifs: divergent correlations primarily rescale temporal noise, while convergent correlations suppress temporal chaos by converting nonzero mean activity into quenched heterogeneity. Finally, analyses of the Lyapunov spectrum and participation-ratio dimension show that motif structure changes the geometry of chaotic activity, reducing entropy production and attractor dimensionality even when the effective spectral edge is held fixed. Together, these findings establish second-order motifs as a fundamental structural mechanism governing the dynamical regimes of local cortical circuits.

We study classical Maxwell fields with non-trivial sources in four-dimensional Minkowski spacetime. In particular, contact and symplectic geometric aspects are discussed. As a point of departure, it is shown that a few classes of solutions with sources are constructed from the so-called Beltrami fields, where these fields are contact forms on three-dimensional Riemannian manifolds. In addition, several applications in these classes are provided. One is to give a solution to the London equations for superconductors. Another one is that, if there is a non-trivial conserved quantity along the magnetic vector field, then the Maxwell system can be viewed as a Liouville integrable Hamiltonian system on a four-dimensional symplectic manifold, where this manifold is obtained by a symplectization of the contact manifold. As examples, Maxwell fields with the Lundquist model, a restricted case of the ABC flow model, and so on, are shown to be integrable in the above sense.

We consider the effect of light decoherence in a Fabri-Perot (FP) microcavity. We show that, when present, it may significantly change its linear response to the incident light.The optical properties of the bounding mirrors are described using the classical electrodynamics, and the light scattering causing the phase breaking is treated as a multichannel scattering problem employing a model introduced by Büttiker to describe dephasing in electron transport. We show that the dephasing causes a gradual erosion of the cavity photon mode and thus impedes the formation of molecular polaritons. Consequently, the polaritons signatures in the transmission and absorption optical spectra of the microcavity are fading away as the scattering intensifies.

Advances in solid-state physics, materials science, and device engineering have accelerated the development of superconducting qubits. Among emerging platforms, van der Waals (vdW) materials and their heterostructures are potentially attractive building blocks for quantum devices, yet their realization in qubit architectures remains largely underexplored. Here we report an all-vdW superconducting qubit based on a NbSe$_2$-hBN-NbSe$_2$ junction, in which a thin hBN layer simultaneously provides Josephson coupling and capacitive shunting between two NbSe$_2$ islands, forming a "merged-element" transmon. Temporal characterization using circuit quantum electrodynamics (cQED) techniques yields an average energy-relaxation time $T_{1,\mathrm{avg}} = 55 ~\mu s$, Hahn-echo coherence time $T_{2\mathrm{E},\mathrm{avg}} = 21 ~\mu s$, and Ramsey coherence time $T_{2\mathrm{R},\mathrm{avg}} = 1.9~\mu s$. The relatively low Ramsey time is primarily attributable to an enhanced sensitivity to charge noise consistent with the realized device parameters and not a fundamental limitation. These results show that lumped-element superconducting qubits based on vdW heterostructures can achieve coherence times comparable to those of conventional Al-AlO$_\mathrm{x}$-Al qubits, while offering a reduced device footprint and suppressed stray capacitive coupling.

Interaction effects and fluctuations govern the phase diagram of systems with multiple competing phases. In particular, as individual phases are destroyed by increasing temperature, fluctuations can still produce a composite `vestigial' order given by a product of individual order parameters. Here, we describe vestigial Altermagnetism (AM) from the thermal melting of antiferromagnetic (AFM) and orbital orders (OO) on the square lattice. The coexistence of AFM and OO can give rise to conventional AM with ordering wave vector $\mathbf{Q}=(\pi,\pi)$. We show that a distinct `vestigial AM' phase with $\mathbf{Q}=0$ can arise from thermal melting of AFM and OO, and investigate its generic phase diagram. We find that the transition from the high-temperature disordered phase into the vestigial AM phase can be either first or second order, depending on the AFM and OO bare susceptibilities and their interactions. We then investigate the unique experimental signatures by calculating the electron spectral function for a minimal two-orbital model. Despite the fact that the vestigial AM order parameter does not couple to electrons directly, fluctuations dominate the self-energy corrections giving rise to a spin- and orbital-dependent quasi-particle lifetime with the AM symmetry.

Relativistic $5d$ Mott insulators host a rich variety of exotic hidden multipolar order, whose microscopic nature remains heavily debated. A broken local point-symmetry (BLPS) phase followed by antiferromagnetism was previously observed in the doped compound Ba$_2$Na$_{0.1}$Ca$_{0.9}$OsO$_6$, where mixed Os valence places the system toward the $5d^2$ end of the $5d^1$-$5d^2$ regime. In contrast, pristine $5d^2$ Ba$_2$CaOsO$_6$ has shown a single octupolar transition with average cubic symmetry, raising the question of whether BLPS arises from chemical disorder in the doped systems. Here, we discover the BLPS phase in pristine Ba$_2$CaOsO$_6$ emerging at $T^* \approx 50$ K, precisely coincident with the octupolar transition. Beyond standard ${}^{43}$Ca nuclear magnetic resonance (NMR) spectral analysis, our spin-echo nutation measurements detect a finite electric field gradient, demonstrating spontaneous symmetry breaking despite the cubic average structure. While our NMR data support the previously identified octupolar order, the BLPS phase reveals a subdominant quadrupolar contribution, establishing that the hidden order in Ba$_2$CaOsO$_6$ is intrinsically multicomponent. Such mixed multipolar states lie beyond conventional theoretical descriptions of the $5d^2$ ground state. Our results establish local symmetry breaking as an intrinsic property of the clean $5d^2$ limit and provide a new constraint on microscopic theories of strongly spin-orbit-coupled Mott insulators.

High quality factor ($Q$) and overtone operation enable narrow-linewidth acoustic devices with multiple discrete frequencies in a single cavity. Maintaining both high $Q$ and sufficient electromechanical coupling at higher mode orders remains challenging. Here, we demonstrate a bimorph periodically poled piezoelectric film (P3F) lithium niobate (LN) platform for high-order thickness-shear (TS) overtone excitation. The device comprises a bonded 80-$\mu$m-thick single-crystal X-cut LN bimorph with opposite polarizations, patterned top and floating bottom electrodes, and a suspended air cavity. The P3F configuration mitigates charge cancellation from the alternating stress distribution of higher-order TS modes, enabling measurable coupling across a broad sequence of overtones. The thick LN acoustic cavity and increasingly confined high-order mode profiles support low-loss operation. Measured TS overtones extend to 1.75 GHz. At room temperature, representative overtones at 0.77 and 0.89 GHz exhibit 3-dB $Q$ values of 11,338 and 11,917, corresponding to $fQ$ products of $8.74\times10^{12}$ and $1.06\times10^{13}$ Hz, respectively. Cooling from 297 to 12 K systematically enhances $Q$, yielding a peak 3-dB $Q$ of 20,507 at 779 MHz and a maximum $fQ$ product of $1.98\times10^{13}$ Hz at 1.379 GHz. These results establish bimorph P3F LN as a promising platform for high-$Q$, frequency-scalable micro-acoustic resonators in the sub-GHz and low-GHz regimes.

We investigate primordial black hole (PBH) formation during an early matter-dominated era using fully nonlinear numerical relativity. The initial condition is set by a functional form of the curvature perturbation including ellipticity, which makes the configuration triaxial. Two kinds of matter descriptions are considered: dust fluid and collisionless particles. In the dust fluid description, numerical computation crashes associated with the appearance of a singularity at which the fluid density diverges, unless the singularity is hidden well inside the apparent horizon. We found that, for the dust fluid description, to observe the horizon formation before calculations crash, the initial amplitude must be larger than the previous analytic estimation by a factor of 2. On the other hand, with the particle system description, calculations do not crash, and we may observe black hole formation after subsequent evolution of the system. Then the threshold of black hole formation is significantly smaller than the previous analytic estimation by an order of magnitude.

We elaborate a scheme for controllable shaping of self-trapped vortex states in a quasi-phase-matched three-dimensional photonic crystal with the combination of self-focusing quadratic and defocusing cubic material nonlinearities. The setting gives rise to sturdy droplet-like vortex modes, capable to adapt to externally imposed strong geometric constraints. The application of a square-shaped modulation in the transverse $\left(x,y\right) $ plane and periodic quasi-phase-matching to the quadratic nonlinear coefficient $d_{z}$ along the propagation direction $z$ leads to the formation of square vortex droplets (VDs) with fourfold rotational symmetry ($C_{4}$). These states preserve the vortical phase circulation and exhibit robust propagation in a broad parameter region. In the oversaturated regime dominated by the cubic self-defocusing, the square-shaped VDs obey the anti-Vakhitov–Kolokolov stability criterion. The results, which are produced, chiefly, for the VDs with topological charge $S=1$, and also, in a partial form, for $S=2$ and $4$, reveal an unexpected universality: the vortex robustness is not contingent upon the circular symmetry. Thus, the combination of the competing nonlinearities and geometric confinement provides not only an effective method for the formation of self-trapped vortex states, but also new insight into generality of the topological protection in nonlinear optical fields.

We introduce a graph invariant obtained from Pauli decompositions of Hamiltonians derived from local graph neighborhoods. Given a rooted h-hop neighborhood, we construct a local adjacency operator, embed it into a common Hilbert space dimension, and define its Pauli-support set as the collection of Pauli strings appearing with nonzero coefficients. For periodic graphs, we prove invariance under lattice-compatible graph equivalence and establish converse results under root-separation hypothesis. The framework naturally extends to Lie closures, commutants, and Cartan-type structures generated by the associated Pauli supports. We further discuss extensions to aperiodic graphs with finite local complexity and make connections to cut-and-project models of quasicrystals and notably, Penrose tilings. From a quantum information perspective, the resulting invariants provide a operator-theoretic description of graph-based Hamiltonians and offer a new mechanism for comparing graph-based quantum systems through Pauli-support data.

Using the Swift-Perley sample, Le, Ratke, & Mehta performed a study of the rate density of LGRBs with an assumed broken power-law GRB spectrum. They obtained a GRB-burst-rate functional form that fits the preSwift~and Swift~redshift cumulative distributions at all redshifts with an assumed Hubble constant of $H_0 = 72 \, {\rm km \, s^{-1} \, Mpc^{-1}}$. Further analysis indicated that the cumulative redshift distribution is weakly sensitive to variations in the Hubble constant $H_0$, whereas the corresponding differential burst-rate distribution exhibits greater sensitivity. In this paper, we extend this analysis by comparing model predictions for different values of $H_0$ with the observed cumulative and differential redshift and jet-opening angle distributions, while adopting the same GRB framework and observational samples. We find that both the cumulative and differential distributions depend only weakly on variations in $H_0$, and the model predictions using $H_0 \approx 68 - 80 \, {\rm km \, s^{-1} \, Mpc^{-1}}$ provide agreement with the observed LGRB distributions.

Let $\rho$ and $\sigma$ be density operators on a separable Hilbert space. For $0<\alpha<1$, we study the directed trace-norm overlap $\Phi_\alpha(\rho,\sigma)=\|\rho^\alpha\sigma^{1-\alpha}\|_1$ and its symmetrized form $\mathcal F_\alpha(\rho,\sigma)=\frac12\bigl(\Phi_\alpha(\rho,\sigma)+\Phi_{1-\alpha}(\rho,\sigma)\bigr)$. At $\alpha=\tfrac12$, both quantities coincide with the root Uhlmann–Jozsa fidelity. Our aim is not to introduce a new notion of fidelity, but to understand how these overlaps vary with the parameter and when equality occurs in the resulting inequalities. We first prove that $\alpha\mapsto\Phi_\alpha(\rho,\sigma)$ is log-convex. This yields a sharp lower bound for $\mathcal F_\alpha$ in terms of the root fidelity, together with a stronger intermediate geometric-mean bound. We also show that $\Phi_\alpha$ is the trace functional $Q_{\alpha,1/2}$ associated with the $\alpha$-$z$ Renyi divergence, which connects the directed overlap with the known $\alpha$-$z$ Renyi theory. We then determine the exact data-processing behavior of the symmetrized family. Universal monotonicity under quantum channels holds only at $\alpha=\tfrac12$; for every other value of $\alpha$, it already fails under diagonal pinching of faithful real qubit states. In finite dimensions, we give a complete spectral description of the equality cases and provide explicit noncommuting examples. We also discuss some natural questions about overlap-preserving maps. Finally, we prove that the difference between the Petz overlap and the directed trace-norm overlap vanishes exactly when $\rho$ and $\sigma$ commute, without requiring either faithfulness or any additional support assumption.

We prove a lower comparison for disorder-averaged ferromagnetic XY correlations: independent nonnegative random couplings $K_e$ can be replaced by $-\frac12\log\mathbb{E}e^{-2K_e}$. Ginibre's inequality makes each normalized correlation convex in $1-e^{-2K_e}$, so conditional Jensen and thinning compare Bernoulli bond densities; two star-wise Jensen passes handle site dilution on bipartite graphs. Together with the phase-existence theorem of Dario and Garban, these comparisons give local Lipschitz regularity of both the averaged algebraic-phase and susceptibility-divergence thresholds throughout the supercritical density intervals on $\mathbb{Z}^2$. The clean finite-domain criterion of van Engelenburg and Lis also yields explicit finite-size susceptibility lower bounds in a weak-dilution region. For bounded centered bond noise, the possible suppression of the algebraic-phase temperature is at most quadratic in the noise amplitude. Finally, at finite positive thresholds we prove total-variation continuity for bounded iid coupling laws whose essential supremum equals the common support cap, with local Lipschitz control when the reference law has an atom at that cap.

We develop a general framework for constructing massive black bounce geometries from massless wormhole seeds by introducing a position-dependent mass function while preserving the underlying areal-radius profile. We apply this procedure to the generalized Ellis-Bronnikov wormhole and obtain a new family of generalized Bardeen-like black bounce space-times, which continuously interpolates between traversable wormholes and regular black holes. We investigate the motion of massive particles and photons and show that, in contrast with the simpler orbital structure of the massless generalized Ellis-Bronnikov geometry, the generalized Bardeen-like space-time can exhibit multiple circular orbits and a rich light ring structure, including configurations with two unstable circular photon orbits separated by a stable one. We determine the corresponding photon sphere and shadow radii and compare our predictions with Event Horizon Telescope observations of Sgr A*, deriving observational constraints on the parameter space of the model. We further investigate the optical appearance produced by a geometrically and optically thin accretion disk through ray tracing. Multiple light rings generate characteristic nested structures in the high-resolution intensity profiles, whose relative brightness is strongly affected by the mass deformation and gravitational redshift. However, after modeling the finite angular resolution of the EHT with a Gaussian beam convolution, these fine structures are largely washed out, revealing a strong observational degeneracy between these exotic compact objects and standard black hole geometries at current EHT resolution.

Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within $25 \mathrm{ns}$, with an average gate fidelity exceeding $99.99\%$ and leakage below $10^{-5}$. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately $99.9\%$. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below $10^{-4}$ in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.

We investigate whether quantum metric fluctuations can destroy the differentiable Lorentzian support required for spacetime. We conjecture that non-Lorentzian metric elements are absent from the physical manifold and restrict admissible histories to a single continuing, causally connected four-dimensional geometry. To explore this proposal, we extrapolate the Gaussian transverse-traceless graviton vacuum to an additive metric ensemble with physical Fourier cutoff $k_{\max}=1/q$. A lattice model with local repair and selection of periodically winding differentiable-state components gives a minimum surviving scale $q_{\min}\simeq1.9\,\ell_{\rm P}$ over the simulated duration. We then examine two complementary curvature-induced deformations. For the Schwarzschild electric Weyl field, the smallest boundary radius at the center of a black hole, occurring when $q\simeq2.5\,\ell_{\rm P}$, is $r_{\rm qb}\simeq2.62\,C_W^{1/3}(r_g\ell_{\rm P}^2)^{1/3} \simeq1.91\times10^{-22}\, C_W^{1/3}\left(\rm M/\rm M_\odot\right)^{1/3}\mathrm{m}$, where $r_g=GM/c^2$ and $C_W$ parameterizes the finite-$q$ Weyl response. For homogeneous radiation, a supplementary Gaussian four-metric ensemble subject to linearized de Donder conditions gives $\rho_{\rm qb}/\rho_{\rm P}\simeq1.31\times10^{-2}/C_R$ at $q=2.5\,\ell_{\rm P}$, where $C_R$ is the corresponding Ricci-response coefficient. The local homogeneous criterion is unchanged under reversal of the expansion rate. These model-dependent thresholds motivate a possible replacement of classical singular continuations by finite-curvature quantum boundaries.

I contend that physics should provide a coherent account of reality, in addition to be an efficient algorithm for the prediction of empirical results. This article offers pictures of reality derived from theories of modern physics. In particular it is shown that Bose quantum fields may be interpreted as pure wave fields via the Weyl-Wigner representation. The most relevant result being the existence of a stochastic vacuum field, corresponding to the quantum vacuum fluctuations of the standard, canonical, formulation of field theory. That field provides explanations for the particle (photons) behaviour of the electromagnetic field. Also a realistic interpretation is offered for the interference experiments with actual particles, like atoms. The interpretation of classical general relativity is standard but emphasis is made on the principle of equivalence. Problems like the spacetime singularities (black holes) and the empirical violation of Bell inequalities are touched but slightly. Asides from these problems the main incompleteness of the article is the absence of a realistic interpretation of Fermi fields.

Hyperbolically symmetric wormholes provide a setting in which negative energy densities arise from the throat geometry and finite matter configurations can be matched to the hyperbolic Schwarzschild vacuum. We construct such configurations from a matter-first perspective using an effective Casimir source corrected by a gravitational-memory contribution, $\rho(r)=-\alpha/r^4+\eta/r^7$. The $r^{-7}$ term is motivated by the persistent shift of the Casimir vacuum energy after a transient gravitational perturbation, while its promotion to a radial source is treated phenomenologically. The density determines the shape function, and the temporal geometry is fixed through complexity-based conditions. Full vanishing complexity, $Y_{TF}=0$, is first imposed and then relaxed through a one-parameter deformation, $Y_{TF}=(p-3)r_0/(2r^3)$. Decomposing the complexity factor into local and throat contributions shows that local vanishing complexity occurs at $p=\beta'(r_0)$. At this value, besides the constant-redshift solution of the finite-$r$-derivative branch, a second lapse branch is regular in radial distance. We show that pressure-free Darmois matching in the finite-$r$-derivative family requires $p<\beta'(r_0)$, enforcing tangential null and strong-energy-condition violations at the throat throughout the matching domain. The density remains negative in the matter-supported region, implying weak- and dominant-energy-condition violations independently of the lapse branch. The memory parameter modifies the flare-out domain, redshift profile, and matching data, while finite pressure-free junctions permit smooth matching to the hyperbolic Schwarzschild vacuum without thin shells. The construction combines a memory-corrected Casimir source with a unified complexity framework in which the temporal sectors emerge as related branches of the same radial geometry.

We address two questions posed by Qu and Valkó in their study of the pair correlation function of the $\mathrm{Sine}_\beta$ process. First, we prove that the pair correlation function admits a jointly continuous version in the inverse-temperature and spatial parameters on $(0,\infty)\times\mathbb{R}$, removing the restriction $\beta>2$ in their joint-continuity result. The argument uses a general observation: separate weak continuity of a family of probability laws, together with stochastic monotonicity in one parameter, implies joint weak continuity. Applied to the terminal value of the Qu–Valkó diffusion, their Palm-density formula then gives the result without differentiating the Fourier expansion. Second, for $\beta=2n$ we give a direct proof that the Qu–Valkó matrix-recursion power series agrees with the Selberg-integral representation recorded by Forrester. A Krawtchouk transform converts the Qu–Valkó system into a $(2n+1)$-dimensional differential system with parameter $-(n+1)$, while a centered Aomoto–Selberg trace system has parameter $n+1$. An explicit triangular differential intertwiner reflects the parameter $\eta\mapsto-\eta$. Matching the unique Frobenius branch of exponent $2$ gives exactly the Selberg normalization. As a consequence, every coefficient of the Qu–Valkó recursion is identified with an even centered moment of the corresponding Jacobi–Selberg trace statistic.

Shock fronts and vortex cores often coexist and overlap in compressible flows, where walls, wakes and shear layers also produce strong gradients. Refining a network to detect one structure can therefore degrade its prediction of the other without revealing the loss in the optimized score. We present a task-preserving formulation for simultaneous shock and vortex-core segmentation. The experiments use two solvers and include supersonic diamond-airfoil flows at several incidences and Reynolds numbers, together with circular- and elliptical-cylinder flows. A shared primitive encoder feeds separate shock and vortex decoders with independent sigmoid outputs, allowing the two classes to overlap. Adaptation is confined to the relevant branch: zero-initialized adapters supply rotational diagnostics only to the vortex decoder, while corrected shock supervision updates only the shock decoder. All dependencies of the protected output remain fixed, and bitwise equality is verified on every evaluation field. Compression and conservation-jump (Rankine–Hugoniot) signatures provide weak shock supervision; rotation and topology provide vortex candidates. Analytical oblique-shock rays, Billig's bow-shock correlation and an isentropic vortex supply references independent of these labels. Under the same corrected-target budget, the restricted model and a capacity-matched shared-decoder U-Net obtain comparable shock agreement. Their airfoil vortex-core Dice overlap scores, however, are 0.83 and 0.08, respectively. A soft retention penalty recovers most of the U-Net's lost core agreement. The frozen shock-adapted models locate the tested analytical oblique-shock rays within 0.003 chord. An additional branch identifies expanding-flow regions, which are distinguished from centred Prandtl–Meyer expansion fans through comparison with ideal shock–expansion theory.

We formulate new Barrow holographic dark energy (NBHDE) as a second-order expansion of the Barrow entropy correction near the standard holographic dark energy (HDE) limit, adopting the future event horizon as the infrared cutoff. Writing the Barrow factor in exponential form identifies $(\Delta/2)\ln S_{\rm BH}$, rather than $\Delta$ alone, as the expansion parameter. In a flat universe containing pressureless matter and NBHDE without a cosmological constant, we derive the background equations, establish consistency with the integral definition of the future event horizon, and recover HDE exactly at $\Delta=0$. We assess this approximation against the unexpanded Barrow holographic dark energy (BHDE) density, locally and through independently normalized background evolutions. Across $0.50\leq c\leq1.20$ and $0\leq\Delta\leq0.003$, the maximum fractional density difference remains below $1\%$ over $-0.99\leq z\leq5$, while the normalized Hubble rates differ by less than $0.074\%$ over $0\leq z\leq5$. Within this domain, the Barrow correction modestly changes the expansion rate and acceleration transition but more strongly affects the dark energy equation of state and phantom crossing. At $c=0.80$, $w_{d0}$ shifts from $-1.031$ in HDE to $-0.900$ at $\Delta=0.003$. We perform a conditional comparison with 36 spectroscopic cosmic chronometer (CC) measurements. At fixed $H_0=67.4\,{\rm km\,s^{-1}\,Mpc^{-1}}$ and $\Omega_{m0}=0.30$, the minimum lies on the HDE boundary at $\Delta=0$ and $c=0.8457$. Minimizing over $c$ at $\Delta=0.003$ gives $c_{\min}=0.6879$, with $\Delta\chi_{\rm CC}^2\simeq1.0\times10^{-3}$. NBHDE therefore provides a self-consistent, quantitatively controlled framework near the HDE limit, showing that Barrow corrections can alter dark energy behavior even when their effect on $H(z)$ is largely compensated by changing $c$.

We formulate a Maxwell-Jüttner averaged extension of relativistic nonaffine shear-viscosity theory for a classical gas of massive particles. The starting point is the relativistic nonaffine response formula derived from generalized Langevin dynamics, where proper-momentum dissipation produces a Lorentz-factor enhancement of the viscosity. Since a thermal relativistic gas is not characterized by a single Lorentz factor, we replace this scalar enhancement by an equilibrium momentum average over the Maxwell-Jüttner distribution. Within the scalar transverse mean-field closure used in this work, the minimal relativistic correction is the Maxwell-Jüttner mean of the Lorentz factor and becomes a finite-mass enhancement function of $\zeta=mc^2/(k_BT)$. In the general closure, the averaged object is the full product of the Lorentz factor, the zero-frequency memory kernel, and the nonaffine affine-force correlator. This construction separates kinematic relativistic enhancement from dynamical dissipation encoded in the bath memory and collective mode spectrum. We derive the nonrelativistic and ultrarelativistic limits, show that a specified effective hard-sphere scaling reproduces the classical square-root law as a consistency test, and identify the assumptions under which a cubic high-temperature law follows. Comparison with relativistic kinetic-theory examples clarifies that the memory kernel is not equivalent to a relaxation time unless a microscopic closure is specified. Retaining the full frequency dependence instead yields a relaxation spectrum. A single dominant pole reduces this spectrum to one shear relaxation time and gives the usual transient shear equation.

We propose a new class of sigma models that extend AKSZ sigma models, which we refer to as gauged AKSZ sigma models. These models are constructed using QP-manifolds. The compatibility between the AKSZ structure and gauging is characterized by geometric conditions on the target graded manifold. As an example, we explicitly analyze the gauging of higher Courant sigma models in higher dimensions. When fluxes and boundaries are introduced into gauged higher Courant sigma models, generalizations of momentum maps and Hamiltonian $G$-spaces arise as consistency conditions for the models.