We study embeddings within different scales of generalised smoothness Morrey spaces defined on bounded smooth domains, i.e., in $\mathcal{N}^s_{φ,p,q}(Ω)$, $\mathcal{E}^s_{φ,p,q}(Ω)$, $B^{s,φ}_{p,q}(Ω)$ and $F^{s,φ}_{p,q}(Ω)$ spaces. We prove sufficient conditions for continuity and compactness of the embeddings. In some cases the conditions are also necessary. We generalise and even improve some earlier results known for the classical smoothness Morrey spaces. Our approach is based on wavelet characterisation of the function spaces.

We perform a Bayesian inference of the equation of state (EOS) of cold dense matter within a density-dependent relativistic mean-field (DD-RMF) model. An explicit inverse-mapping procedure reconstructs the density-dependent couplings from a physically interpretable ten-dimensional parameter set while enforcing thermodynamic consistency together with stability and causality conditions. The EOS is constrained by complementary multi-messenger data including chiral effective field theory calculations at low density, heavy-ion collision flow information at intermediate densities, NICER mass-radius posteriors, and the existence of approximately two-solar-mass pulsars. The combined constraints strongly restrict both isoscalar and isovector sectors. In particular, the chiral effective field theory band favors a relatively soft symmetry-energy slope around 38 MeV, corresponding to a compact canonical neutron-star radius of about 11.6 km. To reconcile the intermediate-density softness suggested by heavy-ion data with the high-density stiffness required by massive pulsars, the posterior prefers a moderately large Dirac effective mass at saturation together with correlated high-density limits of the scalar and vector couplings. The resulting sound-speed profile remains causal and shows significant stiffening above the conformal limit at several times nuclear saturation density, indicating strongly interacting matter in neutron-star cores. Evidence diagnostics indicate strong compatibility among the adopted constraints within the present DD-RMF framework.

We derive the existence of solutions for an asymptotically linear equation driven by the spectral fractional Laplacian operator with mixed Dirichlet-Neumann boundary conditions. When the nonlinear term $f$ is odd and a suitable relation between the perturbation parameter, the limit of $f(\cdot,t)/t$ as $t\to 0$ and the eigenvalues occurs, we establish also a multiplicity result via the pseudo-index theory related to the genus.

We investigate a deformable spin-1/2 Ising chain subjected to either a longitudinal or a transverse magnetic field, which incorporates a magnetoelastic coupling linearly dependent on a lattice distortion parameter. Within the harmonic and static adiabatic approximations, the variational Gibbs free energy is evaluated exactly using transfer-matrix and Jordan-Wigner fermionization techniques and then minimized self-consistently with respect to the lattice distortion parameter. This approach enables a unified description of magnetic and elastic properties including the magnetization, magnetic susceptibility, lattice distortion, inverse compressibility, and relative change in the sound velocity. In a longitudinal magnetic field, the deformable Ising chain displays a line of discontinuous thermal phase transitions terminating at a critical point. The discontinuous transitions are accompanied by metastable states, which give rise to a hysteresis loop at low temperatures. In contrast, the deformable Ising chain in a transverse field undergoes exclusively a continuous quantum phase transition at zero temperature with no indication of thermal phase transitions. The magnetic susceptibility and inverse compressibility exhibit cusp- and dip-like anomalies at discontinuous phase transitions, while a diverging susceptibility and vanishing inverse compressibility characterize the continuous phase transitions. An elastic softening of the deformable chain near thermal and quantum phase transitions manifest itself also through a significant sound attenuation.

Sulfur is a redox active element that may have helped mediate an electron flow that kickstarted life and which presently is an essential element for all life on Earth. Despite current uncertainties in global sulfur fluxes, modeling sulfur's abiotic cycling through Earth's deep history is important for understanding the impact of a planet wide biosphere on sulfur geochemical cycling and availability and vice versa. We present here an open-source, dynamical box model for estimating global sulfur fluxes and concentrations among surface and deep Earth reservoirs over Earth history, allowing tracking and estimation of the sulfur distribution in planetary reservoirs over deep time in the absence of life. While the main model presented here does not take into account the abrupt evolution of redox-shunting biosynthetic pathways such as oxygenic photosynthesis, we also modeled the abiotic sulfur cycle before and after a Great Oxidation Event-like transition on Earth-like planets. Our results suggest a considerably distinct chemical makeup of sulfur content in marine sediments in the absence of life on an Earth-like planet, leading to a marine sediment sulfate content two orders of magnitude larger than on present-day Earth and a marine sediment sulfide content 4 orders of magnitude lower than on present day Earth, attributable to the lack of microbial sulfur metabolism. This model could be useful for understanding sulfur cycling on potentially habitable exoplanets.

Serrin's symmetry theorem shows that the classical overdetermined torsion problem forces the domain to be a ball. Extending this rigidity statement to merely Lipschitz (and more generally rough) domains in the weak formulation has been a long-standing and challenging problem, recently resolved by the authors in [12]. In this paper we address the corresponding question in the anisotropic setting: Given a uniformly convex $C^{2,γ}$ anisotropy $H$, we study the overdetermined problem for the anisotropic Laplacian $Δ_H u={\rm div}\big(H(\nabla u)\,DH(\nabla u)\big)$ on a bounded indecomposable set of finite perimeter $Ω$. Assuming the Ahlfors--David regularity of $\partial^*Ω$ and a global $β$-number square-function bound (a weak uniform rectifiability hypothesis), we prove that a weak solution exists if and only if $Ω$ is a translate and dilation of the Wulff shape, in which case the solution is unique and explicit. In particular, the result applies to Lipschitz domains. While our approach follows the rough-domain strategy of [12] at a high level, the key Laplacian-specific ingredients exploited there have no direct analog for $Δ_H$, necessitating the development of new ideas and techniques.

This study explored the association between sleep duration and redistribution preferences. Using an online survey, we propose a hypothetical situation in which the tax paid directly by respondents is redistributed to those earning less than one-fifth of the respondents' income. Next, we asked about the allowable tax rates. We found the following through Tobit and ordered logit regression estimations: (1) The relationship between sleep hours and the allowable tax rate showed an inverted U-shape, where the optimal amount of sleep led to the highest allowable tax rate. (2) High-quality sleep was more positively correlated with the allowable tax rate than was low-quality sleep when the sleep quantity was the same. (3) Sleep hours were more significantly and positively correlated with the allowable tax rate in the high-income group than in the low-income group. (4) Assuming that twice the amount of tax paid goes to those with lower income, individuals who previously preferred a higher tax rate were more likely to increase the allowable tax rate.

Spacetime transformations in any physically viable theory should follow Lie Point symmetry. In this work, we explore the Cuscuton model extended to Galileons, as introduced by de Rham et al in \cite{Rham2017}. We find the true degrees of freedom by converting the model into an equivalent first order model. Despite being a higher derivative model, it possesses only \textit{two} degrees of freedom. We calculate the Noether symmetry parameters corresponding to Lie point transformations, which lead to the vanishing of the original Cuscuton term's coefficient and restrict the potential to an exponential form. Interestingly, the coefficient corresponding to the original Cuscuton term vanish. Additionally, we also use the Killing analysis to find out the charges corresponding to the Killing vectors and the Killing tensors. The cosmological implications are examined through dynamical analysis, revealing that under the condition where the coefficient $a_2$ vanishes, the equation of state parameters exhibit damped oscillatory behavior .

Blazars are a subclass of radio-loud active galactic nuclei (AGNs) that display strong multi-wavelength variability on diverse timescales ranging from years down to minutes. In the last 1.5 decades, there have been occasional detections of quasi-periodic oscillations in several blazars in their time series data. We search for quasi-periodic oscillations (QPOs) in the 37 GHz radio band light curve of the flat-spectrum radio quasar Ton~599 made at the RT-22 radio telescope in Simeiz, Crimea, from 1990 to 2020. To identify and quantify the QPO nature of this radio light curve of Ton 599, we used the Lomb-Scargle periodogram (LSP), REDFIT, and weighted wavelet Z-transform (WWZ) analyses. We report the detection of a likely QPO of about 2.4 years in the 37 GHz radio light curves of Ton 599. We briefly discuss possible emission models for radio-loud active galactic nuclei that could explain such QPOs with periods of a few years.

We use a direct phase-resolved optical technique to study the coherence of spin waves (SWs) that are driven by surface acoustic waves (SAWs) via resonant magnetoelastic coupling. For this, we employ a piezoelectric lithium tantalate (LiTaO$_{3}$) substrate, equipped with micropatterned interdigital transducers for SAW excitation, which interact with SWs in a 5 nm thin and 20 $μ$m wide Co$_{40}$Fe$_{40}$B$_{20}$-waveguide. We detect the SAW and the SW using a phase-locked micro-focused optical polarization detection experiment and use the characteristic polarization dependence to separate the SAW and SW signals. Our measurements directly image the resonant and coherent excitation of the SW by the SAW.

We study the periodic dynamics of a spin-one chain driven using a square-pulse protocol with amplitude $Q_0$ and frequency $ω_D$. The Hamiltonian of the spin chain hosts a thermodynamically large number of $Z_2$-valued conserved quantities $W_{\ell}$ on the links $\ell$. This allows us to study the Floquet dynamics of this chain within a given sector with fixed values of $W_{\ell}$. For the sector with all $W_{\ell}=1$, we find signatures of quantum many-body scar states for $\hbar ω_D \gg Q_0$; they lead to oscillatory dynamics and fidelity revival for specific initial states. Upon lowering $ω_D$, we find an ergodic regime exhibiting fast thermalization consistent with the prediction of the (Floquet) eigenstate thermalization hypothesis. In addition, we identify special drive frequencies $ω_n^{\ast}= Q_0/(2n \hbar)$ (where $n = 1, 2, 3, \cdots$) at which the Floquet Hamiltonian exhibits prethermal strong Hilbert space fragmentation (HSF) with the largest fragment being ergodic; in contrast, a weak HSF is found at $ω'_n= Q_0/[\hbar(2n+1)]$ (where $n = 0, 1, 2, \cdots$). We also study the sector with $W_{\ell} =\{\cdots 1,1,-1,1,1,-1 \cdots \}$ which shows strong HSF at $ω_n^{\ast}$ but no fragmentation at $ω'_n$. Our analysis indicates that the strong HSF in this sector harbors an integrable largest fragment. We provide numerical support for our analytical and perturbative results using exact-diagonalization (ED) studies on finite chains of length $L\le 24$. Our numerical results for entanglement entropy, fidelity, and correlation functions of the driven chain provide definitive signatures of prethermal strong HSF for both sectors.

We prove the discrete Rubio de Francia extrapolation theorem for a pair of quasi non-increasing sequences with $\mathcal{QB}_{β, p}$ weight class. Also, a weight characterization of the boundedness of the generalized discrete Hardy averagin19g operator on the class of quasi non-increasing sequences from $l_w^p(\mathbb{Z}^+)$ is proved.

We investigate stochastic resonance (SR) in an ensemble of coupled overdamped bistable oscillators driven by colored noise. The networks incorporate the weighted contributions of both pairwise coupling and 2-simplex coupling. Our findings show that these higher-order interactions further exacerbate the suppression effect of colored noise on SR, reducing the peak of resonance curves and shifting the optimal noise intensity toward higher values. To clarify the underlying mechanism, we establish a close connection between SR and the four-stage variation in network synchronization level. Specially, the synchronization extremes explain the effect of higher-order coupling and colored noise on SR. Our analysis reveals that higher-order interactions do not reverse, but primarily promote the spatial propagation of suppression effects due to colored noise.

Many popular Python libraries use C-extensions for performance-critical operations allowing users to combine the best of the two worlds: The simplicity and versatility of Python and the performance of C. A drawback of this approach is that exceptions raised in C can bypass Python's exception handling and cause the entire interpreter to crash. These crashes are real faults if they occur when calling a public API. While automated test generation should, in principle, detect such faults, crashes in native code can halt the test process entirely, preventing detection or reproduction of the underlying errors and inhibiting coverage of non-crashing parts of the code. To overcome this problem, we propose separating the generation and execution stages of the test-generation process. We therefore adapt Pynguin, an automated test case generation tool for Python, to use subprocess-execution. Executing each generated test in an isolated subprocess prevents a crash from halting the test generation process itself. This allows us to (1) detect such faults, (2) generate reproducible crash-revealing test cases for them, (3) allow studying the underlying faults, and (4) enable test generation for non-crashing parts of the code. To evaluate our approach, we created a dataset consisting of 1648 modules from 21 popular Python libraries with C-extensions. Subprocess-execution allowed automated testing of up to 56.5% more modules and discovered 213 unique crash causes, revealing 32 previously unknown faults.

Using an individual-level panel dataset from Japan covering the period 2016-2024, we examined how the COVID-19 pandemic, as an unanticipated public crisis, affected preferences for income redistribution. Furthermore, we investigated how the association between redistribution preferences and trust in government changed before and after COVID-19. The major findings are as follows: (1) individuals in the high-income group are less likely to prefer redistribution after COVID-19 than before it; (2) the degree of decline in redistribution preference is lower when trust in government is higher; and (3) generalised trust and reciprocity did not influence the decline in preference.

We prove that fibered hyperbolic $3$-manifolds carrying transitive Anosov flows are abundant. More precisely, for every $g\geq 2$, there is a finite index subgroup~$Γ$ of $ \mathrm{Mod}(S_g)/\mathrm{Tor}(S_g) \simeq \mathrm{Sp}(2g,\mathbb{Z}) $ so that every element of $Γ$ has a representative $φ\in \operatorname{Mod}(S_g)$ such that the mapping torus $ M_φ:= S_g \times [0,1]/(x,1) \sim (φ(x),0) $ carries a transitive Anosov flow. The manifold $M_φ$ is hyperbolic for almost every element of $Γ$. This shows in particular that, in the set of all fibered hyperbolic manifolds, the subset made of the manifolds carrying Anosov flows has positive density up to trivial linear monodromy. Moreover, the subgroup $Γ$ is defined by an explicit set of generators, and our construction yields many examples of simple fibered hyperbolic manifolds carrying Anosov flows.

We consider in this paper a velocity discretized version of the full linear kinetic BGK model and the corresponding limit for small Knudsen number, the linearised Euler or acoustic system. Considering these equations on networks, coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. Here, a degeneracy in the limit equations requires not only the investigation of kinetic layers, but also the discussion of viscous layers. Using the kinetic coupling conditions at the junction and coupling kinetic and viscous layers to the outer problems on the edges one obtains a coupled kinetic half-space problem at each node. A spectral method is developed to solve this coupled kinetic half-space problems. This allows to obtain a detailed picture of the various interface layers near the nodes and to determine the relevant coefficients in the kinetic derived coupling conditions for the macroscopic equations.Numerical results show the accuracy and efficiency of the approach.

We present a long-term broadband study of the Seyfert galaxy Mrk~530 spanning $\sim$24 yr (2001--2024). The source remains largely stable across epochs, except in 2018, when a possible quasi-periodic oscillation is observed simultaneously in the UV and X-ray bands, with characteristic timescales of $\sim$90 and $\sim$60 days, characterized by low coherence. Time-resolved spectral analysis shows that this epoch is characterized by comparable coronal cooling and compressional heating timescales, a condition conducive to oscillatory behavior in the inner accretion flow. Other epochs exhibit a clear mismatch between these timescales, and no such variability is observed. The X-ray spectral properties display significant long-term evolution. The photon index and luminosity vary systematically, while a soft excess is present only in early epochs (2001--2006) and weakens thereafter, consistent with an evolving warm corona. Physically motivated models indicate that changes in the accretion rate regulate both the spectral slope and coronal geometry, with higher disc accretion rates producing enhanced cooling, a more compact corona, and softer spectra, and lower rates yielding an expanded hot flow and harder emission. These results suggest that accretion-driven coupling between the disc and corona governs both the long-term spectral evolution and transient short-timescale variability in Mrk~530.

Accurate quantum chemical calculations are critical for understanding molecular properties, yet their computational cost remains a major challenge. Full Configuration Interaction (FCI) provides exact solutions but is prohibitively expensive for large systems. To address this, quantum computers are expected to be useful, but developing practical quantum computers is still ongoing. Here we introduce an efficient Configuration Interaction (CI) computation algorithm based on classical mechanics, which we call Simulated Bifurcation-based CI (SBCI), because we derive this algorithm from a quantum inspired algorithm for combinatorial optimization called Simulated Bifurcation. Applying it to FCI computations of representative molecular systems and comparing the results with those by a standard method, we demonstrate that SBCI can reduce computation costs such as computation times and/or required memory sizes, while keeping high accuracy comparable to the standard method. Thus, SBCI will be promising for accelerating high-precision electronic structure calculations without compromising reliability.

The well-known Newton-Puiseux Theorem states that each real branch of a planar real analytic curve admits a Puiseux expansion. We generalize this result to characteristic orbit of an isolated singularity of a planar real analytic vector field and prove that each characteristic orbit has a `power-log' expansion.

Using an unprecedented cadence of 30 minutes provided by the Transiting Exoplanet Survey Satellite (TESS), we have examined the optical light curves (LCs) of the blazar S5 0716+714 obtained from its Sectors 40, 47, and 53 over a period of about 75 days. This source exhibited flux variability in each of those sectors, reaching a maximum variability amplitude of 5.6%. The power spectral density (PSD) shapes were tested with a simple power law and two distinct bending power laws and were found to be better fit by bending power laws than simple power laws for all but one of the segments. To look for any periodicities in these LCs, we used weighted wavelet Z (WWZ) transform analysis and generalized Lomb-Scargle periodograms (LSPs). We identified one possible quasi-periodic oscillation (QPO) signature in a portion of sector 40 (period of ~6.5 h), having ~95% global significance. A statistical approach to assess the light curves involving continuous autoregressive moving average (CARMA) was implemented, and the light curves were found to follow more complex processes than the simplest and typical damped random walk process. We briefly discuss the statistical properties of the light curves along with the general variability features and physical processes that could cause these types of fluctuations.

This study investigates shifts in acceptable tax rate for reducing inequality during the COVID-19 pandemic using Japanese data. We find a transition from norm-based, unconditional support for redistribution to conditional altruism. Before the pandemic, support remained high and independent of institutional trust. The pandemic generated an overall decline in altruistic attitudes while increasing their dependence on trust in government, particularly among high-income individuals. This "widening gap" implies that in post-crisis societies, the social contract is no longer anchored in stable social norms but increasingly relies on institutional trust to sustain income redistribution from the rich to the poor.

We present X-ray intraday variability, cross-correlated variability, and power spectrum density analysis of the binary black hole blazar candidate OJ 287. The X-ray pointed observations of the source were carried out on eight occasions by the EPIC-pn camera on board the XMM-Newton satellite from November 2005 to November 2022. These good time intervals range between 3.6 hours and 24.1 hours. Three energy bands -- 0.2-2 keV (soft), 2-10 keV (hard), and 0.2-10 keV (total) -- have been used to estimate variability. Low amplitude variations are observed in 4, 5, and 6 light curves in soft, hard, and total energy bands, respectively. Only two observation IDs has shown variation in the all energy bands. The discrete correlation function of the light curves in soft and hard energy bands peaks at zero lag, suggesting that the emission in both bands was cospatial and came from the same population of leptons. Red noise dominates the power spectral densities of variable light curves. According to our flux and spectrum investigations, both particle acceleration and synchrotron cooling mechanisms contribute significantly to the emission from this blazar.

Recently a new family of enumerative invariants called leaky Hurwitz numbers was introduced by Cavalieri-Markwig-Ranganathan in the context of logarithmic intersection theory. They admit an interpretation via tropical covers where the balancing condition fails. We employ tropical geometry to prove a generalisation of the piecewise polynomiality of Accadia-Karev-Lewanski for leaky completed cycles Hurwitz numbers, and a different wall crossing that is cubic instead of quadratic. Using tropical combinatorics and generatingfunctionology, we also find closed formulae for one-part and two-part completed cycles leaky Hurwitz numbers in genus $0$. Working more generally with a view towards topological recursion, we use Hamiltonian flows to associate spectral curves to very general cut-and-join operators. Under mild analytic constraints, we find the appropriate spectral curves, and in case the leakiness is fixed, we show that the resulting enumerative invariants satisfy topological recursion. This provides a partial inverse to recent work of Alexandrov-Bychkov-Dunin-Barkowski-Kazarian-Shadrin producing differentials satisfying topological recursion for KP $τ$-functions. In particular these results specialise to completed cycles leaky Hurwitz numbers.

We compute the complete set of the leading-twist gluon and sea-quark generalized transverse momentum distributions (GTMDs) in the small-$x$, or eikonal, approximation at vanishing skewness $ξ= 0$. All the gluon GTMDs become expressed in terms of the basic gluon dipole operator featuring also proton helicity-flips. Consequently, we establish universal relations between otherwise distinct GTMDs that hold in the small-$x$ limit. The obtained results are systematically projected onto the transverse momentum dependent distributions (TMD) and the generalized parton distribution (GPD) cases, recovering known results where available. In case of sea-quarks all the GTMDs are given in terms of the gluon dipole convoluted with a hard kernel. We generalize the unpolarized sea-quark GTMD to non-zero momentum transfers and find new results for the proton helicity-flip distributions. We pay special attention to their perturbative, high transverse momentum, tails to confirm that it becomes governed by the small-$x$ gluon GPDs. The obtained results provide guidance to the phenomenological modeling of the GTMDs but also allow for their explicit computations.

In $e^+e^-$ shape-variable studies, and in particular for the case of thrust, fixed-order QCD predictions are typically supplemented with the resummation of contributions enhanced near the two-jet limit. In this work we examine whether different, yet legitimate, resummation prescriptions can induce significant differences in the resulting predictions. This can occur because formally equivalent prescriptions may differ by terms that, although subleading, are characterised by asymptotic expansions and may therefore lead to slow convergence. We first compare two alternative formulations of resummation: the conjugate-space (or Laplace-space) approach, in which resummation is performed in a variable conjugate to thrust, such that the observable factorises exactly in the soft-collinear limit; and the direct-space formulation, where resummation is instead carried out directly in the thrust variable. We show that, at double-logarithmic level, the inverse Laplace transform generates a convergent tower of subleading terms. Starting from leading-logarithmic accuracy, the expansion becomes asymptotic due to the presence of the Landau pole, leading to a mild log-factorial growth of the coefficients. When including the highest available logarithmic order in the resummation, matched to fixed-order results, we still find non-negligible differences between predictions obtained in the two spaces. We then consider a formulation of the resummation that avoids certain approximations commonly used in the derivation of conjugate-space resummation. We observe that this also has a non-negligible numerical impact. In general, we find that the systematics stemming from the adoption of different formalisms typically exceeds the quoted theoretical uncertainties, suggesting the need for more conservative theory-error estimates when using the thrust distribution in determinations of the strong coupling.

We investigate the fractional magnetic $p$-Laplacian operator in the physical dimension case $N=3$, with $0<s<1<p$ and $sp<3$. Our goal is twofold. First, we define and study suitable functional settings for such operator proving significant properties. Then we get the existence of weak solutions for some quasilinear equations involving a weighted critical and subcritical power type nonlinearity. Our technique relies on variational methods and faces various difficulties: the complex quasilinear framework due to the presence of an external magnetic potential, the nonlocal setting, which entails appropriate tools, and the lack of compactness, which requires concentration compactness arguments. In this direction, we state a new concentration compactness principle in the quasilinear magnetic setting that seems to be missing in the literature.

Electroporation is increasingly used as a percutaneous ablation technique for tumours located near vital structures. Although effective, tumour regrowth may still occur. At the same time, in vitro studies on cell monolayers have shown that electroporation can trigger immunogenic cell death (ICD) through the release of damage-associated molecular patterns (DAMPs). These molecules can stimulate the immune system and could counteract tumour regrowth. To fully exploit electroporation, two key questions must be addressed: (1) what dynamics drive tumour regrowth, and (2) how ICD unfolds in space and time within three-dimensional cellular structures, which better mimic in vivo conditions than 2D cultures. Here, we combine in vitro experiments with a hybrid individual-based/continuous computational model to explore tumour spheroid regrowth and ICD potential under different pulse intensities. Experiments quantify spheroid viability, growth rate, and the release of ATP and HMGB1. In parallel, the hybrid model predicts the dynamics of proliferative, quiescent, and necrotic cells. Both approaches show that cell death and DAMP release scale with pulse intensity. The model, validated against experimental data, further highlights the dual role of quiescent cells: some die and free space and resources, while others survive and resume proliferation. Together, these findings demonstrate how spheroid fate depends on pulse strength and emphasize the importance of accounting for quiescent cells when designing electroporation-based therapies.

The distribution of entanglement is a crucial task for quantum communication towards realizing a globe-spanning quantum internet. Recently a protocol for deterministic long-distance distribution of macroscopic entanglement over a network of ensembles of qubits was introduced [Adv. Quantum Technol. 2025, 8, 2400524]. It was shown that this protocol allows for the propagation of macroscopic amounts of entanglement with a protocol complexity that is independent on the ensemble size. However, questions remained on whether the scheme is viable, particularly for a large particle number, which is the case for realistic atomic ensembles. Here we develop improved numerical techniques that allow calculation of realistic ensemble sizes up to 10^6 with a negligible loss of accuracy. We find that moderate dephasing leaves the entanglement largely intact at the magic times, whereas stronger noise monotonically suppresses the entanglement. Our results demonstrate that the protocol retains its functionality towards the macroscopic regime and provides quantitative benchmarks for its robustness under a realistic level of decoherence.

We give an explicit example of a fibration $f \colon X \to Y$ between smooth projective varieties whose "orbifold base" $Δ_f$ in the sense of Campana has the property that the induced morphism $X \to (Y, Δ_f)$ is not a morphism of C-pairs (i.e., it is not an "orbifold morphism"). We however also show that this cannot happen if $f$ is "neat" and $(Y, Δ_f)$ is sufficiently well-behaved. Finally, we discuss the implications of this statement towards conjectures of Campana aiming to give algebro-geometric characterizations of those varieties which either admit a dense entire curve or a potentially dense set of integral points.