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Supermassive black hole binary (SMBHB) candidates with sub-parsec (sub-pc) orbital separations are rare, high-value systems, thought to be the dominant sources of the recently detected nanoHertz (nHz) gravitational wave (GW) background. Alongside pulsar-timing-array searches for localized nHz GW sources from SMBHBs, an increasing number of candidates have been identified from synoptic surveys of large quasar optical light curves over increasingly long baselines. The optical light curve of the quasar PG~1302-102 at a redshift of $z=0.278$ exhibits a pronounced, smoothly varying periodic signal of ~5.2 years over approximately 20 years. Although the cause of this periodicity remains debated, a plausible explanation is a binary system of two SMBHs with a sub-pc separation. At this close distance, the $10^{8.3-9.4} M_{\odot}$ nuclear black holes in PG 1302-102 are expected to merge within $\sim$$10^{5}$ yr solely due to GW emission. We present a multi-frequency radio light curve analysis of PG~1302-102 spanning a $\sim$19-year baseline, with observations between 2005 and 2024 drawn from the Australian Telescope Compact Array (ATCA). The ATCA radio light curve is highly variable at 5.5~GHz but shows no significant evidence of the periodicity seen at optical wavelengths. However, we report fractionally stronger evidence of periodicity in the in-band spectral index time-series at 5.5~GHz, with a period consistent with the optical periodicity. Furthermore, the recently reported change in optical periodicity is also present in the radio in-band spectral index light curve. These two results suggest that radio and optical periodicity may be physically coupled despite very different emission mechanisms. We argue that this radio-optical coupling reinforces the SMBHB interpretation, despite the optical periodicity change, and provides an intriguing case study ahead of the LSST-SKAO era.

The discovery by the James Webb Space Telescope (JWST) of an abundant population of compact little red dots (LRDs) and supermassive black holes at high redshifts poses a severe timing challenge for standard Eddington-limited growth from stellar remnants. In this work, we present a unified hybrid assembly framework in which intermediate-mass seed black holes are formed via hierarchical primordial black hole (PBH) mergers within dense clusters in Hu-Sawicki $f(R)$ gravity, followed by galactic gas accretion. We demonstrate that the screened $f(R)$ fifth force nonlinearly accelerates early seed formation through a quadratic enhancement of the gravitational-wave radiation-capture kernel, while environmental chameleon screening dynamically self-regulates the growth. Because subsequent gas accretion scales multiplicatively with seed mass, the $f(R)$ seed enhancement is preserved throughout the accretion history, drastically reducing the time-averaged Eddington ratios required to assemble $10^{6}\text{-}10^{9}\,M_{\odot}$ LRDs by cosmic dawn. Confronting our active mass functions with JWST data reveals that a small clustered PBH fraction ($f_{\rm PBH} \lesssim 10^{-3}$) under a realistic active galactic nucleus duty cycle ($δ\approx 10^{-2}$) naturally matches observed LRD space densities at $z \sim 5.5\text{-}6.5$ while remaining fully compliant with LIGO-Virgo-KAGRA limits, with modified gravity naturally driving the high-mass tail. Finally, we show that parameter degeneracies between modified gravity and cluster density can be cleanly broken by combining three multi-messenger diagnostics: remnant spin state signatures, a stochastic GW background cutoff, and a scale-dependent inversion in the PBH spatial correlation function.

Vortex pinning is central to the standard interpretation of pulsar glitches, but the mechanical load exerted by a pinned vortex array on the solid crust has received less attention than the angular-momentum reservoir itself. We calculate the axisymmetric elastic response of a continuously stratified neutron-star crust to this load using realistic SLy4 and BSk21 stellar backgrounds and composition-dependent Coulomb shear moduli. The superfluid-crust lag sets the Magnus force, while the mesoscopic pinning force of Seveso et al. (2016) provides a local upper bound. At low lag the response is linear; progressive local saturation then produces a broad transition and a finite high-lag envelope. The stress maximum is robustly located at the deep crustal boundary towards the rotation axis, although the local Magnus force vanishes on-axis, showing that the localization is produced by global elastic-gravitational redistribution. Realistic elasticity changes the stress amplitude by 10-20 per cent relative to the common mu=10^-2 P prescription and reverses the SLy4-BSk21 ordering. At a Vela-motivated lag of 10^-2 rad s^-1, the maximum strain is only 3.1 x 10^-5 (SLy4) and 4.7 x 10^-5 (BSk21), remaining below 1.4 x 10^-4 on the formal plateau. A 1.2-2.0 solar-mass scan changes the stress amplitude by only about 20 per cent and leaves the deep-polar localization unchanged. Pinning therefore supplies a structured and astrophysically relevant crustal pre-stress, but cannot by itself break an initially relaxed crust.

Elastic photon--dark matter scattering attenuates gamma-ray spectra along a line of sight, probing the same operators as dark matter annihilation to photons but at a rate linear, rather than quadratic, in dark matter density. We consider Standard Model gauge-invariant effective operators of mass-dimension 5 to 7, suppressed by a cutoff scale $Λ$, coupling scalar, Majorana or Dirac dark matter to the photon. The leading operators with non-vanishing real-photon amplitudes enter at dimension-5 for Dirac dark matter and dimension-7 for Majorana dark matter. In the electroweak-doublet dipole portal, the inelastic splitting invoked to evade direct detection also closes the CMB annihilation bound, leaving attenuation the only one of the three photon-sector probes that survives. Applying this to a pixel-level reanalysis of 17 years of \textit{Fermi}--LAT Pass~8 data toward the Galactic centre, we derive the first operator-resolved sensitivity estimates for photon--dark matter scattering from the Galactic halo: $Λ\simeq 0.32~\mathrm{GeV}$ for the dimension-5 Dirac dipoles, $0.21~\mathrm{GeV}$ for the dimension-6 scalar Rayleigh operator and $0.79$--$1.06~\mathrm{GeV}$ for the dimension-7 Rayleigh family. The reach is weak: it lies below the EFT-validity threshold across the cold dark matter mass range, and is superseded on the dipole plane by CMB and direct-detection constraints. The framework is calibrated against pseudo-experiments, and recomputes the sensitivity for any instrument that provides a per-bin spectrum with uncertainties and a line-of-sight column density.

Ion-scale waves are believed to play an important role in heating of the solar corona and wind, though their generation mechanism remains unclear. Based on Parker Solar Probe observations, this Letter investigates the occurrence of ion-scale waves in the near-Sun solar wind with heliocentric distances between 0.1 and 0.2 au. Results show that the occurrence rate of left-handed polarized waves significantly depends on the plasma beta ($β$) and cross helicity ($σ_c$). The occurrence rate rapidly increases with decreasing $β$ and increasing $σ_c$. Overall, the occurrence rate exceeds 45$\%$ when $β<0.2$ and $σ_c > 0.7$ are satisfied. These observations are consistent with the direct predictions of the helicity barrier theory that suggests the generation of ion cyclotron waves via imbalanced magnetized turbulence.

Black Holes are the key to solving many unanswered questions in fundamental physics: in particular, the very extreme properties shown by supermassive black holes at the centers of galaxies make them obvious candidates for testing gravity theories in the strong-field regime. Since X-rays are generated by matter under extreme physical conditions, ultra-high resolution X-ray imaging (uXRI) will directly image the region near the event horizon of black holes in X-rays, similar to the Event Horizon Telescope in the radio band, enabling unprecedented tests of General Relativity and alternative theories of gravity near supermassive black holes. On the other hand, clusters of galaxies hold the potential of unveiling many unknowns in cosmology. uXRI will unlock this potential by probing small-scale plasma properties in the intracluster medium, providing the missing link required to establish galaxy clusters as reliable tools for high-precision cosmology. Moreover, uXRI will enable mapping of Dark Matter from galaxy cluster dynamics via proper motion measurements. Finally, uXRI will open a new field of precision X-ray astrometry, allowing for measuring pulsar parallaxes to support nanoHertz gravitational wave searches.

We derive an endpoint-free optical rigidity theorem and use it to separate two rigidity regimes in Bianchi I spacetimes, without assuming that the spatial metric is diagonal in a fixed basis. For a smooth, regular, twist-free null congruence, the affine Raychaudhuri equation expresses a finite null-Ricci integral as an expansion boundary term minus a nonnegative optical bulk. If the past and future cutoffs are removed independently and their two-end liminf is nonnegative, two-sided completeness forces the optical tensor and the null Ricci contraction to vanish pointwise. In Bianchi I this freezes the spatial metric on the fixed kernel of the conserved covector. We classify the resulting saturation geometry: a non-static metric has zero, one, or two unoriented saturated lines, equivalently zero, two, or four oriented rays, and a third line forces staticity. Under the stronger pointwise null convergence condition, the existence of a single two-sided complete null geodesic already forces the spatial metric to be constant and the cosmic-time interval to be all of $\mathbb R$; on the Cartesian universal cover the spacetime is Minkowski. Periodic models attain the four-ray saturation bound in the weaker cutoff-stable regime, with $I_p^{\mathrm{ind}}=-\infty$ in every nonsaturated direction, while pointwise null convergence fails on open time intervals. Matter and achronal averaged-null-energy consequences are stated under an explicit matching assumption on field equations and cutoff prescriptions.

In this paper, we investigate the late-time accelerated expansion of the Universe in power law $f(Q)$ gravity, where a logarithmic dark energy parametrization is considered: $ω_{de}(z)=ω_0+ω_1\ln(1+z)$. This description gives a smooth deviation from a constant equation of state within the complete range of redshifts. We obtain an analytical expression for the Hubble parameter and we use a Markov Chain Monte Carlo to compare the model with the most recent observational data obtained from Pantheon$^+$ Type Ia supernovae, Baryon Acoustic Oscillation measurements from the second data release (DR2) of the Dark Energy Spectroscopic Instrument, and Cosmic Chronometers. We then perform a statistical comparison between our model and the standard $Λ$CDM model using the Akaike Information Criterion and the Bayesian Information Criterion. From our results, we conclude that the use of logarithmic parametrization in the $f(Q)$ gravity model $f(Q)=Q+6γH_0^2\left(\frac{Q}{Q_0}\right)^n$ is a valid and more flexible alternative to standard dark energy models, as it provides a richer phenomenology at low redshifts.

Inspired by interaction of gravitational waves, dark matters and dark energy, we study the Einstein scalar field equations with the nonzero cosmological constant for the Bondi-Sachs metrics. We provide the asymptotic expansions under the outgoing radiation condition. Unlike the case of the zero cosmological constant, the asymptotic expansions depend on four additional $Λ$-independent functions $B(u, θ, φ)$, $\tilde{X}(u, θ, φ)$, $\tilde{Y}(u, θ, φ)$ and $\tilde{I}(u)$. We show that, under suitable coordinate transformation, we can make $B(u, θ, φ)=0$. We prove the peeling property for the Einstein scalar field equations if $\tilde{I}=0$, and derive a loss formula of the Bondi energy-momentum for the nonzero cosmological constant. We remark that, for certain real data from gravitational waves, the loss formula is likely to indicate the loss property of the Bondi energy-momentum.

Quantum resonances and black-hole quasinormal modes (QNMs) are described by closely related mathematics: radiative boundary conditions, analytic continuation of Green functions or resolvents, poles on nonphysical sheets, and non-self-adjoint spectral representations. This article does not introduce that equivalence but reconstructs its genealogy. Nuclear resonance theory grew from radioactive decay, reaction cross sections, metastable compound states, and complex energies, whereas black-hole perturbation theory grew from spacetime stability and causal response. We place the two developments on a common chronology, from Sommerfeld's radiation condition and early nuclear-decay theory through Regge--Wheeler perturbations, Vishveshwara's 1968 dissertation and 1970 papers, Press's 1971 quasi-normal terminology, and the independent Aguilar--Balslev--Combes theory of analytic dilation, then follow their later mathematical reunification in scattering-resonance theory. Alongside the chronology, we give a working dictionary relating no-incoming and horizon-ingoing/infinity-outgoing conditions, pole energy and complex frequency, width and damping rate, residues and excitation factors, and nonresonant background with branch-cut and prompt contributions. The aim is to make the cross-disciplinary equivalence operational without flattening its history, and to distinguish mathematical equivalence from historical genealogy.

In this work we investigate how exotic spinorial topology modifies the propagation of fermionic modes in the Schwarzschild geometry. By incorporating a topological gradient, $\partial_μ\varphi$, into the Dirac operator through a tetrad deformation, we show that the exotic spinorial sector naturally induces an effective geometric deformation of the Schwarzschild background. The central consequence of this construction is the emergence of a topological impedance surface at $\rtopo=1/q$, which suppresses the radial group velocity of the exotic spinorial modes, yielding a birefringent propagation pattern. Using a spinorial perturbation we discuss the greybody factor and the quasinormal response. The quasinormal spectrum shows the stability of the background metric and the absence of isospectrality for the superpartner potentials.

We systematically investigate the zoom-whirl periodic orbits of a small compact object orbiting a magnetically charged black hole in $f(R, T)$ gravity coupled with Euler-Heisenberg nonlinear electrodynamics. We evaluate the impact of the magnetic charge $Q_m$ and the Euler-Heisenberg parameter $a$ on the characteristics of the innermost stable circular orbit (ISCO) and the marginally bound orbit (MBO). Particularly, we focus on the precession parameter q and systematically examine how the magnetic charge and other parameters affect the trajectories of periodic orbits. Using the numerical kludge method, we generate gravitational waveforms for these periodic orbits. The results presented in our work demonstrate that the magnetic charge can significantly modify not only the precession parameter but also the orbital trajectories of the periodic orbits. Moreover, changing the magnetic charge $Q_m$ could cause a significant phase shift in the gravitational waveforms, while other parameters exert a relatively weaker influence on the gravitational waves.

Runaway stars ejected from the Galactic disc span a range of velocities, with two extreme regimes of particular interest. Hyper-runaway stars reach velocities approaching the local Galactic escape speed while remaining gravitationally bound to the Galaxy, while hypervelocity stars (HVS) have speeds which exceed the escape speed, leaving them formally unbound. Studying both populations places stringent constraints on star cluster formation, supernova explosions in massive binaries, and the shape of the stellar halo. Here we present a spectroscopic search for such extreme-velocity stars using data from the first data release of the Dark Energy Spectroscopic Instrument (DESI DR1). Because these objects are typically located at distances beyond the range where \textit{gaia} parallaxes are reliable, we derive stellar parameters through a combined analysis of spectroscopy and spectral energy distributions (SEDs). These parameters are then compared with stellar evolutionary tracks to infer distances, which are subsequently used to compute the kinematics of the candidates. We identify a sub-sample of eight stars that appear unbound to the Galaxy, likely of extragalactic origin. These stars exhibit projected rotational velocities exceeding $50$ km s$^{-1}$, consistent with a main-sequence nature. An additional eleven stars are identified as potential HVS candidates under the assumption that they are main-sequence stars. This interpretation is not supported by their rotational velocities, making their unbound status less secure. Finally, $26$ stars show evidence of being main-sequence runaway stars ejected from the Galactic disc. The fastest object in the sample is a metal-poor HVS candidate with a Galactocentric velocity upper-limit of $934 \pm 110$ km s$^{-1}$. The star with the largest measured radial velocity of $513$ km s$^{-1}$ is most likely a slowly pulsating B-type runaway star.

The increasing precision and complementarity of late-time cosmological observations provide new opportunities to test modified gravity against the observed expansion history of the universe. The combination of DESI DR2 BAO measurements with cosmic chronometers (CC) and independent Type Ia supernova compilations provides a data-driven test of cosmic acceleration. Motivated by this progress, we investigate late-time dark energy dynamics in symmetric teleparallel $f(Q)$ gravity by adopting the power-law form $f(Q)=βQ^{m+1}$ and characterizing cosmic evolution through the effective equation of state (EoS) parameter. The model is constrained using CC, DESI DR2 BAO and three independent Type Ia supernova compilations, namely Pantheon+, DES-SN5YR and Union3. The inferred Hubble constant values are mutually consistent, yielding $H_0=67.60^{+1.60}_{-1.66}$, $67.08^{+1.66}_{-1.61}$ and $68.16^{+1.46}_{-1.43}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$, respectively. Statistically, the proposed $f(Q)$ model yields lower $χ^2_{\min}$ values and is favored by the AIC for all dataset combinations, whereas the BIC favors $Λ$CDM for the CC + DESI DR2 + Pantheon+ and CC + DESI DR2 + DES-SN5YR combinations and indicates no meaningful preference between the two models for the CC + DESI DR2 + Union3 dataset combinations. The reconstructed EoS indicates quintessence-like behavior, while the negative deceleration parameter confirms the current accelerated expansion. The transition from deceleration to acceleration occurs within $0.680\leq z_t\leq0.745$. Higher-order cosmographic parameters and the Statefinder and $Om(z)$ diagnostics consistently support this quintessence-like behavior, with the Statefinder trajectories approaching the $Λ$CDM fixed point in the far future. Overall, the power-law $f(Q)$ model provides a viable and competitive description of late-time cosmic acceleration.

We study the holographic duality between free vector models and Higher-Spin Gravity in 4-dimensional de Sitter space. On both the bulk and boundary sides, we introduce new reality conditions, which allow us to include odd spins in the bulk, and to extend the duality from type-A to type-B (i.e. from boundary scalars to spinors). The new reality conditions are closely related to a higher-spin-symmetric Hilbert-space norm for the single-particle (super)multiplet in de Sitter space. We construct two alternative viewpoints on the type-A and type-B theories. In one view, the two co-exist in "parallel universes", specifically in even vs. odd antipodal identifications of de Sitter space. In the other view, type-A and type-B are Legendre-transformed descriptions of the same twistor-space theory in Euclidean AdS (this involves the observation that the higher-spin partition function is Legendre-dual to itself). In this way, higher-spin holography reconciles the two-boundary nature of de Sitter space with the one-boundary nature of Euclidean AdS. The supersymmetric theory that unifies type-A and type-B with bulk fermions fails to be consistent under the appropriate reality conditions.

We present a chemo-kinematical, structural, and photometric analysis of the old open cluster Berkeley 36 using Gaia DR3 astrometry and photometry together with high-resolution spectroscopy from the Gaia-ESO Survey DR5.1. Applying a Gaussian Mixture Model to Gaia astrometry, we identify 946 high-probability cluster members. We derive a core radius of 2.63 +/- 0.21 arcmin and a tidal radius of 14.84 +/- 0.47 arcmin, indicating a moderately concentrated and dynamically relaxed system. By fixing the cluster metallicity to the spectroscopic value of [Fe/H] = -0.19 +/- 0.02 dex and adopting an independently determined geometric distance of 4377 +/- 510 pc, we minimize the classical age-reddening-metallicity degeneracy and derive a robust isochrone age of 6.8 +/- 0.5 Gyr. Independent Ba-based chemical clocks yield a mean age of 7.75 +/- 1.94 Gyr, supporting the isochrone solution. The cluster exhibits a high main-sequence binary fraction of 48.0 +/- 1.7% and hosts 83 blue straggler star candidates with an extended spatial distribution, contrary to classical mass segregation. Orbit integration shows that Berkeley 36 follows a nearly circular orbit in the outer Galactic disc at R_GC = 11.42 +/- 0.44 kpc. Accounting for the Galactic warp and disc flare increases the cluster's maximum vertical excursion by 86% and the local disc scale height by 17%, respectively. Comparison with its chemically inferred birth radius at R_b = 6.71 +/- 0.66 kpc indicates an outward radial migration of approximately 5 kpc, predominantly driven by churning. These results establish Berkeley 36 as a benchmark for investigating radial migration, secular evolution, and the dynamical history of old Galactic open clusters.

We introduce \emph{latent geometry} in BFSS/BMN models. Before an emergent geometry evaporates at the geometric transition, large-$d$ Gaussianization encodes its information in the exceptional $N=2$ sector selected by the baby fuzzy sphere, a single active spin-$1/2$ Pauli block. Dimensional reduction, finite-$N$ Gaussianization and exact Molien--Weyl projection transport this encoding to mass-deformed BFSS$_2$. At $N=2$, the same stable BFSS$_2$ oscillator admits inequivalent unitary $\mathbf{H}^2_θ=\mathbf{EAdS}^2_θ$ and $\mathbf{dS}^2_θ$ decodings, realizing spacetime transmutation and the emergence of Lorentzian time.

The No-Scale gravity is a compelling framework to describe particle physics, gravity and cosmology, in which all mass scales are an illusion given by the value of a scalar field $φ$. This theory, however, falls under the umbrella of more general scalar-tensor theories, which propagate different modes depending on the scalar field, and faces the extensive debate regarding the equivalence between its Jordan and Einstein frame descriptions. In this work we advocate that by excluding the singular point in the transformation between the two frames (e.g., $φ=0$) we can have the classical equivalence between them. To show the merit of removing this singular point, we argue the Jordan frame makes the symmetries of the model manifest, which creates a suitable playground for the particle-physics model building which we illustrate by showing the emergence of discrete symmetries which leads to a high-quality axion and also naturally incorporate the seesaw mechanism.

On a compact connected section ${\cal S}$ of a supersymmetric $M$-horizon the Killing-spinor bilinears give a pointwise identity relating the warp factor $Δ$, the rotation one-form $h$ and the two spinor norms, with nothing assumed about the norm of the Killing spinor. We derive three consequences of that unreduced identity. First, a single-point rigidity theorem: if $Δ$ and $h$ vanish at one point of the section, then the flux vanishes identically, ${\cal S}$ is Ricci-flat and the horizon is $\mathbb{R}^{1,1}\times{\cal S}$. A single point replaces the usual global spinorial hypothesis. Second, the ${\rm Spin}(7)$ decomposition of the flux fixes $h$ algebraically and exhibits the invariant flux content of the scalar square $Δ=4Φ^2$ known in an adapted gauge, $Δ=\frac{1}{108}\|w_{\bf 7}\pmσ({\cal Y}_{\bf 7})\|^2$. Only the two ${\bf 7}$-summands $w_{\bf 7}$, ${\cal Y}_{\bf 7}$ reach the warp factor, and the square is degenerate rather than definite: it vanishes on the linear subspace $w_{\bf 7}=\mpσ({\cal Y}_{\bf 7})$ rather than at the origin, so positivity of $Δ$ yields no case list. Third, the two combine into a pointwise budget: the single constant of supersymmetry is shared between the deviation from staticity and the ${\rm Spin}(7)$ mismatch of the flux, each bounded by that constant. The same identities characterise the constancy hypothesis, equivalent to $V=-fh$ for the bilinear one-form $V$, which fails on the static branch of known warped $AdS_2$ solutions; they fix a weighted integral of the warp factor; and they reduce the Komar angular momentum of the horizon to a positive bilinear integral. Two no-go statements, for hidden symmetries built from the Killing spinor and for a second isometry from its bilinears, are stated with their hypotheses.

The internal structure of galaxies encodes the complex baryon cycle driven by gas accretion, star formation, and feedback, together with secular evolution and environmentally driven processes such as mergers and tidal interactions. We present a population-level census of massive nearby galaxies ($\log(M_\star/M_\odot) > 10$) by comparing Hyper Suprime-Cam Subaru Strategic Program observations with matched mock images from IllustrisTNG, EAGLE, and SIMBA. Using a consistent, like-for-like imaging pipeline, we construct structural abundance functions (SAFs) for key morphological parameters, revealing a structural abundance crisis. Across Sérsic index, concentration, size, and ellipticity, all simulations exhibit large, systematic discrepancies ($>5σ$; RMSE $\sim 0.2$--$1.8$\,dex), typically corresponding to abundance differences of factors of several. While individual simulations display diverse failures---underproducing or overproducing compact spheroids, extended or round galaxies ---all underproduce highly flattened disks. Although TNG shows the closest agreement and SIMBA the largest offsets, this shared failure indicates that current models---despite matching global demographics such as the stellar mass function---do not uniquely constrain internal galaxy structure. Our results demonstrate that agreement in integrated observables can mask fundamental shortcomings in the modelling of mass and angular momentum redistribution. We therefore establish SAFs as a stringent, multidimensional, and observationally accessible benchmark for testing and calibrating next-generation galaxy formation models in the era of upcoming deep, wide-field surveys.

The cross section for galaxy-galaxy strong lensing (GGSL) events in galaxy clusters has repeatedly been found to be higher in observations than in cosmological simulations. We revisit this discrepancy using updated simulation methodology and investigate the dependence of the GGSL probability, $P_{\rm GGSL}$, on host-cluster lensing properties, baryonic physics, and correlated and uncorrelated line-of-sight structure. We find that correlated material within $\sim 35$ cMpc of the cluster along the line of sight enhances $P_{\rm GGSL}$ by a few percent for typical systems and by up to $\sim15\%$ for the most efficient lenses. At fixed cluster mass, dark-matter-only simulations yield GGSL probabilities up to an order of magnitude lower than hydrodynamical simulations. We also find a strong dependence on the host-cluster Einstein radius, with an approximate scaling $P_{\rm GGSL} \propto θ_{\rm E}^{2}$. Matching simulated and observed clusters in both mass and Einstein radius seems to reduce the discrepancy relative to previous comparisons. However, our analysis does not clearly resolve the GGSL discrepancy, as the inferred tension depends strongly on the field-of-view definition: square fields are approximately consistent with simulations, while cluster member-bounded fields yield observed probabilities a factor of $\sim 2-3$ higher. Until observations and simulations share a matched selection function and matched measurement methodology, the residual tension cannot be cleanly attributed to either astrophysics or cosmology.