Carrier-phase (CP) ranging is a key enabler of high-precision positioning in modern wireless systems. In multi-frequency OFDM-based sensing, phase observations across subcarriers provide information about the underlying propagation geometry. However, in realistic industrial and urban environments, these observations exhibit non-Gaussian and asymmetric characteristics due to deterministic multipath components, violating standard circular statistical assumptions. In this work, we analyze CP-based ranging as an estimation problem over circular phase observations. We show that conventional model-based estimators, such as circular averaging under von Mises assumptions, become biased under 3GPP-compliant propagation conditions. Using a QuaDRiGa-based simulation framework, we evaluate empirical phase distributions in Industrial Factory (InF) and Urban Microcell (UMi) scenarios and quantify their deviation from classical statistical models. To address these limitations, we propose a learning-based estimator that operates directly on empirical phase distributions without assuming a predefined statistical model. Experimental results show improved accuracy compared to classical estimators, particularly under multipath conditions.

Quantifying the coherence properties of complex optical fields is essential for applications ranging from high power laser arrays to quantum coherent systems. Here, we present a new paradigm for coherence retrieval inspired by the Gerchberg Saxton framework, enabling reconstruction of the first order spatial coherence function (mutual intensity) of partially coherent light from intensity measurements in the near and far fields. We introduce two complementary approaches: a four dimensional Tensor GS algorithm that directly reconstructs the mutual intensity with high accuracy, and a Monte Carlo GS variant that significantly reduces computational cost at the expense of controlled approximation. We validated both methods by reconstructing partially coherent fields in simulated linear and ring arrays of up to 600 beams with prescribed Gaussian decaying coherence. Experimentally, we applied the Tensor GS method to a triangular array of 130 coupled lasers with inhomogeneous spatial coherence, achieving good agreement with theory and a root mean square phase error as low as 2pi over 250.

Sub-Saturn mass planets with extremely low bulk densities $(ρ\lesssim0.3)\mathrm{g/cm^3}$, or ``super-puffs'', are one of the most interesting and least understood populations of exoplanets. While many short-period super-puffs can be attributed to the effects of high irradiation and star-planet interactions, cold super-puffs appear to challenge the expectations of core accretion theory. We constrain the possible properties of 34 cold super-puffs by computing hydrostatic interior structures using PlanetSolver. We find that 28 planets in our sample can be reproduced by models consistent with core accretion based on their observed masses and radii and adjusting for planet age. We identify HIP 41378 f, Kepler-30 d, Kepler-51 d, Kepler-177 c, TOI-1420 b, and WASP-107 b as planets inconsistent with core accretion theory which necessitate a non-standard explanation (e.g. exo-rings). With the exception of TOI-1420 b, core accretion-compatible solutions are possible for these planets if an additional heat source is present. We modify planetary evolution models to determine whether enhanced radiogenic heating or late impacts with sub-planetary mass objects can plausibly inflate sub-Neptunes enough to achieve super-puff densities. We find that the effects of radiogenic heating are insufficient to produce super-puff densities, but that impacts can in many cases produce the necessary inflation for upwards of 1Gyr. We also compile and present here an index of all currently known super-puffs.

In this paper we present the chemical screening of the complex stellar population discovered in the Bulge Fossil Fragment Liller 1. This study is part of the Bulge Cluster Origin (BulCO) survey based on a Large Program at the ESO-VLT with the high resolution spectrograph CRIRES+. The survey is aimed at performing an unprecedented chemical screening of 17 stellar systems orbiting the Milky Way bulge, with the ultimate goal of unveiling their origin and true nature. We measured precise chemical abundances of iron, CNO, iron-peak, $α$- other light-elements, and neutron-capture elements for a sample of 30 red giant branch stars, kinematic members of Liller 1. The presented analysis provides the high-resolution spectroscopic proof of the complex chemistry of this massive stellar system, with multi-metallicity sub-populations of different ages that nicely fits into a self-enrichment scenario. We find no evidence for the Na-O anticorrelation associated with genuine globular clusters; rather the overall abundance trends are similar to those seen in the bulge field and in Terzan 5, providing definitive evidence of an in-situ formation of Liller 1 within the Galactic bulge.

The integration of green hydrogen in local energy markets is often analyzed from a technical flexibility perspective, while the effect of market design rules remains less explored. This paper proposes a coordinated local electricity-hydrogen market framework in which hydrogen participation is regulated by explicit renewable access mechanisms. A mixed-integer linear programming model is developed to co-optimize electricity trading, battery operation, wind allocation and hydrogen production under centralized coordination. Six regulatory cases are examined including hydrogen supply options and access of local wind. Results are obtained for representative seasonal weeks for Norwegian energy community. Electrolyzer, when connected as rigid load, increases grid dependence, but also improves system cost when price-based participation is activated. Direct renewable access reduces grid imports, enhances wind allocation and introduces competition with households for energy distribution and system cost optimization. Furthermore, findings show that (i) hydrogen integration in local energy systems is essentially a market design problem and (ii) renewable access rules critically determine system behaviour, flexibility interactions and seasonal performance.

In this paper, we study the sharp bounds of the first three logarithmic inverse coefficients for Janowski convex class $\mathcal{C}(A, B)$. We also derive sharp upper and lower bounds of $\bigl|\,γ_2 \,\bigr|-\bigl|\,γ_1\,\bigr|$ and $\bigl|\,Γ_2 \,\bigr|-\bigl|\,Γ_1\,\bigr|$ for functions in the class $\mathcal{C}(A, B)$. Furthermore, a sharp estimate for the second Hankel determinant associated with the logarithmic inverse coefficients for functions in $\mathcal{C}(A, B)$ is obtained.

Magnetic fields permeate the multiphase interstellar medium (ISM), yet their phase-dependent structure remains poorly constrained by observations. Dust polarization and \ion{H}{1} emission together offer complementary probes of the plane-of-sky magnetic field and cold neutral medium (CNM) gas structure, respectively. Recent observational work has shown that in the diffuse ISM, the dust polarization fraction correlates positively with the CNM mass fraction ($f_{\rm CNM}$) but not with total \ion{H}{1} column density, suggesting a phase-dependent magnetic field geometry. Here, we use extremely high-resolution ($2048^3$) simulations of the turbulent, magnetized, multiphase ISM to investigate the physical origin of this trend. By constructing synthetic \ion{H}{1} and dust polarization maps, we directly compare our simulations to the observational results of \citet{Lei:2024}. We recover a positive $f_{\rm CNM}$-polarization correlation most clearly for sightlines intersecting fewer than $\sim$20 discrete CNM clouds, while the trend becomes weak or intermittent for larger cloud counts, consistent with the expectation that high-Galactic-latitude sightlines contain relatively few independent cold structures. We show that this correlation reflects genuine phase-dependent magnetic structure: CNM clouds tend to be elongated along the local magnetic field and, when normalized by column density, exhibit lower magnetic disorder than the warm neutral medium (WNM). We further demonstrate that apparent discrepancies between simulation- and observation-based measures of magnetic disorder arise from whether disorder is quantified per unit path length or per unit mass. Our results support a picture in which CNM structures host relatively ordered magnetic fields, producing higher polarization fractions along CNM-dominated sightlines in the diffuse ISM.

Event Horizon Telescope (EHT) images of black holes appear as rings with a brightness asymmetry. Here, we expand on our previous study of the asymmetry magnitude $a_1$ to study the position angle of the peak brightness asymmetry $\mathrm{PA}_1$ in general relativistic magnetohydrodynamic (GRMHD) models. For larger spin magnitudes ($a_{*}>0$ and $a_{*}\lesssim-0.5$), the mean $\mathrm{PA}_1$ falls within $1σ$ of the approaching limb of the black hole, regardless of viewing inclination, disk magnetization, or source. By comparing the $(a_1, \mathrm{PA}_1)$ distribution in M87* observations with models, we demonstrate that we can mildly disfavor low-magnitude spins and strongly disfavor all spin vectors that point toward Earth. The alignment of $\mathrm{PA}_1$ relative to the large-scale jet axis may suggest that M87*'s disk does not have a large tilt. By combining $\mathrm{PA}_1$ with the pattern speed measured in optimistic 2026 M87* video conditions, the EHT can constrain whether M87* is prograde or retrograde with $\sim 84\%$ accuracy. In Sgr A*, we show that a detection of $(a_1, \mathrm{PA}_1)$ could constrain the magnitude and direction of the galactic center spin vector. Finally, if future EHT expansions increase the sample of horizon-scale sources, a simple set of observables (ring diameter, asymmetry magnitude, and asymmetry angle) could enable robust constraints on black hole mass, spin, and inclination.

The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [10]. In [7], He and Jiang studied the Terwilliger $\mathbb{F}$-algebras of factorial association schemes. In this paper, we continue studying the Terwilliger $\mathbb{F}$-algebras of factorial association schemes. We get all block idempotents of the Terwilliger $\mathbb{F}$-algebras of factorial association schemes. We get the $\mathbb{F}$-dimensions, the centers, the Jacobson radicals of the block algebras of the Terwilliger $\mathbb{F}$-algebras of factorial association schemes.

We consider a continuous time investment problem in a multi-asset Black-Scholes market with the following features: The assets' drifts are not known and constitute a source of model ambiguity. However, there is a prior distribution (knowledge) on the possible drifts. Our investor is ambiguity averse and wants to maximize a mean-variance criterion for the terminal wealth where ambiguity aversion is incorporated in a smooth way. We consider here the criterion introduced in Maccheroni et al. 2013 where the variance is decomposed and each part is weighted differently to account for different levels of market risk and model ambiguity aversion. We use a novel approach to find the optimal dynamic investment strategy within the class of all adapted strategies which allow for learning. We also present a number of numerical results which help to understand how the model parameters affect the optimal investment strategy. In general it turns out that ambiguity averse investors invest less in the risky assets.

These lecture notes are intended as a coherent introduction to conformal field theory in general, and composite operators in particular, through a semiclassical framework for computing scaling dimensions, with emphasis on operators of the form $ϕ^n$. In doing so, they aim to fill a gap in the literature and to help decode some of the relevant concepts. The physical idea is that at large $n$ an (heavy) operator creates a highly occupied state. Through the state-operator correspondence, this state lives on the cylinder $\mathbb{R}\times S^{d-1}$, and its scaling dimension is the corresponding energy of the theory on the cylinder. The notes are organized as a self-contained route from conformal symmetry to semiclassical dynamics. Part I reviews the conformal group, primary operators, radial quantization, the state-operator correspondence, and operator mixing. Part II builds the semiclassical framework, first in the free scalar theory, where the dimension of $ϕ^n$ is recovered in three independent ways, and then through the double-scaling limit, the action variable, and Bohr-Sommerfeld quantization. Part III develops the general machinery of periodic saddles, Floquet theory, fluctuation determinants, the Gel'fand-Yaglom method, and the Gutzwiller trace formula. Part IV applies the framework to the $O(N)$ $ϕ^4$ theory in $d=4-ε$ at the Wilson-Fisher fixed point, deriving the classical elliptic solution, the Lamé fluctuation spectrum, the zero modes, and the one-loop contribution to the large-$n$ scaling dimensions. Beyond the explicit computation, the notes emphasize the role of composite operators as probes of collective sectors of quantum field theory, with extensions to gauge theories, conformal windows, and asymptotically safe field theories.

The properties of spiral galaxies in the early universe remain poorly studied and, as such, little is known about their nature and evolution. We use JWST data to measure the pitch angles of spiral galaxies across cosmic time. Our sample consists of 593 spiral galaxies with stellar masses ($M_*$) greater than $10^{10} M_\odot$ up to $z \sim 3.5$, drawn from the CEERS and JADES surveys. Spiral galaxies are identified by fine-tuning a Zoobot deep-learning model. We use SpArcFiRe to identify spiral arms and measure their pitch angles. We find no significant redshift evolution in the average pitch angle across the full sample. However, in the most massive systems (log$(M_*/M_\odot)=11-12$), spiral arms slightly wind up with time. We show that at $z>1.25$, pitch angle does not correlate with some key internal galaxy properties (stellar mass, bulge mass, disk mass, specific star formation rate [sSFR]). In contrast, at $z<1.25$, pitch angle shows a weak but statistically significant negative correlation with stellar mass, bulge mass, and disk mass, and a positive correlation with sSFR at $z<0.75$. We also find no dependence of pitch angle on the tidal strength applied by nearby companions. These results indicate a transition epoch at $z\sim1$: above this redshift, spiral structures appear to be primarily locally driven and not correlated with global galaxy properties; and below this redshift, spiral arms are regulated by global gravitational potential, consistent with the predictions of the density wave theory.

Low surface brightness tidal debris around galaxies, such as tails, streams, and shells, together with other interaction-driven morphological disturbances, serve as valuable indicators of past or ongoing galaxy mergers. With the growing data volume from surveys like the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), automated detection methods are essential. This paper evaluates the performance of two automated methods, a Self-Supervised Learning (SSL) model and the Concentration-Asymmetry-Smoothness (CAS) parameter method, in tracing interaction-driven disturbances and merger signatures, with visual classification used as the benchmark. Visual classification yields a high-confidence disturbance fraction of 25.1 +/- 1.5% in our sample and serves as the reference standard for assessing the completeness and precision of the automated approaches. Visual classification is affected by galaxy distance and image resolution, which limit the detectability of faint low surface brightness structures. The SSL model achieves high recall (0.86 +/- 0.04) and low contamination (0.2) by retraining only its linear classifier on a small labelled dataset, making it suitable for identifying a broad set of disturbed systems, including faint tidal debris and other interaction-driven morphological disturbances, thereby providing a more complete census of merger-related features. The CAS method, using the traditional threshold A > 0.35, shows higher precision (0.77) but lower recall (0.20), indicating a conservative approach that captures cleaner but less complete samples. Visual classification and the SSL model show a significant positive correlation between stellar mass and disturbance fraction, while the CAS method exhibits a much weaker trend.

We present cosmological constraints from the Dark Energy Survey Year 3 (DES Y3) weak lensing data using hierarchical hybrid statistics within a Bayesian simulation-based inference framework that is based on the Gower Street simulations. To maximize the precision of the inference, we have developed a new, information-theory based, data compression of the weak lensing maps to just seven highly informative summary statistics. The hybrid scheme exploits the high information content of the power spectrum, compressing both the power spectrum and neural-based summaries that are designed to extract further information. Our simulation-based approach enables principled forward modelling of all major sources of systematic uncertainty and survey properties into realistic mock observations, including the survey mask, photometric redshift uncertainties, intrinsic galaxy alignments, multiplicative shear calibration bias, source galaxy clustering, non-Gaussian shape noise, and non-linear structure formation. The summary statistics are then used in a Bayesian simulation-based inference pipeline. The inference is validated through coverage tests and checks for robustness against baryonic feedback. Assuming a $w$CDM cosmology, our analysis yields $S_8 = 0.808 \pm 0.017$, $Ω_{\rm m} = 0.325 \pm 0.024$, and $w < -0.766$ (marginalized posterior 68 per cent credible intervals). This rigorous combination of information theory, physics- and neural network-based extreme data compression, and principled Bayesian analysis improves the figure of merit for $(Ω_{\rm m}, S_8, w)$ by 60 per cent over the previous state-of-the-art, and by almost a factor of 3 over two-point analyses of the same data. They are the most precise joint constraints on $(Ω_{\rm m}, S_8, w)$ from weak gravitational lensing data alone of any survey to date. We intend to apply this analysis to the more recent DES Y6 data.

The physical processes that shape a galaxy's spectrum are strongly degenerate in observations, obscuring which processes act independently. Leveraging the pop-cosmos generative galaxy population model, we investigate how many independent degrees of freedom the rest-frame optical SED contains. We use a $β$-variational autoencoder (VAE) to compress a 16-parameter stellar population synthesis (SPS) description into a disentangled latent representation interpreted through mutual information (MI). We find that five independent dimensions suffice, corresponding to stellar mass, recent star formation, dust, and two -- not the three or four assumed by standard nebular models -- degrees of freedom in the ionization state of the gas. Stellar metallicity and stellar age are not among these primary drivers; their spectral effects are distributed across the others rather than independently encoded. By tying each dimension to specific spectral features, this decomposition breaks the star-formation--dust--metallicity degeneracies that limit broadband photometry, and recovers the physical conditions of the gas more cleanly than the line-ratio diagnostics in standard use.

Synchrotron self absorption (SSA) is seen across a variety of astrophysical sources, and observation of an SSA peak in the spectrum is a powerful tool for estimating the physical conditions and the minimum energy of the emitting region. We begin with the (re)derivation of the usual SSA parameter estimates, carefully considering dependencies and assumptions, obtaining the most accurate traditional SSA minimum energy equations currently available. Traditional methods rely on the assumption that the emitting region is quasi-spherical and homogeneous. However, many observations of SSA show that the spectral index at frequencies below the peak is less than the expected $+2.5$ (non-thermal) or $+2$ (thermal). We argue that an inhomogeneous emitting region is the most likely explanation in many cases. Power law inhomogeneous cylindrical slab and broken power law inhomogeneous sphere models are used to investigate how the presence of inhomogeneity affects parameter estimates using traditional SSA methods. We find that in some cases inhomogeneity can lead to traditional SSA methods underestimating the minimum energy and the size of the emitting region by over an order of magnitude. Quantitative correction factors are found which can be applied to traditional estimates to correct for inhomogeneity, depending on the value of the observed flattened spectral index and the range in frequency over which this value is observed. Furthermore, we derive simple correction factors for non-spherical homogeneous emitting regions. Finally, we explore the effects of inhomogeneity on measurements of polarisation around the spectral peak, and on lightcurves for expanding emitting regions.

While Hamiltonian Lattice Gauge Theory is gaining traction, today's limited numerical capacity leaves simulations affected by discretization errors. This motivates the implementation of renormalization group (RG) techniques to find discretization-error-free operators. To this end, we introduce VAPOR, a variational quantum algorithm that decomposes operators into Pauli strings, identifies RG flow orbits, and determines fixed points of a naively discretized operator. We illustrate this using a toy model of a kinematic operator in a symmetry-restricted SU(2) Yang-Mills theory.

For broadband imaging surveys, filter-substrate refraction causes light at different wavelengths to follow slightly different paths through the filter substrate before reaching the detector. This effect produces two chromatic perturbations to the point spread function (PSF): a shift in the effective focal position along the optical axis (longitudinal shift), which manifests as a defocus-like perturbation, and a wavelength-dependent displacement of the image position in the focal plane (lateral shift), which manifests as image decentering. Using image simulations, we provide the first study of these two effects independently across all eight Roman imaging bands and over the full focal plane. We compute the resulting PSF and photometric errors from images with and without the effect included, and compare the magnitude of the effect to the Roman science requirements. We find that the lateral shift is the dominant contribution, producing PSF size and ellipticity residuals in most bands of order ~0.3-0.4%. These exceed the Roman science requirements for weak lensing by roughly an order of magnitude. The effect is also strongly field dependent, increasing toward the edges of the focal plane. By contrast, flux residuals remain below one third of the 1% requirement for most bands, except in R062 and W146. We find the longitudinal shift to be subdominant and negligible in most bands, including the weak lensing bands. Finally, we implement the dominant lateral-shift effect in a framework suitable for large-scale image simulations and validate that the resulting PSF size and shape changes are accurately reproduced. Overall, we find that filter-substrate refraction is a relevant chromatic effect for Roman PSF modeling, and we provide tools to model and incorporate it in large-scale image simulations.

We investigate the nonequilibrium dynamics of a one-dimensional interacting system across a transition from a charge-density-wave (CDW) phase to a symmetry-protected topological (SPT) phase. Starting from a CDW initial state, we study both sudden quenches and slow ramps into the SPT regime. While the CDW order melts under both protocols, the fate of topological order is sharply different. Following a sudden quench, long-range SPT order does not emerge because the post-quench state contains a finite density of excitations above the topological ground state. In contrast, slow ramps allow the system to follow the instantaneous ground state away from the critical region, enabling the buildup of SPT order with deviations governed by Kibble-Zurek defect production. The dynamics is solvable via a unitary mapping to a quadratic fermionic Hamiltonian, allowing us to compute the Loschmidt echo, correlation functions, and string correlator. The Loschmidt rate function exhibits cusps signaling dynamical quantum phase transitions, while the correlation dynamics reveal the contrasting mechanisms governing quenches and ramps across the transition. These results demonstrate that entering the topological regime is not sufficient for the emergence of topological order; the decisive factor is the suppression of excitation production during the evolution.

We present a mechanism for ferromagnetism in narrow bands consisting of Anderson-localized states. We exploit single-particle localization to derive a controlled theory of exchange interactions within the narrow band. For quasiperiodic systems with a half-filled moiré band, we show that the critical interaction strength for ferromagnetism is highly sensitive to the geometry of real-space overlaps between localized orbitals: we find well-defined resonances at which ferromagnetism sets in for interaction energies that are far lower than the gap to other bands. Near these resonances, all the approximations in our theory are controlled, so our critical point predictions are quantitative. We show examples both in one and two dimensions. Our work identifies a route to ferromagnetism based on the geometry of real-space wavefunctions, distinct from previously found mechanisms based on the quantum geometry of Bloch bands.

We study the Alexander polynomials of the 4-strand Turk's head knots $Th(4,2n+1)$, defined as the closures of the braid $(σ_1σ_2^{-1}σ_3)^{2n+1}$. Using the reduced Burau representation, we derive an annihilating recurrence of order at most 8 and a rational generating function for the resulting polynomial sequence. By executing a multivariable resultant elimination over the reciprocal constraint, we obtain an exact factorization of the normalized Alexander polynomial in terms of Chebyshev polynomials. This factorization produces a binomial convolution formula for an associated coefficient sequence and a representation by a terminating ${}_4F_3$ hypergeometric series. We evaluate the continuous approximation of this representation using the saddle-point method, demonstrating negative curvature in the asymptotic main term. Finally, we describe analytic obstructions to extracting global discrete error bounds via this method, leaving the formal proof of Fox's Trapezoidal Conjecture for this family open.

Parity-violating physics in the Universe can generate correlations between the Cosmic Microwave Background (CMB) $E$- and $B$-modes, but detecting such signals requires extremely accurate calibration of instruments. We describe a data-driven method to calibrate the relative polarisation angle between CMB experiments using cross-correlations of observations over a common sky region. Unlike standard self-calibration approaches, this method does not assume vanishing isotropic cosmic birefringence or primordial $EB$ correlations when estimating the relative misalignment angle, and therefore preserves sensitivity to parity-violating physics. As a proof of concept, we forecast the performance of this method using the Simons Observatory (SO) Small Aperture Telescopes (SATs) as a calibrated reference. If they can be calibrated to an uncertainty of $0.08^\circ$, as anticipated from the SO wire grid calibration system, we show that the SO Large Aperture Telescope and Planck could be calibrated to uncertainties of $0.10^\circ$ and $0.17^\circ$, respectively, at $\sim 145$ GHz. This approach relies on the availability of at least one well-calibrated instrument, and provides a complementary path to improving polarisation calibration across experiments, enabling more robust searches for parity-violating physics in the CMB, such as cosmic birefringence.

We conduct a global general relativistic neutrino-radiation-transfer magnetohydrodynamics simulation of a $1.35$-$1.35M_\odot$ binary neutron star with the unprecedented spatial resolution of $6.25$\,m on the Japanese supercomputer FUGAKU. The total consumed CPU time is $\approx 530$ million core hours. We initialize the binary neutron star's magnetic field to be $3.16\times 10^{12}$~G at maximum, which is compatible with the upper end of the observed binary pulsars. We demonstrate that the Kelvin-Helmholtz instability that emerges when the two neutron stars touch amplifies the magnetic field to an expected electromagnetic saturation energy of $\sim 10^{50}$~erg within $3$~ms after the merger. The spectral analysis indicates that the Kazantsev and Kolmogorov spectra are reproduced in the magnetic and kinetic power spectral densities, respectively. We also find that it induces stellar-scale magnetic field amplification by at least a factor of $316$. We conclude that a magnetar may form at least temporarily following neutron star mergers in a few ms.

We contribute to the systematic analysis of New Physics effects in neutrino experiments using Effective Field Theory (EFT) methods. We review and extend the quantum field-theoretical formalism for generic neutrino interactions, discussing the inclusion of matter effects and deriving the connection with the density matrix formalism. On the phenomenological side, we apply this framework for the first time to medium-baseline reactor neutrino experiments. We derive analytical expressions for the relevant oscillation observables and perform a first EFT analysis of the recent JUNO dataset, extracting bounds on the leading non-standard interaction parameters.

We investigate the existence and implications of ``bouncing geodesics'' in asymptotically flat Schwarzschild and Schwarzschild--de Sitter black holes. These trajectories, which probe the high-curvature regions near the black hole singularity, correspond to specific ``bouncing singularities'' in the bulk retarded Green's function. We provide a precise description of these singularities by combining the local Hadamard form with the global propagation of singularities theorem. We then derive the critical times at which the bulk retarded correlator becomes singular, considering all possible anchorings of the bouncing geodesics, including null infinity and the cosmological horizon. Finally, for black holes enclosed in a reflecting cavity, we establish a universal connection between the locations of the bouncing singularities and the spectrum of cavity quasinormal modes (QNMs) by deriving a cavity version of the thermal product formula, analogous to the one known for anti-de Sitter black holes. This relation allows one to extract information about the black hole interior from the asymptotic QNM spectrum measured at a reflecting hypersurface, even when the cosmological constant is zero or positive. We confirm this prediction through explicit examples by computing the cavity QNMs of scalar and electromagnetic fields, as well as gravitational waves, in spacetimes with asymptotically flat and de Sitter black holes.

Three-body interactions exhibit phases of strong chaotic evolution as well as hierarchical motion where one body separates from a binary and follows a hyperbolic or elliptic trajectory around it. The binaries produced during phases of hierarchical motion may lead to gravitational wave (GW) inspirals, but this depends on the outcomes of the chaotic states. In this paper we re-derive the elliptic outcome distribution using equilibrium statistical mechanics and explore it together with the hyperbolic distribution. When comparing to N-body simulations, we find that we can reduce the elliptic outcome model to one free parameter instead of the previously used two and that the predicted disintegration probabilities agree except for very low angular momentum triples. We then use both outcome distributions along with a star cluster model to design a Monte Carlo algorithm for repeated binary-single scatterings within dense star systems. We explore star cluster masses of $[10^5 - 10^7] M_{\odot}$, with the goal of quantifying observably eccentric merger (OEM) GWs, visible to instruments such as LIGO and Virgo. Assuming an OEM detection sensitivity of $f_{\rm min}=10 {\rm Hz}, e_{\rm min} = 0.1$, we find the elliptic OEMs are about $\sim (32 - 63)\%$ of the total elliptic mergers and that the total cluster mass greatly impacts the fraction of ejected binaries. The OEM to total merger fraction (OEM fraction) is found to be $(2.6 - 4.4)\%$. Considering the detection sensitivity that GW interferometers have today $(f_{\rm min} \simeq 34.4 {\rm Hz})$ we obtain the OEM fraction in the $(1.6 - 3.1)\%$ range.

The explosion of a white dwarf (WD) in a close binary can launch a surviving runaway star at velocities of $\gtrsim 1000\, \rm km\,s^{-1}$. Such runaways provide a direct probe of thermonuclear supernovae (SNe) in double-degenerate binaries. Several candidate runaways are known, but their evolutionary states and the demographics of the broader population are uncertain. To enable robust population inference, we carry out a systematic survey for hypervelocity runaways with a simple selection function, selecting candidates based on large Gaia-inferred tangential velocities and blue colors. We classify 100% of the resulting 92 candidates using a combination of spectroscopic follow-up and archival data. The search yields ten suspected D$^6$ stars and three LP 40-365 stars. Three D$^6$ stars are new discoveries, including two hot ($T_{\rm eff} > 50,000$ K) objects and one cool ($T_{\rm eff}\approx 7,000$ K) object. We forward-model our survey under several proposed D$^6$ star evolutionary models, coupling each to a Galactic model and the survey selection function. No single model reproduces the observed diversity of D$^6$ stars, which likely reflects a range of remnant masses, ages, and heating mechanisms. Models in which runaway companions are heated by SN shocks alone are too faint and short-lived to explain most of the observed sample, while fully reheated models are too luminous and long-lived. Models with intermediate heating, as occurs in some simulations of violent mergers and partially disrupted remnants, best match the observed magnitude, distance, and kinematic-age distributions. The inferred D$^6$ star birth rate is model dependent, but the models that best match the observed population require rates of only a few percent of the Galactic SN Ia rate, perhaps implying that most SNe Ia result from WD binaries in which both components explode.

Observations suggest that the hot Neptune desert contains the remnants of destroyed gas giants. Recent theoretical work has shown that gas giant destruction via Roche lobe overflow (RLO) can indeed populate the desert with remnant planets, but only if mass transfer removes most of the planet's orbital angular momentum ("lossy" RLO). Motivated by the fact that stellar accretion naturally gives rise to such lossy RLO, in this Letter we examine how planet-to-star mass and angular momentum transfer manifests in the distribution of stellar obliquities. We find that RLO tilts host stars into spin/orbit alignment (within a few ${\sim}$tens of degrees) regardless of initial conditions. Obliquity damping by RLO can only be reversed by the presence of misaligned companion planets within ${\lesssim}$2 au. While tides and mass transfer usually produce stellar spin up, host stars can also emerge from RLO slowly rotating if systems begin strongly retrograde; retrograde RLO reconciles theory with the anomalously slow rotation of the desert dweller host, LTT 9779. Predicted spin/orbit alignment may differentiate RLO from alternative giant planet destruction mechanisms, in particular hot Jupiter disruption during high eccentricity migration (which tends to produce broadly distributed stellar obliquities). We summarize other population-level predictions that can further distinguish RLO from high eccentricity migration. Our work suggests that follow-up obliquity measurements may reveal the formation pathways of desert dwellers, and potentially open a window into gas giants' exposed interiors.

Based on its predominantly thermal X-ray emission and long spin period, the isolated neutron star eRASSU J131716.9-402647 is one of the most promising candidates for membership in the still small class of X-ray dim isolated neutron stars (XDINSs). Confirmation of this classification, however, requires a more detailed characterisation of the source's timing and spectral properties. In this work, we present new NICER observations which, together with previous X-ray follow-up, allow us to constrain the timing properties and long-term evolution of eRASSU J131716.9-402647. We obtain a coherent timing solution with a spin period of $P\sim12.8$ s and a period derivative of $\dot{P}\sim9\times 10^{-14}$ s s$^{-1}$, which best-describes the spin evolution of the source. These parameters imply a dipolar magnetic field strength of $3\times10^{13}$ G and a spin-down luminosity of order $10^{30}$ erg s$^{-1}$. Spectral modelling reveals no significant change in the spectral state over the 15 months of observational monitoring and indicates a thermal luminosity that likely exceeds the rotational energy loss. This suggests a thermal evolution that has been significantly influenced by past reheating. The energy dependence of the double-humped pulse profile closely resembles that observed in the XDINS RX J1308.6+2127, with the pulsed fraction increasing towards higher energies. Taken together, these results unambiguously confirm the XDINS nature of eRASSU J131716.9-402647, making it the first newly confirmed XDINS in more than two decades.

Classical Game Theory underpins much of AI and multiagent research, but hybrid Human AI systems require a framework in which execution authority can alternate within a digital environment. We introduce NeoGame Theory, an extension of classical Game Theory for hybrid Human AI coalitions operating under Virtual Nature, the algorithmic analogue of classical (physical) Nature. The framework combines a lexicographic coalition utility with a delegation rule based on the Jensen-Shannon divergence between Human and AI policies. Two thresholds define agreement, contextual, and disagreement regions. In the contextual region, execution follows a scenario specific rule. Apart from the theory, in this paper we develop the first regime, Human arbitration, in which the AI learns by observation and frequency matching while the Human retains final execution authority. We establish the axiomatic basis of the framework and characterize a frequency convergence equilibrium, providing the foundation for later extensions and computational validation.