This is a preface to Fields, Gravity, Strings and Beyond, a special issue collection of articles published in J. Phys. A in memory of Stanley Deser.

Introduction to the theoretical foundations of gravitational waves: from general relativity to detection and binary system waveforms. Lecture notes prepared for the MaNiTou summer school on gravitational waves. Draft chapter for the CNRS contemporary Encyclopaedia Sciences to be published by ISTE.

Magic state distillation enables universal fault-tolerant quantum computation by implementing non-Clifford gates via the preparation of high-fidelity magic states. However, it comes at the cost of substantial logical-level overhead in both space and time. In this work, we propose a very low-cost magic state distillation scheme for biased-noise qubits. By leveraging the noise bias, our scheme enables the preparation of a magic state with a logical error rate of $3 \times 10^{-7}$, using only 53 qubits and 5.5 error correction rounds, under a noise bias of $\eta \gtrsim 5 \times 10^6$ and a phase-flip noise rate of $0.1\%$. This reduces the circuit volume by more than one order of magnitude relative to magic state cultivation for unbiased-noise qubits and by more than two orders of magnitude relative to standard magic state distillation. Moreover, our scheme provides three key advantages over previous proposals for biased-noise qubits. First, it only requires nearest-neighbor two-qubit gates on a 2D lattice. Second, the logical fidelity remains nearly identical even at a more modest noise bias of $\eta \gtrsim 80$, at the cost of a slightly increased circuit volume. Third, the scheme remains effective even at high physical phase-flip rates, in contrast to previously proposed approaches whose circuit volume grows exponentially with the error rate. Our construction is based on unfolding the $X$ stabilizer group of the Hadamard 3D quantum Reed-Muller code in 2D, enabling distillation at the physical level rather than the logical level, and is therefore referred to as $\textit{unfolded}$ distillation.

We present new VLTI/GRAVITY astrometry and updated orbit fits for the directly imaged companions YSES 1 b and HR 2562 B, substellar objects straddling the planet-brown dwarf boundary. Using high-precision astrometry, radial velocity (RV) data, and proper motions, we derive revised orbital parameters with orbitize! arXiv:1910.01756. For YSES 1 b, the inclusion of GRAVITY astrometry and a relative radial velocity measurement from arXiv:2409.16660 overcomes the traditional challenge of constraining eccentricities for distant companions, enabling the first orbit fit and yielding a constrained eccentricity of 0.44 (0.20). This represents the first full orbit fit for the system. Additionally, we calculate a median line-of-sight stellar obliquity of 12 (+11, -8) degrees, providing further insight into the system's dynamical architecture. For HR 2562 B, our analysis agrees with arXiv:2302.04893, confirming a low-eccentricity orbit (0.34 (0.20)) and an inclination of 87 (1) degrees. We find HR 2562 B's orbit to be nearly coplanar with the debris disk, with a mutual inclination of 3.7 (0.3) degrees. For both YSES 1 b and HR 2562 B the lower eccentricities favor an in situ formation scenario over extreme scattering or cloud fragmentation.

Nonreciprocal interactions are widely observed in nonequilibrium systems, from biological or sociological dynamics to open quantum systems. Despite the ubiquity of nonreciprocity, its impact on phase transitions is not fully understood. In this work, we derive criteria to perturbatively assess whether nonreciprocity changes the universality class of pairs of asymmetrically coupled systems undergoing a phase transition. These simple criteria are stated in terms of the unperturbed critical exponents, in the spirit of the Harris criterion for disordered systems, and agree with numerical simulations. Beyond nonreciprocity, our approach provides guidelines for assessing how dynamical phase transitions are affected by perturbations.

One of the first exoplanet hosts discovered thirty years ago, the star 55 Cnc has been constantly observed ever since. It is now known to host at least five planets with orbital periods ranging from 17 hours to 15 years. It is also one of the most extreme metal rich stars in the neighbourhood and it has a low-mass secondary star. In this article, we present data obtained at the Canada-France-Hawai'i Telescope with the SPIRou spectropolarimeter on both components of the 55 Cnc stellar system. We revisit the long-period radial-velocity signals of 55 Cnc A, with a focus on the role of the magnetic cycle, and propose the existence of a sixth planet candidate, whose period falls close to that of the magnetic cycle, or half of it. The other massive outer planet has a revised period of 13.15 years and a minimum mass of 3.8 MJup. Although some uncertainty remains on these outer planets, the characterization of the four inner planets is very robust through the combination of many different data sets, and all signals are consistent in the nIR and optical domains. In addition, the magnetic topology of the solar-type primary component of the system is observed by SPIRou at the minimum of its activity cycle, characterized by an amplitude ten times smaller than observed during its maximum in 2017. For the low-mass component 55 Cnc B, we report the discovery of two exoplanets in the system, with a period of 6.799+-0.0014 and 33.75+-0.04 days and a minimum mass of 3.5+-0.8 and 5.3+-1.4 MEarth, respectively. The secondary magnetic field is very weak and the current data set does not allow its precise characterization, setting an upper limit of 10 G. The system 55 Cnc stands out as the sixth binary system with planetary systems around both components, and the first one with non equal-mass stellar components.

The distribution of close-in exoplanets is shaped by the interplay between atmospheric and dynamical processes. The Neptunian Desert, Ridge, and Savanna illustrate the sensitivity of these worlds to such processes, making them ideal to disentangle their roles. Determining how many Neptunes were brought close-in by early disk-driven migration (DDM; maintaining primordial spin-orbit alignment) or late high-eccentricity migration (HEM; generating large misalignments) is essential to understand how much atmosphere they lost. We propose a unified view of the Neptunian landscape to guide its exploration, speculating that the Ridge is a hot spot for evolutionary processes. Low-density Neptunes would mainly undergo DDM, getting fully eroded at shorter periods than the Ridge, while denser Neptunes would be brought to the Ridge and Desert by HEM. We embark on this exploration via ATREIDES, which relies on spectroscopy and photometry of 60 close-in Neptunes, their reduction with robust pipelines, and their interpretation through internal structure, atmospheric, and evolutionary models. We carried out a systematic RM census with VLT/ESPRESSO to measure the distribution of 3D spin-orbit angles, correlate its shape with system properties and thus relate the fraction of aligned-misaligned systems to DDM, HEM, and atmospheric erosion. Our first target, TOI-421c, lies in the Savanna with a neighboring sub-Neptune TOI-421b. We measured their 3D spin-orbit angles (Psib = 57+11-15 deg; Psic = 44.9+4.4-4.1 deg). Together with the eccentricity and possibly large mutual inclination of their orbits, this hints at a chaotic dynamical origin that could result from DDM followed by HEM. ATREIDES will provide the community with a wealth of constraints for formation and evolution models. We welcome collaborations that will contribute to pushing our understanding of the Neptunian landscape forward.

All future lunar missions require a definition of the lunar reference system and a realization in the form of the lunar reference frame to ensure consistent products for positioning, navigation, cartography, and timing. This paper defines the origin, orientation, and scale of the Lunar Reference System (LRS), as well as provides numerical solutions for the first realization of the International Lunar Reference Frame (ILRF). ILRF is defined as the Principal Axis (PA) system, attached to the surface and co-rotating with the Moon, with its origin in the lunar center of mass (lunocenter). The ILRF realization is based on variance component estimation of the three lunar ephemeris solutions: INPOP21a, DE430, and EPM2021 for the series of the position of the lunar center of mass and rotation Euler angles -- precession, nutation, and proper rotation. The solution is valid starting with the period covered by Lunar Laser Ranging (LLR) data in 1970 and ending with extrapolated ILRF realizations in 2052 for future lunar missions. Results. The combined ILRF is characterized by the mean error of 17.6 cm for 2010-2030, where 15.3 cm comes from the origin and 8.6 cm from the orientation realization. The error in the realization of the origin is mainly caused by a poor geometry of the retroreflector network, resulting in a high correlation between the scale and the X component of the lunocenter in PA. The LLR post-fit residuals in ILRF are at the level of 2-3 cm in terms of the standard deviations of one-way ranges for best-performing LLR stations. The mean errors of the transformation between ILRF and other reference frame realizations in PA are at the level of 3 cm, whereas the mean transformation error to the DE421 Mean Earth frame equals 5 cm.

Transformers exhibit compositional reasoning on sequences not observed during training, a capability often attributed to in-context learning (ICL) and skill composition. We investigate this phenomenon using the Random Hierarchy Model (RHM), a probabilistic context-free grammar that generates sequences through recursive rule application. Models are trained on subsets of sequences and evaluated across four generalization conditions: memorization, in-distribution generalization, out-of-distribution generalization with the same rules, and cross-layer transfer. Behaviorally, performance improves systematically with task complexity and the number of in-context examples, with out-of-distribution tasks requiring substantially more examples than in-distribution scenarios. Mechanistically, we identify a progressive emergence of layer specialization during training that correlates with generalization performance. Principal component analysis and attention pattern clustering reveal that transformers develop structured, hierarchically organized representations in specialized layers. These results demonstrate that transformers develop modular, interpretable mechanisms supporting compositional reasoning, linking internal algorithmic structure to observed behavioral capabilities.

The galaxy gas-phase metallicity gradients have been extensively studied over the past four decades, both in the local and high-redshift universe, as they trace the baryon cycle and growth of galaxies. With the unprecedented spatial resolution and sensitivity of JWST, it is now possible to measure metallicity and its radial gradients out to redshifts as high as $z = 9$. Here, we present a sample of 455 spectroscopically confirmed galaxies from redshifts $1.7 \lesssim z \lesssim 9$ that are spatially resolved on sub-kiloparsec (kpc) scales by deep JWST NIRCam or NIRISS Wide Field Slitless Spectroscopy (WFSS). Synthesizing these new JWST observations with legacy observations from the literature, we observe that at redshift $z > 5$, galaxy centers are more metal-rich, exhibiting negative metallicity gradients of $\sim-0.4$ dex kpc$^{-1}$. These gradients flatten over time, reaching near-zero around $z \approx 2$, coinciding with the peak of the cosmic star formation rate. Beyond this point, the gradients become negative again at lower redshifts approaching $z=0$. This evolution likely reflects transitions in galaxy formation modes: an inside-out growth phase dominated by intense central star formation with inefficient feedback and limited gas mixing during ``cosmic dawn", enhanced gas mixing due to feedback-driven wind and gas accretion at ``cosmic noon", and a later phase of slow evolution and reduced feedback toward the present day. These physical processes, including gas accretion and feedback, not only regulate star and galaxy formation on a cosmic scale but also shape the evolutionary pathways of individual galaxies over cosmic time.

The Kepler mission, despite its conclusion over a decade ago, continues to offer a rich dataset for uncovering new astrophysical objects and phenomena. In this study, we conducted a comprehensive search for exocometary transit signatures within the Kepler light curves, using a machine learning approach based on a neural network trained on a library of theoretical exocomet transit light curves. By analyzing the light curves of 201,820 stars, we identified candidate events through the neural network and subjected the output to filtering and visual inspection to mitigate false positives. Our results are presented into three catalogs of increasing ambiguity. The first-tier catalog includes 17 high-confidence exocometary transit events, comprising 7 previously reported events and 10 newly identified ones, each associated with a different host star. The second-tier catalog lists 30 lower-confidence events that remain consistent with possible exocometary transits. The third-tier catalog consists of 49 more symmetric photometric events that could be either exocometary transits, exoplanet mono-transits, or false positives due to eclipsing binaries mimicking transits. Contrary to previous studies, which suggested that the cometary activity was favored by stellar youth, we find a broad age distribution among candidate host stars, including several red giants. This challenges the general idea of a decline in cometary activity with stellar age and underlines the need for further investigation into the temporal evolution of exocometary activity in planetary systems.

Rotating hairy black holes (RHBHs) are axisymmetric equilibrium solutions of the Einstein-Klein-Gordon equations, consisting of a spinning black hole surrounded by a toroidal distribution of complex scalar field. Despite their potential astrophysical relevance, the stability of these configurations -- naturally expected to form through superradiant growth of light bosonic fields -- remains uncertain. In this work, we investigate the stability of RHBHs by performing fully non-linear numerical evolutions of several configurations that differ in the relative mass contribution of the scalar-field torus. We find that configurations in which the scalar field mass is subdominant compared to the black hole mass remain stable throughout the evolution. In contrast, when the scalar-field mass dominates, the system develops an instability akin to the non-axisymmetric instability observed in rotating boson stars. Given the expected limits on the scalar-field mass growth achievable through superradiance, our results suggest that rotating hairy black holes formed predominantly by this process are expected to be stable.

Gaussian smoothing combined with a probabilistic framework for denoising via the empirical Bayes formalism, i.e., the Tweedie-Miyasawa formula (TMF), are the two key ingredients in the success of score-based generative models in Euclidean spaces. Smoothing holds the key for easing the problem of learning and sampling in high dimensions, denoising is needed for recovering the original signal, and TMF ties these together via the score function of noisy data. In this work, we extend this paradigm to the problem of learning and sampling the distribution of binary data on the Boolean hypercube by adopting Bernoulli noise, instead of Gaussian noise, as a smoothing device. We first derive a TMF-like expression for the optimal denoiser for the Hamming loss, where a score function naturally appears. Sampling noisy binary data is then achieved using a Langevin-like sampler which we theoretically analyze for different noise levels. At high Bernoulli noise levels sampling becomes easy, akin to log-concave sampling in Euclidean spaces. In addition, we extend the sequential multi-measurement sampling of Saremi et al. (2024) to the binary setting where we can bring the "effective noise" down by sampling multiple noisy measurements at a fixed noise level, without the need for continuous-time stochastic processes. We validate our formalism and theoretical findings by experiments on synthetic data and binarized images.

In this letter, we study grand-canonical symmetric orbifolds of conformal field theories on the sphere. We show that a consistent operator product expansion can be defined, provided the Hilbert space is taken to be the direct sum of symmetric orbifolds of all degrees. This Hilbert space contains a tower of central operators of conformal dimension zero, one of which represents the central charge of the Virasoro algebra. Our construction thus provides a conformal field theory interpretation of the central charge operator $\mathcal{I}$ in $AdS_3$ string theory.

Exoplanet imaging is a major challenge in astrophysics due to the need for high angular resolution and high contrast. We present a multi-scale statistical model for the nuisance component corrupting multivariate image series at high contrast. Integrated into a learnable architecture, it leverages the physics of the problem and enables the fusion of multiple observations of the same star in a way that is optimal in terms of detection signal-to-noise ratio. Applied to data from the VLT/SPHERE instrument, the method significantly improves the detection sensitivity and the accuracy of astrometric and photometric estimation.