We present a 'multiple-pass' data-reduction tool designed for Euclid, based on software developed for the Hubble Space Telescope (HST), which improves the astrometric and photometric precision for faint sources and in crowded fields. In this work, we apply it to Euclid Early Release Observations of the Galactic globular cluster NGC 6397. By combining our new catalogue with archival HST data, separated by a time span of approximately 20 years, we were able to measure high-precision proper motions and investigate the radial variations in the energy equipartition and velocity anisotropy of the cluster. The combination of deep and wide-field observations also allowed us to derive the present-day local mass function of NGC 6397 and to study the radial dependence of mass segregation and binary fraction. Finally, we report the discovery of a subtle under-density of stars in the colour-magnitude diagram of NGC 6397 around a stellar mass of 0.35 M$_\odot$ with a more than 5$σ$ confidence level. This feature is consistent with the Gaia M-dwarf gap discovered in Galactic field stars, but it has never previously been observed in a globular cluster. The gap is caused by the onset of full convection in stellar interiors. We demonstrate that the properties of the gap provide tight constraints on the distance to NGC 6397 and its intrinsic metallicity dispersion, offering a new benchmark for stellar evolution models.

Primordial black holes (PBHs) in the asteroid mass window ($10^{17}-10^{23}\,{\rm g}$) remain viable dark matter candidates and can be captured by stars. We develop the first global framework for the evolution of stars that capture PBHs, combining analytic calculations, stellar evolution models, 3D general-relativistic magnetohydrodynamic simulations, and Monte Carlo population synthesis. We find that the fate of these systems bifurcates: PBHs that form an accretion disk before consuming the host drive explosive disruption, whereas PBHs captured too late or growing too slowly consume the star quietly. Capture is dominated by three-body interactions with planetary or stellar companions. For a solar-type host with a Jupiter analog, inspiral within a main-sequence lifetime requires $M_{\rm BH}^{\rm crit}\gtrsim 10^{22}\,{\rm g}$, while lighter PBHs generally require tighter companions. Once deposited at the center, the PBH grows through inefficient quasi-spherical Bondi accretion; if it reaches the angular-momentum threshold before consuming the host, the inflow circularizes into a disk. Our Monte Carlo calculations yield sizable quiet-consumption and explosive-disruption populations, with final PBH masses $M_{\rm BH}\sim0.01-1\,M_\odot$ and disk-forming PBH spins $a_\ast\approx0.8$. Disk formation is the point of no return: disk winds and relativistic jets of $\sim10^{45}-10^{50}\,{\rm erg\,s^{-1}}$ disrupt the star within minutes. The resulting transients may include a $\sim$day-long UV/blue signal, radio afterglow, and, if the jet escapes, an X-ray-flash/low-luminosity gamma-ray-burst (XRF/llGRB) signal. For an $O(1)$ PBH dark matter fraction and optimistic capture assumptions, the event rate can reach that of llGRBs. The low-mass, high-spin remnants offer a complementary PBH probe and possible source for subsolar BH mergers.

Using the first spectroscopic data release from the Dark Energy Spectroscopic Instrument (DESI DR1), we search for AGN signatures in 1,678,787 low-redshift ($0.001 \le z \le 0.45$) line-emitting galaxies. Based on the [NII]-BPT emission-line ratio diagnostic, we identify AGN in 314,245/1,211,573 (25.9%) high-mass ($\log (M_{\star}/M_{\odot}) > 9.5$) and 9648/467,214 (2.1%) dwarf ($\log (M_{\star}/M_{\odot}) \le 9.5$) galaxies. Among these AGN, 17,949 are broad-line candidates (BL-AGN) with broad H$α$ emission, enabling black hole (BH) mass estimates using single-epoch virial methods. We find that the AGN fraction in line-emitting galaxies increases monotonically with stellar mass, rising from $\sim$1.4% at the low-mass end to $\sim$93.3% at the high-mass end. Using the large BL-AGN sample, we extend the $M_{\rm BH} - M_{\star}$ scaling relation down to $\log (M_{\star}/M_{\odot}) \approx 7.8$ and $\log (M_{\rm BH}/M_{\odot}) \approx 4.4$. In the context of high-redshift overmassive BHs, our results suggest that galaxies and their central BHs may follow two distinct evolutionary pathways across cosmic time. With this paper, we release the EmFit value-added catalog, containing emission-line flux and width measurements for $\sim$7.4 million galaxies, the largest catalog with emission-line decomposition into narrow, broad, and outflow components to date. This work significantly expands upon the early DESI results and provides a statistical sample for probing the galaxy$-$BH connection in the low-mass galaxy regime.

The discovery of a population of massive, ancient quiescent galaxies within the first 2 Gyr of the Universe's history has led to significant tensions with models of galaxy formation. However, these analyses are often based on slit spectroscopy, which typically captures only the center-most region of these galaxies and, crucially, assumes these cores are representative of the entire galaxy. To illustrate the varying stellar populations present throughout these galaxies, we present an analysis of color gradients in four $z>3$ $\log(M_\star/M_\odot)>11$ quiescent galaxies which previous works have argued are in tension with models. Using medium-band photometry from MINERVA JWST observations, we measure resolved photometry in a series of elliptical annuli out to $0.7^{\prime\prime}$ ($\sim4~R_e$). We find negative color gradients in three galaxies, and for the most extreme color gradient ($Δ(U-V)/ΔR=-0.126\pm0.030~{\rm mag~kpc^{-1}}$), we find the stellar mass is 0.1 dex lower when compared to photometry measured within NIRSpec slits. In the limiting case where these color gradients are entirely driven by age, we find lessened tensions with extreme value statistics models out to $z\sim9.5$, though different stellar population modeling choices also contribute significantly. Ultimately, these findings highlight the need for integral field unit spectroscopy. Spatially-resolved spectra can provide the evidence needed to break the age-dust-metallicity degeneracy, and reliably separate the effects of the observed color gradients from the effects of different physical modeling assumptions on the formation histories of these galaxies.

ESA's Ariel Space Mission will characterise the atmospheres of approximately 1000 exoplanets to quantify population-level trends. We present HERMES (HiERarchical Modelling for Exoplanet Science), a multidimensional Bayesian framework that probes population-level correlations across multiple axes of diversity. The specific use case we present is the multidimensional relation between stellar metallicity, planetary mass, and atmospheric metallicity. Starting from the Ariel Mission Candidate Sample (Edwards & Tinetti 2022), we select confirmed planets with available masses and stellar metallicity, inject plausible multidimensional trends and demonstrate successful parameter recovery. Simulated surveys are generated with a variety of leverage and sample size, in the presence of intrinsic astrophysical scatter and measurement noise. By fitting independent Bayesian models to each survey, we confirm that survey leverage remains a reliable predictor of trend precision even in multiple dimensions and in the presence of intrinsic astrophysical scatter. For an Ariel Tier 2 transit survey of at least 400 planets, HERMES robustly recovers the correlation between stellar and planetary metallicity despite intrinsic scatter in planetary abundances as large as 1.2 dex. These results establish HERMES as a practical tool for survey design and science yield forecasting in preparation for Ariel and other surveys probing population-level trends.

The repeated tidal stripping of a star by a supermassive black hole, known as a repeating partial tidal disruption event (rpTDE), can give rise to a transient that rebrightens months to years after the first outburst. Among the rpTDE candidates so far observed, some exhibit dimmer peak luminosities during each successive outburst, which is a trend that has not been reproduced from theoretical models when the star survives more than one encounter with the black hole. Here we suggest that this trend can be recovered if the partially disrupted star is initially (i.e., prior to its first mass-stripping event) rapidly rotating, which is expected if the star was placed on its orbit through the Hills breakup of a tidally locked and tight binary. We test this hypothesis with hydrodynamical simulations of high-mass ($\geqslant 1 M_{\odot}$) main sequence stars repeatedly partially disrupted by a $10^6 M_{\odot}$ black hole, and demonstrate that successively dimmer outbursts are indeed recovered for high (tens of percent breakup) and prograde (i.e., aligned with the orbital angular momentum) stellar spins. Our results provide strong indirect evidence for the operation of the Hills mechanism in seeding the stars in rpTDEs.

Gamma-ray burst (GRB) afterglows are thought to arise when relativistic ejecta launched by a compact central engine drive a blast wave into the surrounding circumburst medium, producing broadband synchrotron emission. We present a rigorous assessment, based on high-resolution special relativistic hydrodynamics simulations, of a widely adopted `two-zone model' for approximating the dynamics of the early afterglow phase. Before the onset of the Blandford-McKee (BMK) self-similar solution, the outflow generally produces two emission components, associated with the forward-shocked circumburst medium and the reverse-shocked ejecta. The subsequent evolution depends on whether the reverse shock significantly decelerates the ejecta as it crosses the shell, separating the so-called relativistic and Newtonian reverse shock regimes. We show that when the reverse shock is Newtonian, it crosses the ejecta shell long before BMK self-similarity is established, leaving a prolonged interval that can span $\sim$ hours in observer time in which the true hydrodynamic evolution is not captured by standard semi-analytic prescriptions. We demonstrate that this mismatch can substantially overpredict the reverse-shock emission from radio through ultraviolet frequencies, or overpredict the forward-shock emission at X-ray frequencies, depending on how the transition away from the two-zone model is prescribed.

We present a deep, high-resolution CO(4-3) IRAM-NOEMA observation of a main sequence, barred, spiral galaxy at $z\approx1.12$, with an on-source integration time of $\approx37$ hours and a beam FWHM of $\approx0.\!\!^{\prime\prime}3$. We use the molecular gas data in conjunction with the available deep multi-band JWST and HST imaging, covering restframe UV to near-IR wavelengths, to quantitatively study the gas flows in the disk plane of this cosmic noon barred spiral. We find that this target is a massive ($\log(M_{\rm{baryons}}/M_\odot)\approx10.96$), baryon-dominated ($f_{\rm{dm}}(<R_e)=u^2_{\rm{circ,dm}}(R_e)/u^2_{\rm{circ}}(R_e)\sim4\%$), gas-rich ($f_{\rm{gas}}=M_{\rm{gas}}/(M_{\rm{\star}}+M_{\rm{gas}})\approx40\%$) disk, hosting a long ($a_{\rm{bar}}\approx4.2$ kpc), strong ($Q_{\rm{b}}\approx0.37$), and fast ($\mathcal{R}=R_{\rm{CR}}/a_{\rm{bar}}\approx1.05$) bar, which rotates at an angular speed of $Ω_{\rm{pattern}}\approx$ 50 km/s/kpc. This bar is driving molecular gas inflows with a net inflow rate of $\dot{M}\sim30$ $M_\odot$/yr, based on three estimates, which is of the same order as the galaxy-integrated star formation rate ($\rm{SFR}\approx36$ $M_\odot$/yr). We additionally identify evidence of a well-defined dust lane shock at the northwestern side of the bar, with gas motions parallel to this feature, in agreement with expectations for an established bar-driven flow. Our study highlights the possible role of bars as key drivers of galaxy evolution for a significant fraction of cosmic noon galaxies, offering a detailed picture of well-defined, bar-driven inflows in a high-$z$ barred spiral.

We present the discovery of two disky titans in the first data release of the Euclid satellite. These sources are massive ($M>10^{11} M_\odot$) star-forming (SFR $\sim 20 M_\odot$/yr) discs located in strong over-densities at intermediate redshift ($z\sim 0.75$). They represent an small fraction of the massive galaxies in over-dense regions (just four candidates in more than 20 deg2 analysed in this study), and their existence is puzzling considering the abundance of passive and bulge-dominated sources commonly found at the centre of groups and clusters at low redshift. Firstly, our analysis shows that these objects are located in massive groups ($M_h\sim 10^{13.8} M_\odot$), where rapid accretion of cold gas should be prevented from the formation of a static hot halo. Despite this, a millimetre follow-up with NOEMA shows significant cold gas reservoirs $M_{h_2} \sim 10^{10.3} M_\odot$) within these sources. Secondly, our morphological analysis shows the presence of a massive and passive bulge in these galaxies, which is expected to stabilise the disc against fragmentation thereby suppressing further star formation. However, these sources lie on the Schmidt-Kennicutt relation or even slightly above. Building on these observations, we propose a scenario where these disky titans are the product of a merger-induced rejuvenation episode, in which the most massive galaxy of a group accretes cold gas from another member and briefly restarts star-formation. Such scenario is supported by a comparison with the TNG300 simulation and easily explains the surviving of star-formation activity in massive galaxies in over-dense environments as temporary stages in a more complex evolution. More in general, our study showcases the ability of Euclid to find rare objects thanks to the unprecedented statistics offered by its surveys and the scientific potential residing in the synergy between Euclid and other facilities observing at longer wavelengths.

The rapid accumulation of massive dust reservoirs in the early Universe remains a major challenge in astrophysics. While core-collapse supernovae can inject large dust grains ($a \gtrsim 0.1\,μ{\rm m}$) on short timescales, explaining the total dust budgets in the early Universe likely requires efficient grain growth in the interstellar medium (ISM). Such growth depends critically on an abundant population of small grains, which maximize the surface area available for accretion and may be generated by rapid dust-processing or dust-formation channels. Here, we report the discovery of a QSO UDS-27023 at $z=4.556\pm0.003$, identified using JWST/NIRSpec spectroscopy. By quantitatively comparing the spectra to QSO composite templates, we find that UDS-27023 displays an exceptionally steep far-UV extinction curve ($A_{1500}/A_V \approx 8$) but notably lacks the 2175 Angstrom bump, indicating a dominance of small silicate dust grains. We interpret this phenomenology as evidence for active small-grain production and processing in the QSO environment. Mechanical shattering of pre-existing large grains by QSO-driven shocks and outflows provides one natural pathway, while in-situ condensation of silicate grains inside dense QSO-driven winds may offer an additional route. Such a population of steep-extinction QSOs (SEQs) may therefore reveal a short-lived phase in which luminous AGN generate, process, and redistribute small grains, potentially facilitating rapid ISM grain growth and enriching the circumgalactic medium.

Asteroids preserve the solar system's earliest history and pose real threats to Earth. Strengthening the UK's capabilities to detect, track, and characterise Near-Earth Objects (NEOs) is vital for national security, world-leading planetary science, and future space resource opportunities. The UK has been an influential contributor to planetary defence, from establishing the UK NEO Task Force in 2000 to active roles in the International Asteroid Warning Network (IAWN), the Space Mission Planning Advisory Group (SMPAG), and the development of the National Space Operations Centre (NSpOC). UK scientists contribute to major international asteroid missions including NASA's OSIRIS-REx, DART, Lucy, and Psyche; ESA's Hera and RAMSES; and JAXA's Hayabusa2 and MMX. However, the UK currently lacks dedicated funding streams to deliver asteroid missions. Ground-based observations of asteroids cannot definitively determine the physical characteristics of these objects, which are crucial for impact-risk assessment, deflection strategy, and resource evaluation. This white paper proposes UK leadership in autonomous, low-cost asteroid-rendezvous missions, leveraging technologies developed through the UKRI-funded REMORA programme. We outline four priorities: (1) strengthen NEO detection capabilities; (2) reinforce UK participation in international planetary defence missions; (3) develop autonomous rendezvous and in-situ characterisation technologies; and (4) enable the future space resource economy through targeted asteroid exploration. Together, these actions position the UK to lead rapid, affordable deep-space missions and secure a long-term strategic advantage.

Wideband radio interferometers increasingly rely on analog quadrature hybrids to synthesize circular polarization from linear feeds. These systems are typically calibrated under the assumption that instrumental polarization leakage can be represented as a static complex offset, independent of parallactic angle. In this work, we demonstrate that this assumption breaks down in the presence of realistic hybrid imperfections. We show that amplitude and phase errors in the hybrid $\mathbf{H}(ν)$ introduce a non-commutative interaction with parallactic rotation $\mathbf{R}(χ)$, such that [$\mathbf{H}(ν)\mathbf{R}(χ) \neq \mathbf{R}(χ)\mathbf{H}(ν)$] leading to a time-dependent effective leakage term that rotates in the Stokes $(Q,U)$ plane. This effect causes systematic distortions in polarization angle and introduces frequency-dependent biases that can mimic or corrupt Faraday rotation measurements. We derive a first-order analytic model for this leakage and demonstrate that it manifests as a deterministic, geometrically modulated error proportional to total intensity. To mitigate this effect, we introduce a Static Offset Pre-correction (SOP) method that operates in the antenna frame, inverting the hybrid response prior to parallactic de-rotation. Unlike conventional calibration approaches, SOP removes the non-commutative error in the Jones domain, preventing its projection into the sky frame. Our results show that hybrid-induced leakage is not merely a calibration artifact but a fundamental systematic error that must be addressed to achieve high-fidelity wideband polarimetry.

We test whether compact objects in the so called mass gap ($2.5 < M_{\rm max}/M_\odot < 5.0$) can be hybrid stars. Using a generic hybrid equation of state with a first-order deconfinement transition, we map the allowed parameter space in a Seidov-type diagram and confront it with modern mass--radius constraints. We find that mass-gap hybrid stars require an extremely early onset of deconfinement and very stiff quark matter. The Bayesian analysis, however, favors equations of state with deconfinement at typical neutron-star masses around $1.4\,M_\odot$ with mass-twin stars that, if confirmed, would rule out hybrid stars as candidates for observed mass-gap compact objects.

We present a reduced dimension theoretical framework for studying quantum field theories at finite density, providing a tractable model for investigating non-Fermi liquid (NFL) behavior near quantum phase transitions. Our approach departs from the standard paradigm by placing bosons and fermions in different spatial dimensions: bosonic fields reside in a $(d+1)$-dimensional bulk, while fermionic fields are confined on a $d$-dimensional boundary. This dimensional separation significantly simplifies the renormalization group (RG) analysis of gapless boson-fermion coupling. We demonstrate that the tree-level boson exchange contributions, which typically exhibit logarithmic divergences, become finite in our reduced-dimension scheme. Furthermore, the $\log^2$ and $\log^3$ divergences that characterize 1-loop four-fermion interactions in conventional treatments are reduced to logarithmic divergences within this framework, substantially improving the convergence properties of the perturbative expansion and allowing controlled theoretical analysis of NFL physics.

Although cosmic acceleration is well established, its physical origin remains contentious. Most explanations invoke either a non-zero vacuum energy, i.e. a cosmological constant, or new fields. We propose instead a mechanism arising purely from quantum mechanics, without additional constants or local sources. The key point is that quantum theory permits both initial and final boundary conditions on a state, here the wave function of the universe. Pre- and post-selected systems are familiar in laboratory quantum mechanics; we extend the idea to minisuperspace quantum cosmology. As a warm-up, we show that a free non-relativistic particle, initially in a semiclassical wave packet and conditioned on a final quantum state, can have an intermediate peak which accelerates even though the Hamiltonian is free. A semiclassical observer would infer a contrived classical force. We then implement the analogous construction in quantum cosmology using connection variables and unimodular time. A forward semiclassical packet, taken for simplicity to describe pure radiation, is post-selected by a normalizable Chern-Simons soliton. The resulting two-boundary amplitude has a peak which leaves the radiation trajectory and enters an accelerating regime, while the forward Hamiltonian has $Λ=0$. A classical model can mimic this trajectory only by introducing a contrived effective component: near the transition it resembles $w\simeq -1$, but when extrapolated it evolves towards strongly phantom behaviour, $w<-1$. The acceleration is therefore more naturally interpreted as a quantum boundary-condition effect than as a local classical source. We also discuss why the Chern-Simons soliton is a clean final state, the small overlap between initial and final states, and possible tell-tale signatures.

Recent advances in Automatic Speech Recognition (ASR) and Large Language Models (LLMs) have significantly improved speech understanding capabilities. However, multi-speaker speech transcription remains challenging task, constrained by highly similar speaker voices, rapid turn-taking transitions, overlapping utterances and inaccurate speaker boundary segmentation. These challenges become particularly pronounced in real-world conversational audio, where speaker dynamics and acoustic conditions are highly variable. This technical report presents SoulX-Transcriber, a unified multi-speaker transcription system that jointly models speaker diarization (SD) and ASR within an LLM-based framework. SoulX-Transcriber adopts a two-stage training strategy to improve both speaker discrimination and transcription robustness. In the first stage, speaker-aware multi-task continuous pre-training enhances speaker representation learning and boundary perception. In the second stage, supervised fine-tuning further optimizes the model for accurate end-to-end speaker-attributed transcription under complex multi-speaker conditions. SoulX-Transcriber delivers strong performance and robustness across multiple public benchmarks, including AliMeeting, AISHELL-4, and AMI, while maintaining high adaptability to multi-domain scenarios.

Possible violations of the equivalence principle are investigated within the framework of metric-affine gravity and their connection to finite-temperature effects are highlighted. Thermal corrections to particle dynamics, originally derived in a quantum-field-theory setting, can be evaluated in a purely Riemannian framework and lead to a shift in the gravitational-to-inertial mass ratio. We show that the ensuing departure from universality of free fall can be also formulated in metric-affine gravity, where the presence of the non-metricity tensor modifies the Newtonian law in a way that closely parallels the finite-temperature scenario. Furthermore, we introduce a generalized Fermi-Walker derivative adapted to non-Riemannian contexts, which naturally reveals that no orthonormal tetrad can be propagated along an observer worldline. Although metric-affine gravity admits a pointwise realization of the Einstein equivalence principle in its gauge-theoretic, elementary-matter form, the new operator offers a direct geometric signature that this principle, in its modern formulation, is not retained in general. Potential tests of the analyzed effects are also discussed.

Continuous-variable quantum key distribution (CV-QKD) requires highly efficient reconciliation techniques to operate at low signal-to-noise ratios and long distances. Multidimensional reconciliation addresses this challenge by transforming the physical Gaussian quantum channel into a virtual binary-input additive white Gaussian noise (BIAWGN) channel, enabling the use of modern errorcorrecting codes. In this work, we review the principles of multidimensional reconciliation, with a particular focus on high-dimensional constructions beyond the algebraic dimensions 1, 2, 4, 8. We describe the construction of the virtual channel, discuss practical coding schemes for reverse reconciliation, and analyse their integration with linear error-correcting codes. We also present an opensource simulation framework, HDirac, implementing multidimensional reconciliation for arbitrary dimensions, and use it to evaluate state-of-the-art LDPC codes. The results highlight key trade-offs between dimension, reconciliation efficiency, and frame error rate, providing practical guidance for CV-QKD system design.

Let $n$ be an integer not equal to $-2$, $0$ or $2$. We consider the unit equation $\varepsilon + δ= n$ in units $\varepsilon, δ$ of cubic fields. We show that this equation has no solutions for 100% of cubic fields, when ordered by discriminant. This is consistent with a recent conjecture of the authors.

This paper presents the Domain-Agnostic Incremental Learning for Audio Classification Task of the DCASE 2026 Challenge. Incremental learning refers to sequentially learning new tasks with the same system while maintaining its knowledge and performance on the previously learned task. Domain-incremental learning for sound classification refers to learning the same sound classes but in different acoustic domains, and was formalized as a data challenge for the first time in DCASE 2026. Participants will train a system to learn ten sound classes in three different domains, with learning at each incremental task not having access to previous task data. Submitted systems will be ranked by the overall average accuracy calculated over the three domains. During the development stage, the provided baseline system obtains a modest performance of 52.5\% accuracy over the last two domains, mostly due to erroneous inference of the domain for the test sample.

Identifying minimum-energy structures of lattice proteins is a challenging discrete optimization problem. Quantum approaches such as analog quantum annealing and the gate-based quantum approximate optimization algorithm (QAOA) can address this problem after mapping it to a binary representation, which typically involves introducing penalty terms to enforce valid chain configurations. However, in this and many related problems, the use of quadratic penalty terms can be avoided by restricting the search space to independent sets in a conflict graph and using a QAOA mixer designed for the maximum independent set problem. In this work, we implement and explore this QAOA variant for lattice protein folding. Here, the objective function consists solely of the protein energy together with a simple linear bias term, without quadratic penalties. We validate this approach through classical simulations of the quantum circuits for lattice proteins of lengths $N=4$ and $N=6$. To explore larger systems, we further introduce a heuristic iterative local-search scheme, with which we successfully fold lattice proteins with lengths up to $N=14$ using local subgraphs with at most 26 qubits.

This paper investigates the secrecy sum rate (SSR) of rate-splitting multiple access (RSMA)-based visible light communication (VLC) systems considering internal eavesdropping, where legitimate users may intercept private data intended for others. We formulate an optimization problem to maximize the SSR of the system, which is inherently non-convex due to the complex coupling of the objective function and constraints. To this end, two different approaches based on the convex-concave procedure (CCCP) and semidefinite relaxation (SDR) are leveraged to solve the non-convex parameterized problem. A central focus of this work is the investigation of channel similarity (CS), which serves as a metric for quantifying spatial correlation, and its impact on SSR performance. To mitigate the performance degradation caused by high spatial correlation, we propose a channel similarity reduction (CSR) clustering strategy that proactively minimizes CS to restore the system's degrees of freedom (DoF). Numerical results are provided to demonstrate the performance of the two proposed algorithms under various levels of CS. More importantly, the findings reveal that our proposed CSR-clustering strategy significantly outperforms existing baselines, effectively overcoming the secrecy performance ceiling caused by high spatial correlation.

Diagnosing Quality-of-Experience (QoE) degradations in operational Radio Access Networks (RANs) is a critical but notoriously complex task, traditionally requiring labor-intensive expert analysis over high-dimensional, cross-layer telemetry. While Large Language Models (LLMs) offer unprecedented reasoning capabilities, they are fundamentally unsuited for raw RANs troubleshooting: they fail at numeric time-series analysis, hallucinate protocol-violating causal links, and lack the stateful rigor required for multi-step fault localization. To bridge this gap, we present QoEReasoner, an end-to-end, LLM-driven agentic system designed for automated and explainable QoE diagnosis. QoEReasoner tames the inherent unpredictability of LLMs by grounding their reasoning in the physical realities of the network. It employs deterministic tools to reliably translate raw numeric KPIs into structured evidence, enforces protocol-consistent fault propagation through a domain-specific Knowledge Base, and leverages a Historical Bank of expert-validated cases to guide hypothesis generation. A stateful central planner orchestrates this closed-loop process across anomaly detection, causal tracing, and root-cause localization. Evaluations on real-world operational RANs datasets demonstrate that QoEReasoner outperforms strong baselines by 18\%-40\% in accuracy across multiple diagnostic tasks. Furthermore, it reduces diagnostic time from approximately 30 minutes of manual expert analysis to just 3 minutes per session, delivering highly interpretable, expert-grade reports while remaining robust across diverse LLM backbones.

In our previous work, we generalized the concept of Galois points for irreducible plane curves to the case of reduced plane curves. We also introduced the concept of simultaneous Galois points, which is an equivalent concept to Galois points, and studied their number when the irreducible components are nonsingular. In this paper, we consider the remaining cases where the irreducible components are of degree $d=2$ or $3$. For the case of $d=2$, we establish a generalized version of the theorem in our previous paper. For the case of $d=3$, we classify simultaneous Galois points into the first and second kinds. We give a necessary condition for the former and provide examples for the latter.

We report an experiment in autoformalisation of Gödel's second incompleteness theorem in Agda using Claude. The theorem is formalised for Church's Basic Recursive Arithmetic, following the proof outline given in Guard's 1963 lecture notes. The entire Agda development, comprising approximately 50,000 lines and containing no postulates, was produced through interaction with Claude; the author did not write any Agda code. Beyond the formalisation itself, the project provides a case study of the strengths and limitations of current large language models in mathematics. An initial autonomous attempt based on a paper of Rose failed because of a false Lemma; the resulting formal development produced by Claude established a statement superficially resembling Gödel's theorem but mathematically unrelated to it. This failure was traced to an insufficient specification of the internal provability predicate, illustrating how an LLM may reason correctly from an incorrect formal specification. The final development follows Guard's proof and required the reconstruction of several implicit mathematical arguments, including the role of the internal numeral-encoding operation and the specification of substitution. The resulting formalisation clarifies a number of details left implicit in the original presentation and provides a fully machine-checked proof of Gödel's second incompleteness theorem for Basic Recursive Arithmetic.

We present the first machine-checked correctness proof of the OpenZeppelin reentrancy-guard pattern against a Lean 4 state-machine model of production-deployed Solidity source. All thirteen theorems are machine-checked with zero sorry, zero user-introduced axioms, and an axiom footprint bounded by [propext] (a standard mathlib4 axiom), gated under continuous integration. Smart contract reentrancy has caused over US$500M in documented losses since 2016, with the DAO 2016 attack draining ~3.6M ETH and forcing the hard fork that split Ethereum. The OpenZeppelin ReentrancyGuard pattern is the de facto defense across production DeFi, yet no prior work has established its discriminating power: that the guard blocks attacks on vulnerable instances, preserves correct execution for non-attacking transactions, and distinguishes adjacent safe and vulnerable variants. Prior efforts formalized either guard correctness on toy contracts or attack feasibility on isolated instances - not both directions plus boundary cases against production source. We verify three production instantiations - DAO 2016, Compound v2, and Aave V3 flashLoan - plus a minimal-diff mutant of Aave V3's flashLoan (flashLoanVulnerable) isolating one security-critical difference, via mutation testing. The tridirectional structure pairs (a) attack reproduction of the DAO 2016 pattern, (b) a correctness proof for Compound v2, and (c) a boundary-case proof distinguishing Aave V3's CEI-correct flashLoan from the mutant. A capstone meta-theorem composes the three under a no-retrofit discipline, demonstrated at the first cross-protocol stress test (Compound v2 to Aave V3); broader-family portability is future work. Full Lean 4 source, CI config and reproduction commands are at https://github.com/rayiskander2406/qanary-contracts, reproducible at v1.6-phase7-closure (substrate: v1.3-layer6-closure).

This study evaluates the pedagogical viability of LLM-generated English as a Foreign Language (EFL) learning content. Utilising log data from Japanese junior high school students practicing on a grammar drilling application, we analysed how different question modalities impact student performance and whether theoretical localised CEFR difficulty tiers accurately predict empirical task difficulty. Results reveal a clear performance hierarchy: multiple-choice questions carried the lowest cognitive load, cloze tasks posed the greatest barrier to active recall, and drag-and-drop exercises incurred the heaviest time penalties. Furthermore, learner data validated the CEFR-J grammar framework, showing a steady decline in accuracy and increased response times as proficiency levels advanced. These findings demonstrate that LLMs can successfully generate learning content, while highlighting the need for developers to strategically sequence question modalities to transition learners from passive recognition to active linguistic production.

We present a non-convergence theory for probabilistic direct search, a randomized derivative-free optimization method, where non-convergence means the failure to produce iterates that achieve stationarity asymptotically. The motivation is to understand whether the submartingale-like assumption in the existing convergence theory is essential or merely an artifact of the analysis techniques. For convex objectives, we prove that the probability of non-convergence is positive, provided that the polling directions satisfy a probabilistic ascent condition that is essentially the opposite of the submartingale-like convergence condition. Furthermore, we establish a lower bound for the non-convergence probability. For the typical implementation of this method, where each iteration draws a fixed number of random polling directions independently and uniformly from the unit sphere, our theory implies that the method is not globally convergent if the number of directions is below the threshold specified in the convergence theory, and the submartingale-like assumption is confirmed to be essential for convergence. Our theory is obtained by examining two random series that control the distance from any iterate to the starting point and estimating the probability for these series to stay below certain bounds.

Since the discovery of new kinds of celestial bodies known as $dark~comets$, scientists have speculated about their ontology. A curious hybrid of comet and asteroid, these objects show significant non-gravitational accelerations (NGAs) yet exhibit absolutely no signs of cometary outgassing in the form of a coma or tail. The planned rendezvous of the Hayabusa2 spacecraft with 1998 KY$_{26}$ in July 2031 elevates the question of this so-called dark comet's nature beyond a purely research exercise, as the true nature of the object may have practical implications for the scientific return of the mission. This study examines the hypothesis that 1998 KY$_{26}$ may be of technogenic origin, in fact a relic of a historical Russian mission to Mars, the Phobos 1 probe, which suffered a failure 2 months after the launch in July 1988, due to upload of a faulty command. We find that two propulsive DeltaVs combined at 1.9 km/s, the first just after loss of mission and the second in May 1996, allow the orbits and phases of the two bodies to align, with an arbitrarily low $Mahalanobis~distance$ using the covariance of the dark comet in 6D phase space. There is also evidence that 1.9 km/s was within the performance envelope of Phobos 1, which had a powerful nitric acid and amine-based autonomous thruster for Mars Orbital Insertion (MOI).

In recent years, there has been a renewed interest in the search for low density minimizer schemes. These schemes take a window of $w$ consecutive $k$-mers, and sample one of them: the smallest under some specific order. Schemes such as the mod-minimizer provide a low density (fraction of sampled $k$-mers) when $k \gg w$, while schemes such as the greedy minimizer work well for explicit small parameters roughly in the regime $k \leq 2w$, for $k$ and $w$ up to $15$ or so. When $k < \log_σw$ is very small, minimizer schemes cannot do well, and more general sampling schemes are needed that can be richer than just comparing $k$-mers. Bidirectional-string anchors (bd-anchors) form one such scheme. Inspired by bd-anchors, we introduce the smallest unique substring or SUS-anchor: Given a window, this considers all suffixes that do not occur as a substring elsewhere in the window. It then samples the start position of the smallest suffix according to the new anti-lexicographic order that minimizes the first character and maximizes the remaining characters. We give a linear-time and $O(w)$ space streaming algorithm to compute all SUS-anchors of a string. For alphabet size $σ=4$ and $k=1$, the anti-lexicographic SUS-anchor empirically has density $<1\%$ away from the density lower bound, significantly improving over bd-anchors that are often $>15\%$ above it. For alphabet size $σ=2$, the density is at most $10\%$ above the lower bound, which again improves over the $>50\%$ overhead of bd-anchors.