In this article we will discuss a few aspects of the spacetime description of matter and fields. In Section:1 we will discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric continuum. According to this definition, points are not regarded as the basic constituents of a line segment and a line segment is considered to be a fundamental geometric object. This definition is in particular suitable to coordinatize different points on the straight line preserving the order properties of real numbers. Geometrically fundamental nature of line segments are required in physical theories like the string theory. We will discuss the cardinality of rational numbers in the later half of Section:1. We will first discuss what we do in an actual process of counting and define functions well-defined on the set of all positive integers. We will follow an alternate approach that depends on the Hausdorff topology of real numbers to demonstrate that the set of positive rationals can have a greater cardinality than the set of positive integers. This approach is more consistent with an actual act of counting used in statistical mechanics. This article indicates that the axiom of choice is a better technique to prove theorems that use second-countability. This is important for the metrization theorems and physics of spacetime. In Section:2 we will discuss an improved proof of the Poisson's equation. We will show that the self energy of a point charge can be zero in the potential approach to evaluate it. In Section:3 we will discuss a few aspects of the equivalence of the Schwarzschild coordinates and the Kruskal-Szekeres coordinates. In Section:4 we will make a few comments on general physics including the special theory of relativity and hydrodynamics.

Dance serves as both a cultural cornerstone and a medium for personal expression, yet the rapid growth of online dance content has made personalized discovery increasingly difficult. Text-based dance retrieval offers a natural interface for users to search with choreographic intent, but it remains underexplored because dance requires simultaneous reasoning over linguistic semantics, musical rhythm, and full-body motion dynamics. We introduce TD-Data, a large-scale open dataset for text-dance retrieval, containing about 4,000 12-second dance clips, 14.6 hours of motion, 22 genres, and annotations from professional dance experts. On top of this dataset, we propose CustomDancer, a multimodal retrieval framework that aligns text with dance through a CLIP-based text encoder, music and motion encoders, and a music-motion blending module. CustomDancer achieves state-of-the-art performance on TD-Data, reaching 10.23% Recall@1 and improving retrieval quality in both quantitative benchmarks and user preference studies.

Ensuring the safe and efficient operation of Advanced Air Mobility (AAM) in low-altitude airspace requires a reliable, robust, and resilient surveillance system capable of continuously detecting, identifying, and tracking aircraft under both normal and off-nominal conditions. To address this need, this study develops a comprehensive 3R modeling framework, reliability, robustness, and resilience, for the Surveillance for Advanced Air Mobility (SAM) system, with a focus on the optimal design and operation of a multi-type sensor network. Under normal operating conditions, the reliability model determines the baseline sensor types, quantities, and locations required to satisfy surveillance coverage and detection requirements. To address external perturbations, such as adverse weather conditions or sudden increases in AAM traffic demand, the robustness model identifies additional sensor requirements needed to maintain system performance. Furthermore, for surveillance outages caused by primary sensor failures, the resiliency model develops backup sensor deployment and dispatch strategies to provide temporary surveillance coverage, minimize operational disruptions, and support the safe continuation of AAM operations.

We present the results of AGN--host-galaxy decomposition using JWST/NIRCam, HST/ACS, and HST/WFC3 imaging of the North Ecliptic Pole Time Domain Field (NEP-TDF). The light-profiles of 36 NIRCam-selected AGN candidates are modeled for measurement of their point sources, and point source-subtracted host-galaxy emission is used in SED modeling for star formation rate (SFR) estimation. Offsets from the canonical star-forming main sequence (SFMS) show that the host galaxies form two distinct groups distinguished by their star formation: a ``bridge'' between the moderate SFRs of radio sources and low SFRs of X-ray sources, and a cleanly-separated ``branch'' above $Δ\rm SFMS = -1$ whose SFR trends positively with AGN fraction. Branch galaxies include late-type galaxies with X-ray and radio detections and more dominant point sources that are most certainly AGN, while bridge galaxies have predominantly early-type morphologies with weaker point sources that may be due to compact stellar bulges. Both groups show evidence of recent transition between star formation and quiescence, but neither group shows preference for higher or lower stellar mass or redshift, suggesting that star formation in NIRCam-selected AGN-hosts is more strongly determined by AGN activity than by stellar mass.

We present a framework for generating lightcone simulations tailored to the analysis of Stage-IV cosmic shear data using Higher-Order Statistics (HOS). We revisit key design choices from previous simulation campaigns and re-optimize several internal parameters, benchmarking accuracy through changes in $χ^2$ of cosmic shear statistics under survey conditions mimicking 10 years of observations from the Legacy Survey of Space and Time (LSST). We find that discretizing the lightcone uniformly in scale factor yields higher accuracy than commonly adopted schemes such as uniform spacing in redshift or comoving distance. While $N_{\rm part} = 1024^3$ simulation particles (corresponding to a mass resolution of $m_{\rm part} = 2.08\times10^{10}M_\odot$) is sufficient to model two-point statistics up to $\ell = 5000$, we observed significant instabilities on our full suite of HOS as the number of mass shells used in the lightcone construction, $N_{\rm shells}$, is varied. In contrast, simulations with $N_{\rm part} = 2048^3$ particles ($m_{\rm part} = 2.60\times10^{9}M_\odot$) robustly reproduce all statistics considered. In this higher-resolution configuration, $N_{\rm shells}$ can be reduced to $\sim50$ with only minor deviations, no larger than $0.1-0.3σ$ relative to our highest-resolution case ($N_{\rm shells}\sim100$). This has been explicitly verified through a comparison between our fiducial lightcone production mode based on slicing particle snapshots and an exact lightcone mode where individual particle trajectories are solved for at runtime. We further show that the particle density per pixel can be downsampled by a significant amount for $z>1.5$, saving large computational resources with no impact on the resulting statistics. These results guide the design of upcoming simulation campaigns geared towards forward-modeling and emulation-based analyses of Stage-IV data.

Precision measurements of top-quark decays provide powerful probes of physics beyond the Standard Model (SM). While the impact of dimension-6 operators in the SM Effective Field Theory (SMEFT) has been extensively studied, the role of dimension-8 contributions remains largely unexplored, despite their potential importance as experimental precision improves. In this work, we present a combined analysis of dimension-6 and a representative subset of dimension-8 SMEFT effects using the W-boson helicity fractions in top-quark decays. We compute the leading-order contributions of these operators to the top-quark decay width and helicity fractions, and perform one-parameter and selected two-parameter $χ^{2}$ fits to the combined ATLAS and CMS measurements at a reference scale $Λ=1$~TeV. From the fit results, we find that the inclusion of dimension-8 contributions affects the allowed parameter space of several dimension-6 coefficients through non-trivial correlations and degeneracies. Since the leading dimension-8 contributions enter at the same order $\mathcal{O}(Λ^{-4})$ as the squared dimension-6 terms retained in our analysis, this highlights the importance of a consistent treatment of the EFT expansion when interpreting SMEFT constraints.

We investigate the impact of baryonic feedback on two-point and three-point correlation functions (2PCFs and 3PCFs hereafter, respectively) involving galaxy density fields (g) and weak lensing shear fields (G), from simulated photometric catalogs of galaxies. Specifically, we baryonify high-resolution simulation using a baryonic correction model (BCM) and explore the consequences down to sub-arcminute (arcmin) scales, varying two model parameters with the largest impact on our probes: $M_{\rm c}$, which governs the amount of gas expelled beyond the halo boundary, and $θ_{\rm ej}$, which encodes the maximal ejection radius relative to halo boundary. We create lensing maps and galaxy catalogs assuming survey properties of the upcoming Year-10 data for the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), and investigate the impact of baryonic feedback on the observed correlations, including the galaxy--galaxy--shear (ggG) and the galaxy--shear--shear (gGG) 3PCFs, which are measured, for the first time from simulations, with \textsc{TreeCorr}. Focusing on equilateral 3PCFs, we find that small scales are more heavily affected by baryonic effects than the corresponding 2PCFs, by up to 90 percent depending on the probe, redshift and BCM model. The galaxy--galaxy--galaxy (ggg) 3PCF is significantly affected at scales smaller than about 4 arcmin; a similar effect occurs at 10 arcmin for the ggG 3PCF, at 40 arcmin for the gGG 3PCF, and at about a degree for the shear--shear--shear (GGG) 3PCF. These four three-point statistics, which are collectively referred to as the $4\times3$PCFs, can be used at large scales to robustly constrain cosmological parameters. At smaller scales, their enhanced sensitivity to baryonic effects provides valuable leverage for constraining the BCM parameters and supplying informative priors. [Abridged]

We determine the limiting density of the largest sum-free subset of the lattice cube $\{1,2,\ldots,n\}^d$ for all $d$, thus resolving the natural conjecture that it is constructed by two appropriate hyperplane slices.

Altermagnets are an emerging class of collinear antiferromagnets that exhibit unconventional spin-polarised electronic bands, potentially unlocking new functionalities that do not rely on spin-orbit coupling (SOC). Experimental signatures traditionally associated with spin polarisation, like X-ray magnetic circular dichroism (XMCD), are thus being used as a validation of altermagnetism. However, unlike altermagnetic spin-splitting, these responses require SOC and are not invariant under spin-space rotations. This brings into question the extent to which they can be considered direct signatures of altermagnetism. Here, we exploit the g-wave altermagnet $α$-Fe$_{2}$O$_{3}$ to demonstrate that XMCD is governed precisely by the spin-direction-induced symmetry breaking that altermagnetic spin groups are designed to ignore. Strikingly, the XMCD is highly anisotropic and is decoupled from the weak magnetic canting. We show that this anomalous XMCD can be described by on-site Faraday tensors capturing the locally uncompensated spin-orbital anisotropies - a scenario that can be applied to other altermagnets. Leveraging this, we reconstruct complete vectorial maps of nanoscale textures in $α$-Fe$_{2}$O$_{3}$ thin films, including domain walls and topological solitons, which are promising for building future spintronics and magnonics devices.

The crossword-like patterns of tiles in Scrabble form connected graphs of occupied sites on a square lattice. We find the most structureless description that reproduces means and covariances observed in real Scrabble games by adapting a maximum entropy approach to connected graphs. This pairwise model captures the data well, and predicts word-length statistics and geometric features of the Scrabble graphs correctly; in addition, the parameters of this model are interpretable and allow us to understand Scrabble playing strategies. Using this pairwise model, we calculate entropy differences and distinguishability of Scrabble graphs across languages, without having access to the letters on the tiles. Notably, we find that the entropy is predicted better by strategic gameplay -- such as word length on the board -- than lexicon size. Finally, we find that we can use the pairwise model to correctly assign Scrabble graphs to languages, avoiding explicit feature selection and at relatively low computational cost.

It is a well-known theorem of homotopy type theory, originally due to Voevodsky, that function extensionality holds inside any univalent universe. We consider a weaker variant of the univalence axiom, asserting that the wild category formed by the universe is univalent, which we call categorical univalence. We show that categorical univalence does not imply function extensionality by an analysis of Von Glehn's polynomial model construction, which produces models of Martin-Löf type theory that always refute function extensionality. We find in particular that when the base model has a univalent universe, its polynomial model has a universe that is categorically univalent but lacks function extensionality.

We propose a conjectural $q$-analogue of the classical duality for iterated integrals on $\mathbb{P}^{1}$ minus four points, arising from the involutive Möbius transformation which exchanges the four marked points in pairs. To this end, we introduce iterated $q$-integrals with position-dependent $q$-shifts of the parameters and define a functional on admissible words in the six pairwise letters. The conjecture states that this functional is invariant under a natural anti-automorphism of the word algebra. We relate the conjecture to Yamamoto's duality for one-variable multiple $q$-polylogarithms. Finally, we prove the conjecture in several special cases.

Let $p$ be an odd prime. We describe a method to compute the Schur multiplier of finite $p$-groups $G$ of nilpotency class $2$ such that $G/[G,G]$ is isomorphic to direct product of copies of $\mathbb{Z}_{p^s}$ for $s \in \mathbb{N}$, generalizing a method of Blackburn and Evens, who treated the case $s=1$. As an application, we investigate which abelian $p$-groups can occur as the Schur multiplier of a non-abelian $p$-group. We further introduce the notions of $s$-special $p$-groups of rank $k$ generalizing the notion of special $p$-groups of rank $k$. We study the structural properties, compute the Schur multipliers of $s$-special $p$-groups of rank $1$.

We construct a new class of self-similar implosion profiles for the multi-dimensional compressible Euler equations. These profiles are smooth, genuinely non-isentropic, radially/spherically symmetric, and have explicit (closed-form) similarity exponents. We prove that the exact Euler solution corresponding to the ground state implosion profile is stable to radially symmetric perturbations, as a solution to the full nonlinear compressible Euler equations, modulo a one-dimensional compatibility condition on the initial data. For perturbations of the Euler solution corresponding to the ground state implosion profile of a monatomic or diatomic gas, that do not obey any symmetry assumptions, we provide a complete characterization of the set of initial data that yield nonlinear stability.

The cascaded variational quantum eigensolver (CVQE) circumvents the need for iterative communication between the quantum and classical processing units that is necessary in the conventional VQE algorithm. While CVQE offers complete freedom to choose the guiding state as input, not all guiding states suffice for solution accuracy, as well as resource efficiency. Our work presents a process based on trapezoidal-state preparation for selecting guiding states that yield accurate many-electron ground-state solutions with minimal resource consumption. By analyzing the state probability distributions at different stages of the CVQE calculations, we determine the optimal guiding-state parameters for given resource constraints. We demonstrate the process by comparing electronic energies along the minimal-energy path for a prototypical bimolecular reaction, $\mathrm{H}_2 + \mathrm{H}_2^+ \rightarrow \mathrm{H}_3^+ + \mathrm{H}$, using Noisy Intermediate-Scale Quantum (NISQ) computing.

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are observed over many spatial locations. This paper develops a structured estimation procedure for high-dimensional multivariate VAR processes that explicitly incorporates spatial information. We decompose each block transition matrix into a cross-variable dependence coefficient and a spatial transition matrix, and constrain the spatial transition matrices through a pre-specified spatial graph. The resulting estimator is formulated as a weighted $\ell_1$-regularized least-squares problem, where the weights encode spatial proximity or topological similarity and induce stronger shrinkage on spatially implausible interactions. Since the objective function is bi-convex, we estimate the cross-variable dependence matrix and the spatial transition matrices through an alternating convex-search algorithm implemented with ADMM. Under stability and restricted-eigenvalue-type conditions for high-dimensional VAR processes, we establish convergence to a blockwise stationary point in the subgradient sense and derive high-probability estimation error bounds for both components of the model. Simulation studies demonstrate that the proposed estimator accurately recovers sparse transition structures and improves over existing two-step $\ell_1$-regularized methods in support recovery and estimation accuracy. An application to North American climate data illustrates that the method recovers interpretable variable-dependence networks and spatial interaction patterns across different climate regions.

In this paper, we study the long time behavior of solutions of Klein-Gordon-Zakharov system. We show that there exists a solution with special characteristics, which we shall refer to as a dipole solution, that is, there exists a solution $\vec{u}$ such that $$\left\|\vec{u}(t)-\sum_{k=1}^{2}\vec{R}_{k}\right\|_{X} \to 0 \, \, \text{as}\, \, t\to \infty,$$ where $\vec{R}_{k}$ represents a solitary wave for each $k$, with a translation $z_k$ with respect to its position, satisfying that $$|z_1(t)-z_2(t)| \sim 2\log(t)\, \, \text{as} \, \, t\to \infty.$$ Our approach will initially focus on the spectral analysis of the Hamiltonian operator associated with our system. Subsequently, we aim to establish a coercivity estimate that will allow us to derive conditions ensuring the existence of our solution. It is important to note that, in this problem, our objective is to obtain approximate solutions by solving a final data problem. These approximate solutions will then be used, through uniform estimates and compactness results, to derive the desired conclusions via density arguments.

Mixed Reality (MR) aims to blend digital and physical worlds, but the absence of haptic feedback often breaks visual-tactile consistency. We introduce Prop-Chromeleon, a MR system based on generative artificial intelligence (AI) that dynamically transforms everyday objects into adaptive passive haptic props through user-provided text prompts. Our AI pipeline performs generation and anchoring of virtual assets that align with the shape of physical props, allowing us to study how virtual content generation behaves under geometric and prompt-based constraints. We evaluate Prop-Chromeleon's effectiveness through a generation study using varied object shapes and user prompts, combining quantitative shape similarity metrics with qualitative prompt fidelity analysis. Our user study further showcases Prop-Chromeleon's improvements in perceived realism, immersion, and enjoyment compared to static baselines. These results show that shape-aware generation can support both believable haptic interaction and creative engagement in MR.

We have developed Density Functional Tight Binding (DFTB) models for cerium that accurately predict both the electronic band structure and energetic ordering of different allotropes. We show that global optimization of the electronic confining potentials minimize the errors in the predicted Kohn-Sham energies while facilitating determination of a many-body repulsive energy. Our results illustrate the ability of DFTB to accurately reproduce complex f-electron interactions for multiple phases while leveraging minimal Density Functional Theory data.

Dislocation core chemistry in oxides critically influences mechanical behavior and functionality; yet the evolution of core chemistry during the dislocation motion in them has not been directly observed. Here, using SrTiO3 as a model material, we combine aberration-corrected scanning transmission electron microscopy and electron energy-loss spectroscopy with atomic-level molecular dynamics (MD) simulations to correlate the <110>{1-10} dislocation core structure, oxygen vacancy density, charge state, and mobility with each other. We find that the mechanically induced dislocation loops exhibit dissociated cores, whose oxygen vacancy density depends on the gliding distance: short loops are Ti-reduced and oxygen-deficient at the edge dislocation core, whereas longer loops remain close to stoichiometry in both the edge and screw components. MD simulations reveal that kink-assisted edge dislocation glide in SrTiO3 leaves oxygen-deficient trails behind, modulating the oxygen content inside the edge core. These results demonstrate that oxygen-vacancy evolution at the dislocation core intrinsically couples with plasticity in ionic crystals, suggesting a mechanism for oxygen vacancy-dependent dislocation mobility in plastically deformed oxides.

In the fully dynamic maximal matching problem, the goal is to maintain a maximal matching in a graph undergoing an online sequence of edge insertions and deletions. The problem has been studied extensively in the oblivious-adversary setting, where randomized algorithms with polylogarithmic worst-case and constant amortized update time have been known for some time. A major challenge in this area has been designing an algorithm with non-trivial update time against an adaptive adversary. In a recent breakthrough, Bernstein, Bhattacharya, Kiss, and Saranurak (STOC 2025; hereafter, BBKS25) obtained the first algorithms with sublinear update time for this setting: namely, a randomized algorithm with $\tilde{O}(n^{3/4})$ amortized update time, and a deterministic algorithm with $\tilde{O}(n^{8/9})$ amortized update time. Our main result is a deterministic algorithm for fully dynamic maximal matching with amortized update time $n^{1/2+o(1)}$. A powerful tool in dynamic matching is the use of matching sparsifiers: sparse subgraphs that preserve enough information to recover matchings with desired properties. Sparsifiers, such as the EDCS data structure, have been successfully used for approximate maximum matching. For maximal matching, however, this paradigm is not as natural, since maximality must hold with respect to the entire graph. Nevertheless, BBKS25 showed that EDCS can be repurposed as a verification-and-repair mechanism for fully dynamic maximal matching against adaptive adversaries. We introduce a new deterministic framework, referred to as the subgraph system, which, in contrast to EDCS, is purpose-built for verification and maintenance of maximality. It is also designed to allow efficient recursive refinements leading to stronger and stronger parameters, that yield our deterministic algorithm with $n^{1/2+o(1)}$ amortized update time.

We prove the compactness of weighted Sobolev trace operators in outward cuspidal domains by using composition operators on Sobolev spaces. This result allows us to formulate the non-linear Steklov problem in outward cuspidal domains in a correct functional setting and to establish the existence of its non-trivial solution.

Complex contagions describe systems where the probability or rate of contagious transmission is a nonlinear function of the exposure to contagious agents. These models were first studied theoretically but have since been used to capture effects such as nonconformism, social reinforcement or peer pressure in empirical data. However, recent studies have shown that local correlations (e.g., group structure or temporal burstiness) and heterogeneity (e.g., diversity of parameters or covariates) can give the illusion of nonlinear effects even when the dynamics is actually linear. We briefly review these studies to inform a new model and explanation for these effective models of complex contagions. We find global threshold dynamics and superlinear complex contagions even in populations where agents are distributed across social groups described solely by linear or even sublinear contagions. This effect can be understood as a manifestation of Simpson's paradox. Incidence data from heterogeneous groups can look superlinear once averaged over all groups, since the sampling of groups represented at high incidence is biased towards those with stronger local transmission. We then define what we call a Simpson's contagion: a contagion process that looks superlinear when observed over an entire population, but is mechanistically linear or even sublinear in all of its subgroups. By exploring these Simpson's contagions over mathematical case studies, our work contributes to the growing body of literature on the ubiquity of threshold and complex contagions as effective models, and our results stress the pitfall of model selection that ignores correlations and heterogeneity in populations.

Characterizing quantum many-body phase structure is a major goal for quantum simulation. Here, we employ an unsupervised learning approach based on diffusion maps to learn phase transitions in bosonic lattice systems described by Bose-Hubbard type models, which can be realized in ultracold atoms and related quantum simulation platforms. We demonstrate that this approach identifies phase structure across distinct settings without prior knowledge of order parameters or handcrafted observables, including ground-state transitions involving symmetry-protected topological phases and nonequilibrium regimes distinguishing ergodic and many-body localized behavior. Our results indicate that the approach has the potential for direct application to experimentally accessible measurement data for learning quantum phases in current quantum simulators.

Public image diffusion models are now powerful enough that an attacker without the resources to train a tabular-specific generator may repurpose one off the shelf. This study tests that possibility directly. An unmodified Stable Diffusion U-Net is applied to the UCI Adult Income dataset by reshaping each row into a small single-channel pseudo-image. The architecture's inductive bias toward spatial locality makes feature placement a design variable, and several layouts are tested. However, this is only the beginning of the story, as this paper also draws two philosophical distinctions. One separates statistical from perceptual realism: whether synthetic content holds up to a machine's correlation audits or a human's sensory inspection. The other introduces synthetic evidence as a category alongside synthetic media: AI-generated material whose consumer is a machine in a closed evidentiary pipeline rather than a person in an open information system. An attacker succeeds with synthetic evidence by thinking like the machine that will receive it. And the more the attacker succeeds, the more they can induce ground truth drift: the silent reclassification of AI-generated outputs as authentic when reused in pipelines that do not interrogate their provenance.

We study recursive maximum likelihood estimation for stochastic interacting particle systems based on continuous observation of a single particle. In this regime, consistent estimation of the finite-particle log-likelihood is not possible, even in the limit as the number of particles $N\rightarrow\infty$ and the time horizon $t\rightarrow\infty$. We thus seek to optimise the stationary log-likelihood of the limiting mean-field system. We achieve this via a form of stochastic gradient estimate in continuous time, with stochastic gradient estimates computed using the continuous trajectory of the single observed particle, alongside a virtual interacting particle system and a virtual tangent interacting particle system, which are integrated with the online parameter estimate. For fixed numbers of real and virtual particles, we show that the resulting algorithms drive the gradient of a finite-particle surrogate objective to zero as $t\to\infty$. We then prove that, in the iterated limit $t\to\infty$ followed by $N,M\to\infty$, these surrogate gradients converge uniformly to the gradient of the stationary log-likelihood of the limiting mean-field system, yielding convergence to its stationary points. We illustrate the method on several numerical examples, including a model with quadratic confinement and interaction potentials, a model of interacting FitzHugh--Nagumo neurons, and a stochastic Kuramoto model.

We investigate the physical origin and location of high-energy neutrino emission in active galactic nuclei (AGN) using the blazar GB6 J1542+6129 as a case study, testing whether neutrinos are produced in compact regions near the black hole or in parsec-scale jets. This question is central to understanding the conditions under which hadronic processes become efficient in AGN environments. We perform a multimessenger analysis combining ~17 years of Fermi-LAT gamma-ray data, including a 5% adaptively binned light curve and Bayesian block decomposition, with ~14 years of VLBI/MOJAVE observations to derive the Doppler factor evolution of the radio core. These are compared to the temporal properties of a suspected IceCube neutrino flare with a duration of $147^{+110}_{-25}$ days. We find that the suspected neutrino flare precedes both a gamma-ray flare and a pronounced increase in the VLBI core Doppler factor by ~1 year. This delay is consistent with the propagation time of a disturbance from the central engine to the 15GHz radio core. The duration of the post-flare gamma-ray activity is similar to that of the neutrino flare. The broadband gamma-ray spectral energy distributions remain consistent in shape across the full, flare, and post-flare intervals, indicating stable particle acceleration conditions. The temporal ordering favors neutrino production upstream of the VLBI core. GB6 J1542+6129 provides evidence for spatially separated neutrino and gamma-ray/radio emission regions in AGN. The observations are consistent with a disturbance-driven, multi-zone scenario in which neutrinos are produced in a compact, photon-rich region near the central engine, while the same disturbance later enhances Doppler-boosted leptonic emission at the parsec-scale VLBI core. These results demonstrate the power of multimessenger observations in constraining the origin of astrophysical neutrinos.

Let ${\mathcal H}_1$ be a finite dimensional complex Hilbert space. Let $ψ\mapsto Z(ψ)$ be a canonical anti-commutation relations (CAR) field over ${\mathcal H}_1$ acting irreducibly on a Hilbert space ${\mathord{\mathscr K}}$. The $*$-algebra ${\mathscr A}_{{\mathcal H}_1}$ generated by the $Z(ψ)$, $ψ\in {\mathcal H}_1$, is simply all operators on ${\mathscr K}$. However, the CAR field endows ${\mathscr A}_{{\mathcal H}_1}$ with additional structure, and we are concerned with quantum operations whose acting in harmony with this structure. In particular, there is a gauge automorphism group generated by ``second quantizing'' $ψ\mapsto e^{it}ψ$. The fixed point algebra of the gauge group, ${\mathscr G}_{{\mathcal H}_1}$, is a sub-algebra of ${\mathscr A}_{{\mathcal H}_1}$ studied by Araki and Wyss. It contains the density matrices of an important class of states, the gauge invariant Gaussian states, ${\mathfrak S}_{GIG}$. Our focus is on semigroups $\{e^{t{\mathscr L}}\}_{t\geq 0}$ of quantum operations on ${\mathscr A}_{{\mathcal H}_1}$ that map ${\mathfrak S}_{GIG}$ into itself. Each $e^{t{\mathscr L}}$ is one-to-one, and our first main result is a structure theorem forsuch quantum operations on ${\mathscr G}_{{\mathcal H}_1}$ that map ${\mathfrak S}_{GIG}$ into itself. We apply this to study semigroups of quantum operations on ${\mathscr G}_{{\mathcal H}_1}$ that map ${\mathfrak S}_{GIG}$ into itself. Our second main result is a structure theorem showing that they are parameterized by pairs $(G,A)$ where $G$ is a contraction semigroup generator on ${\mathcal H}_1$, and $0 \leq A \leq -G -G^*$. We then show that each of these semigroups has a natural extension to the full CAR algebra ${\mathscr A}_{{\mathcal H}_1}$. Further results are obtained under further assumptions on the pair $(G,A)$.

We develop a theory of completeness for weight structures on stable categories, dual to the theory of complete t-structures. As in the bounded case, we show that complete weight structures are determined by their weight heart, giving rise to a universal construction $A \mapsto K(A)$ that assigns a complete weight category to an additive category and recovers classical examples such as homotopy categories of chain complexes. We also give a general construction of weight structures on presentable stable categories generated by a small set of objects, generalizing a result of Bondarko. This recovers the standard weight structure on spectra and an exotic one related to Anderson duality. We identify their completions with Bousfield--Kan completions arising in Adams-type spectral sequences. To treat naturally occurring examples - such as derived categories of abelian categories and module categories over ring spectra - which are often only partially weight complete, we introduce the notion of weak t-structures. Within this framework, we prove that any stable category equipped with compatible weight and weak t-structures, and satisfying left weight completeness and right t-completeness, can be reconstructed from its heart via a two-step completion process $A \mapsto \widehat{K}(A)$.

We study black hole formation and evaporation in a four-dimensional semiclassical model that preserves diffeomorphism invariance and reproduces the one-loop trace anomaly. Solving the quantum-corrected Einstein equations for the collapse of a spherically symmetric null shell, we follow the formation and evaporation of a black hole with back-reaction included. The semiclassical solutions develop a spacelike thunderbolt singularity that emerges after the apparent horizon has receded and extends far from the black hole where the semiclassical curvature is a priori expected to be parametrically small. This behavior arises from a nonlinear instability of the higher-derivative semiclassical equations and is generic in models with anomaly-induced quantum corrections. The thunderbolt signals a breakdown of semiclassical effective field theory over macroscopic distances and undermines the standard formulation of the black hole information paradox.