Dissipatively stabilized cat qubits are promising for fault-tolerant quantum information processing, yet their non-Hermitian (NH) spectral topology remains largely unexplored. We uncover rich Liouvillian exceptional structures in a cat-qubit mode stabilized by two-photon drive (TPD) and engineered two-photon loss, in the presence of single-photon drive (SPD) and single-photon loss. In the parameter space spanned by SPD strength and detuning, we identify both second- and third-order Liouvillian exceptional points (LEP2s and LEP3s). Remarkably, we show that the phase $θ$ of TPD provides coherent control over these exceptional points: the LEP3 diverges and vanishes at $θ=π/2$, while remaining stable and tunable elsewhere. We introduce a topological invariant based on the winding number of a resultant vector, which robustly identifies LEP3s with unit topological charge. Full master-equation simulations confirm that the system dynamics remains confined to the logical subspace with near-unity fidelity. Our results bridge dissipative stabilization, phase-coherent control, and NH topology, demonstrating controllable higher-order LEPs in open quantum systems.

We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes, eight GABAergic interneuron classes), forty-seven compartments, multi-rule plasticity (recurrent Hebb, BCM anti-saturation, mossy-fiber short-term, endocannabinoid iLTD, burst-gated Hebb), and a bimodal cholinergic encoding/consolidation cycle. Evaluated on pattern completion across auto-associative, associative, and temporal regimes, and on a controlled inhibitory-proportion manipulation at $N{=}256$, the full architecture exhibits \emph{three qualitative signatures absent from a minimal Hopfield baseline}: (i)~multi-attractor cross-seed behaviour at $K{=}5$ with biologically realistic inhibitory proportions, where two of five seeds converge to positive attractors with margin ${+}0.10{-}0.22$ (Cohen's $d{=}0.71$, one-sided $p{=}0.08$); (ii)~target-selective associative recall in paired $(A, B)$ memory at $K{\geq}5$, where the full model retrieves $B$ from a partial cue of $A$ while the minimal model echoes $A$ (Pearson margin $Δ{=}{+}0.163$ at $K{=}5$); (iii)~reduced cross-seed variance of the full model below the minimal baseline under clean upstream, with ratios $1.0{-}3.0$. These three signatures are architecture-specific: they appear consistently across independent regimes and are absent from the minimal control.

Orientation and relaxation dynamics of rod-like colloids under flow govern the optical and mechanical properties of many emerging soft materials. In polydisperse suspensions, particles of different lengths exhibit distinct rotational diffusion timescales, yet how this polydispersity influences relaxation following flow cessation remains unclear. In particular, it is not well understood how the pre-shear rate determines the subsequent orientation relaxation dynamics. To address this question, we performed simple shear on dilute cellulose nanocrystal (CNC) suspensions in a narrow-gap Taylor-Couette cell and measured birefringence relaxation after flow cessation using high-speed polarization imaging. To interpret the experiments, we formulated a polydisperse Fokker-Planck model parameterized by the measured length distribution. As a result, the average orientation relaxation time systematically decreases with increasing pre-shear rate. Moreover, when organized by the Péclet number based on the rotational diffusion coefficient of the weighted average rod length, the data agree well with the theory over a wide range of shear rates. This trend arises because the rod sub-population contributing most strongly to the orientation shifts from longer rods to shorter rods as the pre-shear rate increases, showing that the flow history governs the orientation relaxation dynamics. In polydisperse systems, the orientation relaxation time is no longer a material-specific constant but is determined by both the flow conditions and the polydispersity. This study provides a quantitative framework for understanding orientation dynamics in polydisperse rod suspensions and for interpreting rheo-optical measurements.

Stellar binaries may form through several formation pathways, including disk or core fragmentation. Their spin-orbit angles are a signature of formation, although individual measurements for visual binaries are limited and broad. A seminal work by A. Hale (1994) found that visual binaries with separations $\lesssim 30$ AU tend to be more aligned, which laid the groundwork for binary formation theories. However, A. B. Justesen & S. Albrecht (2020) found that underestimated stellar radii lead to inaccurate spin-orbit angles and that KS statistics do not provide meaningful population-level constraints even with updated radii. Using a hierarchical Bayesian model to reanalyze their dataset, we find evidence with a Bayes factor of 12 for two subpopulations of spin-orbit angles separated by a $\sim 31-38$ AU cutoff. Binaries inside (outside) the cutoff are more (less) aligned, consistent with a Fisher distribution with $κ=48$ ($κ=6$). We also find possible indications of a secondary cutoff at $\sim 10-17$ AU, although more data is required to resolve this prediction. These cutoffs may mark transitions between formation pathways: closer-in binaries tend to form aligned in a shared protostellar disk, while wider binaries tend to form less aligned through turbulent fragmentation.

Transient, star-like point sources that appear and vanish over short timescales are described in astronomical images prior to launch of Sputnik. We have reported that transient numbers diminish significantly in Earth's shadow (shadow deficit) and are more likely within (plus/minus) one day of nuclear testing (nuclear window). These findings remain debated with some arguing that transients identified via existing automated pipelines are simply plate defects. Therefore, we use machine learning (ML) to enhance transient identification accuracy and validate the phenomenon. The model was trained against 250 transient image pairs taken 30 minutes apart that were classified as real versus plate defect by expert visual review; the model demonstrated good discrimination (out-of-fold AUC$=$0.81; sensitivity$=$0.71, specificity$=$0.71). After deployment in a dataset of 107,875 previously-identified transients, the model assigned each a probability of being real. After controlling for ML-identified artifacts, transient counts were significantly elevated for dates within a nuclear window (p$=$.024); transients with the highest probability of being real were more likely to occur within a nuclear window (p$<$.0001). The shadow deficit was significant (p$<$.0001) and largest in the highest probability transients relative to lower probability transients (p$=$.003). Results strongly support existence of an unrecognized population of transient objects in historical astronomical plates warranting further study.

Formal verification of masking in post-quantum cryptographic (PQC) hardware relies on SMT solvers over finite domains. Our prior work established structural dependency analysis at scale [1] and quantified the security margin of partial NTT masking [2]. QANARY, our structural dependency analysis framework, verified 1.17 million cells across 30 modules of the Adams Bridge ML-DSA/ML-KEM accelerator [3, 4], but its core soundness result (Theorem 3.9.1) was machine-checked only at $q = 5$ via $2^{25}$ Boolean wire functions. This left portability to ML-KEM ($q = 3{,}329$, FIPS 203 [5]) and ML-DSA ($q = 8{,}380{,}417$, FIPS 204 [6]) as an open gap. NIST IR 8547 [7] (March 2025) motivates closing such gaps. We present the first machine-checked universal proof of the $r$-free sub-theorem of Theorem 3.9.1: for every $q > 0$, every wire function, and every pair of secrets, value-independence implies identical marginal distributions. The proof, in Lean 4 [8] with Mathlib [9], requires five lines versus $2^{25}$ finite evaluations. It is sorry-free, reducing the trusted base from {Z3 [10], CVC5 [11], Python} to the Lean 4 kernel. We provide nine theorems (T1--T6, T1', T3') covering reparametrization, bijectivity, overflow bounds, RNG bias, and a universal non-tightness counterexample for all $q \geq 2$. The results establish commutative ring axioms of $\mathbb{Z}/q\mathbb{Z}$ as the natural abstraction layer for arithmetic masking verification.

The micro-newton cusped field Hall thruster is an electric propulsion device that employs microwave-assisted ionization control. It serves as an actuator in drag-free control systems, ensuring control accuracy and stability by providing continuously adjustable thrust over a wide range. However, a mode transition occurring during the regulation process can lead to a sudden change in anode current, degrading control precision and stability. Therefore, it is necessary to investigate the underlying patterns of mode transition. This study examines the variations in internal plasma parameters and discharge characteristics of the thruster before and after microwave mode transition, primarily through probe diagnostics.Experimental results indicate that before the mode transition, the plasma luminous region is primarily concentrated within the electron cyclotron resonance (ECR) area, approximately 1-3 mm upstream of the anode. After the transition, the luminous region moves further upstream, and the plasma density near the anode exceeds the cutoff density, dropping sharply along the axial direction. The fundamental cause of the change in electron heating mechanism is the alteration in the propagation characteristics of fundamental waves due to this plasma density variation.When the plasma density rises to the cutoff density, the R wave and O wave, which drive ionization, are rapidly attenuated or reflected. At this point, the R-wave cannot reach the resonance layer, causing the dominant ECR ionization to become ineffective. The ionization mechanism shifts from being dominated by the R wave and O wave to being dominated primarily by the O wave. Consequently, the electron heating mechanism transitions from volume heating to surface wave heating......

Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the computation of any sparse tensor algebra expression across parallel execution units. Our algorithm generalizes parallel merging algorithms to any number of operands, and to multi-dimensional, hierarchical sparse data structures. We implement our algorithm within an existing sparse tensor algebra compilation framework to automatically generate parallel sparse tensor algebra kernels that target multi-core CPUs and GPUs. We show that our generated code is competitive with hand-implemented parallelization strategies used by vendor libraries like Intel MKL and NVIDIA cuSPARSE (geo-means of $0.73$--$3.4\times$) and \textsc{Taco} (geo-means of $1.0$--$2.4\times$), and significantly outperforms general-purpose strategies for sparse tensor expressions where specialized algorithms have not been developed (geo-means of $2.0$--$6.4\times$).

Diffusion models have emerged as powerful generative priors for solving PDE-constrained inverse problems. Compared to end-to-end approaches relying on massive paired datasets, explicitly decoupling the prior distribution of physical parameters from the forward physical model, a paradigm often formalized as Plug-and-Play (PnP) priors, offers enhanced flexibility and generalization. To accelerate inference within such decoupled frameworks, fast neural operators are employed as surrogate solvers. However, directly integrating them into standard diffusion sampling introduces a critical bottleneck: evaluating neural surrogates on partially denoised, non-physical intermediate states forces them into out-of-distribution (OOD) regimes. To eliminate this, the physical surrogate must be evaluated exclusively on the fully denoised parameter, a principle we formalize as the Manifold Consistency Requirement. To satisfy this requirement, we present Diffusion Latent Optimization (DiLO), which transforms the stochastic sampling process into a deterministic latent trajectory, enabling stable backpropagation of measurement gradients to the initial latent state. By keeping the trajectory on the physical manifold, it ensures physically valid updates and improves reconstruction accuracy. We provide theoretical guarantees for the convergence of this optimization trajectory. Extensive experiments across Electrical Impedance Tomography, Inverse Scattering, and Inverse Navier-Stokes problems demonstrate DiLO's accuracy, efficiency, and robustness to noise.

Efficient classical simulation of noisy intermediate-scale quantum (NISQ) circuits has been a topic of intense study over the past few years. The majority of results on efficient simulation assume that the circuits undergo some variant of unital noise or involve sufficient randomness. However, there are limited results for circuits undergoing non-unital noise in the absence of randomness. In this work, we present a polynomial-time classical algorithm to sample from the output distributions of amplitude-damped instantaneous quantum polynomial (IQP) circuits. Our algorithm works for circuits generated by arbitrary $l$-local diagonal gates with depth $d = Ω(\log(n))$, undergoing constant amplitude-damping noise.

A single photon in a superposition of $d$ modes naturally encode a $d$-dimensional quantum system, a so-called qudit. We show that such superpositions can be leveraged to achieve a quantum speed-up of remote remote state preparation (RSP): a primitive for several quantum network protocols. For a superposition over $d\geq 2$ modes, the photon state can encode up to ${\rm Log}_2(d)$ qubits, which we exploit in a proposed reflection based RSP protocol with multiple variations. For single qubit RSP, we achieve a performance comparable to the best known existing schemes but with reduced requirements for phase stabilization. For many qubit RSP the achievable success rates remain high despite needing exponentially many temporal modes, since only one photon needs to be transmitted and detected to prepare multiple qubits. By simultaneously preparing many qubits at once, we bypass limited qubit lifetimes limited qubit lifetimes and improve fidelities beyond what is achievable with existing RSP protocols.

We characterize possible pairs $(u_\varepsilon,c)\in C(\mathbb{R}^n\backslash\varepsilon\mathbb{Z}^n,\mathbb{R})\times\mathbb{R}$ addressing the homogenization problem for Hamilton--Jacobi equations $$ H\left(\frac{x}{\varepsilon}, d u_\varepsilon, u_\varepsilon\right)=c, \quad \left({\mathrm resp.} \quad H\left(\frac{x}{\varepsilon}, d u_\varepsilon, u_\varepsilon\right)=\varepsilonΔu_\varepsilon+c \right) $$ for all $\varepsilon>0$. Under a (not necessarily strict) monotonicity assumption on the Hamiltonian, we proposed certain criteria (based on the structure of Mather measures), under which all possible solutions $u_\varepsilon$ converge to a uniquely identified limit $u\in C(\mathbb{R}^n,\mathbb{R})$ solving the effective equation \[ \overline H( du,u)=c,\quad ({\mathrm resp.}\quad \overline H(du,u)=Δu+c) \] as $\varepsilon\rightarrow 0_+$ with a uniform rate $\mathcal{O}(\varepsilon)$.

We establish a lower bound for the surface area of a closed, convex hypersurface in Euclidean space in terms of its displacement under continuous maps. As a result, a hypothesized lower bound for the volume of a Riemannian $n$-sphere, proved by Berger in dimension $n=2$ and disproved by Croke in dimensions $n \geq 3$, is valid for convex hypersurfaces in all dimensions. We also establish a sharp lower bound for the mean width of a convex hypersurface.

This paper introduces PowerDAG, an agentic AI system for automating complex distribution-grid analysis. We address the reliability challenges of state-of-the-art agentic systems in automating complex engineering workflows by introducing two innovative active mechanisms: adaptive retrieval, which uses a similarity-decay cutoff algorithm to dynamically select the most relevant annotated exemplars as context, and just-in-time (JIT) supervision, which actively intercepts and corrects tool-usage violations during execution. On a benchmark of unseen distribution grid analysis queries, PowerDAG achieves a 100% success rate with GPT-5.2 and 94.4--96.7% with smaller open-source models, outperforming base ReAct (41-88%), LangChain (30-90%), and CrewAI (9-41%) baselines by margins of 6-50 percentage points.

This is a survey of the diversity of problems in additive number theory. Equity requires the consideration of less currently popular problems, and suggests their inclusion in the additive canon. Of particular interest are problems about the sizes of sumsets of finite sets of integers and problems about the arithmetical structure of intersections of sumsets.

Experimental measurements of the radial spreading of photoelectrons emitted from a multi-alkali photocathode in a MCP-based photomultiplier tube have shown that, for photon wavelengths of 455 nm, 515 nm and 625 nm, the maximum initial energies of the emitted photoelectrons are approximately 0.3 eV, 0.2 eV and 0.1 eV respectively. Combining these experimental results with simulations performed using the SIMION simulation package, a compact radio-frequency photoelectron multiplier tube with a temporal resolution better than 10 ps is proposed. The device would be suitable for applications in several fields, particularly in medical optical instruments employing time-correlated single-photon counting.

We present an automated framework to search for optical counterparts of LIGO-Virgo-KAGRA (LVK) gravitational wave (GW) superevents using public Zwicky Transient Facility (ZTF) alerts processed through the ALeRCE broker. The goal is to filter and identify optical transients potentially associated with binary black hole (BBH) mergers during the LVK O4a and O4b observing runs. Using the Automatic Learning for the Rapid Classification of Events (ALeRCE) infrastructure, we spatially query ZTF alerts within GW localization regions and apply machine learning classifiers, host-galaxy crossmatching, and temporal cuts within 200 days post-merger to isolate plausible candidates. Our search yielded one candidate in O4a and four in O4b, several consistent with the supernova or tidal disruption event regime. This work demonstrates that public alert brokers can establish a robust baseline for systematic searches for electromagnetic counterparts to GW superevents in current and future observing runs. Our algorithm provides a systematic approach to search for BBH counterparts for all significant LVK GW superevents using survey telescope alerts. The search, together with the accompanying analysis, demonstrates the significance of the counterpart candidates, with one candidate ultimately identified as a transient event consistent with a Bowen fluorescence flare in a now discarded active galactic nucleus (AGN).

Estimating thermal expectations of local observables is a natural target for quantum advantage. We give a simple classical algorithm that approximates thermal expectations for Gibbs states of local Hamiltonians, and we show it has quasi-polynomial cost $n^{O(\log (n/ε))}$ for all temperatures above a phase transition in the free energy. For many natural models, this coincides with the entire fast-mixing, quantumly easy phase. Our results apply to the Sachdev-Ye-Kitaev (SYK) model at any constant temperature due to its absence of a phase transition -- despite its entanglement, sign problem, and polynomial quantum circuit lower bounds. Beyond SYK, we rigorously establish a universal classically easy high-temperature phase for all local, bounded-degree Hamiltonians and show that it extends to temperatures strictly colder than the death of entanglement transition.

Generative AI chatbots enable personalized problem-solving, but effective learning requires students to self-regulate both how they seek help and how they use AI-generated responses. Considering engagement modes across these two actions reveals nuanced reliance patterns: for example, a student may actively engage in help-seeking by clearly specifying areas of need, yet engage passively in response-use by copying AI outputs, or vice versa. However, existing research lacks systematic tools for jointly capturing engagement across help-seeking and response-use, limiting the analysis of such reliance behaviors. We introduce RelianceScope, an analytical framework that characterizes students' reliance on chatbots during problem-solving. RelianceScope (1) operationalizes reliance into nine patterns based on combinations of engagement modes in help-seeking and response-use, and (2) situates these patterns within a knowledge-context lens that accounts for students' prior knowledge and the instructional significance of knowledge components. Rather than prescribing optimal AI use, the framework enables fine-grained analysis of reliance in open-ended student-AI interactions. As an illustrative application, we applied RelianceScope to analyze chat and code-edit logs from 79 college students in a web programming course. Results show that active help-seeking is associated with active response-use, whereas reliance patterns remain similar across knowledge mastery levels. Students often struggled to articulate their knowledge gaps and to adapt AI responses. Using our annotated dataset as a benchmark, we further demonstrate that large language models can reliably detect reliance during help-seeking and response-use. We conclude by discussing the implications of RelianceScope and the design guidelines for AI-supported educational systems.

We introduce a metric-dependent geometric variant of factorization homology in conformally flat Riemannian geometry for $d \geq 2$. Its coefficients are symmetric monoidal functors from a disk category in conformal Riemannian geometry to the ind-category of Hilbert spaces, which we call conformally flat $d$-disk algebras. We prove that their left Kan extensions define symmetric monoidal invariants of conformally flat manifolds. Under suitable positivity and continuity assumptions, the value on the standard sphere reproduces the sphere partition function of the associated conformal field theory. For $d>2$, we construct explicit examples from unitary representations of $\mathrm{SO}^+(d,1)$.

How do cost shocks pass through to prices in markets with price dispersion? We decompose the problem into two layers. In the competition layer, consumers' consideration sets determine equilibrium distributions of normalized margins. In the curvature layer, demand elasticity maps these margins into prices and pass-through rates. We prove the pricing game is strategically equivalent to a game over normalized margins, so equilibrium margin distributions are invariant to demand and costs. This separation yields closed-form pass-through formulas at each quantile of the price distribution, robust bounds across demand specifications, and sharp comparative statics linking market structure to incidence.

We introduce the variable coherence model (VCM) for simulating free-electron laser (FEL) pulses generated through self-amplified spontaneous emission. Building on the established partial coherence model of [T. Pfeifer et. al, Opt. Lett. 35, 3441 (2010)], we demonstrate that the implementation of a variable coherence width allows for continuous control over the pulses' characteristic noise, while keeping the average pulse parameters such as the bandwidth fixed. We demonstrate this through systematic statistical analyses of the intensity and number of sub-pulses in VCM pulses, in both time and frequency. In particular, we analyze how the sub-pulse statistics are affected by the coherence width parameter. We perform our analyses across three distinct regimes of FEL parameters and demonstrate how the VCM can generate pulses that range from maximally random to fully coherent. Finally, we illustrate the effect of the VCM variable coherence width on an absorption simulation.

The Casimir interaction in salted water contains a universal contribution of electromagnetic fluctuations that makes it of a longer range than previously thought. The universal contribution dominates non universal ones at the distances relevant for actin fibers inside the cell. We discuss universal and non-universal contributions with a model mimicking biological matter. We also show that the universal Casimir effect should have important implications at the cell scale.

Multielectron tunneling ionization creates ionic coherence crucial for lasing and driving electron motion in molecules. While tunneling is well understood as a single active electron process, less emphasis has been placed on theoretical descriptions of bound electrons during tunneling. This work systematically investigates multielectron tunneling ionization based on the strong field approximation, establishing a theoretical foundation and demonstrating the equivalence of wave function and density matrix approaches for subcycle ionic dynamics. An accurate subcycle nonadiabatic ionization rate is also derived and incorporated into the theory to improve its quantitative accuracy. Applying the theory to N$_{2}$ and CO$_{2}$, this work showcases how an intense laser field can induce ionic coherence in molecules as observed in previous experiments. These findings encourage future investigations into multielectron tunneling ionization and its applications in lasing and in controlling chemical reactions.

This article focuses on smooth, projective, and geometrically integral varieties $X$ defined over a number field $k$ with torsion-free geometric Picard groups. We establish an isomorphism between the Brauer groups of $X$ and its symmetric products. As applications, we deduce the relationship between the Brauer--Manin obstruction to the Hasse principle and to weak approximation for $0$-cycles of degree $n$ on $X$ and the corresponding obstruction for rational points on smooth projective models of its $n$-fold symmetric product.

We study the class structure of finite-alphabet Markov chains with arbitrary memory length. To capture the structural constraints induced by prohibited transitions, we introduce the skeleton of a higher-order transition kernel, defined as a reduced set of contexts encoding all essential zero-probability patterns. To each skeleton we associate a binary transition matrix. We show that the communicating class structure of this matrix completely determines the recurrent classes of the original higher-order Markov chain, along with their periods. As a consequence, simple criteria for essential irreducibility and periodicity follow directly from the skeleton, without constructing the full first-order representation on the enlarged state space. From a practical perspective, this approach can yield significant computational gains. An example illustrates how the skeleton may have substantially smaller order than the original chain.

It is a common belief that any relativistic nonlocal quantum field theory encounters either the problem of renormalizability or unitarity or both of them. It is also known that any local relativistic quantum field theory (QFT) possesses the CPT symmetry. In this Letter we show that a previously proposed nonlocal Lorentz invariant QFT, which violates the CPT theorem, is both renormalizable and unitary, thus being a first presented example in the literature of such a nonlocal theory. The theory satisfies the requirement of causality as well. A further generalization of such a nonlocal QFT to include the gauge theories is also envisaged. In particular, dressing such a Standard Model with a CP violating phase, will make the theory satisfying most of the necessary criteria to finally explain the baryon asymmetry of the universe by a viable QFT. As for the necessity of baryon number violation, there are hopefully several possibilities such as by GUT and electroweak baryogenesis, leptogenesis or sphalerons.

We investigate the electronic transport properties of a superconductor-quantum dot-superconductor Josephson junction coupled to a ferromagnetic metal reservoir in the presence of an external magnetic field. The device is described by an effective non-Hermitian Hamiltonian, whose complex eigenvalues encode the energy (real part) and the broadening (imaginary part) of the Andreev quasi-bound states. When extending the Andreev current formula to the non-Hermitian case, a novel contribution arises that is proportional to the phase derivative of the levels broadening. This term becomes particularly relevant in the presence of exceptional points (EPs) in the spectrum, but its experimental detection is not straightforward. We identify optimal Andreev spectrum configurations where this novel current contribution can be clearly highlighted, and we outline an experimental protocol for its detection. We point out that the phase dependence in the levels imaginary part originates from the breaking of a time-reversal-like symmetry. In particular, spectral configurations in the broken phase of the symmetry and without EPs can be obtained, where this novel contribution can be easily resolved. The proposed protocol would allow to probe for the first time a fingerprint of non-Hermiticity in open junctions that is not strictly related to the presence of EPs.

The Quick Look data products from the Very Large Array Sky Survey (VLASS) contain widespread imaging artifacts arising from the simplified imaging algorithm used in their production. The catalog of double radio sources associated with active galactic nuclei (DRAGNs) found in the VLASS first epoch Quick Look release using the DRAGNhunter algorithm suffers from contamination from these artifacts. These sources contain two or three individual components, each of which can be an artifact. We train random forest models to classify these DRAGNs based on the number of artifacts they contain, ranging from zero to three artifacts. We optimize our models and mitigate the class imbalance of our dataset with judicious training set selection, and the best of our models achieves a weighted F1 score of $97.01\%^{+1.12\%}_{-1.32\%}$. Using our classifications, we produce a catalog of VLASS DRAGNs from which an estimated 99.3% complete catalog of 97.7% artifact-free sources can be extracted.

The Bustling Universe Radio Survey Telescope in Taiwan (BURSTT) is a new-generation wide-angle radio telescope specifically designed to survey Fast Radio Bursts (FRBs), energetic millisecond-duration pulses of unknown extragalactic origin. To realize its scientific potential, which includes detecting approximately 50 FRBs per year and sub-arcsecond localization capability, the system is designed to perform real-time beamforming and pulse search over the \SI{60}{\degree} $\times$ \SI{120}{\degree} field of view. This paper provides a detailed account of the design, implementation, and performance validation of the BURSTT back-end System. The system employs an efficient multi-stage processing architecture: initial beamforming is executed on the Xilinx ZCU216 RF System-on-Chip (RFSoC) platform; data is then transferred to Intel Xeon servers, where AVX-512 and AMX instruction sets are utilized for the second stage of beamforming and channelization, achieving high computational efficiency to ensure real-time capability. A highly optimized \texttt{bonsai} de-dispersion algorithm performs a real-time pulse search and triggering across 256 beams, which, upon detection, issues commands to the distributed outrigger system to save voltage data for very-long baseline interferometry (VLBI) precise localization. System performance has been validated through beamforming tests using bright radio sources and real-time detection of known pulsars, confirming the high fidelity of the signal processing pipeline.