Quantum computing is a new approach to computation that utilizes superposition, entanglement, interference, and tunneling to solve problems too complex for classical computers. This paper discusses the basic concepts and development of quantum computing, exploring its potential applications in the built environment and urban microclimate research. In buildings, quantum computing may help optimize energy management, control HVAC systems, and plan electric vehicle charging networks more efficiently. For urban microclimates, it could accelerate renewable energy planning and support multi-objective design, making it easier to balance urban building performance with climate conditions. Since current quantum hardware is still in the Noisy Intermediate-Scale Quantum (NISQ) stage, we propose the "BITE" principle to guide researchers in choosing suitable problems for quantum acceleration: B (Big search), I (Input-light), T (Tiny computation), and E (Evaluation polish). Although quantum computing still faces challenges such as noise and hardware limits, it offers great potential for developing more climate-resilient, sustainable, and energy-efficient cities of the future.

This paper introduces the separable covariance mixture model, which assumes a data-matrix $Y$ to be of the form $$ \sum\limits_{r=1}^R A_r X B_r $$ for one random $(d \times n)$-matrix $X$ with independent centered variance-one entries, and for two families of deterministic matrices $A_1,\dots,A_R \in \mathbb{C}^{d \times d}$ and $B_1,\dots,B_R \in \mathbb{C}^{n \times n}$. Under certain assumptions, it is shown that the resolvents $(\frac{1}{n} Y Y^* - z \operatorname{Id}_d)^{-1}$ and $(\frac{1}{n} Y^* Y - z \operatorname{Id}_n)^{-1}$ respectively approximate the deterministic matrices $$ -\frac{1}{z}\Big( \operatorname{Id}_d + \sum\limits_{r,s=1}^R δ^{(B)}_{r,s}(z) A_{r} A_{s}^* \Big)^{-1} \ \ \text{ and } \ \ -\frac{1}{z}\Big( \operatorname{Id}_n + \sum\limits_{r,s=1}^R δ^{(A)}_{r,s}(z) B_{s}^*B_{r} \Big)^{-1} \ , $$ where $δ^{(A)}, δ^{(B)} \in \mathbb{C}^{R \times R}$ are uniquely defined solutions to a certain dual system of equations. The results are non-asymptotic and do not require simultaneous diagonalizability of the families $(A_r)_{r \leq R}$ or $(B_r)_{r \leq R}$, as was required in previous works such as [Hazarika and Paul (2025)] or [Mei et al. (2023)]. An asymptotic application, which describes the limiting spectral distribution of the sample covariance matrix analogues $\frac{1}{n} Y Y^*$ or $\frac{1}{n} Y^* Y$, is included.

Electronic voting systems must balance public verifiability with voter privacy and coercion resistance. Existing cryptographic protocols typically achieve end-to-end verifiability by revealing vote distributions, relying on trusted clients, or enabling transferable receipts - design choices that often compromise trust or privacy in real-world deployments. We present ACE, a voting protocol that reconciles public auditability with strong privacy guarantees. The protocol combines a publicly verifiable, tally-hiding aggregation mechanism with an Audit-or-Cast challenge that enforces cast-as-intended even under untrusted client assumptions. Tallier-side re-randomization eliminates persistent links between voters and public records, yielding information-theoretic receipt-freeness assuming at least one honest tallier. We formalize the security of ACE and show that it simultaneously achieves end-to-end verifiability, publicly tally-hiding results, and strong receipt-freeness without trusted clients.

We describe the equation of state (EoS) of a warm ion plasma as obtained by performing microscopic many-body simulations using Molecular Dynamics computational techniques. Using the cold one-component plasma (OCP) composition in the Neutron Star (NS) outer crust assumed in Murarka et al. (2022) with a representative heavy nucleus for each density, we refine previous calculations. We include electron screening and modeling of ions as finite-size Gaussian distributions in the interaction potential, together with an efficient Ewald energy summation procedure. From this, the EoS relation $P(n_B,T)$ is obtained as a function of baryonic density and temperature in the NS outer crust under conditions $n_B\in[7.48\times 10^{-10},2.09\times10^{-4}]$ $ \rm fm^{-3}$ , $k_{B}T\in[1,5]$ MeV. In order to improve the usability of our results we provide tabulated data values along with a neural network parametrization available in the Zenodo repository, see https://zenodo.org/records/15348712. We find that even at moderate temperatures, thermal effects of ions are key in the higher density region closer to the inner crust, when described using a thermal effective parametrization based on the thermal adiabatic index $Γ_{th}$. We compare our results with other EoS in the literature performing a critical discussion.

We prove a suitable fibration theorem over quasi-trivial tori that, through an approach developed by Harpaz and Wittenberg, implies so-called solvable descent. In particular, this gives a positive answer to the Grunwald problem for solvable groups up to the necessary Brauer--Manin obstruction, providing a generalizion of Shafarevich's positive answer to the Inverse Galois Problem for solvable groups. This also provides an alternative proof of Shafarevich's result that avoids his "shrinking procedure". For the fibration theorem, we first adapt the starting ideas of Shafarevich for the creation of local lifts. To deal then with the Brauer--Manin obstruction (i.e. the relevant local-to-global obstruction), we compute its "triple variation" on grids of fibers. The resulting expression is a linear combination of Redéi symbols on the base. Customizing these and employing a combinatorial principle first noted by Alexander Smith in the context of Class and Selmer Groups, one infers the vanishing of the obstruction in at least one fiber.

Gas delivery to galactic centers powers nuclear starbursts and active galactic nuclei (AGNs), yet bar-driven inflow is generally expected to stall in a nuclear ring a few hundred parsecs across. Using three-dimensional Lagrangian hydrodynamic simulations in a fixed barred potential, we identify a bypass channel in which a fraction of the inflowing gas acquires vertical momentum, vaults across the ring, and reaches the inner few tens of parsecs. This pathway is absent in two-dimensional calculations, which instead predict long-lived stagnation at the ring. We find that the circumnuclear material within $\sim 50$ pc originates from gas initially located outside the ring ($\gtrsim 300$ pc), rather than from secondary inflow out of the ring itself. Successful delivery requires both a sufficiently large vertical excursion, $|z| \sim 100$ pc before encountering the ring, and substantial loss of azimuthal angular momentum $L_z$. The resulting inflow is organized rather than chaotic: center-reaching trajectories are confined to a limited spatial region set by the scale height of the ring gas. Most bar-driven gas still accumulates near the resonance and fuels star formation in the nuclear ring, but the vaulting stream selects a modest yet sufficient fraction that penetrates to the circumnuclear disk. These results suggest that intrinsically three-dimensional gas motions help link nuclear starbursts, AGN fueling, and the frequent misalignment of nuclear disks with respect to their host galaxies.

Program debloating aims to remove unused code to reduce performance overhead, attack surfaces, and maintenance costs. Over time, debloating has evolved across multiple layers (container, library, and application), each building on the principles of application-level debloating. Despite its central role, application-level debloating continues to rely on imperfect proxies for measuring performance, such as test-case-driven evaluation for correctness, code size for runtime efficiency, and gadget count reduction for estimating security posture. While there is widespread skepticism about using such imperfect proxies, the community still lacks standardized methodologies or benchmarks to assess the true performance of application-level software debloating. This experience paper aims to address the gap. We revisit the foundations of application-level debloating through a ground-truth-based evaluation paradigm. Our analysis of eight state-of-the-art debloaters - Blade, Chisel, Cov, CovA, Lmcas, Trimmer, Occam, and Razor - uncovers insights previously unattainable through traditional evaluations. These tools collectively span the spectrum of source-to-source, IR-to-IR, and binary-to-binary transformation paradigms, characterizing a holistic reassessment across abstraction levels. Our analysis reveals that while dynamic analysis-based tools often remove up to 94% of code that should be retained, static analysis-based approaches exhibit the opposite behavior, showing high false retention rates due to coarse-grained dependency over-approximation. Additionally, static analyses may add code by introducing specialized variants of functions. False retentions and removals not only cause functional incorrectness but may also lead to systematic inconsistency, robustness failures, and exploitable vulnerabilities.

Fan-array wind generators (FAWGs) provide controlled turbulent inflow conditions that cannot be reproduced in conventional wind tunnels. Despite their increasing use in experimental studies, numerical modeling of FAWG-generated flows remains largely unexplored. The present study assesses the capability of Reynolds-Averaged Navier-Stokes (RANS) modeling to predict jet interaction in a 10x10 fan-array wind generator. Numerical predictions are compared against experimental measurements of axial velocity and turbulence intensity from a reference configuration. Individual fan units are represented using a pressure-jump boundary condition based on a reconstructed performance curve derived from manufacturer data. Grid convergence is verified, and the influence of fan representation, operating point and inflow turbulence conditions is examined. The results show that RANS modeling captures the global jet interaction topology and downstream velocity decay with reasonable accuracy. However, systematic magnitude discrepancies are observed in the near-field injection region and peripheral shear layers. Turbulence intensity predictions exhibit larger deviations, reflecting limitations of the eddy-viscosity closure in highly mixing-dominated flows. A low-aspect-ratio flat plate is included as a demonstrative application to illustrate the aerodynamic impact of FAWG-generated inflow. Overall, the study shows that RANS modeling, combined with a pressure-jump fan representation, provides a computationally efficient framework for predicting the mean-flow structure of FAWG systems, while exhibiting clear limitations in resolving localized turbulence characteristics.

Possibilities are considered to simplify the computation of several statistical functions used to test statistical hypotheses when processing observations: the inverse normal distribution, the Student's t-distribution, and the criterion for rejecting outliers. For these three cases, simple approximation expressions are proposed for the quantiles of these statistical distributions, which are accurate enough for most practical applications.

Prior work has demonstrated that functionally correct yet vulnerable outputs arise systematically in threat-oriented settings, where adversarial or implicit channels are used to induce security failures in code agents and automated patching workflows. This note introduces a complementary but distinct framing: False Security Confidence (FSC), which studies the same surface phenomenon from a measurement-first perspective in ordinary, non-attack-framed generation tasks. Our interest is not in whether attacks can produce such outputs, but in how frequently and in what forms they appear absent explicit attack pressure, and whether conventional functional evaluation reliably detects them. We formalize FSC rate as the prevalence of security failure within the set of functionally correct outputs, distinguish it from prior joint functional-security metrics such as SAFE and outcome-driven evaluation frameworks such as CWEval, define a three-ecosystem task view for studying how FSC manifests across general-purpose programming, deployment-context tasks, and security-explicit programming, and identify FSC-hard as a practically important refinement layer in which static analyzers miss vulnerabilities that remain dynamically triggerable. This technical report is intentionally scoped as a framework statement rather than a full empirical paper: its purpose is to establish terminology, measurement boundaries, and study design commitments for subsequent large-scale evaluation.

We introduce a family of metric-deformed Heisenberg algebras $M_1$ and $M_2$, where the commutation relations are expressed directly in terms of the components of a diagonal Lorentzian metric. We show that these algebras unify several known $q$-deformed Heisenberg algebras, including the $q$-$\hbar$ algebra, the new $q$-Heisenberg algebra, and the $q$-generalized Heisenberg algebra, which embed as special cases. Using Sylvester's theorem of inertia, we establish a connection between the metric signature and the deformation parameters. We construct a $q$-Dirac operator $D_q$ from the deformed D'Alembertian and prove that $D_q^2$ recovers the deformed Klein-Gordon operator. Furthermore, we relate this construction to the quadratic $q$-Dirac operator previously introduced by the author, providing a unified framework that bridges spacetime geometry and $q$-deformed quantum algebras.

Phys. Rev. B 113, 165102 (2026) proposed the conjecture that, for quantum quenches within the same phase, the overlap between the initial ground state and postquench eigenstates is maximal for the postquench ground state. We show that this conjecture is not valid in general. An explicit local, translationally invariant, gapped free-fermion counterexample exists even though the pre- and postquench Hamiltonians are connected by a symmetry-preserving gapped path and the thermodynamic-limit spectrum is continuous.

The presence of degeneracies plays a crucial role in describing the behavior of non-Hermitian (NH) systems. In these systems, there are two key types of degeneracies: $n$-bolical degeneracies, which are analogous to Hermitian degeneracies, and various forms of exceptional points, each associated with different orders that correspond to sizes of the Jordan blocks. These types of degeneracies may coalesce at the same energy level, forming multi-block degeneracies. To understand how a multi-block degenerate NH system responds to perturbations, one should address how each types of involved degeneracies disperse. In this work, we systematically characterize the asymptotic behavior of all types of multi-block degeneracies in NH systems using a rigorous mathematical formulation. Through a range of examples, we demonstrate that our algebraic approach can facilitate the analysis of NH degeneracies in various settings relevant to experiments.

The emergence of various types of degeneracies plays a crucial role in optimizing and engineering different physical phenomena in non-Hermitian physics. In our work, we focus on the derogatory Exceptional Points (EPs), which are characterized by multiple Jordan blocks corresponding to the same eigenvalue. We demonstrate that, under certain infinitesimal perturbations, a derogatory EP can be converted into an EP of different structure without varying the total order of degeneracy. In particular, such conversion can increase the size of the largest Jordan block and, hence, the sensitivity of the eigenspectrum to parameter variation, which is an important feature for practical applications. Furthermore, by analyzing all possible conversions, we introduce hierarchies of degeneracies of the same order that appear when perturbing non-Hermitian systems. We systematically explore hierarchies in the absence of any symmetry and when pseudo-Hermitian symmetry is present. Our study facilitates engineering various degeneracies of non-Hermitian systems, paving the way to extending the implications of non-Hermitian physics.

Classical latent-score ranking models often fail to distinguish objects' intrinsic scores from contextual effects, which are typically nonlinear and can dominate the observed outcomes. To address this, we introduce a semiparametric ranking framework in which the log-score of each object is modeled as the sum of a utility parameter and a nonparametric covariate effects. Within this framework, we establish model identifiability under mild regularity and connectivity conditions. For estimation, we approximate the covariate effects using a neural network and estimate the parameters via maximum likelihood. Under random design assumptions, we prove that the resulting estimator exists with high probability and derive non-asymptotic error bounds that achieve minimax optimality for both the parametric and nonparametric components. Numerical experiments on both synthetic data and an ATP tennis dataset are conducted to support our findings.

We present a first-principles explanation of the recombination requirement for benign termination of relativistic electron (RE) beams in tokamaks. Kinetic modeling including neutrals shows that the injection of neutrals over a finite quantity window, together with recombination, increases bulk resistivity. Nonlinear MHD simulations using the JOREK code demonstrate that this preferentially amplifies edge tearing modes, producing a more stochastic edge magnetic field during RE deconfinement, resulting in a larger RE wetted area. We identify resistivity, not the free electron density, to govern access to benign termination. This provides the first broadly applicable and experimentally consistent picture of the MHD mechanisms behind the benign scenario, critical to its extrapolation to next-step devices.

Representations play a central role in the study of both biological and artificial intelligence, as well as philosophy of mind. Across neuroscience, computer science, and philosophy, a recurring theme is that representations not only carry information but should be ``useful'' for or ``usable'' by an agent in some sense. Here, we review how the ``usefulness'' of representations has been conceptualized and how it figures into different conceptions of representation. We identify and explore four aspects of use and usability: representations generally carry \textit{information}; that information may or may not be \textit{useful} and it may or may not be encoded in a usable \textit{format}; and the representations may or may not be \textit{used downstream}. Building on these four aspects of information and use, we then organize existing perspectives on neural representations into three levels: Representations as Information (Level 1); Representations as Usable (Level 2); and Representations as Used (Level 3). Our account is meant to give readers an appreciation for the diversity of notions of ``neural representation,'' help them navigate the vast and multi-disciplinary literature on the topic, and help them clarify the appropriate notion of representation for their own investigations.

We study replica symmetry breaking (RSB) for multi-entropy in the random-tensor-network (RTN) domain-wall spin model. Our main result is that, within this framework, multi-entropy has a structural obstruction to RSB for any Rényi index $n$ and any multipartite number $\mathtt{q}$. This obstruction arises because the boundary permutations relevant to multi-entropy are organized along mutually incompatible coordinate directions of the replica hypercube, and therefore do not admit a nontrivial common geodesic intermediate permutation $τ$ in the Cayley graph of $S_N$. This is in sharp contrast to entanglement negativity, which does admit such a $τ$-mediated saddle and exhibits RSB in the same framework. As a robustness check, we also consider a toy $\mathbb{Z}_2$ gauge extension of the spin model with a minimal bulk gauge constraint. Numerical evidence in this gauged model indicates that multi-entropy continues to show no sign of RSB at $n=2$ and $n=3$, while negativity continues to exhibit RSB. Our results show that, within the RTN spin-model description, multi-entropy is not "RSB-friendly'': its boundary data are structurally incompatible with a nontrivial common geodesic intermediate permutation, unlike negativity.

We present a comprehensive theoretical analysis of ultrafast entanglement generation between two Rydberg-blockaded atoms, explicitly accounting for realistic laser noise. Using femtosecond Gaussian pulses as a baseline, we systematically evaluate Bell-state fidelity sensitivity to amplitude and phase noise across white, pink (1/f), and Ornstein-Uhlenbeck spectra using Monte Carlo ensemble simulations. Our results show that amplitude noise is well tolerated, with fidelities above 90% even at 30% noise levels, while phase noise is the primary limiting factor, causing fidelity to drop rapidly beyond about 1% noise amplitude. The spectral structure of the noise is also important: pink noise consistently causes less fidelity loss than white noise of the same amplitude. By applying quantum optimal control theory (QOCT) with the D-MORPH algorithm under multiple equality constraints, we obtain a double-pulse structure with a spectral notch that achieves approximately 99% fidelity in the noise-free case and maintains high fidelity under moderate amplitude noise. A breakdown threshold near 1% amplitude noise is identified, beyond which even optimized pulses cannot sustain coherent control. These results offer practical benchmarks for the development of ultrafast neutral-atom quantum processors operating in the femtosecond regime.

In the context of selective inference, confidence envelopes for the false discoveries allow the user to select any subset of null hypotheses while having a statistical guarantee on the number of false discoveries in the selected set. Many constructions of such envelopes have been proposed recently, using local test families (Genovese and Wasserman, 2006; Goeman and Solari, 2011), paths (Katsevich and Ramdas, 2020) or interpolation (Blanchard et al., 2020a). All those methods have in common that they have been well-studied for the homogeneous case where all p-values under the null have a uniform distribution over [0, 1]. However, in many applications the data are heterogeneous and discrete, hence the p-values have heterogeneous, discrete distributions, and the previous constructions may incur a loss of power, in the sense that they over-estimate the number of false discoveries. In this paper, we bridge the previous constructions under the homogeneous case with new tools. We also apply these tools to propose several confidence envelopes based on tools tailored for heterogeneous data, like the Bretagnolle inequality, or a new variant of the Simes inequality. We compare these new envelopes to their homogeneous counterparts on simulated data.

The almost Golomb equation of order $r$ is the implicit functional equation $$a\Bigl(\sum_{j=0}^{r-1} a(n{-}j)\Bigr) = n$$ for nondecreasing sequences of positive integers with $a(1)=1$. Its earliest solution, the almost Golomb sequence of order $r$, is $r$-regular in the sense of Allouche and Shallit and has oscillating ratio $a(n)/n$. We prove that for every $r\ge 2$ that is not an even perfect square, the equation admits a second monotone solution given by an inhomogeneous Beatty sequence of slope $1/\!\sqrt{r}$. Composing the equation with $a$ leads to a triple-nested identity which admits a continuous one-parameter family of inhomogeneous Beatty solutions, parametrised by a shift $d$ ranging over an explicit interval. We determine these intervals sharply for $r=2$ and $r=3$, each proved by a local regime analysis combined with equidistribution of an irrational orbit. The endpoints of these intervals sit naturally inside the Pell--Ostrowski framework of Fokkink, and the defect set at the upper endpoint for $r=2$ is characterised as the return-time set of an irrational rotation to an explicit interval.

A single operational protocol based on free evolution and projective measurements yields inequivalent quantum time distributions through distinct post-processing procedures. We construct an activity-based time-of-flow (TF) distribution and a presence-based quantum stroboscopic (QS) distribution, providing complementary operational notions of time. Applied to tunneling, the regional QS mean saturates, whereas the TF mean first decreases in the Hartman regime and then grows for larger barrier widths. Within this framework, we provide an operational interpretation of the Hartman effect in terms of quantum time distributions associated with flow through the exit region and occupation within the barrier, capturing the mechanism of early penetration, dominant reflection, and spectrally filtered transmission.

Liquid crystal (LC) is a promising hardware solution for implementing large RISs, as it is cost-effective, energy efficient, scalable, and capable of providing continuous phase shifts with low power consumption. However, the phase shift response of LC-based RISs is inherently frequency dependent. If unaddressed, this characteristic leads to performance degradation, particularly in wideband scenarios. This issue is especially critical in secure communication applications, where minor phase shift variations across elements can result in considerable information leakage. This paper addresses these frequency-induced variations by developing a physics-based model for an LC unit cell across varying frequencies and proposing a novel phase shift design framework that maximizes secure communication across all subcarriers. Given the large number of elements in millimeter wave (mmWave) LC-RISs, acquiring full channel state information (CSI) is often impractical. Therefore, we optimize the phase shifts based solely on the locations of the legitimate mobile users (MUs) and potential eavesdroppers. Rather than targeting a single user point, the RIS is designed to illuminate a broader area. This approach enhances communication reliability for the MUs and mitigates performance degradation caused by location estimation errors. To solve the problem, we introduce both a semi-definite programming (SDP)-based solution and a low complexity heuristic method. While the SDP-based approach yields superior performance, it incurs higher computational complexity. Conversely, the scalable method exhibits a much slower scaling of complexity, which makes it highly suitable for extremely large RISs. Simulation results demonstrate that both algorithms improve the secrecy rate compared to baseline methods. Finally, the proposed design is validated through experimental evaluations on an LC RIS setup.

How should researchers conduct causal inference when the outcome of interest is latent and measured imperfectly by multiple indicators? We develop a general nonparametric framework for identifying and estimating average treatment effects on latent outcomes in randomized experiments. We show that latent-outcome estimation faces two distinct noncomparability challenges. First, across studies, different measurement systems may cause estimators to target different empirical quantities even when the underlying latent treatment effect is the same. Second, within a study, different indicators may have different and possibly nonlinear relationships with the same latent outcome, making them not directly comparable. To address these challenges, we propose a design-based approach built around nonparametric bridge functions. We show that these bridge functions can be characterized and identified. Estimation relies on a debiasing procedure that permits valid inference even when the bridge functions are weakly identified. Simulations demonstrate that standard methods, such as principal components analysis and inverse covariance weighting, can generate spurious cross-study differences, whereas our approach recovers comparable latent treatment effects. Overall, the framework provides both a general strategy for causal inference with latent outcomes and practical guidance for designing measurements that support identification, comparability, and efficient estimation.

The design of polarization-encoded quantum interfaces relies on the assumption that solid-state emitters possess static transition dipoles defined by the host lattice symmetry. Here, we demonstrate that the transition dipole moment of single hexagonal boron nitride quantum emitters is not a static property but rotates as a function of photon energy. Through high-resolution energy-resolved spectroscopy, we reveal a continuous rotation of the emission dipole orientation reaching up to $40^{\circ}$ across the vibronic manifold at room temperature, driven by coupling to the phonon bath. This spectral rotation is effectively suppressed at cryogenic temperatures (6 K), where the acoustic phonon population is negligible, identifying thermally activated lattice vibrations as the primary driver of the reorientation. First-principles calculations on two representative defects spanning weak and strong electron-phonon coupling regimes confirm that phonon-displaced geometries produce a systematic deviation of the transition dipole orientation from the zero-phonon line, with the magnitude scaling with vibronic coupling strength. The experimental observations and calculations demonstrate that single quantum emitters can operate beyond the Condon approximation, with the transition dipole acquiring a dependence on the instantaneous nuclear configuration. Our results identify a fundamental limit for polarization fidelity in solid-state quantum networks and connect solid-state single-emitter physics to a class of effects previously accessible only in ensemble measurements in molecular and biological spectroscopy.

We consider a verification problem for opinion dynamics based on binary observations. The opinion dynamics is governed by a Friedkin-Johnsen (FJ) model, where only a sequence of binary outputs is available instead of the agents' continuous opinions. At every time-step we observe a binarized output for each agent depending on whether the opinion exceeds a fixed threshold. The objective is to verify whether an FJ model with a given set of stubbornness parameters and initial opinions can generate the observed binary outputs up to a small error. The FJ model is formulated as a transition system, and an approximate simulation relation of two transition systems is defined in terms of the proximity of their opinion trajectories and output sequences. We then construct a finite set of abstract FJ models by simplifying the influence matrix and discretizing the stubbornness parameters and the initial opinions. It is shown that the abstraction approximately simulates any concrete FJ model with continuous parameters and initial opinions, and is itself approximately simulated by some concrete FJ model. These results ensure that consistency verification can be performed over the finite abstraction. Specifically, by checking whether an abstract model satisfies the observation constraints, we can conclude whether the corresponding family of concrete FJ models is consistent with the binary observations. Finally, numerical experiments are presented to illustrate the proposed verification framework.

We establish uniform diameter estimates and volume non-collapsing estimates for the Chern-Ricci flow on smooth Hermitian minimal models of general type, assuming the initial metric is Kähler in a neighborhood of the null locus of the canonical bundle. This yields subsequential Gromov-Hausdorff convergence, partially resolving a conjecture of Tosatti and Weinkove. When the underlying manifold is Kähler, we further prove the uniqueness of the limit space. Analytically, we overcome the difficulties posed by non-Kähler torsion in the Green's formula by exploiting our local Kähler assumption, successfully adapting recent estimates of Kähler Green's function to the Hermitian setting. To prove the uniqueness of the limit, we introduce Perelman's reduced length to the Chern-Ricci flow. By establishing a uniform Chern scalar curvature bound and an almost monotonicity formula for the reduced volume, we deduce an almost-avoidance principle for the singular set, allowing us to effectively compare the flow distance with the canonical limit distance.

We study the Plücker degree of the main component of the Quot scheme of length $l$ quotients of a locally free sheaf on a smooth projective scheme $\mathrm{S}$ of dimension $d\geqslant 1$. This degree is determined by classes in the Chow ring of the symmetric product $\mathrm{S}^{(l)}$, which are given by the pushforward of the powers of $c_{1}(\mathcal{O}^{[l]})$ with respect to the canonical morphism from the Quot scheme to $\mathrm{S}^{(l)}$. We describe a decomposition of these classes, allowing us to compute the (in a certain sense) leading term of the Plücker degree. We also obtain a higher-dimensional analogue of a classical result of Schubert.

Clusters can provide propitious environments for bar formation in galaxies. This work studies the formation and evolution of 15 bar-like galaxies in the most massive cluster of the TNG50 simulation from the IllustrisTNG suite. The selection includes galaxies from the last simulation output from well-resolved subhalos with a strongly prolate stellar component. Eleven galaxies form or strongly enhance their bars during a pericenter passage around one or more progenitors of the brightest cluster galaxy (BCG). Two form their bars early as a result of minor mergers, one via an interaction with another massive galaxy, and one via disk instability. The bar formation times differ considerably, ranging between 3-11 Gyr. The lengths of the bars also differ, ranging between 2-6 kpc, and do not correlate with the amount of tidal forcing experienced. All galaxies have at least one pericenter passage around a BCG progenitor, but the number of interactions varies strongly and is reflected in the different amount of mass stripping the galaxies experience. Most bar formation events take place before the BCG is fully formed. In three cases, they occur just before different progenitors of the BCG merge. For six bar-like galaxies, the merger events leading to the final formation of the BCG cause significant changes of their orbits. Their diverse evolutionary histories illustrate the different paths to bar formation in clusters and emphasize the complex nature of the process, which includes coevolution with BCG progenitors.

These proceedings start with a discussion of my recent experiences with large language models and potential implications for their usage in our field. This is followed by an AI generated summary of my talk at the workshop ``Recent Progress in Computational String Geometry,'' held at the Chennai Mathematical Institute in January 2026. The focus is on four-dimensional $\mathcal{N}=1$ Minkowski vacua in type IIB compactifications that live deep in the interior of moduli space and admit an exact worldsheet description in terms of Landau--Ginzburg models. The main examples are the $1^9$ and $2^6$ models, mirror to rigid Calabi--Yau threefolds and therefore free of Kähler moduli. This makes them ideal laboratories for testing whether fluxes can stabilize all fields and for probing conjectures about the string landscape and the swampland. Based mostly on arXiv:2406.03435, arXiv:2407.16756, we review how higher-order terms in the flux superpotential can stabilize fields that remain massless at quadratic order, how isolated Minkowski vacua arise in the $2^6$ model, and why these constructions provide sharp data for the tadpole and massless Minkowski conjectures. We also emphasize the role of arXiv:2407.16758 by other authors, where the first Minkowski vacua of this type with all fields massive were identified.