New sources of charge-parity (CP) violation beyond those described in the Standard Model (SM) are required to explain the observed matter--antimatter asymmetry of the Universe. The Standard Model Effective Field Theory (SMEFT) provides a framework to introduce additional electroweak sources of CP-odd physics in a model-independent manner. However, these CP-violating signatures are mostly degenerate to CP-even SMEFT operators in polarisation-blind observables, distinguishable only in the SM-New Physics (NP) interference using the azimuthal decay angle. Using Quantum Tomography techniques, we present a new approach to constraining these NP effects. Reconstructing the spin density matrix (SDM) of a diboson system, we go beyond `interference resurrection' to exploit the full signature of the Beyond-SM physics, including the pure quadratic NP terms. We show that this approach provides superior simultaneous sensitivity to characteristic features of CP-even and CP-odd contributions, including effects not fully captured by traditional angular observables.

We have considered the problem of the influence of inhomogeneity of gravitational field on transport effects predicted by the field theory describing massless Dirac fermions in the Maxwell and dark matter background. As a model of dark sector one takes into account dark photon model, where the hidden sector is described by the auxiliary U(1)-gauge field coupled to the visible sector. Elaborating the model we restrict our considerations to the case when Weyl type conformal transformation slightly differs from the Minkowski spacetime. This assumption simplifies the calculations and enables us not to use complicated methods of the quantum field theory in the curved background. The resulting currents stemming both from visible and dark sectors are proportional to the adequate beta functions appearing in the elaborated systems. For charge-less dark sector we predict corrections to the scale conductivities in both sectors: linear in α in the dark sector and quadratic in the visible one.

In this paper, we have studied the impact of two different formalisms of quantum decoherence in determining the sensitivities of the two future long-baseline experiments DUNE and P2SO. In Formalism-A, we will assume that the decoherence matrix is defined in a matter mass eigenstate basis which is the basis that diagonalizes the Hamiltonian for neutrinos in matter, with a constant matter density. In Formalism-B, we will define the decoherence matrix in the vacuum mass eigenstate basis and then rotate it to matter mass basis via an unitary transformation. By using different values of the decoherence parameter $Γ$, we will show how these two formalisms differ at the probability level and then we will demonstrate how the sensitivities can differ at the $χ^2$ level. Our results show that if the values of $Γ$ is small, then these two formalisms yield same probability in vacuum. However, if the values of $Γ$ is large or if there is strong matter effect, then these two formalisms yield very different results.

We construct a quantum low-density parity-check code family from a length-$512$ Calderbank--Shor--Steane base matrix pair. The base pair is permutation-equivalent to the known SPC(3) product CSS code, and the present affine-coset description gives a direct proof that both Tanner graphs are $(3,8)$-regular with girth $8$. The base code has parameters $[[512,174,8]]$. We then apply circulant permutation matrix (CPM) lifts. The main decoding experiment uses the CPM-lifted code with lift factor $P=32$, which has parameters $[[16384,4142,\le 40]]$, under the code-capacity depolarizing model. A belief-propagation decoder with post-processing achieved frame error rate about $10^{-8}$ at $p=0.085$, and one observed logical residual of weight $40$ gives a decoder-derived upper bound $d\le 40$.

We prove quenched and annealed statistical stability, linear response, and differentiability of asymptotic moments for parametric families of partially hyperbolic skew products, with random hyperbolic maps on the fibers. The main novelty is that the base maps also depend on the parameter, which leads to different formulas in the linear response and the derivative of the asymptotic moments with respect to the parameter. Our annealed results apply to partially hyperbolic maps that are not covered in \cite{BashCastro26,Dol,DS}.

Optical wireless communication (OWC) has emerged as a promising candidate for future high-capacity indoor wireless networks, driven by its large unregulated spectrum, high spatial reuse, and ability to support multi-gigabit data rates. However, OWC systems are highly sensitive to user mobility, as link performance depends strongly on the spatial alignment between transmitter and receiver. Accurate modelling of user position and device orientation is therefore essential for reliable channel estimation and system evaluation. To that effect, this paper proposes a hybrid Gauss--Markov and long short-term memory (GM--LSTM) mobility model for indoor OWC environments. The Gauss--Markov component captures the temporal correlation of user motion, while the LSTM learns residual behaviour to model non-linear movement patterns and orientation dynamics. The proposed model jointly predicts user position and device orientation, enabling improved representation of mobility in OWC channels. Performance is evaluated using prediction accuracy and per-user data rate evolution. Results show that the proposed hybrid GM--LSTM model outperforms conventional Random Waypoint and Gauss--Markov models, providing more accurate mobility prediction and more stable communication performance in dynamic indoor environments.

We introduce a framework for pulling back Cartier modules and their associated invariants along regular $F$-finite morphisms. To achieve this, we construct a relative Cartier isomorphism and operator for an arbitrary regular $F$-finite map of locally noetherian schemes. As an application, we obtain new results on the constancy regions of mixed test ideals, based on the work of Felipe Pérez.

Large language models with long context windows can answer complex questions directly from full-length academic, technical, and policy documents, but passing entire documents is often costly, slow, and can degrade answer quality while increasing the risk of unnecessary data leakage. This paper targets the common setting of answering many heterogeneous questions over long document(s), where fixed position heuristics and standard retrieval-augmented generation (RAG) can fail due to document structure variability and weak query-chunk semantic similarity, which often requires task- and domain-specific tuning of embedding retrievers. We propose {Selective Attention-Guided Extraction} (\ourmethod), a training-free, plug-and-play context reduction framework that uses a lightweight local LLM to perform a single prefilling pass and convert language model attention signals into a query-specific relevance heatmap at configurable granularities. \ourmethod\ further introduces \emph{differential attention} strategies to better isolate question-relevant evidence, then selects the top-scoring units under a user-defined token budget and forwards only this reduced context to a downstream LLM for answer generation. \ourmethod\ surpasses traditional reduction techniques across multiple long-document QA benchmarks, notably securing a top-4 rank on QuALITY-hard while constrained to a 10\% context budget. This enables a 90\% reduction in tokens with competitive accuracy, without the need for model fine-tuning or complex calibration.

We give an independent eta-product derivation of the level-8 Apery limit lim B_n^{(8)}/s_n = (7/32) zeta(3), where s_n = sum_{k=0}^n C(n,k)^2 C(2k,n)^2 and B_n^{(8)} is the rational companion sequence satisfying the same cubic recurrence with initial values B_0^{(8)}=0, B_1^{(8)}=1. This value was identified numerically by Almkvist-van Straten-Zudilin and was proved by Golyshev via Beukers's Atkin-Lehner modular method; it was later recomputed by Golyshev-Kerr-Sasaki in the motivic/normal-function framework. The continued fraction PCF((2n+1)(3n^2+3n+1),-n^6) = 8/(7 zeta(3)) already appears in Batut-Olivier and was later rediscovered by the Ramanujan Machine as conjecture Z1. The contribution of the present paper is an explicit rederivation, in the eta-product normalization, of the already-known level-8 Apery limit. We spell out the eta-product verification of the Wronskian identity, the normalization of the Eichler integral, the residue computation of the Fricke period polynomial, and the elementary continuant conversion.

Two-dimensional ferromagnets with strong perpendicular magnetic anisotropy exhibit magnetic order down to the monolayer thickness, beneficial for energy-efficient spintronic devices. In this work, molecular beam epitaxy has been employed to realize controlled Ni-doping in Fe$_{3}$GeTe$_{2}$ (FGT) epitaxial films. MBE not only enables a large-scale growth of 2D films, but also allows a precise control over thickness and doping. X-ray diffraction and scanning transmission electron microscopy (STEM) reveal the formation of high-quality epitaxial films of pristine and Ni-doped FGT on graphene via van der Waals (vdW) epitaxy. Integrated differential phase contrast STEM images further provide in-depth information on Ni substitution and intercalation into the vdW gaps. Ni incorporation in doped films results in the shrinking of both in-plane and out-of-plane lattice parameters. Superconducting Quantum Interference Device, Hall, and X-ray magnetic circular dichroism measurements were utilized to probe the ferromagnetic properties of the films. Due to both Ni substitution and intercalation into the vdW gaps for Ni-doped FGT films, we observed a suppression of PMA and a drastic reduction in the Curie temperature down to 50 K. Our density functional theory based calculations of structural and magnetic properties further supports and provide deep insights into the variations of magnetic exchange interaction parameters and atom-projected magnetocrystalline anisotropy energies due to Ni doping to understand the experimental observations.

We study delegated Bayesian persuasion: a principal incentivizes an intermediary to design information via outcome-contingent transfers, while the intermediary privately chooses the experiment subject to convex costs. We characterize first-best implementability through a pair of alignment conditions on the principal's and intermediary's payoff indices. A local condition on the support of the target experiment is necessary; a global affine alignment condition is sufficient. We show that the gap between them is non-empty and provide a partial characterization of the intermediate region. When the first-best is unattainable, the principal's problem admits a virtual Bayesian persuasion representation: the second-best experiment maximizes the same concavified objective as the first-best, with the principal's payoff index distorted by a single scalar shadow price that summarizes the entire agency friction. Under entropy costs, moral hazard compresses posterior dispersion whenever the intermediary's utility differs across the actions it recommends. Explicit closed-form solutions for posteriors, mixing weights, and the optimal transfer schedule are derived for binary environments.

The scale evolution of parton distributions is governed by splitting functions. We compute the four-loop splitting functions in perturbative QCD that control the evolution of quark non-singlet distributions. We confirm previous partial results and obtain, for the first time, fully analytic expressions for all non-singlet contributions at this order. These allow us to extract the analytic form of the four-loop virtual and rapidity anomalous dimensions entering logarithmic resummation. We provide precise numerical representations of the splitting functions suitable for parton evolution.

Periodic boundary conditions are not always used in the study of disordered systems, but it can be advantageous to apply them to mimick thermodynamically large systems. In this case, polarization and its cumulants can not be obtained directly, but through the tools of the modern theory of polarization. This theory casts the polarization in crystalline systems as a geometric phase, rather than an operator expectation value. We develop disorder averaging techniques within the context of this theory which can calculate the variance of the polarization, its higher order moments, and the excess kurtosis (or Binder cumulant). We also derive an indicator of delocalization based on the degeneracy as a function of boundary conditions. We apply the computational techniques to two model systems. To test localization, we use a one-dimensional disordered model which is fully Anderson localized. Our calculations verify this. We also apply our techniques to the one dimensional de Moura-Lyra model, developed to study power law correlated (controlled by a parameter, $α$) disorder. While this model is a pathological one, our method is validated. We also point out the significance of pairwise degeneracies found in the parameter range, $α>2$ and near the band center (or near half filling), where the model was conjectured to exhibit a mobility edge.

The structures and dynamics of the interstellar medium are governed by a combination of self-gravity, external gravity, and various sources of ordered and random motions on different spatial scales. This paper uses ALMA CO (3-2) observations at 0.1" $\approx$ 5 pc resolution to examine the scale dependence of molecular gas structure and dynamics in the central molecular zone (CMZ) of a nearby galaxy, NGC 3351. We use the dendrogram technique to characterize hierarchical molecular gas structures spanning two decades in spatial scales and measure their size, gas mass, and velocity dispersion. Their size-linewidth relation shows a power-law slope of 0.58, comparable to measurements for CMZs in other galaxies and suggestive of significant contribution from ordered motion on large scales. We further decompose the observed velocity dispersion in each gas structure into ordered versus random motions. The former appears stronger in gas structures at $\gtrsim$ 30 pc while the latter becomes more dominant at $\lesssim$ 30 pc. Modulo uncertainties with the CO-to-H$_2$ conversion factor, the estimated gravitational free-fall time is comparable to the crossing time of ordered motions for structures on all spatial scales, and both becomes longer than the crossing time of random motions at small, $\lesssim$ 10 pc scales. Our results highlight the varying sources and drivers of gas motions on different spatial scales in the CMZ of a Milky Way-like galaxy.

Proliferating cell collectives often develop an active growth layer near their boundary that regulates expansion and morphology, as observed in systems ranging from bacterial biofilms to epithelial tissues and tumor spheroids. While such layers have been attributed to diverse mechanisms, their microscopic origin remains unclear in many situations. Here, we show that micromechanical feedback alone provides a minimal mechanism for their emergence. We introduce a particle-based model of non-motile proliferating cells in which growth is locally inhibited by compressive stress, coupling division to mechanical interactions and generating an active growth layer without biochemical regulation. An emergent mechanical length scale, denoted by $χ$, sets the extent of the proliferative region and controls the system's behavior across scales, governing growth dynamics, morphology and organizing internal stress and velocity fields. Coarse-graining the model yields a continuum description with no adjustable parameters, providing a microscopic foundation for existing approaches. When the colony expands into a passive environment, we observe and characterize fingering instabilities driven purely by mechanical feedback. These instabilities can be tuned through the system geometry relative to $χ$, and leads to an exponential acceleration of colony growth, enhancing the collective growth rate. We further establish a correspondence with nutrient-depletion models, providing a route to study the statistical properties of expanding fronts within a minimal microscopic framework.

The properties of the first metal-free stars remain largely unknown, and so far, the only data-driven constraints on their mass distribution (IMF) come from near-field cosmology. Here, we interpret new observations of the C1 and C2 components of Hebe, the HeII emitter near the galaxy GN-z11. Using a locally calibrated model, we robustly confirm the pristine (PopIII) nature of both components, showing that the measured upper limits on metal lines can only be reproduced by galaxies with $>50\%$ of their stellar mass in PopIII stars. We find that C1 is consistent with a purely PopIII system and adopt a simple parametric approach to infer the implications for the PopIII IMF and stellar mass. The observed $\rm HeII/H_γ$ ratio excludes steep IMFs, favoring top-heavy distributions, especially for young stellar ages ($\leq 1$ Myr). Combined with the HeII luminosity, this implies a total PopIII stellar mass of $2 \cdot 10^4 < M_\star/M_\odot < 6 \cdot 10^5$. While degeneracies between IMF, stellar mass, and age remain, adopting the lower stellar masses predicted by simulations ($M_\star < 10^5\,M_\odot$) strengthens the preference for top-heavy IMFs. Combining these results with near-field constraints, which instead exclude the flattest IMFs, we define a data-driven range of viable PopIII IMFs, linking characteristic mass and slope. This work demonstrates that direct observations of high-$z$ PopIII systems can place independent constraints on the IMF of the first stars, opening a new window on their formation and properties.

Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating solvers. In this paper, we measure the end-to-end performance of a hybrid quantum-classical framework designed to accelerate Finite Element Analysis (FEA) by integrating a quantum solver for GPP into Synopsys/Ansys' LS-DYNA multiphysics simulation software. The quantum solver we use is based on Iterative-QAOA, a scalable, non-variational quantum approach for optimization. We focus on two specific classes of FEA problems, namely vibrational (eigenmode) analysis and transient simulation. We report numerical simulations on up to 150 qubits done on NVIDIA's CUDA-Q/cuTensorNet and implementation on IonQ's Forte quantum hardware. The potential impact on LS-DYNA workflows is quantified by measuring the wall-clock time-to-solution for complex problem instances, including vibrational analysis of large finite element models of a sedan car and a Rolls-Royce jet engine, as well as transient simulations of a drill and an impeller. We performed end-to-end performance measurements on meshes comprising up to 35 million elements. Measurements were conducted using LS-DYNA in distributed-memory mode via Message Passing Interface (MPI) on AWS and Synopsys compute clusters. Our findings indicate that with a quantum computer in the loop, amortized LS-DYNA wall-clock time can be improved by up to 14.6% for specific cases and by at least 5.9% for all models considered. These results highlight the significant potential of quantum computing to reduce time-to-solution for large-scale FEA simulations within the Noisy Intermediate-Scale Quantum (NISQ) era, offering an approach that is scalable and extendable into the fault-tolerant quantum computing regime.

Microwave sounding is the leading driver of global numerical weather forecasting, but is limited by the scalability of such instruments. With modern machining and commercial microwave components, it is now possible to design low size, weight, power, and cost (SWaP-C) microwave spectrometers while maintaining wide bandwidth performance. Here we report on the status of CubeSounder, a spectrometer tailored for water vapor radiometry that utilizes passive wave guide filter banks. After developing a prototype and high altitude balloon payload, we demonstrated CubeSounder on commercial stratospheric balloon flights. We report on our design process, especially the simulation and fabrication of the custom millimeter-wave filter banks. We also report the initial results of the data collected from the balloon flights.

We investigate self-dual radially symmetric configurations in the $CP^1$ model coupled to a Maxwell and Chern-Simons (CS) gauge fields through nonminimal interactions. Starting from the nonlinear $O(3)$-sigma model, we explicitly construct its classical mapping to the $CP^1$ formulation, highlighting the emergence of a local $U(1)$ gauge symmetry intrinsically associated with the Fubini-Study geometry of the target space. In the static regime, the combined effects of the Chern-Simons term and the Pauli-like nonminimal coupling modify the effective gauge connection, render the electric sector unavoidable, and give rise to magnetized and electrically polarized BPS lump configurations. By implementing the Bogomolnyi procedure, we determine the self-interaction potential required for self-duality and derive the corresponding BPS equations. We show that the magnetic flux remains quantized and is completely fixed by the asymptotic behavior of the gauge field, even in the presence of the Chern-Simons and nonminimal couplings. A detailed asymptotic analysis further reveals that finite-energy solutions necessarily correspond to lump-like configurations in which the $CP^1$ scalar field vanishes at spatial infinity. Numerical solutions of the BPS equations confirm that the resulting configurations are regular, spatially localized, and free of singularities, exhibiting confined magnetic flux together with a nontrivial localized electric field. These results show that the generalized $CP^1$-Maxwell-CS model supports self-dual solitons whose internal structure is rigidly governed by the target-space geometry rather than by spontaneous symmetry breaking.

Given a cooriented branched surface $\mathcal B$ fully carrying a foliation $\mathcal F$, we use the dual graph of $\mathcal B$ to define a simplicial 1-cycle $Γ_m(\mathcal B)$ representing the Poincaré dual of the Euler class of $\mathcal F$ relative to the boundary. As an example, we complete the classification of which homology classes in the Whitehead link exterior are realisable as relative Euler classes of taut foliations. We also show how our formula generalises previous results of Lackenby and Dunfield. Finally, we observe that cooriented branched surfaces whose complement is a union of balls satisfy a Combinatorial Transverse Surface Theorem, in the sense of Landry--Minsky--Taylor.

Diffusion recommender systems achieve strong recommendation accuracy but often suffer from popularity bias, resulting in unequal item exposure. To address this shortcoming, we introduce A2G-DiffRec, a diffusion recommender that incorporates adaptive autoguidance, where the main model is guided by a less-trained version of itself. Instead of using a fixed guidance weight, A2G-DiffRec learns to adaptively weigh the outputs of the main and weak models during training, supervised by a fairness-aware regularization that promotes balanced exposure across items with different popularity levels. Experimental results on three public datasets show that A2G-DiffRec is effective in enhancing item-side fairness at a marginal cost of accuracy reduction compared to existing guided diffusion recommenders and other non-diffusion baselines.

Decentralized protocols claim immutable, rule-based execution, yet many embed emergency mechanisms such as chain-level freezes, protocol pauses, and account quarantines. These overrides are crucial for responding to exploits and systemic failures, but they expose a core tension: when does intervention preserve trust and when is it perceived as illegitimate discretion? With approximately \$10 billion in technical exploit losses potentially addressable by onchain intervention (2016-2026), the design of these mechanisms has high practical stakes, but current approaches remain ad hoc and ideologically charged. We address this gap by developing a Scope $\times$ Authority taxonomy that maps the design space of emergency architectures along two dimensions: the precision of the intervention and the concentration of trigger authority. We formalize the resulting tradeoffs of standing centralization cost, containment speed, and collateral disruption as a stochastic decision support framework, and derive three empirical hypotheses from it. Assessing the framework against 705 documented exploit incidents, we find that containment time varies systematically by authority type, that losses follow a heavy-tailed distribution ($α\approx 1.33$) concentrating risk in rare catastrophic events, and that community sentiment plausibly modulates the effective cost of maintaining intervention capability. Using scope breadth as a practical proxy for blast potential, we also find that narrower interventions (Account/Module) do not underperform broader ones (Protocol/Network) on containment success and are slightly faster at the median, giving partial empirical support to the scope-blast hypothesis. The analysis yields design guidance for emergency governance and reframes the problem as one of engineering tradeoffs rather than ideological debate.

An $ω$-regular language is Eve-positional if, in all games with this language as objective, the existential player can play optimally without keeping any information from the previous moves. This notion plays a crucial role in verification, automata theory and synthesis. Casares and Ohlmann recently gave several characterisations of Eve-positionality of $ω$-regular languages. For this, they introduce the notion of $\varepsilon$-complete parity automaton and show (among other results) that an $ω$-regular language is Eve-positional if and only if it can be recognised by some $\varepsilon$-completion of a deterministic parity automaton. Colcombet and Idir built on their work, and obtained a more direct algebraic characterisation of Eve-positionality. We introduce a new formalism that characterises the Eve-positional languages, consisting of a restriction of non-deterministic Büchi automata. This allows us to complete a missing implication in Casares and Ohlmann's work. We then use this formalism to describe a determinization procedure for non-deterministic Büchi automata recognising such languages, with size blow-up at most factorial. We also show that this construction is state-wise optimal for languages over sufficiently complete alphabets.

Generalized neutrino interactions (GNI) are emerging as a convenient framework for describing effective scalar, vector, and tensor interactions. Such interactions arise naturally from extensions of the Standard Model that aim to explain neutrino properties and their mass origin. In this paper, we carefully study the two more common parametrizations for GNI and how to relate them. This allows us to compare bounds obtained from CEvNS and deep-inelastic scattering under the same footing. In addition, we present the current bounds from CEvNS measurements by COHERENT and compare them to those obtained from deep inelastic scattering on the same level. Our results focus on neutrino-quark interactions, and illustrate the complementarity between experiments working at different scales for GNI, showing that scalar interactions are better constrained by low-energy experiments like COHERENT, while tensor interactions are robustly constrained from deep inelastic scattering.

We study an extended Kitaev model on the triangular lattice in a limit where the symmetric off-diagonal bond-dependent and Heisenberg interactions together map onto an XXZ model, in addition to the Kitaev interaction. Within the previously identified $\mathbb{Z}_2$ vortex regime, we uncover a ferrichiral skyrmion phase characterized by a sublattice-resolved scalar chirality: two of the three sublattices carry unit skyrmion charge, while the third remains nonchiral. Using classical Monte Carlo simulations, we show that this ferrichiral skyrmion phase emerges at zero temperature and in the absence of both an external magnetic field and Dzyaloshinskii-Moriya interactions, in sharp contrast to conventional skyrmion-hosting systems. The phase is stable over a wide parameter window and persists to relatively high temperatures. Our results reveal an unconventional route to skyrmion physics driven purely by frustrated exchange interactions and highlight the emergence of rich topological structures. Since both XXZ anisotropy and Kitaev interactions originate from the same spin-orbit-coupling mechanism, materials traditionally classified as XXZ magnets are expected to host finite Kitaev interactions as well. The potential for ferrichirality in these systems therefore warrants further investigation.

We show that excitons coupled to cavity photons and phonons admit a generalized Bloch theorem when formulated for the conserved total crystal momentum. In minimal-coupling and Fröhlich representations, the interchange of momenta between fermions and bosons breaks crystalline excitons' translational symmetry. In our symmetry-adapted frame, the Hamiltonian becomes block diagonal, without invoking approximations. The resulting formulation yields dispersions and optical responses of cavity exciton polaron-polaritons, enabling investigations that elucidate material properties in strong coupling.

Rabi oscillations characterize light-matter hybridization in the waveguide quantum electrodynamics~(WQED) framework, with their associated decay rates reflecting excitation damping, yet their behavior remains unresolved when collective emitters are coupled to a collective waveguide mode. This scenario reveals a conceptually novel collective-light-collective-matter interaction, realizable when a timed-Dicke state~(TDS) of subwavelength emitters couples to a slow, delocalized surface-plasmon mode, forming a hybridized plasmon-polariton~(HPP). The HPP acquires its directionality from the TDS via momentum matching. It also exhibits plasmonic characteristics, with excitation frequencies following the surface-plasmon dispersion relation. We obtain a Rabi oscillation and a long-time decay that describe the HPP and use them to reveal weak- and strong-coupling regimes through the emergence of normal-mode splitting. By performing a finite-time Lyapunov-exponent analysis, we show that the HPP also exhibits instantaneous decay and identify three distinct decay regimes: early-time rapid, transient-time oscillatory, and long-time classical. Finally, by analyzing the emission spectrum, we observe an anticrossing of the peak doublets~(a feature also seen in cavity QED setups) which originates from quantum vacuum effects and the resulting non-Markovian HPP evolution in our WQED.

In this work, we investigate the bi-Lipschitz invariance of two fundamental local invariants in singularity theory: the Łojasiewicz exponent and the local Euler obstruction. We draw inspiration from Bivià-Ausina and Fukui, whose framework we extend to ideals in rings of analytic functions defined on affine toric varieties. We establish conditions under which these invariants remain unchanged under bi-Lipschitz equivalence. We also provide an answer, to a particular case, to the open question of whether the local Euler obstruction is a bi-Lipschitz invariant. For hypersurfaces with isolated singularities, we show that the Euler obstruction is preserved under non-degeneracy conditions. These results contribute to the understanding of metric invariants in complex analytic geometry.

We study the space of $A_\infty$-natural transformations between braiding functors acting on the Fukaya category associated to the Coulomb branch $\mathcal{M}(\bullet,1)$ of the $\mathfrak{sl}_2$ quiver gauge theory. We compute all cohomologically distinct $A_\infty$-natural transformations $\mathrm{Nat}(\mathrm{id}, \mathrm{id})$ and $\mathrm{Nat}(\mathrm{id}, β_i^-)$, where $β_i^-$ denotes the negative braiding functor. Our computation is carried out in a diagrammatic framework compatible with the established embedding of the KLRW category into this Fukaya category. We then compute the Hochschild cohomology of the Fukaya category using an explicit projective resolution of the diagonal bimodule obtained via the Chouhy-Solotar reduction system, and use this to classify all cohomologically distinct natural transformations. These results determine the higher $A_\infty$-data encoded in the braiding functors and their natural transformations, and provide the first step toward a categorical formulation of braid cobordism actions on Fukaya categories.

We demonstrate a nondestructive, high-throughput method for observing dislocations in GaN (0001) using phase-contrast microscopy (PCM). The PCM images (359x300 $μ$m$^2$) analyzed in this study were acquired with an exposure time of 3 ms per image. The one-to-one correspondence between threading dislocation (TD) contrasts in PCM images and the corresponding contrasts in multiphoton excitation photoluminescence (MPPL) images provides clear evidence that PCM can detect TDs with in-plane Burgers vector components. The contrast shape in PCM reflects the inclination of dislocations with respect to the surface normal: dot contrasts correspond to vertical dislocations, whereas line contrasts correspond to inclined dislocations. By shifting the focal plane from the top surface to the back surface, the three-dimensional propagation paths of dislocations can be visualized. The PCM image obtained represents a projection of threading dislocations within a thickness of approximately 43 $μ$m. Dislocations spaced as close as 1.3 $μ$m can be individually resolved. In addition, the capability of PCM to detect scratches, subsurface scratches, facet boundaries, and voids was demonstrated. This study establishes PCM as a versatile and laboratory-accessible technique for three-dimensional, nondestructive characterization of dislocations and other defects in wide-bandgap semiconductors.