We study the resolvent \[ G^z = \left(\frac{1}{n}XX^T - zI_p\right)^{-1}, \qquad z\in\mathbb C,\ \Im(z)>0, \] where $X=(x_1,\ldots,x_n)\in\mathcal M_{p,n}$ is a random matrix with independent, but not necessarily identically distributed, columns. Our bounds are expressed in terms of moments of the centered quadratic forms \[ q_i(A):=x_i^TAx_i-\mathbb E[x_i^TAx_i], \] for deterministic matrices $A$ with unit Hilbert--Schmidt norm. In particular, we do not assume independence between the entries of a given column $x_i$. In the quasi-asymptotic regime $p\le O(n)$, the matrix $G^z$ admits a natural deterministic equivalent $\tilde G^z$, depending only on the second moments of the column vectors $x_1,\ldots,x_n$. We show that, for any deterministic matrix $B\in\mathcal M_p$, the trace $\text{Tr}(BG^z)$ is close to $\text{Tr}(B\tilde G^z)$, with error controlled by $\|B\|_{\text{HS}}$ under first-moment bounds on the quadratic forms, and by $\|B\|_{\text{HS}}/\sqrt n$ under suitable second-moment bounds.

Conducting uniform inference on a continuous functional F defined on a compact subset X of R^d involves specifying L_n^d nodes for estimation and the construction of confidence bands. While asymptotically valid inference requires L_n to increase with n, existing fixed-L rules of thumb and heuristic data-driven approaches lack formal justification. This paper shows that, for functions within a Donsker class, the simple grid-growth condition r_n^(1/4)/L_n -> 0, equivalently L_n grows faster than r_n^(1/4), is sufficient for valid inference on twice continuously differentiable functions whose estimators satisfy r_n^(1/2)(F_hat - F) = O_p(1).

Randomness extraction is indispensable for quantum random number generators, serving to eliminate bias and potential information leakage from raw measurement data. Conventional extractors operate in a block-wise fashion, requiring the complete accumulation of raw data before processing. To circumvent the latency and buffering overheads that hinder real-time random number generation, recent work introduced a stream-cipher implementation for the randomness extractor based on the Toeplitz matrix hashing. In this work, we generalize this stream-processing paradigm to the broader family of randomness extractors based on (almost dual) universal$_2$ random hashing. Specifically, we shift the computational burden from a time-consuming block-wise post-processing stage into an offline pre-processing stage that generates a pseudo-random mask. This allows the raw data to be processed by the mask on the fly using a simple bitwise exclusive-OR operation. Crucially, we prove that this stream implementation strictly preserves the security guarantees of the original block-wise protocols. We detail the transformation of three typical constructions -- based on standard Toeplitz, circulant, and modified Toeplitz matrices -- from block to stream implementations, and benchmark their practical performance using realistic quantum experimental data. We anticipate our framework will enhance the efficiency of real-time quantum cryptographic systems.

Modern agentic systems allow Large Language Model (LLM) agents to tackle complex tasks through extensive tool usage, forming structured control flows of tool selection and execution. Existing security analyses often treat these control flows as ephemeral, one-off sessions, overlooking the persistent influence of memory. This paper identifies a new threat from Memory Control Flow Attacks (MCFA) that memory can dominate the control flow, forcing unintended tool usage even against explicit user instructions and inducing persistent behavioral deviations across tasks. To understand the impact of this vulnerability, we further design MEMFLOW, an automated evaluation framework that systematically identifies and quantifies MCFA across heterogeneous tasks and long interaction horizons. To evaluate MEMFLOW, we attack state-of-the-art LLMs, including GPT-5 mini, Claude Sonnet 4.5 and Gemini 2.5 Flash on real-world tools from two major LLM agent development frameworks, LangChain and LlamaIndex. The results show that in general over 90% of trials are vulnerable to MCFA even under strict safety constraints, highlighting critical security risks that demand immediate attention.

We propose a novel phenomenological model of quantum gravitational collapse inspired by loop quantum gravity that ensures a completely regular spacetime evolution. By incorporating quantum gravitational modifications based on local rather than average energy density, our model simultaneously resolves both the central singularity and the shell-crossing singularities. Numerical simulations reveal that the interplay between local quantum repulsion and gravitational attraction leads to the formation of a stable, outgoing solitary matter wave, supported by a dynamical local anti-trapped region. This mechanism allows for a time-like ejection of the entire stellar mass -- a \emph{fuzzy-nova} -- which signals the end of macroscopic black holes. By providing a concrete dynamical mechanism for matter to escape the trapped region, our work sets a new stage for resolving the information paradox and opens a realistic observational window into quantum gravity.

This study develops a hybrid analytical and numerical approach for dynamic user equilibrium (DUE) assignment with simultaneous route and departure time choice (RDTC) for homogeneous users. The core concept of the proposed approach is the generalized queue replacement principle (GQRP), which establishes an equivalence between the equilibrium queueing-delay pattern and the solution to a linear programming (LP) problem obtained by relaxing some conditions in the original DUE-RDTC problem. We first present a method for determining whether the GQRP holds. Based on the GQRP, we then develop a systematic procedure to obtain an exact DUE solution by sequentially solving two LPs: one for the equilibrium cost pattern, including queueing delays, and the other for the corresponding equilibrium flow pattern. Computational results on networks of varying scales confirm the effectiveness of the proposed method.

By aiming to find and characterise dozens of habitable exoplanets through the technique of nulling interferometry, the LIFE space mission will produce transformational science. One of the key parameters for such an interferometric mission is the nulling baseline length - the distance between nulled apertures, which past studies have assumed to be 10-100m. Advances in planet occurrence statistics and simulation tools allow us now to revisit this key assumption with significantly more detail, particularly with the intention to reduce the range of baselines considered due to mission implementation concerns. We utilise the LIFEsim mission simulator along with revised mathematical tools to identify whether the range of baselines could be reduced without significantly affecting planet yield and fringe tracking performance. Along the way, we also determine a new astrophysically motivated technique for choosing which baselines are optimal for a given science target. We find that indeed, LIFE could utilise a considerably shorter range of baselines, such as 25-80m, or even discrete baselines without much (<10%) loss of performance. Nevertheless, careful trade-offs between performance and implementation simplification must be made, especially considering any spectral weighting that may be required by the scientific goals, and the potential loss of target-specific baseline optimisation.

The approximately flat outer parts of spiral galaxy rotation curves are commonly interpreted as evidence for a discrepancy between the observed baryonic mass and the dynamical mass inferred from the measured orbital velocities. In many analyses, simplified mass estimates are often expressed through the relation $v^2(R)=GM(<R)/R$, which is exact only under spherical symmetry. Spiral galaxies, however, are flattened disk systems, for which mass exterior to the galactocentric radius under consideration can contribute non-negligibly to the gravitational field. We introduce the \textit{Lost and Found} (LF) model, a geometrically consistent Newtonian framework based on direct full-disk gravitational integration and a parametrized representation of the disk surface density. This approach is closely related to previous thin-disk treatments that compute the gravitational field from the full mass distribution, while providing a simplified parametrization suitable for systematic fitting across heterogeneous galaxy samples. We apply the LF model to a heterogeneous sample of disk galaxies spanning a broad range of masses and radial extents. The model reproduces the main observed features of the rotation curves, including the inner rise and the approximately flat outer behavior, while yielding systematically lower inferred masses compared to conventional dynamical mass estimates. Across the sample, the LF-inferred mass scales nearly linearly with the conventional dynamical mass, with a characteristic scaling factor $η_{\rm LF}\sim0.67$. These results suggest that part of the inferred mass discrepancy in disk galaxies may be associated with geometric assumptions in standard mass estimates, and highlight the importance of full-disk treatments when interpreting galactic rotation curves.

The Gaia DR3 and Non-Single-Star (NSS) catalogs are currently the definitive sources for binary systems (Gaia Collaboration 2023). While this affords an invaluable asset to the astronomical community, there are suspected limitations. To address these constraints, we introduce a filtering regime that can be applied to raw data. This study introduces the "Triple Constraint" framework for use on Gaia DR3 data through the application of multi-wavelength cogent evidence. Using Topcat, we cross-matched the WDS Supplement with the Gaia DR3, 2MASS, and Pan-STARRS catalogs. The derived "Base-sample" (N = 199,786) and "Quad-sample" (N = 120,418) provide the basis for the examination employed to establish systemic limits within the Gaia single-star model. To verify the results and eliminate any bias introduced by employing the WDSS as the basis for the Base and Quad-samples, we exploited an independent sample of Gaia-2MASS cross-matched audit stars, the "Audit-sample" (N = 22,371). Only stars selected at high northern declinations (delta > 60 degrees) were employed for this sample to avoid potential distortions resulting from crowding. All of these samples manifested a -0.75 magnitude offset, indicating the presence of two stars of equal magnitude, creating a "Detection Gap" across all populations. We conclude, reinforced by a peer-reviewed independent external spectroscopic study, that a 7% floor of global sensitivity exists, representing a limitation of the Gaia pipeline. This suggests that local stellar mass density models require a quantifiable correction to accurately reflect the local baryonic mass budget.

Open-source software (OSS) projects rely on effective newcomer onboarding to sustain their communities. OSS projects widely adopt "good first issue" (GFI) labels to highlight beginner-friendly tasks. As development practices continue to evolve, understanding how these onboarding mechanisms change over time is important for both maintainers and researchers. This study analyzes 406,826 issues and 1,117 newcomer GFI pull requests across 37 popular GitHub repositories (30 of which use GFI labels) over a four-year period from July 2021 to June 2025. We find that while the proportion of issues with GFI labels remained stable during the first three years, it underwent a statistically significant decline beginning in January 2024, with substantial variation across projects not explained by repository age or programming language. Despite this supply-side decline, newcomer engagement with GFI issues remains stable at approximately 27%, suggesting that GFI labels maintain consistent attractiveness. Examining the outcomes of this engagement, we find that the merge rate of newcomer GFI pull requests declined from 61.9% to 42.2%. Initial pull request characteristics such as description length and code size show no significant association with merge outcomes, indicating that success is not predicted by the quantitative characteristics of the initial submission alone. Together, these findings reveal a widening gap between stable newcomer interest in GFIs and the declining availability and success of GFI-based onboarding, underscoring the need for maintainers to sustain both GFI labeling and review support.

Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on the level of the pairwise commuting charges, the underlying quantum group structures had not yet been recognised. In this paper, we provide a quantum group-theoretical description for the family of long-range deformations of arbitrary homogeneous Yang-Baxter integrable spin chains up to first order in the deformation parameter. In particular, we show that the deformations are obtained via a twist of the algebraic structure of the underlying quantum group. This twisting results in a generally non-associative algebra that has a non-trivial Drinfeld associator. The Drinfeld associator is then shown to encode the information about the long-range interaction terms for the integrable spin chain. Moreover, the deformed quantum group is shown to contain a large perturbatively associative substructure, thus ensuring the perturbative integrability of the long-range model. The deformed quantum group provides explicit expressions for the Lax operators and R-matrices of the long-range deformed models, which manifestly satisfy the RLL relation and the Yang-Baxter equation up to first order in the deformation parameter. In order to derive the results, we introduce algebra elements that we call the algebraic charge densities. As a side result, we provide a conjecture for the explicit expressions of the undeformed charge densities in terms of these algebra elements.

The early universe need not be described by an incomplete inflationary phase connected to a separate, more exotic prehistory. Recent results show that, within non-static FRW cosmology, only positive spatial curvature permits a nonsingular, geodesically complete universe with ANEC-respecting matter. We construct a geodesically complete closed $k=+1$ bounce-plus-inflation cosmology in ordinary general relativity, sourced by a single canonical scalar field with a positive vacuum offset. The bounce is supported by curvature rather than exotic stress energy: the matter content satisfies the NEC throughout and violates only the strong energy condition, as in any accelerated expansion. The solved branch remains sub-Planckian and evolves onto a curvature-diluted slow-roll phase with inflationary observables consistent with current constraints. The pivot-scale predictions are $n_s=0.9617$, $r=0.0045$ at $N_*=55$ and $n_s=0.9650$, $r=0.0037$ at $N_*=60$. Direct evolution of closed-universe infrared perturbations shows regular tensor and scalar propagation through the bounce and inflationary era, with the physical curvature perturbation freezing in the standard way. This gives a minimal explicit realization of a complete early-universe cosmology in the closed FRW branch selected by completeness and ANEC compatibility.

The Matérn covariance model is ubiquitous in spatial modelling, but there is no default choice for spatio-temporal modelling. In this paper, we consider the recently proposed ``diffusion-based'' extension of the spatial Matérn covariance model to a spatio-temporal non-separable covariance model that allows fractional smoothnesses in space and in time. The model is described in terms of a space-time fractional stochastic partial differential equation, but currently proposed computational approaches have strong restrictions on the possible smoothnesses in time. We propose a discretization method based on rational approximations in time to handle arbitrary smoothnesses, which leads to a vector autoregressive moving average process (VARMA). We prove that the covariance function of the approximation converges pointwise, determine explicit convergence rates as a function of spatial and temporal resolutions and the accuracy of the rational approximation, and conduct numerical verification to demonstrate small pointwise error for low orders of the VARMA process. Through a simulation study, we demonstrate that the parameters can be estimated back and that correctly specifying the temporal smoothness is especially important for forecasting. The approach is illustrated for three months of daily mean temperatures in mainland France.

This paper introduces a heterogeneous macroeconomic model of a Proof-of-Stake (PoS) network to analyze the long-term centralizing effects of external traditional finance (TradFi) yields. We model a continuum of rational actors divided into two distinct classes: investors, who optimize portfolios between staking and external variance-dominated investments, and consumers, who balance staking yields against the transactional utility of holding liquid assets. By employing a quasi-linear utility function to model consumer behavior, we derive a cubic polynomial that strictly defines the unique macroeconomic equilibrium of the coupled network. The model demonstrates that, at scale, external macroeconomic factors force the complete institutional capture of the PoS consensus layer. Because investors have access to external risk premiums, their wealth compounds exponentially, leading to massive capital inflows that crush the protocol's internal staking yield to effectively zero. We show that as the yield is crushed, consumer wealth becomes strictly upper-bounded. Ultimately, consumers are forced to cease staking entirely and hold all remaining wealth in liquid form to satisfy their transactional constraints.

Direct Device-to-Satellite (D2S) communications, which enable direct satellite connectivity with unmodified user equipment (UE), not only expand global coverage but also reshape the evolution of future access networks. However, D2S links face fundamental challenges due to inherently low signal-to-noise ratios (SNRs) and limited spatial multiplexing gains arising from near line-of-sight propagation, both of which severely constrain achievable spectral efficiency. Despite the lack of spatial multiplexing, this work shows that aggressive non-orthogonal transmissions, where multiple users (e.g., four) transmit concurrently over the same frequency resources, even to a single receive antenna, can unlock substantial capacity gains that remain entirely unexploited by existing systems. Realizing these gains in practice, however, requires receiver architectures that, to the best of our knowledge, have not yet been developed. To this end, we introduce NL-COMM-Sat, an efficient and flexible framework that overcomes this limitation by enabling aggressive non-orthogonal signal transmissions. In contrast to conventional non-orthogonal multiple access (NOMA) schemes, NL-COMM-Sat supports more than two UEs per receive antenna on the same frequency resource. The framework revisits optimal receiver design principles and proposes computationally efficient processing schemes that translate previously unexplored theoretical gains into tangible throughput improvements, even under realistic channel estimation errors and high-mobility Doppler conditions. Our evaluation shows that NL-COMM-Sat achieves up to a 2x increase in spectral efficiency compared to orthogonal multiple access and NOMA baselines across all considered SNR and Doppler regimes, even with a single-antenna receiver and user speeds of up to 500 km/h.

Building on results by Abouzahra and Lewin, McIntosh, and Kirilov we derive new functional dilogarithm equations and consequent diologarithim ladders. By showing that the ratio of a pair of sextic and cubic integrals equals a rational constant, we construct new 3- and 6-term functional equations, from which we derive an analytic proof of an identity by Loxton-Lewin, as well as a pair of quartic-base dilogarithm ladders, also believed to be new, building on Loxton's result. Finally, we prove conjectured 2-term dilogarithm identities of Bytsko, and extend his result for the Bloch-Wigner function using the above methods.

This paper presents two enhancements to cylindrical algebraic decomposition (CAD) based quantifier elimination (QE) for cases in which multiple equational constraints are present in the given input formula $ϕ^*$. The first enhancement provides more detail in the output when there is a conceptual partition of the set of variables of $ϕ^*$ into parameters and unknowns. In such cases, we describe how to partition the parameter space so that: (1) in each open set of the partition the number $ν$ of associated unknowns is a finite constant or is infinite; and (2) for each such open set for which $ν$ is finite, an expression for the unknowns in terms of the parameters is provided. The second enhancement is an efficiency gain achievable in certain situations. Indeed, when certain conditions are met, the second CAD equational projection step can be reduced more significantly than is supported by the prior existing theory. Relevant theorems and worked examples for both enhancements are provided. Application areas include approximation theory, cuspidal manipulator classification, and biological/chemical systems.

A promising approach to unifying functional and imperative programming paradigms is to localize mutation using linear or affine types. Haskell, a purely functional language, was recently extended with linear types by Bernardy et al., in the name of Linear Haskell. However, it remained unknown whether such a pure language could safely support non-local borrowing in the style of Rust, where each borrower can be freely split and dropped without direct communication of ownership back to the lender. We answer this question affirmatively with Pure Borrow, a novel framework that realizes Rust-style borrowing in Linear Haskell with purity. Notably, it features parallel state mutation with affine mutable references inside pure computation, unlike the IO and ST monads and existing Linear Haskell APIs. It also enjoys purity, lazy evaluation, first-class polymorphism and leak freedom, unlike Rust. We implement Pure Borrow simply as a library in Linear Haskell and demonstrate its power with a case study in parallel computing. We formalize the core of Pure Borrow and build a metatheory that works toward establishing safety, leak freedom and confluence, with a new, history-based model of borrowing.

Transition--metal dichalcogenides (TMDs) uniquely combine topological electronic states realized without external magnetic fields with a strong optical response arising from long--lived excitons. Motivated by this confluence, we investigate an interacting fermion--boson system formed by coupling an exciton to a quasihole of a fractional Chern insulator (FCI) at filling fraction $1/3$. We introduce a kagome--lattice fermion--boson model hosting an electronic FCI and a mobile exciton whose dispersion is tunable from a parabolic band to a flatband. Using exact diagonalization, we demonstrate the emergence of exciton--quasihole bound states controlled by the repulsive electron--exciton interaction $V_{\mathrm{FB}}$ and the exciton kinetic energy $t_{\mathrm{B}}$. These states appear as low--lying levels in the fermion--boson spectrum, well separated from the scattering continuum, and arise despite repulsive interactions due to a residual attraction to the local charge depletion associated with a quasihole. Reducing $t_{\mathrm{B}}$ enhances this effect by favoring interaction--dominated binding. Our results provide a model description of moiré TMD heterostructures, including fractional Chern insulating twisted bilayer MoTe$_2$ proximitized by excitonic TMD heterobilayers, where we estimate exciton--quasihole binding energy scales of $0.8$--$1.2$~meV, placing these effects within reach of photoluminescence spectroscopy.

Biomolecular systems are often modeled with partially known nonlinear stochastic dynamics, making state and parameter estimation a central challenge. While Kalman filtering techniques are widely used in this setting, their performance critically depends on the choice of the process noise covariance, which is typically assumed constant and heuristically tuned. Such assumptions are not justified for biomolecular systems, where intrinsic noise arises from underlying reaction kinetics. In previous works, a process noise covariance update based on the Chemical Langevin Equation (CLE) was introduced for Extended Kalman Filter (EKF)-based estimation in Chemical Reaction Networks (CRN). In this work, we analyze the stochastic stability of this filtering framework. In particular, we obtain a conservative upper bound on sampling interval for discrete-time biomolecular systems that ensures mean-square exponential boundedness under stated assumptions. The proposed framework is validated through simulations on a nonlinear gene expression model. The analysis provides theoretical justification for CLE-based process noise covariance modeling in EKF design for biomolecular circuits, reducing reliance on heuristic covariance tuning.

In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only the space dimension but simultaneously the time dimension as well. The proposed a-priori error estimate is developed for a linear parabolic partial differential equation and estimates the error between the numerical solution to a linear parabolic partial differential equation (PDE) and its space-time POD reduced solution. Numerical examples illustrate the occurring errors and analyze them in comparison to the theoretical bounds.

For an elliptic curve E over Q and a natural number j, Cojocaru has shown that there is an explicit constant C_E,j giving (under GRH) the density of primes p of good reduction such that the smallest invariant factor of E(F_p) is j. For E without complex multiplication, we study the question of when C_E,j is positive (a necessary and, on GRH, sufficient condition for there to be infinitely many such p), strengthening a result by Kim. Our arguments are group-theoretic using the image of the adelic Galois representation of E. Experimentally, C_E,j appears to vanish only when there is a coincidence of division fields; we document a number of families of such coincidences arising from abelian division fields.

This work provides a quantum-computing-first derivation of the Unitary Coupled Cluster ansatz, showing that its structure emerges naturally from fermionic algebra under unitary constraints. By explicitly connecting second quantization, Jordan-Wigner mapping, and circuit synthesis, we clarify conceptual gaps between quantum chemistry and quantum computing implementations, particularly regarding operator locality, commutation structure, and hardware realization.

We define a filter of time-frequency anisotropic global singularities of phase space for tempered distributions. The filter contains information from the corresponding anisotropic Gabor wave front set and admits propagation results for the Cauchy problem for certain linear evolution equations of Schrödinger type that generalize the harmonic oscillator.

In the era of high-sensitivity infrared (IR) astronomy, traditional manual diagnostics are no longer sufficient to harvest the complex physical insights hidden within interstellar spectra. We introduce a machine learning paradigm that bypasses the limitations of empirical band ratios by treating the complete IR spectrum of polycyclic aromatic hydrocarbons (PAHs) as a high-dimensional fingerprint. Using a random forest classifier trained on over 23000 spectra, we achieve a robust F1-score of 0.963 across 12 size and charge categories, maintaining high performance on unseen molecular mixtures. Interrogating the model's decision-making process reveals that PAH size diagnostics are charge-dependent. Neutral PAHs are traced by C-H modes, while ionized species rely on 6-8 micron C-C morphology; however, the 12.5micron feature remains a versatile tracer across multiple charge states. This AI-driven paradigm redefines our understanding of IR signatures, providing a transformative lens to probe the chemical complexity of the interstellar medium.

Superconducting altermagnets have proven to be a promising ground for emergent phenomena, but their study has involved two-dimensional systems. In this work, we investigate three-dimensional $d$- and $g$-wave altermagnets with spin-singlet chiral $d$-wave superconductivity and show the formation of crossed surface flat bands due to the interplay between superconducting and altermagnetic symmetries. We find that these crossed flat bands are topologically protected, appear at zero energy in the surface along $z$ due to the superconducting nodal lines in the $xy$-plane, and their number of corners is determined by the crystal symmetry of altermagnets. We also show that the superconducting nodal lines give rise to Bogoliubov-Fermi surfaces, which then affect the appearance of zero-energy arcs in the surface along $x$. Moreover, we demonstrate that the crossed flat bands or surface arcs, and Bogoliubov-Fermi surfaces give rise to the coexistence of three distinct dependences of the charge conductance on the normal transparency, hence offering a solid way for their detection and paving the way for realizing higher-dimensional topological phases using altermagnets.

We first consider nested CLE$_4$ in a simply-connected domain and compute some exact renormalised probabilities: the probability that two points belong to the same CLE$_4$ gasket and the probability that two points belong to the outermost CLE$_4$ gasket. The resulting conformally covariant formulas have a non-trivial modular dependence, expressed explicitly in terms of Jacobi theta functions. We are guided by the conformal field theory of the Ashkin-Teller (AT) model, but our proofs are purely probabilistic using Brownian loop soups, gauge-twisted Gaussian free fields (GFFs) and the level line geometry of the 2D continuum GFF. More generally, we also calculate renormalised probabilities that two points belong to CLE$_4$ gaskets sampled in alternation with certain two-valued sets of the Gaussian free field. These quantities correspond to the two-point function of the conjectured scaling limit of the AT single spins on the critical line. At the decoupling point, our results recover the Ising model correlations; they also suggest a CLE$_4$-based continuum FK representation of the AT single-spin fields along a whole segment of the critical line.

Finite-element simulations of optical cavities are presented, showing frequency splittings in the resonance spectrum. These can be directly compared to and understood by recent theory and experiments presented in van Exter et al. (2022, Phys. Rev. A 106, 013501), Koks et al. (2022, Phys. Rev. A 105, 063502) and Post et al. (2025, Phys. Rev. A 112, 033537). They provide strong evidence for the nonparaxial theory, but point out limitations of predicted mirror-shape corrections. The simulations also provide model-independent predictions of modal losses for optical cavities.

Elemental abundance variations in the solar corona, commonly characterised by First Ionisation Potential (FIP) bias, provide crucial diagnostics of chromospheric processes. The ponderomotive force model, which attributes fractionation to Alfvén wave propagation, has successfully reproduced the observed fractionation patterns in various solar features. However, existing theoretical implementations rely on a static quiet Sun chromosphere, leaving the influence of chromospheric dynamics largely unexplored. We address this limitation by combining hydrodynamic simulations from HYDRAD with ponderomotive force calculations through FIPpy, a new open-source code. Comparing predictions between an initial VAL-C chromosphere and a heated chromosphere following impulsive nanoflare-like events, we show that the ponderomotive force model remains consistent under dynamic chromospheric conditions, while stronger changes in fractionation behaviour arise from variations in acoustic flux and turbulence. Most significantly, when acoustic wave flux drops below $\sim5\times10^6$ erg cm$^{-2}$ s$^{-1}$, mass-dependent thermal velocities dominate the fractionation process, producing counterintuitive patterns where Fe exceeds Ca in FIP bias, while high-FIP Ar shows fractionation. We demonstrate that any source of chromospheric turbulence will act to suppress fractionation. For flares, our results predict that the increased turbulence will suppress FIP bias, potentially explaining the observed abundance variations during flares. These findings suggest that coronal abundances and composition encode a sensitive balance between dominant mechanisms, determined by the ratio of ponderomotive acceleration to turbulent velocity.

The Ichimura-Austern-Vincent (IAV) sum rule formalism for inclusive breakup reactions $a + A \to b + \mathrm{anything}$ treats the detected fragment $b$ as a spectator by replacing its interaction with the target by an optical potential. This assumption becomes questionable when $b$ is a loosely bound composite particle such as a deuteron. I derive a generalization that removes the spectator approximation and retains $b$'s internal degrees of freedom, providing state-resolved inclusive cross sections. Within the DWBA, all non-spectator effects enter through the source function via the operator $V_{bA} - U_{bA}$. The exact sum rule involves the full $x + A$ resolvent $(E_{x,0}^+ - H_{xA})^{-1}$, while a single-channel IAV-like expression is recovered only when the explicit target dependence of $V_{bA}$ is neglected; post-prior equivalence is preserved in both cases. A key conceptual finding is that the standard IAV result for structureless $b$ corresponds, under closure, to the \emph{total} inclusive cross section summed over all of $b$'s internal states, rather than the cross section for $b$ in a specific state. An operator-level estimate for $b = d$ on ${}^{208}\mathrm{Pb}$ shows that the non-spectator correction is not a small perturbation at the nuclear surface. The present work is purely formal: it establishes the theoretical framework and identifies the relevant operators, while quantitative assessment of the cross-section impact awaits a full numerical evaluation of the source integrals.