Decoder-only LLM rerankers struggle with long documents: inference is costly and relevance signals can be diluted by irrelevant context. Motivated by a diagnostic attention analysis suggesting that appended irrelevant context can weaken query-focused interactions, we propose EviRerank, an evidence-based long-document reranking framework for decoder-only LLMs. EviRerank first scores document blocks with a lightweight selector, such as BM25, a bi-encoder, or a cross-encoder. It then constructs a compact reranking context under a hard token cap by dynamically budgeting evidence blocks with Adaptive Evidence Budgeting (AEB) and adding a compact global cue via Summary Augmentation (SA). Finally, the compact evidence context is reranked with a decoder-only LLM. Across TREC DL'19, DL'22, DL'23, and MLDR-zh, EviRerank consistently outperforms full-document LLM reranking and strong block-selection baselines while reducing input length. RankZephyr-7B validation further confirms transfer to listwise reranking. On TREC DL'19, EviRerank reaches up to 0.744 nDCG@10 and 0.307 MAP, improving over RankLLaMA while using a compact evidence context.

We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surface braids and surface links, we also define an invariant that can be used as an indicator of the necessity of Euler fusion or fission between braid systems.

The field of Dynamic Multi-Objective Optimization (DMOO) has witnessed a surge of interest from both academia and industry, as numerous time-evolving real-world applications can be naturally formulated as Dynamic Multi-Objective Optimization Problems (DMOPs). This growing demand thus necessitates advanced benchmarks to rigorously evaluate optimization algorithms under realistic conditions. This paper introduces a comprehensive and principled framework for constructing highly realistic and challenging DMOO benchmarks. The proposed framework incorporates several novel components, including: a generalized formulation that allows the Pareto-optimal Set (PS) to change on hypersurfaces; a mechanism for creating controlled variable contribution imbalances to generate heterogeneous landscapes; and dynamic rotation matrices for inducing time-varying variable interactions and non-separability. Furthermore, we incorporate a temporal perturbation mechanism to simulate irregular environmental changes and propose a generalized time-linkage mechanism that systematically embeds historical solution quality into future problems, thereby capturing critical real-world phenomena such as error accumulation and time-deception. Extensive experimental results validate the effectiveness of the proposed framework, demonstrating its superiority over conventional benchmarks in terms of realism, complexity, and its capability for discriminating state-of-the-art algorithmic performance. Thus, this work establishes a new standard for dynamic multi-objective optimization benchmarking and provides a powerful tool for the development and evaluation of next-generation algorithms capable of addressing the complexities of real-world dynamic systems.

Driving non-superconducting materials into a superconducting state through specific modulation is a key focus in the field of superconductivity. Pressure is a powerful method that can switch a three-dimensional (3D) material between non-superconducting and superconducting states. In the two-dimensional (2D) case, strain engineering plays a similar role to pressure. However, purely strain-induced superconductivity in 2D systems remains exceedingly scarce. Using first-principles calculations, we demonstrate that a superconducting transition can be induced solely by applying biaxial tensile strain in a 2D carbon allotrope, THO-graphene, which is composed of triangles, hexagons, and octagons. Free-standing THO-graphene is non-superconducting. Surprisingly, the electron-phonon coupling in strained THO-graphene is enhanced strong enough to pair electrons and realize superconductivity, with the highest superconducting transition temperature reaching 45 K. This work not only provides a notable example of controlling metal-superconductor transition in 2D system just via strain, but also sets a new record of superconducting transition temperature for 2D elemental superconductors.

Semi-supervised inference assumes access to a labeled dataset together with a large unlabeled dataset in which the outcome variable is missing, and it is widely used to improve statistical efficiency and support generalizability across populations. In many modern applications, however, individual-level unlabeled data may not be directly accessible due to privacy restrictions, data-sharing limits, or storage constraints, while summary statistics such as sample means and covariances from the unlabeled population are often available. In this work, we study this constrained semi-supervised setting where, in addition to labeled data with individualized observations, auxiliary information from the unlabeled population is available only through summary statistics. We propose new semi-supervised inference methods for mean estimation under both covariate-independent and covariate-dependent labeling and show that unlabeled summaries can still improve efficiency and help correct selection bias. The proposed methods apply in high dimensions and are robust to model misspecification. Valid inference is obtained under sparsity conditions comparable to those required by semi-supervised methods that assume access to individual-level unlabeled samples. Our approach relies on a specialized cross-fitting procedure, where sample splitting is applied only to the labeled data, which removes the need for individualized unlabeled covariates. We further extend this framework to average treatment effect estimation, enabling generalizability and transportability of causal conclusions in this constrained semi-supervised setting.

We show that quasinormal modes (QNMs) of a massive scalar field in Kerr-de Sitter and Myers-Perry black holes exhibit an exceptional line (EL), which is a continuous set of exceptional points (EPs) in parameter space, at which two QNM frequencies and their associated solutions coincide. We find that the EL appears in the parameter space spanned by the scalar mass and the black hole spin parameter, and also in the Nariai limit, i.e., $r_{\rm c} - r_{\rm h} \to 0$, where $r_{\rm c}$ and $r_{\rm h}$ denote the radii of the cosmological and black hole horizons, respectively. We analytically study the amplitudes or excitation factors of QNMs near the EL. Such an analytic treatment becomes possible since, in the Nariai limit, the perturbation equation reduces to a wave equation with the Pöschl-Teller (PT) potential. We discuss the destructive excitation of QNMs and the stability of the ringdown near and at the EL. The transient linear growth of QNMs -- a characteristic excitation pattern near an EP or EL -- together with the conditions under which this linear growth dominates the early ringdown, is also studied analytically. Our conditions apply to a broad class of systems that involve the excitation of (nearly) double-pole QNMs.

The Noisy Intermediate-Scale Quantum (NISQ) era of technology in which we currently find ourselves is defined by non-universality, susceptibility to errors and noise, and a search for useful applications. While demonstrations of practical quantum advantage remain elusive in this era, it provides space to develop and analyze the advantages and limitations of systems and their ability to solve problems. In this work, we critically assess a proposed quantum algorithm for the graph isomorphism problem, implemented on a photonic quantum device. Inspired by the nature of this quantum algorithm, we formulate a necessary condition for the isomorphism of graphs encoded in Gaussian boson samplers and a classical algorithm to test for it. Our classical algorithm makes use of efficiently computable statistical properties of a quantum sampling system to show a pair of graphs fail to meet our necessary condition and thus cannot be isomorphic. We analyze our algorithm in the context of the inspiring, sampler-based quantum algorithm of Bràdler et. al., the classical color refinement algorithm, and the state-of-the-art quasi-polynomial Babai algorithm.

In the context of distributed fusion estimation, directly transmitting local estimates to the fusion center may cause a privacy leakage concerning exogenous inputs. Thus, it is crucial to protect exogenous inputs against full eavesdropping while achieving distributed fusion estimation. To address this issue, a noise injection strategy is provided by injecting mutually independent noises into the local estimates transmitted to the fusion center. To determine the covariance matrices of the injected noises, a constrained minimization problem is constructed by minimizing the sum of mean square errors of the local estimates while ensuring (ε, δ)-differential privacy. Suffering from the non-convexity of the minimization problem, an approach of relaxation is proposed, which efficiently solves the minimization problem without sacrificing differential privacy level. Then, a differentially private distributed fusion estimation algorithm based on the covariance intersection approach is developed. Further, by introducing a feedback mechanism, the fusion estimation accuracy is enhanced on the premise of the same (ε, δ)-differential privacy. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed algorithms, and the trade-off between differential privacy level and fusion estimation accuracy.

The optical response of two-dimensional materials has been customarily calculated {\it ab initio} using plane waves basis and the full Bloch wavefunction, without separating the most important orbital contributions. In the family of monolayer transition metal dichalcogenides lacking inversion symmetry, we take advantage of the mostly $d-$orbital content of the Bloch bands around the semiconductor gap to reduce the calculation of their linear and quadratic optical susceptibilities to a very minimal model that includes only three energy bands. As the Bloch wavefunction determines the microscopic response to external fields, this simple approach reproduces well first principles calculations up to roughly 2 eV above the band gap. This could be the starting point for the inclusion of many-body effects with only a few energy bands in a numerically inexpensive way.

Network nonlocality extends Bell nonlocality to settings with multiple independent sources and parties. Certifying it in quantum information processing tasks requires suitable witnesses. However, in contrast to local correlations, the set of network-local correlations is non-convex. This non-convexity makes certifying network nonlocality a highly non-trivial task. Existing approaches involve leveraging network-specific properties, or inflation-based methods whose constraints grow combinatorially in the number of local variables. In this work, we introduce a linear programming witness for network nonlocality built from five classes of linear constraints. These classes are network-agnostic, although the explicit forms of the constraints must be tailored to a specific network's structure. We use the procedure to construct network nonlocality witnesses for a family of ring networks and certify network nonlocality for a concrete example, relying only on observed probabilities and a tunable experimental parameter. Our work advances the search for efficient witnesses to certify network nonlocality across diverse quantum network architectures.

The realization of fractional Chern insulators opens up the possibility of exploring fractionally charged excitations and anyonic statistics in the absence of a magnetic field. A central question is whether lattice-based systems can give rise to radically new states, distinct from those observed in traditional fractional quantum Hall systems. In this work, we investigate a new type of moiré flat band system composed of Bernal bilayer graphene and rhombohedral tetralayer graphene. We discover an unprecedented richness of quantum anomalous Hall insulators with Chern numbers from C = 1 to C = 7 at v = 1 and around v = 3. Remarkably, we observe an exotic fractional Chern insulator with C = 7/3 around v = 2/3 which is beyond all known fractional Chern insulators described by either the Jain sequence or current high Chern theory. Our work expands the understanding of fractionally charged excitations beyond the Landau level basis and offers a new moire platform for exploring anyons.

Organic mixed conductors (OMCs) represent a promising class of materials for applications in bioelectronics, physical computing, and thermoelectrics. Rather unparalleled, OMCs feature dynamics spanning multiple length and time scales, involving an intricate coupling between electronic, ionic, and mass transport. These characteristics set them notably apart from traditional semiconductors and hinder the description by conventional semiconductor theory. In this work, we approach the charge carrier modulation of OMCs using statistical mechanics. We discuss OMCs from a thermodynamic perspective and contrast them with established semiconductor materials, highlighting key differences in their collective charge carrier dynamics. This motivates our description of OMCs as a lattice gas, which we analyze within the grand canonical ensemble. The model exhibits a first-order phase transition analogous to a classical vapor$\unicode{x2013}$liquid transition, governed by temperature and chemical potential. In doing so, it captures the formation of distinct low- and high-density carrier phases, consistent with recently reported experimental observations. It also illustrates how metastability near the phase boundary can give rise to history-dependent characteristics in device operation, a similarly well-reported effect in OMC transistors. This work is intended as a simple motivation for studying OMCs through the lens of statistical mechanics, offering a more natural description than traditional semiconductor models developed for materials of fundamentally distinct character.

High-fidelity spectrum cartography is important for spectrum monitoring and wireless situational awareness, especially in satellite-based wide-area sensing scenarios where measurements are sparse, noisy, and often low-bit quantized. In such settings, two coupled challenges arise: accurate reconstruction from severely incomplete measurements and efficient allocation of additional sensing resources under a limited sensing budget. Existing methods usually address these problems separately, and, for reconstruction, they often rely on priors that are insufficiently expressive under sparse and quantized measurements. This paper proposes Generative Spectrum Cartography (GSC), a diffusion-based posterior inference framework for spectrum cartography with uncertainty-aware active sensing. Specifically, spectrum map recovery is formulated as a Bayesian inverse problem under a learned diffusion model prior, and closed-form posterior mean updates are derived for both linear and quantized measurement models. By embedding these updates into the reverse diffusion process, GSC enables gradient-free and measurement-consistent posterior sampling without relying on computationally costly likelihood-gradient guidance. The resulting posterior samples are further used to estimate spatial uncertainty and to guide diversity-aware selection of additional measurement locations for active sensing. Experiments on simulated electromagnetic maps and a high-fidelity simulated satellite monitoring scenario show that GSC achieves higher PSNR, lower LPIPS, and more efficient sensing than representative baseline methods under sparse, noisy, and low-bit quantized measurements.

Many studies assert that dark matter (DM) subhaloes without a baryonic counterpart and with an inner cusp always survive no matter the strength of the tidal force they undergo. In this work, we perform a suite of numerical simulations specifically designed to analyse the evolution of $V_\mathrm{max}$, $r_\mathrm{max}$ and concentration of low-mass DM subhaloes due to tidal stripping. We employ the improved version of the DASH code, introduced in our previous work arXiv:2207.08652 to investigate subhalo survival. We follow the tidal evolution of a single DM subhalo orbiting a Milky Way (MW)-size halo modeled with a baryonic disc and a bulge replicating the actual mass distribution of the MW. We consider the effect of the time-evolving gravitational potential of the MW itself. We simulate subhaloes with unprecedented accuracy, varying their initial concentration, orbital parameters, and inner slope (both NFW and prompt cusps are considered). Unlike the previous literature, we examine the evolution of subhalo structural parameters -- tidal tracks -- not only at orbit apocentres but also at pericentres, finding in the former case both similarities and differences -- particularly pronounced in the case of prompt cusps. Overall, $r_\mathrm{max}$ shrinks more than $V_\mathrm{max}$, leading to a continuous rise of subhalo concentration with time. The velocity concentration at present is found to be around two orders of magnitude higher than the one at infall, being comparatively larger for pericentre tidal tracks versus apocentres. These findings highlight the dominant role of tidal effects in reshaping low-mass DM subhaloes, providing valuable insights for future research via simulations and observations, such as correctly interpreting data from galaxy satellite populations, subhalo searches with gravitational lensing or stellar stream analyses, and indirect DM searches.

We study the behavior of Du~Bois singularities under base change and fiber products. For embeddable varieties in characteristic zero, we show that Du~Bois singularities descend from any field extension. We also prove that the product of a variety with rational singularities and a variety with Du~Bois singularities again has Du~Bois singularities, and we discuss the case of products of curves.

Strain engineering enables quantum confinement in pristine graphene without degrading its intrinsic mobility and spin coherence. Here, we extend previously proposed strain-induced charge-qubit architectures by incorporating spin degrees of freedom through Rashba spin-orbit coupling (RSOC) and Zeeman fields, enabling spin-qubit operation in single-layer graphene (SLG). In a graphene p-n junction, a strain-induced nanobubble generates a pseudo-magnetic field that forms double quantum dots with gate-tunable level hybridization. Tight-binding quantum transport simulations and a four-band model reveal two distinct avoided crossings: spin-conserving gaps at zero detuning and spin-flip gaps at finite detuning, the latter increasing with SOC strength while the former decreases. Time-domain simulations confirm detuning-dependent Rabi oscillations corresponding to these two operational regimes. These results demonstrate that strain-induced confinement combined with tunable SOC provides a viable mechanism for coherent spin manipulation in pristine graphene, positioning strained SLG as a promising platform for scalable spin-based quantum technologies.

Analogue gravity explores how collective excitations in condensed matter systems can reproduce the behavior of fields in curved spacetimes. An important example is the acoustic black holes that can occur for sound in a moving fluid. In these lecture notes, we focus on atomic Bose-Einstein condensates (BECs), quantum fluids that provide an interesting platform for analogue gravity studies thanks to their accurate theoretical description, remarkable experimental control, and ultralow temperatures that allow the quantum nature of sound to emerge. We give a pedagogical introduction to analogue black holes and the theoretical description of BECs and their elementary excitations, which behave as quantum fields in curved spacetimes. We then apply these tools to survey the current understanding of black-hole superradiance and analogue Hawking radiation, including explicit examples and numerical methods.

We present a computational framework for simulating finite-dimensional ordinary differential equations by combining classical Koopman-Lie product formulas with coordinate-wise frozen subflows. The setting is model-known, since the vector field is assumed to be available, and no data-driven approximation of the Koopman operator is attempted. Under standard assumptions, the Koopman-Lie generator associated with the flow admits a coordinate decomposition into partial generators. This decomposition leads to elementary updates in which all but one state variable are frozen, and the resulting frozen scalar subproblems are evaluated either in closed form or by one-dimensional solves. Lie-Trotter, Strang, and higher-order exponential compositions are then converted into state-update algorithms for two- and three-dimensional systems, with the semigroup and product-formula theory used as background justification for the constructions. We also record the exponential-term counts produced by the recursive constructions used in the implementation. These counts are presented as implementation costs. Numerical experiments on the Lotka-Volterra, Van der Pol, and Lorenz systems compare the coordinate-wise splitting algorithms with high-accuracy RK45 reference solutions using root-mean-square errors and work-precision curves. The results illustrate the practical trade-off between splitting order, number of time steps, number of exponential factors, and runtime.

As anyone who has blown across the mouth of a beer bottle knows, beer bottles have a well-defined fundamental frequency. This paper shows how a beer bottle's acoustical resonance can be modeled as a one-dimensional driven-damped oscillator and includes enough detail to be useful in undergraduate laboratory experiments. While the frequency-domain Green's function of the bottle can be extracted through sequential pure-tone measurements, sufficient data to fit the model's parameters can be collected in just a few seconds when Fourier methods are used.

Inspired by the use of adaptive kernel-based Cohen's class time-frequency distributions (CCTFDs) for cross-term suppression, this paper aims to explore novel adaptive kernel functions for denoising, with a particular focus on non-stationary signal processing in practical applications}. We integrate Wiener filter principle and the time-frequency filtering mechanism of CCTFD to design the least-squares adaptive filter method in the Wigner-Ville distribution (WVD) domain, giving birth to the least-squares adaptive filter-based CCTFD whose kernel function can be adjusted with the input signal automatically to achieve the minimum mean-square error denoising in the WVD domain. {Numerical experiments on typical simulated radar signals and real-world electrocardiogram data comprehensively demonstrate that the proposed adaptive CCTFD outperforms several state-of-the-art methods in noise suppression.

Fast radio bursts (FRBs) are a $\sim$ millisecond-long transient phenomenon that propagate across extragalactic distances and are effectively a point source. Radio wave propagation through inhomogeneous distributions of plasma can act as a lens, generating multiple images of the emitted electric field. A lens can produce images of a point source where the phase of the electric field between images remains coherent when observed by a radio telescope. FRB 20220413B shows a complicated pulse structure with time separated components that may be image copies of the main components due to plasma lensing. We perform several analyses to determine if FRB 20220413B is consistent with expectations of a plasma lensed FRB. We analyze and fit the morphology of the burst to a plasma lens model and find consistency in the spectro-temporal profile but not the observed flux. Using the complex-valued channelized voltage data from the CHIME telescope, we perform a time-lag correlation analysis and report correlation signatures present in the electric field of FRB 20220413B. We find that there exists an excess correlation signature only in absolute power and not in phase. We perform a frequency-lag correlation analysis on the spectra of all subcomponents of the burst and find a consistent scintillation bandwidth across all components. We find the scintillation bandwidth is consistent with expectations of scattering due to the Milky Way. We interpret this as all burst components propagating through the same scintillation screen located in the Milky Way, which would generate the excess variance signature observed, even in the absence of phase coherence between burst components. We find that while the burst morphology can be modeled by a plasma lens, the coherent signature present in the time-lag correlation is consistent with the expectations of a common scattering screen, but not coherent plasma lensing.

We show that a normed linear space is isometrically isomorphic to an inner product space if and only if it is a strongly $n$-point homogeneous metric space for any (or every) $n \geqslant 3$. The counterpart for $n=2$ is the Banach-Mazur problem.

Public blockchains inherently offer low throughput and high latency, motivating off-chain scalability solutions such as Payment Channel Networks (PCNs). However, existing PCNs suffer from liquidity fragmentation-funds locked in one channel cannot be reused elsewhere-and channel depletion, both of which limit routing efficiency and reduce transaction success rates. Multi-party channel (MPC) constructions mitigate these issues, but they typically rely on leaders or coordinators, creating single points of failure and providing only limited flexibility for inter-channel payments. We introduce Hypergraph-based Multi-Party Payment Channels (COALESCE), a new off-chain construction that replaces bilateral channels with collectively funded hyperedges. These hyperedges enable fully concurrent, leaderless intra- and inter-hyperedge payments through verifiable, proposer-ordered DAG updates, offering significantly greater flexibility and concurrency than prior designs. Hence our, design eliminates routing dependencies, avoids directional liquidity lock-up, and does not require central monitoring services such as watchtowers. Our implementation on a 150-node intra-hyperedge achieves a transaction success rate of approximately 94% under heavy load (larger payment sizes), while full hyperedge evaluation over a 15,000-node network sustains success rates in the range of 85% to 95%, without HTLC expiry or routing failures, highlighting the robustness of COALESCE.

The functional renormalization group (fRG) is an established tool in the treatment of correlated electron systems, notably for the description of competing instabilities. In recent years, methodological advancements led to the multiloop extension of the fRG, which systematically includes loop corrections beyond the conventional one-loop truncation and yields a quantitatively accurate description of two-dimensional lattice systems. At the same time, the single-boson exchange (SBE) decomposition of the two-particle vertex has been shown to offer both computational and interpretative advantages paving the way to more affordable approximation schemes. We here apply their combination coined as multiloop SBE fRG to the two-dimensional Hubbard model at weak coupling. After providing a detailed account of the underlying formalism in physical channels, we analyze the results for the frequency- and momentum-dependent vertex functions. We find that the SBE approximation, i.e., neglecting the flow of the multi-boson exchange contributions, accurately reproduces the parquet approximation at loop convergence. The presented algorithmic improvement opens the route for the treatment of more challenging parameter regimes and more realistic models.

Let $p \in \{3, 5\}$ and consider a cyclic $p$-extension $L/\mathbb{Q}$. We show that there exists an effective positive density of elliptic curves $ E $ defined over $ \mathbb{Q} $, ordered by height, that are diophantine stable in $ L $.

We study the possibility of detection of ``spin-boson'' entanglement by qubit only measurements. Such entanglement is impossible to detect by previously proposed schemes that involve a fixed system-environment interaction, because of inherent symmetries within the coupling and the initial state of the environment. We take advantage of the possibility of tuning of qubit-environment coupling, that is available in some qubit realizations. As an example we study a superconducting transmon qubit interacting with a microwave cavity, which is one of such systems and is, furthermore, essential in the context of quantum information processing. We propose suitable Hamiltonian parameters for the preparation and measurement phases of the detection scheme that allow for an experimental test, and verify that the reported signal is nonnegligibly large still at finite temperatures.

When a star passes within the Roche limit of a supermassive black hole (SMBH), it is pulled apart by the BH's tidal field in a tidal disruption event (TDE). The resulting flare is powered by the circularization and accretion of bound stellar debris, which initially returns to the BH on eccentric orbits in a thin debris stream. The returning fluid elements follow inclined orbits that converge near pericenter, resulting in extreme vertical compression to scales $10^{-4}~R_\odot$ and the formation of a nozzle shock. Dissipation at the nozzle shock may affect circularization by altering the properties of the debris stream, but its role is the subject of ongoing debate. We develop an idealized model for the debris stream evolution combining 3D smoothed-particle hydrodynamics simulations, the semi-analytic affine model, and 1D finite-volume hydrodynamic simulations. Because our model is computationally cheap, we can unambiguously resolve the nozzle shock, use a realistic equation of state, and follow the debris stream evolution at many different times. Near peak fallback, Hydrogen recombination and molecular Hydrogen formation broaden the stream by a factor $\sim 5$, enhancing dissipation at the nozzle. However, the dissipation is still insufficient to directly circularize the debris by in-plane pressure gradients. Instead, the thicker stream substantially increases the likelihood that the stream self-intersects on the second orbit, despite relativistic nodal precession. The stream properties at self-intersection are sensitive to dissipation at the nozzle and the timing of focal points where the ballistic trajectories of the debris converge. Our results clarify the nozzle shock's role in circularization in TDEs, providing a foundation for more realistic circularization and emission models.

The construction of non-empirical density functional approximations is typically guided by the satisfaction of exact constraints. An important constraint is the recovery of the gradient expansion for slowly varying electron densities. In prior constructions of semilocal density functional approximations, the $\nabla ζ$-dependent terms in the gradient expansion of the correlation have been dropped, where $ζ$ is the relative spin polarization. We propose a scheme by which such terms can be reintroduced into already constructed functionals without significantly affecting other constraints and norms. We implement this scheme on the Strongly Constrained and Appropriately Normed (SCAN) functional to construct a $\nabla ζ$-corrected version of SCAN. The resulting functional is shown to provide improvements in transition-metal atoms and molecules without significantly affecting SCAN's accurate description of $sp$-systems. For the binding energy curve of the chromium dimer Cr$_2$, the SCAN underbinding is fully corected at large bond lengths and reduced at short bond lengths.

The quantitative impact of strong rotation on the amplitudes and frequencies of the post-bounce gravitational wave (GW) signal from core-collapse supernovae (CCSNe) is still not fully understood. To study trends in frequencies and amplitudes, and possibly spectacular phenomena like resonant amplification, we perform a series of axisymmetric long-duration magnetohydrodynamic CCSN simulations of a 17 $M_\odot$ progenitor using a finely spaced grid in initial rotation rate from 0.29 rad/s to 3.48 rad/s. We find that these rotating models produce GWs at frequencies of up to 3 kHz, higher than in typical non-rotating models in the literature. The high frequencies arise due to small polar radii of rapidly rotating proto-neutron stars and stabilization by angular momentum gradients at lower latitude. GW frequencies and amplitudes tend to decrease with faster rotation. Different from two complementary simulations without magnetic fields, the magnetohydrodynamic models are characterized by an absence of p-modes above the dominant high-frequency emission band. We find no indication of resonant mode amplification for any rotation rate, although a temporo-spatial and space-frequency analysis reveals some interesting couplings of quadrupolar motions across the proto-neutron star and the gain region. Generalized, multi-dimensional perturbative techniques need to be developed to study the mode structure and mode interaction in the collapse of rapidly rotating massive stars.

Understanding how early-universe inflation may emerge from generalized holographic energy densities within modified gravity motivates the present analysis. We develop a self-consistent inflationary scenario in which the Tsallis holographic dark energy (THDE) density effectively acts as the inflaton potential in $f(R,T)$ gravity. Using the Granda-Oliveros infrared cutoff, we derive the corresponding slow-roll relations and identify a broad region of the parameter space $(α,β,δ,λ)$ that remains consistent with ACT DR6 (P-ACT-LB) constraints. By exploiting the dependence of the THDE density on the Hubble rate, we reconstruct the inflaton potential $V(ϕ)$ and show that both the field excursion $Δϕ$ and the normalized potential gradient $|V'|/(V M_{p})$ are predominantly controlled by the matter-geometry coupling $λ$. We demonstrate that $λ\gtrsim \mathcal{O}(10^{2})$ suppresses the field excursion below the Planck scale and ensures $|V'|/(V M_{p}) \ge 1$, thereby satisfying both the distance conjecture and the refined de Sitter swampland bound. We also analyze the reheating stage. In addition to the primordial nucleosynthesis requirement $T_{\rm BBN} \approx 4~\mathrm{MeV}$, which sets a lower limit on the reheating temperature, the observational bound $ΔN_{\rm eff} \le 0.17$ imposes an additional constraint from primordial gravitational waves (PGWs). During stiff reheating phases with $ω_{\rm re} > 1/3$, the high-frequency PGW spectrum is significantly enhanced, producing a distinct signature that may fall within the sensitivity of upcoming detectors. Overall, this work provides an observationally consistent realization of holographic inflation in $f(R,T)$ gravity, jointly constrained by CMB data, swampland criteria, reheating physics, and PGW limits.