In this paper we show that the volume of a maximal globally hyperbolic Cauchy-compact anti-de Sitter $3$-manifold $M$ is at least $π^2|χ(M)|$, and that this minimum value is attained if and only if $M$ is Fuchsian.

A Locally Checkable Labeling (LCL) is a distributed constraint satisfaction problem defined on a bounded-degree graph that relates a finite set of input labels to a finite set of output labels through a finite set of locally checkable constraints. In this work we define labels and local constraints that encode solutions to two classical problems: leader election and spanning tree construction. It is known that leader election cannot be expressed as an LCL in arbitrary graphs using constant-size labels. In fact, it is known that there does not exist a finite set of labels and local constraints for leader election even for the class of rings. On the other hand, there exists a finite set of labels and local constraints characterizing leader election on trees. In this work, we prove that there exists a finite set of labels and local constraints for leader election also in the much larger class of dismantlable graphs. Our labels need one bit per edge or equivalently $O(Δ)$ bits per node (where $Δ$ is the maximum degree in the graph) and are checkable within the graph induced by the 1-neighborhood of each node. To the best of our knowledge, these are the first local labeling results tailored to dismantlable graphs, potentially highlighting structural properties useful for designing labels and constraints for additional LCL problems. Finally, we present a generic transformation that converts any finite set of labels and local constraints into a silent self-stabilizing algorithm by adding only one extra state, assuming a Gouda fair scheduler. This transformation may be of independent interest.

Swift heavy ion (SHI) irradiation generates nanoscale ion tracks through intense electronic excitation, yet the microscopic mechanisms governing their morphology and phase stability in low symmetry oxides remain poorly understood. Here, a multiscale atomistic simulation framework is used to investigate the formation and recovery of SHI-induced tracks in monoclinic $β$-Ga2O3 over a wide range of electronic energy losses (Se) and crystallographic orientations. A sequence of distinct structural responses is identified with increasing Se: (i) complete lattice recovery at low Se; (ii) recrystallization into a metastable $γ$-Ga2O3 phase at intermediate Se; and (iii) the formation of core-shell ion tracks at high Se, consisting of an amorphous core surrounded by a recrystallized $γ$-phase shell. Despite the essentially isotropic initial energy deposition, the final ion-track morphology exhibits pronounced crystallographic anisotropy, governed by orientation-dependent recovery dynamics. The superior recrystallization along the [010] direction is attributed to its exceptionally high elastic stiffness. Notably, SHI irradiation perpendicular to the (100) plane induces a more severe structural response at low Se ($\le$ 10 keV/nm), however, at higher Se, it yields a smaller residual ion track compared to the other orientations. The simulated ion-track sizes show excellent quantitative agreement with the available experimental measurements over a wide range of Se values. These findings establish a unified atomic-scale picture of core-shell track formation and anisotropic recovery in $β$-Ga2O3.

High-dimensional chaotic dynamics can emerge in a large random recurrent neural network when the synaptic gain crosses a threshold. Recent works showed that the kinetic energy of neural activity links the chaotic dynamics and the supporting unstable fixed points (equilibria) in the phase space. Here, we investigate the kinetic-energy-centric properties of random recurrent neural networks by combining dynamical mean-field theory with extensive numerical simulations. We find that the average kinetic energy shifts continuously from zero to a positive value at the known critical value of coupling variance (synaptic gain) and exhibits a cubic scaling behavior near the critical point from above. This scaling behavior is supported by numerical simulations and provides a quantitative characterization of how fast the dynamics change during the onset of chaos as well as how far the chaotic dynamics are away from the unstable fixed points. The steady-state activity distribution is further calculated by the theory and compared with simulations on finite-size systems from the kinetic-energy optimization perspective as well. The activity distribution is also analyzed in a geometric angle, revealing that although the original chaotic dynamics and the gradient dynamics of the kinetic energy are arranged in a shell-like structure, they are well separated in the polar direction. The trajectory length on the chaotic manifold can be derived from the stationary kinetic energy, and the associated stationary behavior is analyzed as well.

Any quantum state is fully specified by the expectation values of a complete set of Hermitian operators. For a system of Majorana fermions, such as the Sachdev-Ye-Kitaev (SYK) model, this set of observables can be taken to be all possible strings of Majorana fermion operators. The expectation values of these fermion strings in a thermal state depend erratically on the microscopic couplings that specify the SYK Hamiltonian, and we study their statistical properties directly in the thermodynamic limit using path integral techniques. When the underlying SYK Hamiltonian is chaotic, we find that these expectation values are well-modeled as real Gaussian random variables with zero mean and a variance that we compute. In contrast, for the integrable variant of SYK, we find that the expectation values are actually non-Gaussian. We then use these results to study measures of magic in the SYK thermal state, including the robustness of magic and the stabilizer Rényi entropy. We also show that our results can be quantitatively reproduced with a dual gravity calculation in the chaotic case at sufficiently low temperature. In this dual gravity model the variance of a given microscopic operator string is related to a wormhole geometry stabilized by a massive particle which is dual to the operator string. Our results thus provide a concrete and quantitative setting in which to study the relationship between randomness, wormholes and closed universes, as well as a holographic dual of quantum magic.

This study introduces a computationally efficient algorithm, delayed acceptance Markov chain Monte Carlo (DA-MCMC), designed to improve posterior simulation in quasi-Bayesian inference. Quasi-Bayesian methods, which do not require fully specifying a probabilistic model, are often computationally expensive owing to the need to evaluate the inverse and determinant of large covariance matrices. DA-MCMC addresses this challenge by employing a two-stage process: In the first stage, proposals are screened using an approximate posterior, whereas a final acceptance or rejection decision is made in the second stage based on the exact target posterior. This reduces the need for costly matrix computations, thereby improving efficiency without sacrificing accuracy. We demonstrate the effectiveness of DA-MCMC through applications to both synthetic and real data. The results demonstrate that, although DA-MCMC slightly reduces the effective sample size per iteration compared with the standard MCMC, it achieves substantial improvement in terms of effective sample size per second, approximately doubling the efficiency. This makes DA-MCMC particularly useful for cases where posterior simulation is computationally intensive. Thus, the DA-MCMC algorithm offers a significant advancement in computational efficiency for quasi-Bayesian inference, making it a valuable tool for robust Bayesian analysis.

We present near- and mid-infrared spectra of eight Low-Luminosity Active Galactic Nuclei (LLAGN), spanning nearly four orders of magnitude in black hole mass and Eddington ratio, obtained with JWST/NIRSpec and MIRI as part of the ReveaLLAGN program along with identical archival data of Cen A. The high spatial resolution of JWST cleanly separates AGN emission from host-galaxy contamination, enabling detections of high-ionization potential lines more than an order of magnitude fainter than previously measured. Emission-line diagnostics reveal a transition at log($L_{bol}/L_{Edd}$) ~ -3.5, where the spectral energy distribution becomes increasingly deficient in ultraviolet photons. We find that rotational H$_2$ excitation temperatures are elevated (~500 K higher) compared to both higher-luminosity AGN and star-forming galaxies, while the H$_2$(0-0)S(3)/PAH$_{11.3 μm}$ ratios are consistent with those observed in the AGN population. We discuss the possible roles of outflows, jets, and X-ray dominated regions in shaping the interstellar medium surrounding LLAGN. Silicate emission at ~10 $μ$m, localized to the nuclear region, is detected in most ReveaLLAGN targets. This dataset offers the first comprehensive JWST-based characterization of infrared emission lines in the nuclear regions of LLAGN.

We derive an integrable reflection matrix for the scattering of excitations from a boundary with a degree of freedom when the reflection process preserves an $SU(1|2)$ symmetry. As this residual symmetry is not sufficient to fully determine the reflection matrix, we use the boundary remnant of the Yangian symmetry invariance and obtain a family of integrable solutions. A concrete realization of this setup is found when studying insertions in the 1/2 BPS Wilson loop in ABJM theory. The boundary degree of freedom appears as a boundary bound state due to poles in the dressing phase of the reflection matrix. We also compare our results with those obtained from the boundary bound state bootstrap procedure. The ABJM Wilson loop example enables us to perform perturbative verifications of our results.

We establish the existence of many holomorphic Hecke eigenforms $f$ of large weight $k$ for the full modular group, for which the least positive integer $n_f$ such that $λ_f(n_f)<0$ satisfies $n_f \ge (\log k)^{1-o(1)}.$ This is believed to be best possible up to the $o(1)$ term in the exponent, and improves on a result of Kowalski, Lau, Soundararajan and Wu, who showed that, when restricted to primes, the least prime $p$ such that $λ_f(p)<0$ can be as large as $(\log k)^{1/2+o(1)}$. We also discuss an extension of our result to primitive holomorphic cusp forms of weight $k$ and squarefree level $N\geq 1$.

Understanding how and when the first stars and galaxies formed remains one of the central challenges in modern cosmology. These structures emerged during the transition from the Dark Ages to the Cosmic Dawn, a period that remains observationally unconstrained despite strong theoretical progress. During this epoch, neutral hydrogen absorbed a fraction of cosmic microwave background photons through its 21-cm hyperfine transition, producing a 21-cm absorption signal whose evolution encodes the early Universe's thermal and ionization history. However, extracting the underlying astrophysical parameters from this signal is limited by severe parameter degeneracies, which cannot be resolved without independent observational probes. The next-generation gravitational wave (GW) detectors, such as Cosmic Explorer (CE), will observe binary black hole (BBH) mergers up to very large redshifts and hence will detect a fraction of them formed within the redshift range $\sim 13-25$. The merger rate of these BBHs will depend on the star formation rate density (SFRD) at these redshifts, together with the BBH formation efficiency and a time delay distribution. Therefore, the merger rate of these BBHs can work as a tracer of the SFRD in the redshift range $\sim 13-25$. In this Letter, we establish a novel multi-messenger framework and present a proof-of-principle concept of how the observations of BBH mergers form next-generation GW detectors can improve the inference of parameters generating the 21-cm cosmic hydrogen signal, and help break degeneracies between them.

We study the maximum regret (MR) of binary treatment choice in a population with observed covariates x, when welfare varies with an uncertain binary event. We study decision making with plug-in probabilistic predictions of the event and pre-specified decision thresholds, which we term the prediction-threshold problem. In this setting, the optimal treatment for persons with covariate value x is B if the conditional probability P(y = 1|x) of a binary outcome y exceeds a particular x-specific threshold and is A otherwise. This structure is common in medical decision making and also arises in non-medical contexts such as criminal justice. Plug-in prediction uses data to estimate P(y|x) and acts as if the estimate is accurate. However, plug-in prediction is often performed with misspecified prediction models and conventional x-invariant thresholds. We aim to shed new light on MR when treatment choice is performed this way. We use a combination of algebraic and computational analysis of limit and sample MR, demonstrating how MR depends on the prediction model, the state space, and the thresholds used to choose treatments.

We prove new arithmetic results for parametric linear recurrence sequences specialized at roots of unity, denoted by $(U_n(ζ))_{n\geq 0}$. In particular, we obtain effective lower bounds for the largest prime ideal divisor and norm of the radical of the principal ideal generated by $U_n(ζ)$. We further derive an effective upper bound for the $S$-part of $U_n(ζ)$, showing that it is strictly smaller than a fixed power of its absolute norm for sufficiently large $n$.

Modified gravity theories offer a well-motivated extension of General Relativity and provide a possible explanation for the late-time accelerated expansion of the Universe. Among them, $f(R)$ gravity represents a minimal and theoretically appealing class, characterized by the Compton wavelength parameter $B_0$, which quantifies deviations from General Relativity. In this work, we explore the capability of future neutral hydrogen (HI) 21 cm intensity mapping (IM) observations to constrain $f(R)$ gravity at low redshifts. We perform Fisher-matrix forecasts for $B_0$ and standard cosmological parameters using upcoming 21 cm IM experiments, including BINGO and SKA1-MID (Band 1 and Band 2), both individually and in combination with Planck cosmic microwave background (CMB) priors. We find that even near-term experiments such as BINGO are able to place nontrivial bounds on $B_0$, $σ(B_0)\simeq 2.27\times 10^{-6}$, while SKA1-MID yields substantially tighter constraints, with SKA Band 2 providing the strongest sensitivity among the considered configurations, $σ(B_0)\simeq 6.37\times 10^{-8}$. We further demonstrate that the combination of low-redshift 21 cm IM data with CMB observations efficiently breaks degeneracies with background cosmological parameters and leads to a significant improvement in the constraints on $B_0$. These results highlight the potential of future HI intensity mapping surveys, in combination with CMB measurements, to provide stringent tests of General Relativity on cosmological scales.

In this work, we present a fast and highly efficient method for the measurement of $^{210}$Pb in metallic archaeological lead using the commercial low-background liquid scintillation counter Wallac Quantulus 1220 installed at the University of Milano-Bicocca (Italy). By combining an optimized chemical preparation with pulse-shape analysis (PSA), the technique achieves sensitivities at the level of a few $10^2$ mBq/kg within one week of measurement, using sample masses below 1 g. The method enables the simultaneous identification of the $β$ decays of $^{210}$Pb and $^{210}$Bi and the $α$ decay of $^{210}$Po, allowing a direct verification of secular equilibrium within the decay chain. With extended acquisition times, detection limits below 100 mBq/kg are reached after approximately 40 days. This approach provides a rapid, accessible, and reliable tool for the radiopurity screening of lead, and is well suited for quality control and R&D activities in next-generation low-background and rare-event physics experiments. Moreover, the method has the potential to be extended to other materials relevant for low-background applications.

A model for the collisional stopping of ions on free electrons in warm dense matter is developed and explored. It is based on plasma kinetic theory, but with modifications to address the warm dense matter regime. Specifically, it uses the Boltzmann-Uehling-Uhlenbeck kinetic equation to incorporate effects of Fermi degeneracy of electrons. The cross section is computed from quantum scattering of electrons and ions occuring via the potential of mean force derived from an average atom model, which incorporates effects of strong Coulomb correlations. Predictions from this model show comparable accuracy to results from time-dependent density functional theory calculations for deuterium near solid density and a temperature of several electronvolts, at a fraction of the computational cost. Further, the model captures the transition of a plasma from the classical limit to the degenerate limit, including qualitative behaviors of solid state theory.

The Hubble tension is one of the most significant challenges in modern cosmology. Developing new approaches to estimate the Hubble constant is therefore crucial, and in this work, we employ a Gaussian process, a fully model-independent method that relies solely on observational data. To determine the Hubble constant, we use not only electromagnetic observations but also include gravitational-wave standard siren data from GWTC3. Our measurements of the Hubble constant are strongly consistent with the SH0ES result, with tensions less than $2σ$, indicating no statistically significant discrepancy. This approach quantifies the impact of gravitational-wave data on the determination of the Hubble constant, examines its consistency with electromagnetic measurements, and explores its potential role in addressing the Hubble tension.

Ultra-relativistic quantum-electrodynamic (QED) plasmas, characterized by magnetic field strengths approaching and even exceeding the Schwinger field of approximately $B_{Q} \approx 4 \times 10^{13}$ gauss, hold significant interest for laser-plasma experiments and astrophysical observations of neutron stars and magnetars. In this study, we investigate the joint modification of normal plasma modes in ultra-relativistic electron-positron plasmas, both charge neutral and non-neutral, by the super-strong magnetic field and plasma relativistic temperature. Our analysis shows that the most substantial modification concerns the reduction of the plasma frequency cutoff, resulting in relativistic and field-induced transparency. Additionally, we observe a temperature-independent modification of the index of refraction of electromagnetic waves, which coincides with the behavior observed in a cold QED plasma.

Multi-vector late-interaction retrievers such as ColBERT achieve state-of-the-art quality, but their query-time cost is dominated by exhaustively computing token-level MaxSim interactions for every candidate document. The MaxSim scores of $N$ candidates against $T$ query tokens form an $N\times T$ matrix whose row-sums are the late-interaction scores, and identifying the top-$K$ rarely requires every entry. We introduce Col-Bandit, a query-time estimator of the exhaustive-MaxSim top-$K$: it reveals matrix entries in batches, maintains a finite-population Bernstein-Serfling confidence interval on each candidate's score, and permanently drops any document whose upper bound falls below the $K$-th largest lower bound, computing only the cells needed to separate the top-$K$. A single relaxation knob $α_{\mathrm{ef}}\in(0,1]$ tunes the compute-fidelity trade-off. We deploy $α_{\mathrm{ef}}{=}0.2$, while $α_{\mathrm{ef}}{=}1$ admits a $δ$-PAC guarantee under a simplified radius. On BEIR and REAL-MM-RAG, Col-Bandit preserves $\geq 90\%$ fidelity to the exhaustive top-$5$ on every corpus while cutting MaxSim FLOPs by up to ${\sim}8\times$, for up to ${\sim}13\times$ single-thread CPU speedups across x86 and ARM. A drop-in reranking layer, it needs no retraining or index changes.

This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind discretizations. It is shown how different sources of errors, in particular modeling errors and discretization errors, can be estimated with respect to a user-defined output functional.

The paper presents results on piecewise polynomial approximations of tensor product type in Sobolev-Slobodecki spaces by various interpolation and projection techniques, on error estimates for quadrature rules and projection operators based on hierarchical bases, and on inverse inequalities. The main focus is directed to applications to discrete conservation laws.

We prove the $L^\infty(L^\infty)$-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree $p\geq 0$ for general scalar conservation laws. The estimate is given for the case of several space dimensions and for conservation laws with initial and boundary conditions.

We establish a relationship between the Davey--Stewartson II (DS II) integrable system in $(2{+}1)$ dimensions and quasi-exactly solvable planar interacting Dirac Hamiltonians that exhibit the super-Klein tunneling (SKT) effect. The Dirac interactions are constructed from the real and imaginary parts of breather solutions of the DS II system. In this framework, the SKT effect arises when the energy is tuned to match the constant background of the soliton, while the resulting Dirac Hamiltonians simultaneously support bound states embedded in the continuum. By imposing the SKT boundary conditions, we employ Darboux transformations to construct a general three-parameter family of DS II breather solutions that can be mapped to Dirac Hamiltonians. At the initial soliton time, the corresponding Dirac systems form a massless two-parameter family of Hermitian models with nontrivial electrostatic potentials. As the soliton time evolves, the systems become $\mathcal{PT}$-symmetric and develop a nontrivial imaginary mass term. Finally, when the soliton time is taken to be imaginary, the construction yields Hermitian Dirac systems that lack time-reversal symmetry. In all cases, we identify the emergence of quasi-symmetry transformations that preserve the SKT subspace of states while not commuting with the full Hamiltonian.

Recent Pulsar Timing Array datasets provide compelling evidence for a nano-Hertz gravitational-wave background, but robust detection requires characterizing statistical fluctuations of the Hellings-Downs (HD) correlation expected from a finite population of discrete sources. Building on the variance calculation of Allen (2023), we derive the third central moment (skewness) of the HD correlation for a single unpolarized point source and an ensemble of many interfering point sources in the confusion-noise regime. To isolate the intrinsic non-Gaussianity of the background, we extend the pulsar-averaging formalism to third order by introducing a three-point averaged correlation function, which allows us to define the cosmic skewness. We find that the skewness remains non-zero in the large-source-number limit and is controlled by a new geometric three-point function. These results suggest that incorporating higher-order moments could provide additional information on source discreteness beyond standard Gaussian analyses.

The linear correlation between RMS radius difference and composition asymmetry in two-component many-body systems is a robust feature observed across nuclear experiments, diverse nuclear structural models, molecular dynamic simulations for bimetallic clusters, and galactic modeling with self-interacting dark matter. We identify the short-range attractive central force as the key ingredient for its emergence, a mechanism underpinned by the coordinate transformation under low-energy harmonic-oscillator approximation, the virial theorem, and Pauli principle/hard core potential, in many-fermion system/classic many-body system.

As Artificial Intelligence (AI) systems proliferate, the need for systematic, transparent, and actionable processes for evaluating them is growing. While many resources exist to support AI evaluation, they have several limitations. Few address both the process of designing, developing, and deploying an AI system and the outcomes it produces. Furthermore, few are end-to-end and operational, give actionable guidance, or present evidence of usability or effectiveness in practice. In this paper, we introduce a third-party AI assurance framework that addresses these gaps. We focus on third-party assurance to prevent conflict of interest and ensure credibility and accountability of the process. We begin by distinguishing assurance from audits in several key dimensions. Then, following design principles, we reflect on the shortcomings of existing resources to identify a set of design requirements for AI assurance. We then construct a prototype of an assurance process that consists of (1) a responsibility assignment matrix to determine the different levels of involvement each stakeholder has at each stage of the AI lifecycle, (2) an interview protocol for each stakeholder of an AI system, (3) a maturity matrix to assess AI systems' adherence to best practices, and (4) a template for an assurance report that draws from more mature assurance practices in business accounting. We conduct early validation of our AI assurance framework by applying the framework to two distinct AI use cases -- a business document tagging tool for downstream processing in a large private firm, and a housing resource allocation tool in a public agency -- and conducting six expert validation interviews. Our findings show early evidence that our AI assurance framework is sound and comprehensive, usable across different organizational contexts, and effective at identifying bespoke issues with AI systems.

In this paper, we address the problem of circumnavigation of a stationary target by a heterogeneous group comprising of $\textbf{n}$ autonomous agents, having unicycle kinematics. The agents are assumed to have constant linear speeds, we control only the angular speeds. Assuming limited sensing capabilities of the agents, only a subset of agents, termed as \textit{leaders}, know the target location. The rest, termed as \textit{followers}, do not. We propose a distributed guidance law which drives all the agents towards the desired objective; global asymptotic stability (GAS) is ensured by using Zubov's theorem. The efficacy of the approach is demonstrated through both numerical simulations and hardware experiments.

It is well known that there is a somewhat mysterious relation between the area of the quartic Fermat curve $x^4+y^4=1$, aka squircle, and the arc length of the lemniscate $(x^2+y^2)^2=x^2-y^2$. The standardproof of this fact uses relations between elliptic integrals and the gamma function. In this article we generalize this result to relate areas of sectors of the squircle to arc lengths of segments of the lemniscate. We provide a geometric interpretation of this relation and an elementary proof of the relation, which only uses basic integral calculus. We also discuss an alternate version of this kind of relation, which is implicit in a calculation of Siegel.

The Kitaev model is exactly solvable in terms of Majorana fermions hopping on a honeycomb lattice and coupled to a static $\mathbb{Z}_2$ gauge field, giving the possibility of $π$-vortices in hexagonal plaquettes. In the vortex-full sector and in the presence of a time-reversal-breaking three-spin term of strength $κ$, the energy spectrum is gapped and the ground state possesses an even Chern number. An isolated vortex-free plaquette acts as a ``dual vortex'' and binds a fermionic mode at finite energy $ε$ in the bulk gap. This mode is equivalent to two coupled Majorana zero modes located on the same dual vortex. In a continuum approximation, we analytically compute the Majorana wavefunctions and their coupling $ε$ in the two limits of small or large $κ$. The analytical approach is confirmed by numerical perturbation theory directly on the lattice. The latter is in excellent agreement with the full numerics on a finite-size system. We contrast our results with states bound to an isolated vortex in a topological superconductor with even Chern number.

Atomic hydrogen (HI) regulates star formation as cold gas fuels star formation. It represents a key phase in the baryon cycle. Redshifted $21$ cm line emission serves as a key tracer for investigating HI in the interstellar medium (ISM) and circumgalactic medium (CGM) in distant galaxies, and enables the study of galaxy evolution. Direct detections of HI are currently limited to $z \leq 0.4$ due to the inherently weak $21$ cm emission line. Ongoing and upcoming large radio surveys aim to detect $21$ cm emission from galaxies up to $z \gtrsim 1$. We present a novel approach for creating optical-HI joint mock catalogues for upcoming SKA precursor surveys: MIGHTEE-HI, LADUMA and WALLABY. Incorporation of optical properties along with HI makes these mock catalogues a powerful tool for making predictions for surveys and provides a benchmark for exploring the HI science (e.g., conditional HIMF and optical-to-HI scaling relations) expected from these surveys. As a case study, we show the use of the joint catalogues for predicting the expected outcome of stacking detection for average HI mass in galaxies that are below the threshold for direct detection. We show that combining stacking observations with only the number of direct detections puts a strong constraint on the HI mass function. We also show that this can be done separately for parts of the color-magnitude diagram for galaxies, enabling a fine grained study of galaxy evolution. This may be used to set priors for the full determination of the HI mass function.

The growing number of gravitational-wave (GW) observations allows for constraints to be placed on the underlying population of black holes; current estimates show that black hole spins are small, with binaries more likely to have comparable component masses. Since general relativistic effects, such as spin-induced orbital precession and higher order multipole moments, are more likely to be observed for asymmetric binary systems, a direct measurement remains unlikely. Nevertheless, we continue to consistently probe these effects by performing Bayesian inference with our most accurate and computationally expensive models. As the number of GW detections increases, it may soon become infeasible to consistently use these models for analyses. In this paper, we provide a selection criterion that determines when less accurate and computationally cheaper models can be used without giving biased estimates for the population properties of black holes in the Universe. We show that when using our selection criterion, comparable estimates can be obtained for the underlying mass and spin distribution of black holes for a simulated "worst-case" scenario population, while reducing the overall cost of performing Bayesian inference on our population by $\sim 20\%$. We anticipate a reduction of up to $78\%$ in the overall cost for an astrophysically motivated population, since there are fewer events with observable spin-precession and higher order multipole power.