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The vibrational modes in Sr$_2$RuO$_4$ easily induce octahedral rotations without tilting. Being on the verge of a magnetic instability, such propensity of octahedral rotation may also produce magnetic fluctuations. In this work, we analyze the long-range magnetic phase diagram incorporating such octahedral rotations and demonstrate the possibility of an altermagnetic phase in Sr$_2$RuO$_4$. Using ab-initio calculations, we first study single layer Sr$_2$RuO$_4$ with octahedral rotations, obtaining an orbital-selective $g$-wave altermagnetic phase. We further provide an effective $t_{2g}$ tight-binding model, demonstrating that the $g$-wave altermagnetism is primarily a product of second and third nearest neighbor interorbital hybridizations between the ${\gamma}z$ ($\gamma=x,y$) orbitals, but only a much longer range intraorbital hybridization in the $xy$ orbitals, establishing a strong orbital-selectiveness for the altermagnetism. Notably, by replacing the $xy$ orbital with the $x^2-y^2$ orbital, a similar tight-biding model may be used to investigate the hole-doped cuprate superconductors. We then study bulk Sr$_2$RuO$_4$, where we find the altermagnetic phase as the magnetic ground state for a range of finite octahedral rotations. In the bulk, interlayer hopping breaks some of the symmetries of the $g$-wave altermagnet, resulting in a $d_{xy}$-wave altermagnet, still with orbital selectiveness. We also include relativistic effects through spin-orbit coupling and obtain that an effective staggered Dzyaloshinskii-Moriya interaction generates weak ferromagnetism. Finally, we discuss the implications of the altermagnetic order on the intrinsic superconductivity of Sr$_2$RuO$_4$. Assuming in-plane and intraorbital pairing, the altermagnetism favors spin-singlet $d_{x^2-y^2}$-wave or $g$-wave pairing, or (nematic or chiral) combinations thereof., Comment: 18 pages, 16 figures

The adoption of Large Language Models (LLMs) has revolutionized AI applications but poses significant challenges in safeguarding user privacy. Ensuring compliance with privacy regulations such as GDPR and CCPA while addressing nuanced privacy risks requires robust and scalable frameworks. This paper presents a detailed study of OneShield Privacy Guard, a framework designed to mitigate privacy risks in user inputs and LLM outputs across enterprise and open-source settings. We analyze two real-world deployments:(1) a multilingual privacy-preserving system integrated with Data and Model Factory, focusing on enterprise-scale data governance; and (2) PR Insights, an open-source repository emphasizing automated triaging and community-driven refinements. In Deployment 1, OneShield achieved a 0.95 F1 score in detecting sensitive entities like dates, names, and phone numbers across 26 languages, outperforming state-of-the-art tool such as StarPII and Presidio by up to 12\%. Deployment 2, with an average F1 score of 0.86, reduced manual effort by over 300 hours in three months, accurately flagging 8.25\% of 1,256 pull requests for privacy risks with enhanced context sensitivity. These results demonstrate OneShield's adaptability and efficacy in diverse environments, offering actionable insights for context-aware entity recognition, automated compliance, and ethical AI adoption. This work advances privacy-preserving frameworks, supporting user trust and compliance across operational contexts., Comment: This paper has been accepted at Deployable AI workshop at AAAI 2025

Galaxy groups with $M_{tot} \lesssim 10^{14}$ $M_\odot$ and up to a few tens of members are the most common galaxy environment, marking the transition between field and massive clusters. Identifying groups plays a crucial role in understanding structure formation and galaxy evolution. Modern deep surveys allow us to build well-characterized samples of groups up to the regime where structures were taking shape. We aimed to build the largest deep catalog of galaxy groups to date over the COSMOS-Web field effective area of 0.45 deg$^2$, leveraging the deep high quality data of the new COSMOS-Web photometric catalog resulted from the James Webb Space Telescope observations of the COSMOS-Web field. We performed the group search with the AMICO algorithm, a linear matched filter based on an analytical model for the group signal. AMICO has already been tested in wide and deep field surveys, including COSMOS data up to $z=2$. In this work, we tested the algorithm performances at even higher redshift and searched for protocluster cores at $z>2$. We compiled a list of known protoclusters in COSMOS at $2 \leq z \leq 3.7$, matched them with our detections and studied the clustering of the detected cores. We estimated purity and completeness of our sample by creating data-driven mocks with the SinFoniA code and linked signal-to-noise to purity. We detected 1678 groups in the COSMOS-Web field up to $z=3.7$, including lists of members extending nearly two magnitudes deeper than the previous AMICO-COSMOS catalog. 756 groups were detected with purity of 80\%. More than 500 groups have their redshift confirmed by assigning spectroscopic counterparts. This group catalog offers a unique opportunity to explore galaxy evolution in different environments spanning $\sim$12 Gyr and to study groups, from the least rich population to the formation of the most massive clusters., Comment: 17 pages, 14 figures, 2 tables (including appendices), submitted to Astronomy & Astrophysics (A&A)

Models predict that the well-studied mass-radius relation of white dwarf stars depends on the temperature of the star, with hotter white dwarfs having larger masses at a given radius than cooler stars. In this paper, we use a catalog of 26,041 DA white dwarfs observed in Sloan Digital Sky Survey Data Releases 1-19. We measure the radial velocity, effective temperature, surface gravity, and radius for each object. By binning this catalog in radius or surface gravity, we average out the random motion component of the radial velocities for nearby white dwarfs to isolate the gravitational redshifts for these objects and use them to directly measure the mass-radius relation. For gravitational redshifts measured from binning in either radius or surface gravity, we find strong evidence for a temperature-dependent mass-radius relation, with warmer white dwarfs consistently having greater gravitational redshifts than cool objects at a fixed radius or surface gravity. For warm white dwarfs, we find that their mean radius is larger and mean surface gravity is smaller than those of cool white dwarfs at 5.2{\sigma} and 6.0{\sigma} significance, respectively. Selecting white dwarfs with similar radii or surface gravities, the significance of the difference in mean gravitational redshifts between the warm and cool samples is >6.1{\sigma} and >3.6{\sigma} for measurements binned in radius and surface gravity, respectively, in the direction predicted by theory. This is an improvement over previous implicit detections, and our technique can be expanded to precisely test the white dwarf mass-radius relation with future surveys.

There is increasing evidence for the presence and variability of circumstellar dust and gas around white dwarfs that are polluted with exoplanetary material, although the origin of this dust and gas remains debated. This paper presents the first near-simultaneous observations of both circumstellar dust (via broadband emission) and gas (via emission lines) around a polluted white dwarf. From the optical spectra the gaseous emission lines, notably the calcium infrared triplet and magnesium lines, show significant increases and decreases in their strength over timescales of weeks, while the oxygen and iron lines remain relatively stable. Near-infrared JHKs photometry reveals dust emission changes of up to 0.2 magnitudes in the Ks band over similar timescales, marking the shortest variability timescales observed to date. The two epochs with the strongest emission were correlated between the dust (Ks band brightening) and gas (strengthened calcium and magnesium lines), showing for the first time that the dust and gas must be produced near-simultaneously with a common origin, likely in collisions., Comment: Accepted for publication in MNRAS: Letters 7 pages, 3 figures, 2 tables and 2 supplementary tables

WD\,0141--675 was reported as the first astrometrically detected white dwarf planet host candidate as part of the third data release from \textit{Gaia}, just to be later retracted via a news item on the \textit{Gaia} web site$^1$. We present time-resolved, high-resolution optical ESPRESSO spectroscopy of \obj. A radial velocity analysis of the \Ion{Ca}~K absorption line reveals a tentative periodic signal of $15.6\pm0.9$\,d. Phase-folding the ESPRESSO spectroscopy on this signal exhibits weak variability in the morphology of \Ion{Ca}~K close to the core of the line. A violet-to-red ratio analysis of the Ca~K line shows a periodic signal of $16.1\pm0.9$\,d. The periods from both methods agree, within their uncertainties, with half the period of the astrometric planet candidate, however, both measurements are of low statistical significance. Nonetheless, our results imply possible solutions to the mass function within the planetary regime. And when combined with existing infrared photometry, which rules out a brown dwarf companion, yield a lower limit on the orbital inclination of $\sim7^\circ$. Our study demonstrates that ESPRESSO observations are well capable of detecting short-period (days to weeks) giant planets orbiting white dwarfs., Comment: 6 pages

Pulse profile stability is a central assumption of standard pulsar timing methods. Thus, it is important for pulsar timing array experiments such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) to account for any pulse profile variability present in their data sets. We show that in the NANOGrav 15-yr data set, the integrated pulse profile of PSR J1022+1001 as seen by the Arecibo radio telescope at 430, 1380, and 2030 MHz varies considerably in its shape from observation to observation. We investigate the possibility that this is due to the "ideal feed assumption" (IFA), on which NANOGrav's routine polarization calibration procedure relies. PSR J1022+1001 is $\sim 90\%$ polarized in one pulse profile component, and also has significant levels of circular polarization. Time-dependent deviations in the feed's polarimetric response (PR) could cause mixing between the intensity I and the other Stokes parameters, leading to the observed variability. We calibrate the PR using a mixture of Measurement Equation Modeling and Measurement Equation Template Matching techniques. The resulting profiles are no less variable than those calibrated using the IFA method, nor do they provide an improvement in the timing quality of this pulsar. We observe the pulse shape in 25-MHz bandwidths to vary consistently across the band, which cannot be explained by interstellar scintillation in combination with profile evolution with frequency. Instead, we favor phenomena intrinsic to the pulsar as the cause., Comment: 18 pages, 16 figures, 4 tables. Submitted to ApJ

We study the dynamics of solutions for a family of nonlinear Schroedinger equations on the circle, with a smooth convolution potential and Gevrey regular initial data. Our main result is the construction of an asymptotically full measure set of small-amplitude time almost-periodic solutions, which are dense on invariant tori. In regions corresponding to positive actions, we prove that such maximal invariant tori are Banach manifolds, which provide a Cantor foliation of the phase space. As a consequence, we establish that, for many small initial data, the Gevrey norm of the solution remains approximately constant for all time and hence the elliptic fixed point at the origin is Lyapunov statistically stable. This is first result in KAM Theory for PDEs that regards the persistence of a large measure set of invariant tori and hence may be viewed as a strict extension to the infinite dimensional setting of the classical KAM theorem., Comment: 46 pages

Precisely modeling radio propagation in complex environments has been a significant challenge, especially with the advent of 5G and beyond networks, where managing massive antenna arrays demands more detailed information. Traditional methods, such as empirical models and ray tracing, often fall short, either due to insufficient details or because of challenges for real-time applications. Inspired by the newly proposed 3D Gaussian Splatting method in the computer vision domain, which outperforms other methods in reconstructing optical radiance fields, we propose RF-3DGS, a novel approach that enables precise site-specific reconstruction of radio radiance fields from sparse samples. RF-3DGS can render radio spatial spectra at arbitrary positions within 2 ms following a brief 3-minute training period, effectively identifying dominant propagation paths. Furthermore, RF-3DGS can provide fine-grained Spatial Channel State Information (Spatial-CSI) of these paths, including the channel gain, the delay, the angle of arrival (AoA), and the angle of departure (AoD). Our experiments, calibrated through real-world measurements, demonstrate that RF-3DGS not only significantly improves reconstruction quality, training efficiency, and rendering speed compared to state-of-the-art methods, but also holds great potential for supporting wireless communication and advanced applications such as Integrated Sensing and Communication (ISAC). Code and dataset will be available at https://github.com/SunLab-UGA/RF-3DGS., Comment: in submission to IEEE journals

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15-year pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese PTAs. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational wave background. To explore the internal consistency of this result we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic gravitational wave background in the NANOGrav 15-year data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data., Comment: 21 pages, 11 figures, 2 tables

Quantum differential equation solvers aim to prepare solutions as $n$-qubit quantum states over a fine grid of $O(2^n)$ points, surpassing the linear scaling of classical solvers. However, unlike classically stored vectors of solutions, the readout of exact quantum states poses a bottleneck due to the complexity of tomography. Here, we show that the readout problem can be addressed with quantum learning tools where we focus on distilling the relevant features. Treating outputs of quantum differential equation solvers as quantum data, we demonstrate that low-dimensional output can be extracted using a measurement operator adapted to detect relevant features. We apply this quantum scientific machine learning approach to classify solutions for shock wave detection and turbulence modeling in scenarios where data samples come directly from quantum differential equation solvers. We show that the basis chosen for performing analysis greatly impacts classification accuracy. Our work opens up the area of research where quantum machine learning for quantum datasets is inherently required., Comment: 5 pages, 4 figures

The dissociative photoionization of \textit{tert}-butyl methyl methacrylate, a monomer unit found in many ESCAP resists, was investigated in a gas phase photoelectron photoion coincidence experiment employing extreme ultraviolet (EUV) synchrotron radiation at 13.5 nm. It was found that the interaction of EUV photons with the molecules leads almost exclusively to dissociation. However, the ionization can also directly deprotect the ester function, thus inducing the solubility switch wanted in a resist film. These results serve as a building block to reconstruct the full picture of the mechanism in widely used chemically amplified resist thin films, provide a knob to tailor more performant resist materials, and will aid interpreting advanced ultrafast time-resolved experiments.

Free electrons in the interstellar medium refract and diffract radio waves along multiple paths, resulting in angular and temporal broadening of radio pulses that limits pulsar timing precision. We determine multifrequency, multi-epoch scattering times for the large dispersion measure millisecond pulsar J1903+0327 by developing a three component model for the emitted pulse shape that is convolved with a best fit pulse broadening function (PBF) identified from a family of thin-screen and extended-media PBFs. We show that the scattering time, $\tau$, at a fiducial frequency of 1500 MHz changes by approximately 10% over a 5.5yr span with a characteristic timescale of approximately 100 days. We also constrain the spectral index and inner scale of the wavenumber spectrum of electron density variations along this line of sight. We find that the scaling law for $\tau$ vs. radio frequency is strongly affected by any mismatch between the true and assumed PBF or between the true and assumed intrinsic pulse shape. We show using simulations that refraction is a plausible cause of the epoch dependence of $\tau$, manifesting as changes in the PBF shape and $1/e$ time scale. Finally, we discuss the implications of our scattering results on pulsar timing including time of arrival delays and dispersion measure misestimation., Comment: 16 pages, 14 figures, submitted to ApJ

The accurate flux calibration of observational data is vital for astrophysics and cosmology because absolute flux uncertainties of stellar standards propagate into scientific results. With the ever higher precision achieved by telescopic missions (e.g. JWST) in the infrared (IR), suitable calibrators are required for this regime. The basis of the Hubble Space Telescope (HST) flux scale is defined by model fits of three hot (Teff > 30000 K) hydrogen-atmosphere (DA) white dwarfs, which achieve an accuracy better than 1 per cent at optical wavelengths but falls below this level in the IR range. We present a network of 17 cooler DA white dwarfs with Teff < 20000 K as spectrophotometric flux standards that are equally, if not more, accurate at IR wavelengths. Cooler white dwarfs do not suffer from non-local thermal equilibrium (NLTE) effects in continuum flux or from UV metal line blanketing, have a larger sky density, are generally closer to Earth with little or negligible interstellar reddening, and have energy distributions peaking in the optical or near-IR. Using the latest grid of DA LTE atmosphere models with three-dimensional (3D) convection, the observed Space Telescope Imaging Spectrometer (STIS) and Wide Field Camera three (WFC3) fluxes of our network are accurate to 3 per cent over most of the range 1450 - 16000 AA, with a median standard deviation of 1.41 per cent. Fitting the HST STIS and WFC3 white dwarf SEDs and Balmer lines independently yields SEDs that agree within 3$\sigma$, which demonstrates the precision of the models for our network., Comment: 24 pages, 18 figures. Published by MNRAS

As the descendants of stars with masses less than 8 M$_{\odot}$ on the main sequence, white dwarfs provide a unique way to constrain planetary occurrence around intermediate-mass stars (spectral types BAF) that are otherwise difficult to measure with radial-velocity or transit surveys. We update the analysis of more than 250 ultraviolet spectra of hot ($13{,}000$ K $< T_{\mathrm{eff}} <$ $30{,}000$ K), young (less than $800$ Myr) white dwarfs collected by the Hubble Space Telescope, which reveals that more than 40% of all white dwarfs show photospheric silicon and sometimes carbon, signpost for the presence of remnant planetary systems. However, the fraction of white dwarfs with metals significantly decreases for massive white dwarfs (M$_{\rm WD}~>$ 0.8 M$_{\odot}$), descendants of stars with masses greater than 3.5 M$_{\odot}$ on the main sequence, as just $11^{+6}_{-4}$% exhibit metal pollution. In contrast, $44\pm6$% of a subset of white dwarfs (M$\rm _{WD}~<$ 0.7 M$_{\odot}$) unbiased by the effects of radiative levitation are actively accreting planetary debris. While the population of massive white dwarfs is expected to be influenced by the outcome of binary evolution, we do not find merger remnants to broadly affect our sample. We connect our measured occurrence rates of metal pollution on massive white dwarfs to empirical constraints into planetary formation and survival around stars with masses greater than 3.5 M$_{\odot}$ on the main sequence., Comment: 21 pages, 5 figures, accepted to The Astrophysical Journal (ApJ)

One of the greatest challenges in galaxy evolution over the last decade has been constraining the prevalence of heavily dust-obscured galaxies in the early Universe. At $z>3$, these galaxies are increasingly rare, and difficult to identify as they are interspersed among the more numerous dust-obscured galaxy population at $z=1-3$, making efforts to secure confident spectroscopic redshifts expensive, and sometimes unsuccessful. In this work, we present the Extended Mapping Obscuration to Reionization with ALMA (Ex-MORA) Survey -- a 2mm blank-field survey in the COSMOS-Web field, and the largest ever ALMA blank-field survey to-date covering 577 arcmin$^2$. Ex-MORA is an expansion of the MORA survey designed to identify primarily $z>3$ dusty, star-forming galaxies while simultaneously filtering out the more numerous $z<3$ population by leveraging the very negative $K$-correction at observed-frame 2mm. We identify 37 significant ($>$5$\sigma$) sources, 33 of which are robust thermal dust emitters. We measure a median redshift of $\langle z \rangle = 3.6^{+0.1}_{-0.2}$, with two-thirds of the sample at $z>3$, and just under half at $z>4$, demonstrating the overall success of the 2mm-selection technique. The integrated $z>3$ volume density of Ex-MORA sources is $\sim1-3\times10^{-5}$ Mpc$^{-3}$, consistent with other surveys of infrared luminous galaxies at similar epochs. We also find that techniques using rest-frame optical emission (or lack thereof) to identify $z>3$ heavily dust-obscured galaxies miss at least half of Ex-MORA galaxies. This supports the idea that the dusty galaxy population is heterogeneous, and that synergies across observatories spanning multiple energy regimes are critical to understanding their formation and evolution at $z>3$., Comment: 13 pages, 5 figures, submitted to ApJ; fully reduced mosaic will be shared upon publication

We present the properties of two candidate massive ($M_\star\sim10^{11}M_\odot$) and dusty ($A_{\rm v}>2.5$ mag) galaxies at $z=5-7$ in the first 0.28 deg$^2$ of the COSMOS-Web survey. One object is spectroscopically confirmed at $z_{\rm spec}=5.051$, while the other has a robust $z_{\rm phot}=6.7\pm0.3$. Thanks to their extremely red colors ($F277W-F444W\sim1.7$ mag), these galaxies satisfy the nominal color-selection for the widely-studied ``little red dot" (LRD) population with the exception of their spatially-resolved morphologies. The morphology of our targets allows us to conclude that their red continuum is dominated by highly obscured stellar emission and not by reddened nuclear activity. Using a variety of SED-fitting tools and star formation histories, we estimate the stellar masses to be $\log(M_\star)=11.32^{+0.07}_{-0.15}$ $M_\odot$ and $\log(M_\star)=11.2^{+0.1}_{-0.2}$ $M_\odot$, respectively, with a red continuum emission dominated by a recent episode of star formation. We then compare their number density to the halo mass function to infer stellar baryon fractions of $\epsilon_\star\sim0.25$ and $\epsilon_\star\sim0.5$. Both are significantly higher than what is commonly observed in lower-z galaxies or more dust-obscured galaxies at similar redshifts. With very bright ultra-high-z Lyman-Break Galaxies and some non-AGN dominated LRDs, such ``extended" LRDs represent another population that may require very efficient star formation at early times., Comment: 11 pages, 4 figures, 1 table. Accepted for publication in ApJL

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index \gamma. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, \gamma_run(f) = \gamma + \beta \ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter \beta consistent with no running, \beta \in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero \beta. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA., Comment: 18 pages, 4 figures, 2 tables. v2: matches version published in ApJ Letters

JWST has enabled detecting and spatially resolving the heavily dust-attenuated stellar populations of sub-millimeter galaxies, revealing detail that was previously inaccessible. In this work we construct a sample of 289 sub-millimeter galaxies with detailed joint ALMA and JWST constraints in the COSMOS field. Sources are originally selected using the SCUBA-2 instrument and have archival ALMA observations from various programs. Their JWST NIRCam imaging is from COSMOS-Web and PRIMER. We extract multi-wavelength photometry in a manner that leverages the unprecedented near-infrared spatial resolution of JWST, and fit the data with spectral energy distribution models to derive photometric redshifts, stellar masses, star-formation rates and optical attenuation. The sample has an average z=2.6, A_V=2.5, SFR=270 and log(M*)=11.1. There are 81 (30%) galaxies that have no previous optical/near-infrared detections, including 75% of the z>4 sub-sample (n=28). The faintest observed near-infrared sources have the highest redshifts and largest A_V=4. In a preliminary morphology analysis we find that ~10% of our sample exhibit spiral arms and 5% host stellar bars, with one candidate bar found at z>3. Finally, we find that the clustering of JWST galaxies within 10 arcseconds of a sub-mm galaxy is a factor of 2 greater than what is expected based on either random clustering or the distribution of sources around any red galaxy irrespective of a sub-mm detection., Comment: 37 pages (15 for RGBs + references), 14 figures, submitted to ApJ

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Those analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions are idealizations that may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks: after fitting our fiducial model to real data, we generate a population of simulated data-set replications, and use them to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients assume extreme values for the real data when compared to the replications. We confirm that the NANOGrav 15 yr data set is consistent with power-law and Hellings--Downs assumptions. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2\ $\sigma$ and 3\ $\sigma$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background as reported by NANOGrav., Comment: 20 pages, 14 Figures

Based on the rate of change of its orbital period, PSR J2043+1711 has a substantial peculiar acceleration of 3.5 $\pm$ 0.8 mm/s/yr, which deviates from the acceleration predicted by equilibrium Milky Way models at a $4\sigma$ level. The magnitude of the peculiar acceleration is too large to be explained by disequilibrium effects of the Milky Way interacting with orbiting dwarf galaxies ($\sim$1 mm/s/yr), and too small to be caused by period variations due to the pulsar being a redback. We identify and examine two plausible causes for the anomalous acceleration: a stellar flyby, and a long-period orbital companion. We identify a main-sequence star in \textit{Gaia} DR3 and Pan-STARRS DR2 with the correct mass, distance, and on-sky position to potentially explain the observed peculiar acceleration. However, the star and the pulsar system have substantially different proper motions, indicating that they are not gravitationally bound. However, it is possible that this is an unrelated star that just happens to be located near J2043+1711 along our line of sight (chance probability of 1.6\%). Therefore, we also constrain possible orbital parameters for a circumbinary companion in a hierarchical triple system with J2043+1711; the changes in the spindown rate of the pulsar are consistent with an outer object that has an orbital period of 80 kyr, a companion mass of 0.3 $M_\odot$ (indicative of a white dwarf or low-mass star), and a semi-major axis of 2000 AU. Continued timing and/or future faint optical observations of J2043+1711 may eventually allow us to differentiate between these scenarios.