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The river Ganga is one of the Earth's most critically important river basins, yet it faces significant pollution challenges, making it crucial to evaluate its vulnerability for effective and targeted remediation efforts. While the Analytic Hierarchy Process (AHP) is widely regarded as the standard in decision making methodologies, uncertainties arise from its dependence on expert judgments, which can introduce subjectivity, especially when applied to remote sensing data, where expert knowledge might not fully capture spatial and spectral complexities inherent in such data. To address that, in this paper, we applied AHP alongside a suite of alternative existing and novel variants of AHP-based decision analysis on remote sensing data to assess the vulnerability of the river Ganga to pollution. We then compared the areas where the outputs of each variant may provide additional insights over AHP. Lastly, we utilized our learnings to design a composite variable to robustly define the vulnerability of the river Ganga to pollution. This approach contributes to a more comprehensive understanding of remote sensing data applications in environmental assessment, and these decision making variants can also have broader applications in other areas of environment management and sustainability, facilitating more precise and adaptable decision support frameworks.

In ultra-fast astronomical observations featuring fast transients on sub-$\mu$s time scales, the conventional Signal-to-Noise Ratio (SNR) threshold, often fixed at $5\sigma$, becomes inadequate as observational window timescales shorten, leading to unsustainably high False Alarm Rates (FAR). We provide a basic statistical framework that captures the essential noise generation processes relevant to the analysis of time series data from photon-counting detectors. In particular, we establish a protocol of defining detection limits in astronomical photon-counting experiments, such that a FAR-based criterion is preferred over the traditional SNR-based threshold scheme. We develop statistical models that account for noise sources such as dark counts, sky background, and crosstalk, and establish a probabilistic detection criterion applicable to high-speed detectors. We compare the performance of several detector technologies, including photon-counting CMOS/CCDs, SPADs, SiPMs, and PMTs, in detecting faint astronomical signals. These findings offer insights into optimizing detector choice for future ultra-fast astronomical instruments and suggest pathways for improving detection fidelity under rapid observational conditions.

Fuzzy dark matter (FDM) is a compelling candidate for dark matter, offering a natural explanation for the structure of diffuse low-mass haloes. However, the canonical FDM model with a mass of $10^{-22}~{\rm eV}$ encounters challenges in reproducing the observed diversity of dwarf galaxies, except for possibly scenarios where strong galactic feedback is invoked. The introduction of multiple-field FDM can provide a potential resolution to this diversity issue. The theoretical plausibility of this dark matter model is also enhanced by the fact that multiple axion species with logarithmically-distributed mass spectrum exist as a generic prediction of string theory. In this paper we consider the axiverse hypothesis and investigate non-linear structure formation in the two-field fuzzy dark matter (2FDM) model. Our cosmological simulation with an unprecedented resolution and self-consistent initial conditions reveals the diverse structures of dark matter haloes in the 2FDM model for the first time. Depending on the formation time and local tidal activities, late-time haloes can host solitons of nested cores or solitons of one dominant species., Comment: 9 pages, 5 figures. Comments welcome!

We compare the abundant prolate shaped galaxies reported beyond z$>$3 in deep JWST surveys, with the predicted {\it stellar} appearance of young galaxies in detailed hydro-simulations of three main dark matter contenders: Cold (CDM), Wave/Fuzzy ($\psi$DM) and Warm Dark Matter (WDM). We find the observed galaxy images closely resemble the elongated stellar appearance of young galaxies predicted for both $\psi$DM and WDM, during the first $\simeq$ 500Myr while material steadily accretes from long, smooth filaments. The dark mater halos of WDM and $\psi$DM also have pronounced, prolate elongation similar to the stars, indicating a shared, highly triaxial equilibrium. This is unlike CDM where the early stellar morphology is mainly spheroidal formed from fragmented filaments with frequent merging, resulting in modest triaxiality. Quantitatively, the excess of prolate galaxies observed by JWST matches well WDM and $\psi$DM for particle masses of 1.4KeV and $2.5\times 10^{-22}$ eV respectively. For CDM, several visible subhalos are typically predicted to orbit within the virial radius of each galaxy from subhalo accretion, whereas merging is initially rare for WDM and $\psi$DM. We also verify with our simulations that $\psi$DM may be distinguished from WDM by the form of the core, which is predicted to be smooth and centered for WDM, but is a dense soliton for $\psi$DM traced by stars and measurably offset from the galaxy center by random wave perturbations in the simulations. We emphasise that long smooth filaments absent of galaxies may prove detectable with JWST, traced by stars and gas with comoving lengths of 150kpc predicted at z$\simeq$10, depending on the particle mass of $\psi$DM or WDM., Comment: 20 pages, 14 figures

We explore the scales and the extent of disagreement between $Planck$ PR3 and Atacama Cosmology Telescope (ACT) DR4 data. $Planck$ and ACT data have substantial overlap in the temperature anisotropy data between scales corresponding to multipoles $\ell\simeq 600-2500$ with complementing coverage of larger angular scales by $Planck$ and smaller angular scales by ACT. Since the same cosmology should govern the anisotropy spectrum at all scales, we probe this disagreement in the primordial power spectrum. We use a parametric form of power law primordial spectrum that allows changes in the spectral tilt. We also reconstruct the primordial spectrum with a non-parametric method from both $Planck$ and ACT temperature data. We find the disagreement exists within scales 0.08 - 0.16 ${\rm Mpc}^{-1}$ where ACT temperature data prefers a scale invariant/blue spectrum. At scales larger and smaller than this window, ACT data strongly prefers a red tilt, which is consistent with $Planck$. This change in the spectral tilt can be identified in the ACT data at 2$\sigma$ C.L. without using $Planck$ data, indicating that the tension is driven by different preferences for tilts within the ACT data. The addition of $Planck$ data up to intermediate scales ($\ell\le650$) increases this significance to 3$\sigma$. Given the large overlap between $Planck$ and ACT within 0.08 - 0.16 ${\rm Mpc}^{-1}$ and considering the internal consistency between different $Planck$ temperature and polarization spectra, the scope of new physics as a solution to the tension remains limited. Our results -- a strong preference for an intermediate transition in spectral tilt and the variation of this preference in different data combinations -- indicate that systematic effects can be misperceived as new physics emerging from different non-standard cosmological processes., Comment: v1: 25 pages, 10 figures and 3 tables

Microlensed stars recently discovered by JWST & HST follow closely the winding critical curve of A370 along all sections of the ``Dragon Arc" traversed by the critical curve. These transients are fainter than $m_{AB}>26.5$, corresponding to the Asymptotic Giant Branch (AGB) and microlensed by diffuse cluster stars observed with $\simeq 18M_\odot/pc^2$, or about $\simeq 1$\% of the projected dark matter density. Most microlensed stars appear along the inner edge of the critical curve, following an asymmetric band of width $\simeq 4$kpc that is skewed by $-0.7\pm0.2$kpc. Some skewness is expected as the most magnified images should form along the inner edge of the critical curve with negative parity, but the predicted shift is small $\simeq -0.04$kpc and the band of predicted detections is narrow, $\simeq 1.4$kpc. Adding CDM-like dark halos of $10^{6-8}M_\odot$ broadens the band as desired but favours detections along the outer edge of the critical curve, in the wrong direction, where sub-halos generate local Einstein rings. Instead, the interference inherent to ``Wave Dark Matter" as a Bose-Einstein condensate ($\psi$DM) forms a symmetric band of critical curves that favours negative parity detections. A de Broglie wavelength of $\simeq 10$pc matches well the observed $4$kpc band of microlenses and predicts negative skewness $\simeq -0.6$kpc, similar to the data. The implied corresponding boson mass is $\simeq 10^{-22}$eV, in good agreement with estimates from dwarf galaxy cores when scaled by momentum. Further JWST imaging may reveal the pattern of critical curves by simply ``joining the dots" between microlensed stars, allowing wave corrugations of $\psi$DM to be distinguished from CDM sub-halos, Comment: 12 pages, 5 figures

We show that by jointly fitting cosmic microwave background (CMB) and astrophysical data - a compilation of UV luminosity data from the Hubble Frontier Field and neutral hydrogen data from distant sources-, we can infer on the shape of the evolution of the ionized hydrogen fraction with redshift in addition to constraining the average optical depth $\tau$.For this purpose, we introduce here a novel extended model that includes hydrogen ionization histories which are monotonic with redshift, but allow for an asymmetry as indicated from our previous works on a free reconstruction of reionization. By using our baseline data combination, we obtain $\tau=0.0542^{+0.0017}_{-0.0028}$, consistent with our previous works and tighter than the one inferred by Planck 2018 data because of the combination of CMB with astrophysical data. We find that the symmetric hypothesis within our parametrization is disfavoured at 4 $\sigma$.We test our findings by using alternative likelihoods for CMB polarization at low multipoles, i.e. based on the 2020 reprocessing of Planck HFI data or on the joint analysis of WMAP and Planck LFI data, obtaining consistent results that disfavour the symmetric hypothesis of the reionization history at high statistical significant level.These results will be further tested by more precise astrophysical data such as from JWST and Euclid deep fields., Comment: 13 pages, 9 figures

The Pampilhosa da Serra Space Observatory (PASO) is located in the center of the continental Portuguese territory, in the heart of a certified Dark Sky destination by the Starlight Foundation (Aldeias do Xisto) and has been an instrumental asset to advance science, education and astrotourism certifications. PASO hosts astronomy and Space Situational Awareness (SSA) activities including a node of the Portuguese Space Surveillance \& Tracking (SST) infrastructure network, such as a space radar currently in test phase using GEM radiotelescope, a double Wide Field of View Telescope system, a EUSST optical sensor telescope. These instruments allow surveillance of satellite and space debris in LEO, MEO and GEO orbits. The WFOV telescope offers spectroscopy capabilities enabling light curve analysis and cosmic sources monitoring. Instruments for Space Weather are being considered for installation to monitor solar activities and expand the range of SSA services., Comment: 9 pages, 2 figures, Keywords: Dark Sky, radioastronomy, space, space debris, space situational awareness; Draft from Talk presented at Astronomy and Satellite Constellations: Pathways Forward, IAU Symposium 385, October 2023, Ed. C. Walker, D.Turnshek, P.Grimley, D.Galadi-Enriquez & M.Aub\'e, International Astronomical Union Proceedings Series, Cambridge University Press, 2024

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary substantially in difficulty. Moreover, the critical difficulties associated with a given family will generally manifest themselves at the end stages of an attempted proof. We give a conjectured classification system of congruence families for the coefficients of modular eta quotients by studying the topology of the associated modular curve.

In 2012 Paule and Radu proved a difficult family of congruences modulo powers of 5 for Andrews' 2-colored generalized Frobenius partition function. The family is associated with the classical modular curve of level 20. We demonstrate the existence of a congruence family for a related generalized Frobenius partition function associated with the same curve. We construct an isomorphism between this new family and the original family of congruences via a mapping on the associated rings of modular functions. The pairing of the congruence families provides a new strategy for future work on congruences associated with modular curves of composite level. We show how a similar approach can be made to multiple other recent examples in the literature. We also give some important insights into the behavior of these congruence families with respect to the Atkin--Lehner involution which proved very important in Paule and Radu's original proof., Comment: Mathematica supplement may be found online at https://www.d.umn.edu/~jsellers/garvansellerssmoot2024.pdf or through email

Explore alien solar systems via local star power using interstellar photovoltaics, tailored for the particular target star for maximum power and low mass. We consider tailored organic thin-film photovoltaics. Key for sensing, sending more data back and powering A.I. to send back observational summaries and interesting events and observations. This plus other technology developments are necessary for exploring Alien Solar Systems in the not too distant future., Comment: 14 pages

We introduce a finite-bound extension of a partition equinumerosity result which was orignally proposed as a problem by Andrews and Deutsch in 2016, and given a generalized form in 2018 by Smoot and Yang. We also give a simple bijective proof, itself an extension of the proof given of the 2018 generalization.

One of main sources of uncertainty in modern cosmology is the present rate of the universe's expansion, H0, called the Hubble constant. Once again, different observational techniques bring about different results, causing new 'Hubble tension'. In the present work, we review the historical roots of the Hubble constant from the beginning of the twentieth century, when modern cosmology originated, to the present. We develop the arguments that gave rise to the importance of measuring the expansion of the Universe and its discovery, and we describe the different pioneering works attempting to measure it. There has been a long dispute on this matter, even in the present epoch, which is marked by high-tech instrumentation and, therefore, in smaller uncertainties in the relevant parameters. It is, again, currently necessary to conduct a careful and critical revision of the different methods before one invokes new physics to solve the so-called Hubble tension., Comment: 52 pages, 14 figures, 3 tables. We corrected typos and references

To better match drivers to riders in our ridesharing application, we revised Lyft's core matching algorithm. We use a novel online reinforcement learning approach that estimates the future earnings of drivers in real time and use this information to find more efficient matches. This change was the first documented implementation of a ridesharing matching algorithm that can learn and improve in real time. We evaluated the new approach during weeks of switchback experimentation in most Lyft markets, and estimated how it benefited drivers, riders, and the platform. In particular, it enabled our drivers to serve millions of additional riders each year, leading to more than $30 million per year in incremental revenue. Lyft rolled out the algorithm globally in 2021.

Dark matter-dominated cores have long been claimed for the well-studied local group dwarf galaxies. More recently, extended stellar halos have been uncovered around several of these dwarfs through deeper imaging and spectroscopy. Such core-halo structures are not a feature of conventional cold dark matter (CDM), based on collisionless particles where smooth, scale-free profiles are predicted. In contrast, smooth and prominent dark matter cores are predicted for Warm and Fuzzy/Wave Dark Matter (WDM/$\psi$DM) respectively. The question arises to what extent the visible stellar profiles should reflect this dark matter core structure. Here we compare cosmological hydrodynamical simulations of CDM, WDM $\&$ $\psi$DM, aiming to predict the stellar profiles for these three DM scenarios. We show that cores surrounded by extended halos are distinguishable for WDM and $\psi$DM, with the most prominent cores in the case of $\psi$DM, where the stellar density is enhanced in the core due to the presence of the relatively dense soliton. Our analysis demonstrates that such behavior does not appear in CDM, implying that the small-scale cut-off in the power spectrum present for WDM and $\psi$DM provides a core-halo transition. Consequently, we estimate the mass of the $\psi$DM particle at this core-halo transition point. Furthermore, we observe the anticipated asymmetry for $\psi$DM due to the soliton's random walk, a distinctive characteristic not found in the symmetric distributions of stars in Warm and CDM models., Comment: 17 pages and 15 figures

Here we show how $H_0$ can be derived purely from the gravitational waves (GW) of neutron star-black hole (NSBH) mergers. This new method provides an estimate of $H_0$ spanning the redshift range, $z<0.25$ with current GW sensitivity and without the need for any afterglow detection. We utilise the inherently tight neutron star mass function together with the NSBH waveform amplitude and frequency to estimate distance and redshift respectively, thereby obtaining $H_0$ statistically. Our first estimate is $H_0 = 86^{+55}_{-46}$ km s$^{-1}$ Mpc$^{-1}$ for the secure NSBH events GW190426 and GW200115. We forecast that soon, with 10 more such NSBH events we can reach competitive precision of $\delta H_0/H_0 \lesssim 20\%$., Comment: 13 pages, 10 figures

Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complicating factors arise from the topology of the associated modular curve: classical techniques are sufficient when the associated curve has cusp count 2 and genus 0. Recent work has led to new techniques that have proven useful when the associated curve has cusp count greater than 2 and genus 0. We show here that these techniques may be adapted in the case of positive genus. In particular, we examine a congruence family over the 2-elongated plane partition diamond counting function $d_2(n)$ by powers of 7, for which the associated modular curve has cusp count 4 and genus 1. We compare our method with other techniques for proving genus 1 congruence families, and present a second congruence family by powers of 7 which we conjecture, and which may be amenable to similar techniques., Comment: Mathematica supplements online at ,

Light curves are the primary observable of type-I x-ray bursts. Computational x-ray burst models must match simulations to observed light curves. Most of the error in simulated curves comes from uncertainties in $rp$ process reaction rates, which can be reduced via precision mass measurements of neutron-deficient isotopes in the $rp$ process path. We perform a precise Penning trap mass measurement of $^{27}$P utilizing the ToF-ICR technique. We use this measurement to calculate $rp$ process reaction rates and input these rates into an x-ray burst model to reduce simulated light curve uncertainty. We also use the mass measurement of $^{27}$P to validate the Isobaric Multiplet Mass Equation (IMME) for the A=27 T=$\frac{3}{2}$ isospin quartet which $^{27}$P belongs to. The mass excess of $^{27}$P was measured to be -670.7(6) keV, a fourteen-fold precision increase over the mass reported in the 2020 Atomic Mass Evaluation (AME2020). X-ray burst light curves were produced with the MESA (Modules for Experiments in Stellar Astrophysics) code using the new mass and associated reaction rates. Changes in the mass of $^{27}$P seem to have minimal effect on light curves, even in burster systems tailored to maximize impact. The mass of $^{27}$P does not play a significant role in x-ray burst light curves. It is important to understand that more advanced models do not just provide more precise results, but often qualitatively different ones. This result brings us a step closer to extracting stellar parameters from individual x-ray burst observations. The IMME has been validated for the $A=27, T=3/2$ quartet. The normal quadratic form of the IMME using the latest data yields a reduced $\chi^2$ of 2.9. The cubic term required to generate an exact fit to the latest data matches theoretical attempts to predict this term., Comment: 8 pages, 6 figures

This work presents an initial on-sky performance measurement of the Single-Photon Imager for Nanosecond Astrophysics (SPINA) system, part of our Ultra-Fast Astronomy (UFA) program. We developed the SPINA system based on the position-sensitive silicon photomultiplier (PS-SiPM) detector to record both photoelectron (P.E.) temporal and spatial information. The initial on-sky testing of the SPINA system was successfully performed on UT 2022 Jul 10, on the 0.7-meter aperture Nazarbayev University Transient Telescope at the Assy-Turgen Astrophysical Observatory (NUTTelA-TAO). We measured stars with a wide range of brightness and a dark region of the sky without stars $< 18$ mag. We measured the SPINA system's spatial resolution to be $<232\mu m$ (full-width half-maximum, FWHM), limited by the unstable atmosphere. We measured the total background noise (detector dark counts and sky background) of 1914 counts per second (cps) within this resolution element. We also performed a crosstalk mapping of the detector, obtaining the crosstalk probability of $\sim0.18$ near the detector's center while reaching $\sim 50\%$ at the edges. We derived a $5\sigma$ sensitivity of $17.45$ Gaia-BP magnitude in a 1s exposure with no atmospheric extinction by comparing the received flux with Gaia-BP band data. For a $10ms$ window and a false alarm rate of once per 100 nights, we derived a transient sensitivity of 14.06 mag. For a $1\mu s$ or faster time scale, we are limited by crosstalk to a 15 P.E. detection threshold. In addition, we demonstrated that the SPINA system is capable of capturing changes in the stellar profile FWHM of $\pm1.8\%$ and $\pm5\%$ change in the stellar profile FWHM in $20ms$ and $2ms$ exposures, respectively, as well as capturing stellar light curves on the $ms$ and $\mu s$ scales.

Unveiling the true nature of Dark Matter (DM), which manifests itself only through gravity, is one of the principal quests in physics. Leading candidates for DM are weakly interacting massive particles (WIMPs) or ultralight bosons (axions), at opposite extremes in mass scales, that have been postulated by competing theories to solve deficiencies in the Standard Model of particle physics. Whereas DM WIMPs behave like discrete particles ($\varrho$DM), quantum interference between DM axions is manifested as waves ($\psi$DM). Here, we show that gravitational lensing leaves signatures in multiply-lensed images of background galaxies that reveal whether the foreground lensing galaxy inhabits a $\varrho$DM or $\psi$DM halo. Whereas $\varrho$DM lens models leave well documented anomalies between the predicted and observed brightnesses and positions of multiply-lensed images, $\psi$DM lens models correctly predict the level of anomalies left over by $\varrho$DM lens models. More challengingly, when subjected to a battery of tests for reproducing the quadruply-lensed triplet images in the system HS 0810+2554, $\psi$DM is able to reproduce all aspects of this system whereas $\varrho$DM often fails. The ability of $\psi$DM to resolve lensing anomalies even in demanding cases like HS 0810+2554, together with its success in reproducing other astrophysical observations, tilt the balance toward new physics invoking axions., Comment: Updated with accepted version. The Version of Record of this article is published in Nature Astronomy, and is available online at https://www.nature.com/articles/s41550-023-01943-9. Free online version : https://rdcu.be/damHj

Low mass galaxies in the Local Group are dominated by dark matter and comprise the well studied ``dwarf Spheroidal" (dSph) class, with typical masses of $10^{9-10}M_\odot$ and also the equally numerous ``ultra faint dwarfs" (UFD), discovered recently, that are distinctly smaller and denser with masses of only $10^{7-8}M_\odot$. This bimodality amongst low mass galaxies contrasts with the scale free continuity expected for galaxies formed under gravity, as in the standard Cold Dark Matter (CDM) model for heavy particles. Within each dwarf class we find the core radius $R_c$ is inversely related to velocity dispersion $\sigma$, quite the opposite of standard expectations, but indicative of dark matter in a Bose-Einstein state, where the Uncertainty Principle requires $R_c \times \sigma$ is fixed by Planks constant, $h$. The corresponding boson mass, $m_b=h/R_c \sigma$, differs by one order of magnitude between the UDF and dSph classes, with $10^{-21.4}$eV and $10^{-20.3}$eV respectively. Two boson species is reinforced by parallel relations seen between the central density and radius of UDF and dSph dwarfs respectively, each matching the steep prediction, $\rho_c \propto R_c^{-4}$, for soliton cores in the ground state. Furthermore, soliton cores accurately fit the stellar profiles of UDF and dSph dwarfs where prominent, dense cores appear surrounded by low density halos, as predicted by our simulations. Multiple bosons may point to a String Theory interpretation for dark matter, where a discrete mass spectrum of axions is generically predicted to span many decades in mass, offering a unifying "Axiverse" interpretation for the observed "diversity" of dark matter dominated dwarf galaxies., Comment: 45 pages, 36 figures

Instruments such as the ROTSE, TORTORA, Pi of the Sky, MASTER-net, and others have recorded single-band optical flux measurements of gamma-ray bursts starting as early as $\thicksim$ 10 seconds after gamma-ray trigger. The earliest measurements of optical spectral shape have been made only much later, typically on hour time scales, never starting less than a minute after trigger, until now. Beginning only 58 seconds after the \emph{Swift} BAT triggerred on GRB201015A, we observed a sharp rise in optical flux to a peak, followed by a power law temporal decay, $\propto t^{-0.81 \pm 0.03}$. Flux was measured simultaneously in three optical bands, g\p, r\p, and i\p, using our Burst Simultaneous Three-channel Imager (BSTI) on the NUTTelA-TAO telescope. Our data during the decay show strong colour evolution from red to blue, with a change in the optical log slope of $+0.72 \pm 0.14$; during this time the X-ray log slope remained constant. We did not find evidence for a two-component jet structure or a transition from reverse to forward shock or a prompt emission component that would explain this change in slope. We find that the majority of the optical spectral slope evolution is consistent with a monotonic decay of extinction, evidence of dust destruction. Assuming a constant source spectral slope and an SMC-like extinction curve, we derive a change in the local extinction $A_\mathrm{v}^\mathrm{local}$ from $\thicksim$0.8 mag to 0.3 mag in $\thicksim$2500 seconds. This work shows that significant information about the early emission phase is being missed without such early observations with simultaneous multi-band instruments., Comment: 7 pages, 3 figures. MNRAS: Accepted 2023 February 15. Received 2023 February 14; in original form 2022 November 3

The theory of partition congruences has been a fascinating and difficult subject for over a century now. In attempting to prove a given congruence family, multiple possible complications include the genus of the underlying modular curve, representation difficulties of the associated sequences of modular functions, and difficulties regarding the piecewise $\ell$-adic convergence of elements of the associated space of modular functions. However, our knowledge of the subject has developed substantially and continues to develop. In this very brief survey, we will discuss the utility of modular functions in proving partition congruences, both theoretical and computational, and many of the problems in the subject that are yet to be overcome.

The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. We have discovered an infinite congruence family for $d_5(n)$ modulo powers of 5. Classical methods cannot be used to prove this family of congruences. Indeed, the proof employs the recently developed localization method, and utilizes a striking internal algebraic structure which has not yet been seen in the proof of any congruence family. We believe that this discovery poses important implications on future work in partition congruences., Comment: Mathematica supplement can be found online at

In 2021 da Silva, Hirschhorn, and Sellers studied a wide variety of congruences for the $k$-elongated plane partition function $d_k(n)$ by various primes. They also conjectured the existence of an infinite congruence family modulo arbitrarily high powers of 2 for the function $d_7(n)$. We prove that such a congruence family exists -- indeed, for powers of 8. The proof utilizes only classical methods, i.e., integer polynomial manipulations in a single function, in contrast to all other known infinite congruence families for $d_k(n)$ which require more modern methods to prove.

Although most gravitational wave events are claimed to be mergers of unusually massive, $25-65M_\odot$, black holes, it is now clear that 20\% of all reported events comprise modest mass black holes, $5-15M_\odot$, like the stellar black holes in the Milky Way. We show that such stellar mass black hole binaries (BBH) if magnified by lensing galaxies can be detected at high redshift, 1$< $z$ <$5, with chirp masses increased by $1+z$, accounting for the majority of apparently high mass BBH events. This simple lensing explanation is manifested by the evident bimodality of BBH chirp masses now visible, with 80\% of BBH events in a broad peak centered on $m_{chirp} \simeq 35M_\odot$, and 20\% of BBH events in a narrow, low mass peak at $m_{chirp} \simeq 8.5M_\odot$, matching well our prediction for lensed and unlensed events respectively. This lensing interpretation is reinforced by the "graveyard plot" when ranked by chirp mass, revealing a jump in chirp mass at $m_{chirp} \simeq 10M_\odot$ that we show is caused by the large redshift difference between unlensed events with $z<0.3$ and lensed events above $z>1$. Furthermore, nearly all BBH events are seen to share a component mass ratio of $m_1/m_2=1.45\pm0.03$, indicating a common stellar origin for BBH events across all chirp masses. This observed component mass uniformity implies most binary black holes seldom pair up by random capture, instead we may conclude that massive progenitor stars of BBH black holes typically formed in-situ, in a well defined way over the full span of cosmic time accessed through gravitational lensing., Comment: 7 pages, 5 figures

The unusually large "dwarf" galaxy Crater II, with its small velocity dispersion, $\simeq 3$ km/s, defies expectations that low mass galaxies should be small and dense. We combine the latest stellar and velocity dispersion profiles finding Crater II has a prominent dark core of radius $\simeq 0.71^{+0.09}_{-0.08}$ kpc, surrounded by a low density halo, with a transition visible between the core and the halo. We show that this profile matches the distinctive core-halo profile predicted by "Wave Dark Matter" as a Bose-Einstein condensate, $\psi$DM, where the ground state soliton core is surrounded by a tenuous halo of interfering waves, with a marked density transition predicted between the core and halo. Similar core-halo structure is seen in most dwarf spheroidal galaxies (dSph), but with smaller cores, $\simeq 0.25$ kpc and higher velocity dispersions, $\simeq 9$km/s, and we argue here that Crater II may have been a typical dSph that has lost most of its halo mass to tidal stripping, so its velocity dispersion is lower by a factor of 3 and the soliton is wider by a factor of 3, following the inverse scaling required by the Uncertainty Principle. This tidal solution for Crater II in the context of $\psi$DM, is supported by its small pericenter of $\simeq 20$ kpc established by Gaia, implying significant tidal stripping of Crater II by the Milky Way is expected., Comment: Accepted version by MNRAS. 10 pages, 6 figures and 1 table