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1. The Eisenstein ideal at prime-square level has constant rank

   https://doi.org/10.1073/pnas.2500729122  

   Lang, Jaclyn; Wake, Preston (July 2025, Proceedings of the National Academy of Sciences)

   LetNandpbe prime numbers with $p\ge 5$such that $p\mid \mid (N+1)$. In a previous paper, we showed that there is a cuspformfof weight 2 and level ${\mathrm{\Gamma }}_0\left(N^2\right)$whoseℓ-th Fourier coefficient is congruent to $\ell +1$modulo a prime abovepfor all primesℓ. In this paper, we prove that this formfis unique up to Galois conjugacy, and the extension of ${\mathbb{Z}}_p$generated by the coefficients offis exactly ${\mathbb{Z}}_p[{\zeta }_p+{\zeta }_p^{-1}]$. We also prove similar results when a higher power ofpdivides $N+1$. 

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2. HSTPROMO Internal Proper-motion Kinematics of Dwarf Spheroidal Galaxies. I. Velocity Anisotropy and Dark Matter Cusp Slope of Draco

   https://doi.org/10.3847/1538-4357/ad571c  

   Vitral, Eduardo; van_der_Marel, Roeland P; Sohn, Sangmo Tony; Libralato, Mattia; del_Pino, Andrés; Watkins, Laura L; Bellini, Andrea; Walker, Matthew G; Besla, Gurtina; Pawlowski, Marcel S; et al (July 2024, The Astrophysical Journal)

   Abstract We analyze four epochs of Hubble Space Telescope imaging over 18 yr for the Draco dwarf spheroidal galaxy. We measure precise proper motions for hundreds of stars and combine these with existing line-of-sight (LOS) velocities. This provides the first radially resolved 3D velocity dispersion profiles for any dwarf galaxy. These constrain the intrinsic velocity anisotropy and resolve the mass–anisotropy degeneracy. We solve the Jeans equations in oblate axisymmetric geometry to infer the mass profile. We find the velocity dispersion to be radially anisotropic along the symmetry axis and tangentially anisotropic in the equatorial plane, with a globally averaged value $\overline{{\beta }_{\mathrm{B}}}=-{0.20}_{-0.53}^{+0.28}$, (where 1 – ${\beta }_{\mathrm{B}}\equiv 〈v_{\tan }^2〉/〈v_{\mathrm{rad}}^2〉$in 3D). The logarithmic dark matter (DM) density slope over the observed radial range, Γ_dark, is $-{0.83}_{-0.37}^{+0.32}$, consistent with the inner cusp predicted in ΛCDM cosmology. As expected given Draco’s low mass and ancient star formation history, it does not appear to have been dissolved by baryonic processes. We rule out cores larger than 487, 717, and 942 pc at 1σ, 2σ, and 3σconfidence, respectively, thus imposing important constraints on the self-interacting DM cross section. Spherical models yield biased estimates for both the velocity anisotropy and the inferred slope. The circular velocity at our outermost data point (900 pc) is ${24.19}_{-2.97}^{+6.31}\mathrm{km}{\mathrm{s}}^{-1}$. We infer a dynamical distance of ${75.37}_{-4.00}^{+4.73}$kpc and show that Draco has a modest LOS rotation, with $\left(v/\sigma \right)=0.22\pm 0.09$. Our results provide a new stringent test of the so-called “cusp–core” problem that can be readily extended to other dwarfs. 

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3. Structural phase purification of bulk HfO ₂ :Y through pressure cycling

   https://doi.org/10.1073/pnas.2312571121  

   Musfeldt, J. L.; Singh, Sobhit; Fan, Shiyu; Gu, Yanhong; Xu, Xianghan; Cheong, S.-W.; Liu, Z.; Vanderbilt, David; Rabe, Karin M. (January 2024, Proceedings of the National Academy of Sciences)

   We combine synchrotron-based infrared absorption and Raman scattering spectroscopies with diamond anvil cell techniques and first-principles calculations to explore the properties of hafnia under compression. We find that pressure drives HfO ${}_2$:7%Y from the mixed monoclinic ( $P{2}_1/c$) $+$antipolar orthorhombic ( $\mathit{Pbca}$) phase to pure antipolar orthorhombic ( $\mathit{Pbca}$) phase at approximately 6.3 GPa. This transformation is irreversible, meaning that upon release, the material is kinetically trapped in the $\mathit{Pbca}$metastable state at 300 K. Compression also drives polar orthorhombic ( $Pca{2}_1$) hafnia into the tetragonal ( $P{4}_2/nmc$) phase, although the latter is not metastable upon release. These results are unified by an analysis of the energy landscape. The fact that pressure allows us to stabilize targeted metastable structures with less Y stabilizer is important to preserving the flat phonon band physics of pure HfO ${}_2$. 

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4. Sequence modeling of higher-order wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

   https://doi.org/10.1088/1361-6382/ae2bd6  

   Tiki, Victoria; Pham, Kiet; Huerta, E A (December 2025, Classical and Quantum Gravity)

   Abstract Higher-order gravitational wave modes from quasi-circular, spinning, non-precessing binary-black-hole (BBH) mergers encode rich information about the nonlinear dynamics of strong-field gravity. We present a transformer-based sequence-completion surrogate that, given an early-inspiral segment, forecasts the subsequent late inspiral, merger, and ringdown. The intended applications are (i) patching or completing expensive or interrupted numerical-relativity (NR) simulations and (ii) providing late-time cross-checks and rapid hybridization studies. The training set is built from theNRHybSur3dq8surrogate, which provides spherical-harmonic modes up to $\ell \text{⩽}4$(excluding (4, 0) and $(4,\pm 1)$, and including (5, 5)) for mass ratios $q\text{⩽}8$, dimensionless spin components $s_{1,2}^z\in [-0.8,0.8]$, and inclination angles $\theta \in [0,\pi ]$. Waveforms are supplied on the interval $t\in [-5000\mathrm{M},-100\mathrm{M})$and the model autoregressively generates the plus and cross polarizations $(h_{+},h_{\times })$on $t\in [-100\mathrm{M},130\mathrm{M}]$. Training on the Delta supercomputer with 16 NVIDIA A100 GPUs required $\sim 15$ h on more than 14 million hybrid waveforms. Evaluation on a held-out test set of $\mathrm{840,000}$samples yields mean and median overlaps of 0.996 and 0.997, respectively, with respect to the surrogate ground truth. The model generalises reasonably well to out-of-distribution NR simulations from the SXS catalogue: across 521 NR waveforms with mass ratios up toq = 15 and spin magnitudes $|s|\text{⩽}0.998$, we obtain a median overlap of 0.969, rising to 0.998 for face-on/off orientations. Within the surrogate’s training domain, the transformer provides accurate, millisecond-scale sequence completion of BBH waveforms, including higher-order modes, from early inspiral to ringdown. The NR tests indicate promising performance on higher-fidelity, out-of-distribution data, particularly for detector-favourable orientations. 

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5. Characterizing the fundamental bending vibration of a linear polyatomic molecule for symmetry violation searches

   https://doi.org/10.1088/1367-2630/ace471  

   Jadbabaie, Arian; Takahashi, Yuiki; Pilgram, Nickolas H; Conn, Chandler J; Zeng, Yi; Zhang, Chi; Hutzler, Nicholas R (July 2023, New Journal of Physics)

   Abstract Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize the fundamental bending vibration of ${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$ $\to \tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state, and accurately model the state’s structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the $\tilde{X}{}^2{\mathrm{\Sigma }}^{+}\left(010\right)$state and fit the molecule-frame dipole moment to $D_{\mathrm{m}\mathrm{o}\mathrm{l}}=2.16\left(1\right)$Dand the effective electrong-factor to $g_S=2.07\left(2\right)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin–orbit and vibronic perturbations in the excited $\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}\left(000\right)$state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules. 

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