We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the class of Gaussian distributions, and is unique in the larger class of measures with strongly-concave and smooth log-densities. We prove that the flow globally converges toward the target measure when the source's covariance matrix is not singular, and provide counter-examples to global convergence when it is, giving a first answer to an open question raised in [Carlier et al. 2024, \S4.2]. When the covariance matrix of the source distribution commutes with that of the target, we derive more quantitative results that showcase exponential convergence toward the target when the source and the target share their support, but dropping to linear rates (O(t^{-1})) if the target is concentrated on a strict subspace of the source's support.

We compute the Hilbert series of three-dimensional $\mathcal{N}=3$ quiver gauge theories by taking a specific limit of the superconformal index. Our approach introduces auxiliary fugacities associated with symmetries which, while not present in the full theory, arise as effective symmetries on specific branches of the moduli space. By evaluating the index in a limit governed by these parameters, we successfully isolate the Hilbert series of the desired branches. We validate our results against the literature and provide several new extensions. We focus primarily on linear and circular quivers with unitary gauge groups, which originate from Type IIB brane configurations involving generic $(p,q)$ fivebranes. We further generalise this approach to star-shaped and orthosymplectic $\mathcal{N}=3$ quivers. Finally, we investigate the geometric branches of affine Dynkin quivers, demonstrating agreement with known results, while offering new predictions for unexplored cases.

In this paper, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to Hölder continuous maps on the boundary, with Hölder exponent strictly greater than 1/2.

Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new Julia-based implementation that has two important techniques: (1) a general purpose higher-order automatic differentiation engine for derivative evaluation with low overhead; (2) a combined symbolic-numeric approach to generate code for recursively computing the Taylor polynomial of the ODE solution. We demonstrate that the resulting software's compiler-based tooling is transparent to the user, requiring no changes from interfaces required to use standard explicit Runge-Kutta methods, while achieving better run time performance. In addition, we also developed a comprehensive adaptive time and order algorithm that uses different step size and polynomial degree across the integration period, which makes this implementation more efficient and versatile in a broad range of dynamics. We show that for codes compatible with compiler transformations, these integrators are more efficient and robust than the traditionally used explicit Runge-Kutta methods.

Topological materials hold immense promise for exhibiting exotic quantum phenomena, yet achieving controllable topological phase transitions remains challenging. Here, we demonstrate a structurally driven, reversible topological phase transition in the distorted square net material GdPS, induced via in situ potassium dosing. Using angle-resolved photoemission spectroscopy and first principles calculations, we demonstrate a cascade of topological phases in the sub-surface P layer: from a large, topologically trivial band gap to a gapless Dirac cone state with a 2 eV dispersion, and finally to a two-dimensional topological insulator as inferred from theory. This evolution is driven by subtle structural distortions in the first P layer caused by potassium adsorption, which in turn contribute to the band gap closure and topological phase transition. Furthermore, the ability to manipulate the topology of a sub-surface layer in GdPS offers a unique route for exploring and controlling topological states in bulk materials.

Wilson loops are among the most fundamental gauge-invariant observables in quantum field theory, encoding the global structure of gauge fields through their holonomy along closed contours. Originally introduced as order parameters for confinement in non-Abelian gauge theories, they have recently acquired a central role in condensed matter physics, where they characterize topological phases and quantized transport phenomena. In this work we present a unified theoretical picture in which Wilson loops connect nonperturbative gauge dynamics, Berry-phase topology in band theory, and the quantum Hall response of interacting electron systems. We demonstrate explicitly how Wilson loops encode Chern numbers, fractional charge, and anyonic braiding statistics within Chern--Simons effective field theory. Both quantized Hall conductivity and quasiparticle statistics are shown to originate from the same topological invariant -- the linking number of Wilson loops -- establishing a direct correspondence between microscopic topological structure and macroscopic transport.

Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.

Quantum metrology involves the application of quantum resources to enhance measurements. Several communities have developed quantum-metrology strategies that leverage effective time reversals. These strategies, we posit, form four classes. First, echo metrology begins with a preparatory unitary and ends with that unitary's time-reverse. The protocol amplifies the visibility of a small parameter to be sensed. Similarly, weak-value amplification enhances a weak coupling's detectability. The technique exhibits counterintuitive properties captured by a retrocausal model. Using the third strategy, one simulates closed timelike curves, worldlines that loop back on themselves in time. The fourth strategy involves indefinite causal order, which characterises channels applied in a superposition of orderings. We review these four strategies, which we unify under the heading of time-reverse metrology. We also outline opportunities for this toolkit in quantum metrology; quantum information science; quantum foundations; atomic, molecular, and optical physics; and solid-state physics.

This article presents a pedagogical probabilistic exploration of the Newton-Girard identities. We show that the coefficients in these classical relations between power sums and elementary symmetric polynomials can be interpreted as the stable limits of integrals over the unit cube, and as ratios of moments of simple probability distributions. Several classes of integrals are studied, including trigonometric and multiplicative forms. In addition, we discuss the spectral implications via the Le Verrier-Souriau-Faddeev algorithm and Random Matrix Theory, providing a unified framework for the asymptotic algebraic behavior of these identities. While the identities are classical, the probabilistic interpretation of the limits of their normalized forms is the specific focus of the present work.

Combinatorial sputtering is a physical vapor deposition method that enables the high-throughput synthesis of compositionally varied thin films. Using this technique, the effects of stoichiometry on specific properties of alloy thin films with analog composition gradients can be mapped using high-throughput characterization. To obtain specific stoichiometries, such as those desired for an equiatomic, intermetallic, or doped compounds, the sputter power of each target must be simultaneously tuned to optimize the deposition rate of each component. This optimization problem increases in complexity with the number of components, which commonly leads to iterative guess-and-check processing and can limit the intrinsic high-throughput advantages of this synthesis method. To circumvent this challenge, this work introduces a composition optimization procedure that enables the facile synthesis of sputtered combinatorial films with targeted compositions. This procedure leverages the expeditious mapping of composition using wavelength dispersive x-ray fluorescence and is capable of optimizing processing for an arbitrary number of components. As a demonstration, this method is leveraged to sputter a combinatorial Cr$_{v}$Fe$_{w}$Mo$_{x}$Nb$_{y}$Ta$_{z}$ film with an equiatomic composition near the wafer center.

Post-common envelope binaries (PCEBs) consisting of a white dwarf (WD) plus a main-sequence (MS) star can constrain current prescriptions of common envelope evolution (CEE) and calibrate theoretical models of binary formation and evolution. Most PCEBs studied to date have typical orbital periods of hours to a few days and can be well explained by assuming inefficient CEE to expel the envelope. However, there are currently several systems with relatively wide orbital periods ($>$18 days). To explain these wide PCEBs, additional sources of energy have been suggested to be taken into account. Here, we present the discovery and observational characterization of a compact object ($M\,\geq\,0.58\,\rm M_{\odot}$) with a K-type star companion in the solar neighborhood ($d\sim 112$ pc) and an orbital period of $P_{\rm orb}\sim 14$ days. The compact object binary is likely to be a system consisting of a WD and a barium dwarf, making it the shortest-period barium star binary candidate. Such a system with an orbital period within the gap between tight and wide binaries provides a test of whether additional energy sources are required to explain its formation. Using binary evolution models, we investigate the evolutionary history of this wide PCEB system and find that the observed properties of this source can be explained without invoking any extra energy source.

DAMSA (DArk Messenger Searches at an Accelerator) is a novel short-baseline accelerator experiment aimed at probing short-lived physics processes, including searches for evidence of a dark sector of particle physics and well-motivated Standard Model signals. Motivated by open questions in neutrino physics and the absence of conclusive evidence for conventional weakly interacting massive particles, DAMSA targets MeV-to-sub-GeV dark-sector messengers with feeble couplings that can be produced in abundance at the PIP-II LINAC. By employing an ultra-short baseline of order one meter, DAMSA is uniquely positioned to overcome the beam-dump "ceiling" that limits sensitivity to promptly decaying particles in longer-baseline experiments. The conceptual design emphasizes a beam-dump production scheme combined with a compact detector optimized for rare decays while mitigating intense neutron-induced backgrounds inherent to high-power proton beams. To validate the experimental strategy and detector technologies, the Little DAMSA Path-Finder (LDPF) proof-of-concept experiment is proposed, focusing on axion-like particles decaying to two photons and operating with 300 MeV electron beams at FAST. Successful realization of LDPF will establish the feasibility of the DAMSA approach, enabling a broad and powerful program to explore short-lived new physics and precision Standard Model processes in a previously inaccessible regime. This conceptual design document outlines the technical details of DAMSA's physics goals, the beam facility proposals, key experimental challenges and how to overcome them, and the proposed experimental staging campaigns.

Robust machine learning for regulatory genomics is studied under biologically and technically induced distribution shifts. Deep convolutional and attention based models achieve strong in distribution performance on DNA regulatory sequence prediction tasks but are usually evaluated under i.i.d. assumptions, even though real applications involve cell type specific programs, evolutionary turnover, assay protocol changes, and sequencing artifacts. We introduce a robustness framework that combines a mechanistic simulation benchmark with real data analysis on a massively parallel reporter assay (MPRA) dataset to quantify performance degradation, calibration failures, and uncertainty based reliability. In simulation, motif driven regulatory outputs are generated with cell type specific programs, PWM perturbations, GC bias, depth variation, batch effects, and heteroscedastic noise, and CNN, BiLSTM, and transformer models are evaluated. Models remain accurate and reasonably calibrated under mild GC content shifts but show higher error, severe variance miscalibration, and coverage collapse under motif effect rewiring and noise dominated regimes, revealing robustness gaps invisible to standard i.i.d. evaluation. Adding simple biological structural priors motif derived features in simulation and global GC content in MPRA improves in distribution error and yields consistent robustness gains under biologically meaningful genomic shifts, while providing only limited protection against strong assay noise. Uncertainty-aware selective prediction offers an additional safety layer that risk coverage analyses on simulated and MPRA data show that filtering low confidence inputs recovers low risk subsets, including under GC-based out-of-distribution conditions, although reliability gains diminish when noise dominates.

This paper presents the first thermodynamic assessment of binary and pseudo-binary phase diagrams in the Ba--La--S and Ga--La--S systems by means of the CALPHAD method. Experimental phase diagram equilibrium data and thermodynamic properties available from the literature were critically reviewed and assessed using thermodynamic models for the Gibbs energies of individual phases. The associated solution model was used to describe the short-range ordering behavior of the liquid phases. To supplement the limited experimental data reported in the literature, ab initio molecular dynamics calculations were employed to derive mixing enthalpies of the liquid phases in the binary subsystems. The resulting phase diagrams and calculated thermodynamic properties show good agreement with available literature within the investigated compositional ranges of binary and pseudo-binary systems.

In this paper, we establish global $C^{1,α}$-regularity for bounded generalized solutions of elliptic equations in divergence form with Musielak-Orlicz growth and subject to Dirichlet or Neumann boundary conditions. In fact, our findings extend and generalize several important regularity results in cases of special attention such as variable exponent spaces, Orlicz spaces, and some $(p,q)$ situations. We also point out new conditions in the analysis that focus on the interplay between non-standard growth conditions and the boundary behavior in such generalized examples.

We prove that there is no preferential voting method satisfying the Condorcet winner and loser criteria, positive involvement (if a candidate $x$ wins in an initial preference profile, then adding a voter who ranks $x$ uniquely first cannot cause $x$ to lose), and $n$-voter resolvability (if $x$ initially ties for winning, then $x$ can be made the unique winner by adding some set of up to $n$ voters). This impossibility theorem holds for any positive integer $n$. It also holds if either the Condorcet loser criterion is replaced by independence of clones or positive involvement is replaced by negative involvement.

Advanced manufacturing with new bio-derived materials can be achieved faster and more economically with first-principle-based artificial intelligence and machine learning (AI/ML)-derived models and process optimization. Not only is this motivated by increased industry profitability, but it can also be optimized to reduce waste generation, energy consumption, and gas emissions through additive manufacturing (AM) and AI/ML-directed self-driving laboratory (SDL) process optimization. From this perspective, the benefits of using 3D printing technology to manufacture durable, sustainable materials will enable high-value reuse and promote a better circular economy. Using AI/ML workflows at different levels, it is possible to optimize the synthesis and adaptation of new bio-derived materials with self-correcting 3D printing methods, and in-situ characterization. Working with training data and hypotheses derived from Large Language Models (LLMs) and algorithms, including ML-optimized simulation, it is possible to demonstrate more field convergence. The combination of SDL and AI/ML Workflows can be the norm for improved use of biobased and renewable materials towards advanced manufacturing. This should result in faster and better structure, composition, processing, and properties (SCPP) correlation. More agentic AI tasks, as well as supervised or unsupervised learning, can be incorporated to improve optimization protocols continuously. Deep Learning (DL), Reinforcement Learning (RL), and Deep Reinforcement Learning (DRL) with Deep Neural Networks (DNNs) can be applied to more generative AI directions in both AM and SDL, with bio-based materials.

This paper deals with the state estimation of non-linear and non-Gaussian systems with an emphasis on the numerical solution to the Bayesian recursive relations. In particular, this paper builds upon the Lagrangian grid-based filter (GbF) recently-developed for linear systems and extends it for systems with nonlinear dynamics that are invertible. The proposed nonlinear Lagrangian GbF reduces the computational complexity of the standard GbFs from quadratic to log-linear, while preserving all the strengths of the original GbF such as robustness, accuracy, and deterministic behaviour. The proposed filter is compared with the particle filter in several numerical studies using the publicly available MATLAB\textregistered\ implementation\footnote{https://github.com/pesslovany/Matlab-LagrangianPMF}.

We develop a unified charge-dependent solar modulation model by solving the three-dimensional Parker transport equation, incorporating a realistic wavy heliospheric current sheet to treat drift effects self-consistently. Using a local interstellar spectrum from GALPROP constrained by Voyager data, we fit the model to time-resolved proton and antiproton fluxes measured by the Alpha Magnetic Spectrometer - 02 (AMS-02) during the solar-quiet period (May 2011 to June 2022). To enable rapid parameter scans, we employ neural-network-based surrogate models to compute propagation and modulation matrices efficiently. The results demonstrate that the model simultaneously describes the observed proton and antiproton fluxes with physically reasonable parameters, providing a unified account of charge-dependent modulation.

In our paper [1], our numerical simulations showed that, unlike displacement and conventional squeezing, higher-order squeezing exhibits oscillatory dynamics. Subsequently, Gordillo and Puebla pointed out that simulation results depend on whether the size of the state space in the simulations is even or odd [2]. Using additional derivations, they argued that the oscillatory dynamics is unphysical and that the photon number must increase monotonically as a function of the squeezing parameter $r$. We agree with the observation of an even-odd parity dependence in the simulations. We independently noticed the same feature in our simulations after the publication of Ref. [1]. This observation led us to perform a more detailed investigation of the numerical simulation and mathematical aspects of the generalized squeezing problem. Our new findings were reported in Ref. [3]. Further analysis was reported in Ref. [4]. Our conclusion is that the generalized squeezing operator is physically not well defined but can be made well defined when combined with additional information about the physical system under study. We demonstrated this point in the case where we include an additional nonlinear interaction term in the Hamiltonian. We disagree with the claim that the photon number must be a monotonically increasing function of $r$. This claim contradicts the mathematically rigorous results of Ref. [4]. Furthermore, we show that the oscillatory behaviour persists in two closely related, well-behaved models.

Consider an $(n+1)$-dimensional circular cone with opening angle $α\in (0,π)$. Using a free-boundary adaptation of the classical calibration method, we prove that, for $n \geq 4$, there exists a threshold $\barα(n) \in (0,π)$ such that if $α\geq \barα(n)$, that is, the cone is wide enough, the intersection of the cone with an axial hyperplane is area-minimizing with respect to free-boundary variations inside the cone. This provides a counterexample to a recent Vertex-skipping Theorem proved by the author in collaboration with G.P. Leonardi, at least for $n\geq4$.

We present randomized algorithms for estimating the log-determinant of regularized symmetric positive semi-definite matrices. The algorithms access the matrix only through matrix vector products, and are based on the introduction of a preconditioner and stochastic trace estimator. We claim that preconditioning as much as we can and making a rough estimate of the residual part with a small budget achieves a small error in most of the cases. We choose a Nyström preconditioner and estimate the residual using only one sample of stochastic Lanczos quadrature (SLQ). We analyze the performance of this strategy from a theoretical and practical viewpoint. We also present an algorithm that, at almost no additional cost, detects whether the proposed strategy is not the most effective, in which case it uses more samples for the SLQ part. Numerical examples on several test matrices show that our proposed methods are competitive with existing algorithms.

The giant planet-metallicity correlation revealed that planetary formation depends on the stellar properties. There is growing evidence that it is also valid for smaller hot planets, but it is not clear whether elements other than iron also influence the properties of planetary systems. To investigate this, we determined the abundances of 13 chemical elements (Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Co, Ni and Cu) for a sample of 561 Kepler exoplanet-hosting stars using high-resolution Keck/HIRES spectra. We find that stars in systems having only large or hot planets are enriched in some elements relative to those having only small or warm planets, respectively, with this signature being related to the underlying stellar metallicity. This Kepler sample is composed of stars belonging to the Galactic low- and high-$α$ sequences, corresponding to the chemical thin and thick disks. Our results reveal that stars enhanced in $α$-elements may facilitate the formation of large planets in metal-poor environments although the iron abundance is still a limiting factor. We also investigated chemical abundances as a function of elemental condensation temperatures and found that there is a diversity of slopes regardless of the exoplanetary systems hosted by the star. We confirmed that the Sun is depleted in refractory elements relative to the solar twins in our sample, all of which host a diversity of exoplanets, suggesting that this depletion is caused by processes not related to planet formation.

arXiv admin note: This paper has been withdrawn by arXiv due to disputed and unverifiable authorship and affiliation

We investigate a phenomenological extension of the standard $Λ$CDM framework, the $Ω_1Ω_2$-$Λ$CDM model, in which the total energy density of the universe is expanded in powers of $1+z$. This parameterization recovers $Λ$CDM and introduces two additional terms, $Ω_1(1+z)$ and $Ω_2(1+z)^2$, in the dark energy sector alongside the cosmological constant, leading to a physically interpretable and observationally testable effective dark energy dynamics. Using Planck cosmic microwave background (CMB) data, we find that the model allows additional freedom in the late-time expansion history while preserving standard early-universe physics. When DESI baryon acoustic oscillation (BAO) data are included, the inferred Hubble constant is $H_0 = 69.74 \pm 0.77~\mathrm{km\;s^{-1}\;Mpc^{-1}}$ (68% CL), consistent with Tip of the Red Giant Branch (TRGB) measurements from the Carnegie--Chicago Hubble Program (CCHP). The reconstructed dark energy equation of state exhibits a smooth transition across the phantom divide followed by asymptotic de Sitter behavior, modifying late-time dynamics while maintaining standard early-time cosmology. Overall, controlled late-time deviations from $Λ$CDM improve cosmological concordance.

We study the problem of selecting a subset of patients who are unlikely to experience an adverse event within a fixed time horizon by calibrating a screening rule based on a black-box survival model. We consider two complementary, distribution-free frameworks for this task. The first extends classical calibration ideas -- estimating the event rate among selected patients using a hold-out dataset -- by integrating them with the Learn-Then-Test (LTT) framework, yielding high-probability guarantees for data-adaptively tuned screening rules. The second takes a different perspective by reformulating screening as a hypothesis testing problem on future patient outcomes, enabling false discovery rate (FDR) control via the Benjamini-Hochberg procedure applied to selective conformal p-values, and providing guarantees in expectation. We clarify the theoretical relationship between these approaches, explain how both can be adapted to right-censored time-to-event data via inverse probability of censoring weighting, and compare them empirically using simulations and oncology data from the Flatiron Health Research Database. Our results reveal a trade-off between efficiency and strength of guarantees: FDR-based screening is typically more powerful, while LTT-based calibration is more conservative but offers stronger guarantees. We also provide practical guidance on implementation and tuning.

Suppose we have $n$ dice, each with $s$ faces (assume $s\geq n$). On the first turn, roll all of them, and remove from play those that rolled an $n$. Roll all of the remaining dice. In general, if at a certain turn you are left with $k$ dice, roll all of them and remove from play those that rolled a $k$. The game ends when you are left with no dice to roll. For $n,s \in \mathbb{N} \setminus \{0\}$ such that $s \geq n$, let $Y_n^s$ be the random variable for the number of turns to finish the game rolling $n$ dice with $s$ faces. We find recursive and non-recursive solutions for $\mathbb{E}(Y_n^{s})$ and $\mathrm{Var}(Y_n^{s})$, and bounds for both values. Moreover, we show that $Y_n^{s}$ can also be modeled as the maximum of a sequence of i.i.d. geometrically distributed random variables. Although, as far as we know, this game hasn't been studied before, similar problems have.

The analytic hierarchy process (AHP) is one of the most widely used multicriteria decision-making methods, with applications from agriculture to space engineering. Despite its popularity, AHP has been repeatedly criticised for rank reversal, a phenomenon in which the ranking of alternatives changes after the addition or removal of an irrelevant or duplicate alternative. This paper introduces a new type of rank reversal in AHP, arising when the intensity of preferences is uniformly increased. We show that even when all pairwise preferences preserve their direction and are intensified identically, the eigenvector method may produce a different ordering of alternatives. In contrast, the geometric mean (GM) method is robust to this intensity-of-preference (IOP) rank reversal. The applicability of this result is shown through a real decision-making problem taken from a NASA manual concerning capability prioritisation for the planned lunar Gateway orbital station.

Context. Sunspot boundaries are commonly outlined by contours of the continuum intensity. However, their magnetic nature has not yet been fully characterised. Aims. We investigate the properties of the outer boundary of a long-lived sunspot to identify the magnetic property that defines it. Methods. We analysed the magnetic properties of AR NOAA11591 spot during its two passages across the solar disc, using SDO/HMI continuum intensity and magnetic field, and determined their contours to outline the outer boundary. Results. During the 1st disc passage, in which the sunspot is in its stable phase, the intensity contours at 0.9 of the mean quiet Sun intensity and isocontours of the magnetic field strength of 625G provide an almost perfect match between the two contours. With these thresholds, the time-averaged area of mismatch is minimised, yielding an average distance between the contours of 0.58 pixel, corresponding to less than 0.26 arcsec. During the 2nd disc passage, the spot shows clear signs of decay, and we find that the 0.9 intensity and 625G magnetic isocontours detach from each other, coupled to the disappearance of penumbra. In this super-equipartition area, granulation still operates. Conclusions. Based on a comparison with simulation data from our previous work, and in agreement with findings of other authors, we conclude that the outer boundary of stable sunspots is defined by an invariant magnetic field: the equipartition field. From the discrepancy between intensity and magnetic contours during the decaying phase of the sunspot, we surmise that alongside the well-established (magneto-)convective regimes of the photosphere - granular, penumbral, and umbral - a super-equipartition granular regime can be identified. In this regime, bright, but smaller granules occur where the magnetic field exceeds equipartition but remains sub-critical for convection suppression.

We present ClearPotential, a data-driven, three-dimensional measurement of the gravitational potential of the local Milky Way using unsupervised machine learning, without the symmetry assumptions, specific functional forms, and binning required in previous work. The potential is modeled as a neural network, optimized to solve the equilibrium collisionless Boltzmann equation for the observed phase space density of Gaia DR3 Red Clump stars within 4 kpc of the Sun. This density is obtained from data using normalizing flows, and our unsupervised solution to the Boltzmann equation automatically corrects for selection effects from crowding and the dust-driven extinction of starlight. Our fully-differentiable model of the gravitational potential allows us to map the acceleration and mass density of the Galaxy in the volume around the Sun, including in the dust-obscured disk towards the Galactic Center. We determine the dark matter density at the Solar radius to be $(0.84 \pm 0.08)\times 10^{-2}\,{M}_\odot/{\rm pc}^3$, and analyze the structure of the dark matter halo. We find strong evidence for a tilted oblate halo, weak preference for a cored inner profile, and the strongest constraints to date on a possible dark matter disk. We place a bound on the timescale of disequilibrium in the local Milky Way, and find mild evidence for disequilibrium using independent acceleration measurements from timings of binary pulsar systems. This work provides the clearest map of the local Galactic potential to date and marks an important step in the era of data-driven astrometry.