We derive the effective action governing the dynamics of a compact binary system when gravitational radiation is emitted by any mass or current multipole, scattered by the quasi-static field associated with the binary's angular momentum, and then reabsorbed. Among such angular momentum failed-tail processes, the ones involving multipole moments up to mass and current octupoles, which mix also with quadrupoles of opposite parity, contribute to the system dynamics at sixth post-Newtonian order; we display these terms explicitly as a particular case of our general derivation. Additionally, we derive the radiative multipole moments associated to arbitrary angular momentum failed-tails in emission processes.

We prove a no-go theorem for symmetry-based dissipative engineering of collective-spin steady states: in spin-only Lindblad dynamics with jump operators linear in the collective-spin operators, any unique steady state exhibiting at least $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry is necessarily the maximally mixed state. We then show that bath memory lifts this obstruction, enabling unique entangled steady states with a prescribed symmetry and a metrological gain, and providing a steady-state witness of non-Markovianity. Notably, this framework is largely insensitive to the microscopic details of the bath.

To date, the magnetic structure of nuclei has been poorly constrained, with limited information on its spatial distribution. In this work, we address the composition and distribution of nuclear magnetization in a precision study of short-lived $^{47}$K. We measure the Larmor frequency with part-per-million precision using liquid-state $β$-detected nuclear magnetic resonance at CERN-ISOLDE, improving determination of the experimental differential hyperfine anomaly relative to $^{39}$K by more than an order of magnitude. By combining these experimental results with relativistic all-orders atomic calculations and nuclear density functional theory, we obtain the relative spin and orbital contributions to the nuclear magnetic moments. Our analysis reveals an overestimation of the spin contribution predicted by nuclear theory, that persists even after considering two-body currents. Conversely, we show that the measured hyperfine anomaly is reproduced when adopting the spatial distribution of nuclear magnetization provided by density functional theory. The methodology introduced in this work establishes a means to probe the detailed magnetic structure of the nucleus. This is critical for benchmarking nuclear structure theory and calculations of symmetry-violating nuclear moments relevant to searches for physics beyond the Standard Model in atoms and molecules.

Comparison principles for Volterra equations play a role analogous to maximum principles in PDEs: they provide positivity and stability information on the solution and allow one to control the output of bounded inputs. In the continuous setting, such results often rely on Laplace-transform or spectral methods (see Gripenberg, Londen, and Staffans, Volterra Integral and Functional Equations, 1990). However, these tools are not uniform in the discretization step $h$ hence fail in discrete or semi-discrete approximations. The present note introduces a resolvent-free argument yielding uniform $L^\infty(0,T)$-bounds for non-negative kernels. Compactness is a key ingredient in order to show existence of sweeping processes. While in the classical framework it is well established, adding an infinite distribution of delays complicates greatly the obtaining of such a result. In a first step we show a general energy decay estimate, which is then used to establish compactness. The argument is carried out in the discrete setting and that necessitates the introduction of the new comparison principle. In the classical sweeping process the previous position of the particle lies on the boundary of the constraint set, staying $O(h)$ close to the next projection point ($h$ is the discretization step). Our delay model projects the particle's averaged (by a unit measure kernel) past positions to the constraint set. Numerical simulations show that the projected point can lie at $O(1)$ distance from the convex set's boundary.

This article details two studies of Higgs boson properties using the vector-boson fusion production mode and the $γγjj$ final state. Both efforts are based on a data sample corresponding to 164 fb$^{-1}$ of $\sqrt{s}=13.6$ TeV proton--proton collisions recorded by the ATLAS experiment at the Large Hadron Collider. The first study employs matrix element-based optimal observables to constrain CP-odd couplings beyond the Standard Model within the Standard Model Effective Field Theory framework, expressed in the Warsaw basis. The second study exploits angular distributions to probe the Higgs boson's couplings to longitudinally and transversely polarised $W$ and $Z$ bosons in the production of the Higgs boson. To maximise the sensitivity, the constraints of the CP-odd couplings are combined with those from a previous analysis performed in $γγjj$ events in a data sample of proton--proton collisions at $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of 140 fb$^{-1}$. A significant improvement with respect to the previous analysis is achieved through the implementation of a new neural network-based classification algorithm. All measurements are in agreement with the Standard Model prediction of a CP-even Higgs boson with the expected relative coupling strengths to longitudinally and transversely polarised vector bosons.

Programmable photonic quantum processors face a critical challenge: despite significant advances in quantum state preparation and manipulation, measurements remain limited to projective techniques. Here, we demonstrate a programmable measurement processor that overcomes this limitation by enabling arbitrary quantum measurements within a scalable circuit framework. Our large-scale integrated photonic architecture achieves precise coherent control of ancillary quantum systems, realizing a universal four-dimensional quantum measurement device. We benchmark the processor by performing measurement tomography on 100 randomly selected measurements, achieving an average fidelity of 97.7%. The processor's performance exceeds the theoretical limits of projective measurements in three key quantum information tasks: state discrimination (with 23 times lower error), state estimation (with 10.6% higher fidelity), and randomness generation (with 37% more randomness yield), demonstrating its high operational quality. This work establishes a fully programmable quantum measurement processor, advancing the development of universal quantum operations for photonic quantum information processing by providing the key missing component.

We study the giant graviton integrated correlator in SU$(N)$ $\mathcal{N}=4$ super Yang-Mills at finite complexified coupling $τ$. Despite the formidable complexity arising from the heavy nature of the operators considered, the large-$N$ expansion simplifies dramatically and exhibits manifest modular invariance. At each order in $1/N$, the expansion coefficients are linear combinations of non-holomorphic Eisenstein series thus capturing the full spectrum of perturbative and non-perturbative effects in the Yang-Mills coupling. Furthermore, we find additional contributions which are modular functions exponentially suppressed in $N$. In the 't Hooft limit, this yields an all-orders result in the $1/N$ expansion at arbitrary coupling $λ$, extending beyond prior results of leading orders. For the U$(N)$ theory, we obtain a closed-form expression valid for all $N$ and $τ$, and show that the coupling-dependent sector of the large-$N$ expansion is universal between SU$(N)$ and U$(N)$ to all orders. Crucially, we exploit the integrated correlator constraints and determine the giant graviton correlator itself to two-loop order at finite $N$, previously only accessible in the planar limit.

We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise interaction models such as the Ising model, we consider a framework to accommodate more general tensor structures that capture higher-order dependencies. We develop a two-step procedure for low-dimensional linear and quadratic functionals. The first step constructs a regularized maximum pseudolikelihood estimator, for which we establish consistency under high-dimensional features. However, as in other classical high-dimensional regression problems, this estimator is biased and cannot be directly used for valid statistical inference. The second step introduces a bias-correction that yields an asymptotically normal estimator from which one can construct confidence intervals and test hypotheses. Our results move beyond the existing literature, where only estimation guarantees were available or only for pairwise interaction models. We complement our theoretical analysis with simulation studies confirming the effectiveness of the proposed method.

In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite-dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the \( \ell^q \)-sphere. This choice makes the \(q\)-root transform an \emph{isometry} and allows us to construct the \(\ell^2\)- and \(\ell^q\)-Fisher--Rao geometries, including \emph{Amari--Čencov \(α\)-connections} and a \emph{Chern connection} in the \(\ell^q\)-setting. We then apply this framework to an infinite-dimensional linear optimization problem. We show that the corresponding gradient flow with respect to the \(\ell^2\)--Fisher--Rao metric can be solved explicitly, converges to a maximizer under a natural monotonicity assumption, and admits an interpretation as the geodesic flow of an \emph{exponential connection}. In particular, we prove that this \(e\)-connection is \emph{geodesically complete}. We further relate these flows to a \emph{completely integrable Hamiltonian system} through a \emph{momentum map} associated with a Hamiltonian torus action on infinite-dimensional complex projective space. Finally, inspired by the \(\ell^2\)-theory, we outline an analogous Fisher--Rao geometry for \( \mathrm{Dens}(M) \) on possibly noncompact Riemannian manifolds, showing that, with a suitable spherical differentiable structure, the square-root transform remains an \emph{isometry}.

The Microstrip Silicon Detector (MSD) is one of the subsystems of the FragmentatiOn Of Target (FOOT) experiment whose goal is to measure double differential nuclear fragmentation cross sections for applications in particle therapy and radioprotection in space. The MSD, composed of six 150 $μ$m-thick silicon sensors arranged in three X-Y measuring planes, is part of the FOOT experiment tracking region. In this work, we propose a new method to set the MSD thresholds for the clustering algorithm independently of the other detectors of the experiment. The obtained values can be used as reference values from which to perform a threshold scan in order to evaluate the single-ion detection efficiency of each MSD sensor and to orient the clustering analysis using tracking information.}

We consider $M/G/\infty$ queues with gated service and obtain results on the distribution of the stage length and the number of customers served in a stage when the system is stationary. The stage length density is expressed as an infinite series of terms, involving the solution of an infinite system of linear equations. The convergence of a sequence of solutions arising from truncations of the infinite system is established in the light traffic case. Analogous results are established for a similar $GI/M/\infty$ gated system.

The ST1 diamond color center was experimentally demonstrated to involve a substitutional oxygen atom (O$_C$) and carbon vacancy (V$_C$), has a spin singlet ground-state, and a metastable electron spin ancilla: a triplet. ST1's structure was left unsolved for more than a decade. With embedded multiconfigurational quantum mechanical theory, we investigate O$_C$-V$_C$-derived diamond defects, specifically both 0 and +2-charged coupled O$_C$V$_C$, and O$_C$ surrounded by V$_C$s along the [110] axis (V$_C$O$_C$V$_C$). We found both O$_C$V$_{C}^{2+}$ (C$_{3v}$) and V$_C$O$_C$V$_{C}^{2+}$ (C$_{2v}$) to have a spin-singlet ground state (1$^1$A$_1$) and metastable spin triplets. We demonstrate ST1 to be V$_C$O$_C$V$_{C}^{2+}$. The calculated vertical excitation energies of V$_C$O$_C$V$_{C}^{2+}$'s first (1$^1$B$_2$) and second (2$^1$A$_1$) bright spin-singlet excited states closely match ST1's experimental zero phonon line (2.2-2.3 eV). O$_C$V$_{C}^{2+}$ ($^1$E) absorbs much higher (2.8 eV). The two O lone pairs favor V$_C$O$_C$V$_C$ over O$_C$V$_C$, in a similar manner as the single N lone pair favors formation of N$_C$V$_C$ centers.

This paper is concerned with the construction of prior free posterior distributions which rely on the use of one step ahead predictive distribution functions. These are typically more straightforward to motivate than prior distributions. Recent interest has been with Hill's $A_n$ prediction model through what has become known as conformal prediction. This model predicts the next observation to lie with equal probability in the intervals created by the observed data. The prediction model generates complete data sets which can be used to provide posterior inference on any statistic of interest.

Over the last decades, two distinct approaches have been instrumental to our understanding of the computational complexity of statistical estimation. The statistical physics literature predicts algorithmic hardness through local stability and monotonicity properties of the Franz--Parisi (FP) potential \cite{franz1995recipes,franz1997phase}, while the mathematically rigorous literature characterizes hardness via the limitations of restricted algorithmic classes, most notably low-degree polynomial estimators \cite{hopkins2017efficient}. For many inference models, these two perspectives yield strikingly consistent predictions, giving rise to a long-standing open problem of establishing a precise mathematical relationship between them. In this work, we show that for estimation problems the power of low-degree polynomials is equivalent to the monotonicity of the annealed FP potential for a broad family of Gaussian additive models (GAMs) with signal-to-noise ratio $λ$. In particular, subject to a low-degree conjecture for GAMs, our results imply that the polynomial-time limits of these models are directly implied by the monotonicity of the annealed FP potential, in conceptual agreement with predictions from the physics literature dating back to the 1990s.

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these approximate posteriors so that they appropriately capture uncertainty. vWe introduce two methods that extend simulation-based calibration checking (SBC) to widen approximate posterior uncertainty intervals to aim for marginal calibration. We demonstrate these methods in several experimental settings, and we discuss the challenge of calibration using posterior inferences and the potential for posterior recalibration of hierarchical models.

This paper presents a comparative optimization framework for smart charging of electrified vehicle fleets. Using heuristic sequential dynamic programming (SeqDP), the framework minimizes electricity costs while adhering to constraints related to the power grid, charging infrastructure, vehicle availability, and simple considerations of battery aging. Based on real-world operational data, the model incorporates discrete energy states, time-varying tariffs, and state-of-charge (SoC) targets to deliver a scalable and cost-effective solution. Classical DP approach suffers from exponential computational complexity as the problem size increases. This becomes particularly problematic when conducting monthly-scale analyses aimed at minimizing peak power demand across all vehicles. The extended time horizon, coupled with multi-state decision-making, renders exact optimization impractical at larger scales. To address this, a heuristic method is employed to enable systematic aggregation and tractable computation for the Non-Linear Programming (NLP) problem. Rather than seeking a globally optimal solution, this study focuses on a time-efficient smart charging strategy that aims to minimize energy cost while flattening the overall power profile. In this context, a sequential heuristic DP approach is proposed. Its performance is evaluated against a full-fleet solver using Gurobi, a widely used commercial solver in both academia and industry. The proposed algorithm achieves a reduction of the overall cost and peak power by more than 90% compared to uncontrolled schedules. Its relative cost remains within 9\% of the optimal values obtained from the full-fleet solver, and its relative peak-power deviation stays below 15% for larger fleets.

A new library VecAmpFit for multidimensional amplitude analyses in high-energy physics has been developed for an ongoing amplitude analysis at Belle II experiment. It includes a fitter performing likelihood calculation and explicitly-vectorized subprograms for amplitude implementation. The fitter supports explicit gradient calculation and simultaneous fitting of multiple data sets.

The nonlinear asymptotic stability of shear flows in the 2D Euler equations has traditionally been linked to inviscid damping in the periodic setting. Since Gevrey regularity is required to suppress the ``echo'' phenomenon, asymptotic stability is known to be impossible in Sobolev spaces. In this paper, we identify a distinct stabilizing mechanism available in the infinite channel: the advection of vorticity to spatial infinity. We establish nonlinear asymptotic stability for the 2D Euler equations in the infinite channel $\mathbb{R}\times[0,1]$ at the minimal regularity of the Yudovich class ($L^{\infty}$ vorticity). Specifically, for a class of non-negative shear flows with a curvature bound, any $L^\infty$-small, compactly supported vorticity perturbation leads to decay on compact subsets and weak convergence to zero.

Chiral active matter, which breaks both parity symmetry and time-reversal symmetry, is ubiquitous in living systems. Here, we introduce a minimal two-dimensional chiral active lattice gas by incorporating stochastic, biased local rotations. At low temperatures, the system coarsens into condensates with chiral orientations and faceted, crystal-like shapes. The interfaces align at characteristic angles with respect to the lattice axes and exhibit edge currents that are persistent, unidirectional, and angle-dependent. To generalise these findings, we propose a continuum theory by adding an active chiral edge current term to Model B, which reveals the essential role of active chiral transport in the interfacial dynamics of phase separation. Edge currents with $n$-fold symmetry produce condensates whose shapes resemble regular $n$-sided polygons. In the thin-interface limit, we construct an effective interface potential governing edge currents, from which the steady-state condensate geometry can be obtained, both in the lattice model and the continuum description.

This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of $d$ randomly-chosen options is selected. We investigate what happens when the largest of $d$ randomly-chosen options is selected. This process generates a power-law-like distribution: the $i^{th}$-smallest value scales with $i^{d-1}$, where $d$ is the number of randomly-chosen options, with high probability. We give a formula for the expectation and show the distribution is concentrated around the expectation

Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations, such as the continuous wavelet transform (CWT), are widely used to construct these cross-spectra. However, it is well known that the frequency resolution is inherently limited by the localized nature of the convolving wavelet. Moreover, the functional form of the CWT cross-spectrum is not a proper correlation measure and typically requires post-processing smoothing. Conversely, quadratic representations achieve joint time-frequency resolution approaching the Gabor-Heisenberg limit while also providing an adequate measure of similarity between the signals. Motivated by these advantages, we propose a time-delay estimation method based on the Wigner-Ville Distribution (WVD). Considering nonstationary signals arising from two typical wave-physics scenarios, we show that the WVD yields more accurate time-delay estimates with lower uncertainty, particularly in the most energetic frequency bands.

Artificial intelligence (AI) is increasingly embedded in vocational education systems, yet empirical evidence linking institutional AI readiness to student learning outcomes remains limited. This study develops and tests a 2-2-1 cross-level mediation framework examining how school-level AI readiness is associated with student AI literacy through aggregated teacher mechanisms. Using linked survey data from 1,007 vocational institutions, 156,125 teachers, and 2,379,546 students nationwide, multilevel models were estimated to assess direct, indirect, and contextual effects. Results indicate that overall school AI readiness is positively associated with student AI literacy after adjusting for institutional and regional characteristics. When examined independently, all readiness dimensions show positive associations, while simultaneous modelling suggests that readiness operates as an integrated organisational configuration. Cross-level mediation analyses reveal that aggregated teacher-perceived AI capability partially mediates the relationship between institutional readiness and student literacy, whereas general attitudinal acceptance measures do not demonstrate stable transmission effects. Robustness analyses further show that this readiness-capability-literacy pathway remains structurally stable across heterogeneous regional AI development contexts and under alternative modelling specifications. These findings reposition institutional AI readiness as a multilevel organisational condition linked to student AI literacy, identify collective teacher capability as its central transmission mechanism, and underscore the need to align infrastructural investment with sustained professional capacity development.

We study minimal del Pezzo surfaces of degree 1 with a conic bundle over a finite field $\mathbb{F}_q$ according to the action of the absolute Galois group on the singular fibers (which is known as their type). We give a lower bound on the size of the field over which they exist, and determine values of $q$ for which certain types cannot exist. In particular, we solve the inverse Galois problem for certain types of minimal del Pezzo surfaces of degree 1 over finite fields with a conic bundle structure. Additionally, we give bounds on the values of $q$ for which del Pezzo surfaces of degree 1 of index 8 exist over $\mathbb{F}_q$.

In combinatorial representation theory, Kostant's weight multiplicity formula $m(λ,μ)$ is a tool that provides a means of determining the multiplicity of a weight $μ$ in the adjoint representation of a simple Lie algebra $\mathfrak{g}$, and in this work we consider the case of $\mathfrak{g}=\mathfrak{sl}_{r+1}(\mathbb{C})$. In practice, performing calculations of Kostant's weight multiplicity formula is computationally intense, as the number of terms in this alternating sum grows factorially as the rank $r$ increases, of which most terms provide zero contribution to the overall sum. In this work, we determine the Weyl alternation set, that is the terms in the alternating sum with nonzero contribution, for integral weights $λ$ the highest root of $\mathfrak{sl}_{r+1}(\mathbb{C})$, and $μ$ any nonempty collection of distinct simple roots. We show that the alternation set is enumerated by a product of Fibonacci numbers, with the product being dependent on the choice of distinct simple roots. Then we compute the weight $q$-multiplicity for any nonempty collection of distinct simple roots.

Ensembles of regional-global climate model combinations show substantial spread in projected wind and solar resources. Using 31 RCM-GCM pairs, we quantify the sources of this spread with a spatially and seasonally resolved variance decomposition, separating contributions from RCMs and GCMs. For both wind speed and solar radiation, RCMs dominate the variability in the absolute historical fields. In contrast, projected changes in wind speed are largely controlled by the driving GCMs, except in mountainous regions where RCM-induced variance becomes larger than that induced by GCMs. For solar radiation, contributions are strongly season-dependent, with RCMs dominating in summer and GCMs in winter. Our findings support that GCM and RCM variability together define the uncertainty of wind and solar climate projections. This provides guidance for designing climate model ensembles that better support uncertainty-aware energy system decisions under climate change.

Let $S$ be a family of sequences of positive numbers that decrease to 0, let $X$ be a metric space and $A \subset X$. $A$ is said to be $S$-dominated if, for every $s\in S$, a countable cover $\{E_n\}$ of $E$ can be found such that $diam E_n < s_n$ for all $n$. We examine the family of all $S$-dominated sets, denoted by $\mathcal{D}(S)$. In particular, we examine the connections between $\mathcal{D}(S)$ and families of sets with zero Hausdorff measure for some gauges.

Thermomigration is the driving force for hydrogen transport due to a temperature gradient. It can compete with hydrogen transport induced by stress gradients. While stress-driven hydrogen migration is well established, thermomigration remains comparatively underexplored, largely due to limited mechanistic understanding and a scarcity of experimental data. In this work, we develop a thermodynamically consistent framework for hydrogen transport, incorporating a mechanistic model for thermomigration. This is implemented within a finite element framework using an effective chemical potential. Using case studies of iron and nickel heat exchangers and zirconium alloy nuclear fuel cladding, we quantify the competing and synergistic effects of thermomigration and stress-driven transport. We show that thermomigration often dominates hydrogen redistribution in heat-carrying components, even in the presence of significant thermal incompatibility stresses. However, stress-driven transport is shown to become decisive near sharp stress concentrators. A graphical method is introduced to rapidly identify the dominant transport mechanism without requiring fully coupled simulations. The results provide practical guidance for assessing hydrogen redistribution and embrittlement risk in heat-carrying structural components.

We deduce pertinent relations between the elements of the CKM matrix, and find that not all of these are totally compatible with experiment and/or the assumption of the $3 \times 3$ unitarity. We identify complex phases in the CKM-elements which may signal deviations from unitary (DU). We focus on DUs induced by VLQ-singlets, and the possibility of having significant DUs of the first and second rows of the CKM matrix, together with DUs in its columns. We make a thorough analysis of models with the lowest amount of singlets and find a useful set of parametrizations crucial in coherently exploring the parameter-space of the proposed cases. We test the feasibility of each model, confronting them with the restrictions imposed by several important flavor observables. Special attention is given to the neutral kaon and $D^0$-meson sectors, particularly to the parameters $ε_K$ and $x_D$. We find that for the most elementary VLQ-singlet cases, the DUs in the second row must roughly accompany the DUs of the first row. However, in cases with more elaborate combinations of VLQ-singlets, the DUs in the second row may be very large, and even substantially exceed those of the first row. This is what happens in models with sufficient mingling of the two sectors, e.g. in a 2-up-1-down VLQ-singlet scenario. Until now, the analysis of this joining of the up and down sectors with VLQs has not been described in the literature in great detail.

At a distance of 5.1 pc, the 70 Oph AB binary star system is one of the most favorable targets for future direct imaging and astrometry missions surveying mature, terrestrial planets. We present new radial velocities (RVs) obtained with the Planet Finder Spectrograph (PFS) on the 6.5\,m Magellan II Clay Telescope in Chile. We collected 499 measurements of 70 Oph A and 334 measurements of 70 Oph B during 2023--2025. Combining these data with decades of archival RVs and astrometry, we derive an updated orbital solution for the binary and dynamical masses of $0.88 \pm 0.004\,M_\odot$ and $0.73 \pm 0.003\,M_\odot$ for the primary and secondary components, respectively. We find that the long-term RV variability of both components is consistent with stellar activity modulated by rotation periods, and we detect no coherent planetary signals in either component. We place upper limits on any planets orbiting in the plane of the binary. The 27 yr RV baseline for 70 Oph A excludes Jupiter-mass planets interior to 5 au and reaches a sensitivity of $0.3\,M_{\rm Jup}$ at 1 au or $0.5\,M_{\rm Jup}$ at 2 au. For 70 Oph B, with PFS data we rule out planets more massive than $0.25$--$0.3\,M_{\rm Jup}$ inside 0.5 au. We show that stable S-type orbits around 70 Oph A extend to $\sim2.5$ au, covering the habitable zone. Thus, Saturn-mass planets or smaller on stable orbits in the habitable zone of 70 Oph A are allowed. Overall, our results provide important guidance for future planet searches around this stellar system.

Thermodynamic uncertainty relations (TURs) impose a universal trade-off between current precision and entropy production in autonomous steady states, constraining in particular the power, efficiency, and constancy of heat engines. We demonstrate strong violations of the long-time TUR in a minimal autonomous heat engine composed of a discrete ratchet generating work against a constant bias and an underdamped harmonic oscillator acting as an internal stochastic control. In the regime of time-scale separation, the model becomes exactly solvable and yields a closed analytical expression for the TUR ratio, where the influence of the continuous degree of freedom is fully captured by the Fano factor of oscillator zero crossings. We show that increasingly deterministic internal control drives the TUR ratio arbitrarily close to zero while the engine operates near maximal current and efficiency. In an appropriate limit, the model reduces to the classical pendulum-clock system of Pietzonka, Phys. Rev. Lett. 128, 130606 (2022).