With initial state radiation, the multi-TeV muon collider can be regarded as an electroweak boson collider. The dominant production mode of the certain process becomes the vector boson fusion channel, because the corresponding cross section typically increases logarithmically at high energies. This also holds true for new physics beyond the standard model. Within the $U(1)$ gauged extension of seesaw models, the heavy neutral lepton has additional interactions with the new gauge boson $Z'$ and heavy Higgs $H$. In this paper, we investigate the production of heavy neutral lepton $N$ via the new vector boson fusion processes $Z'Z'\to H\to NN$ with and $Z'Z'\to NN$ without heavy Higgs at the multi-TeV muon collider. Different from the canonical vector boson fusion processes $WW/ZZ\to H\to NN$, the new process $Z'Z'\to H\to NN$ is not suppressed by the small mixing angle $α$ between the Higgs bosons. Meanwhile, the pair production process $Z'Z'\to NN$ is also viable even for heavy Higgs $m_H> \sqrt{s}$. Therefore, these new avenues provide alternative pathways to probe the intrinsic feature of the heavy neutral lepton. We then perform a detailed analysis of the lepton number violation signals via the new vector boson fusion with heavy Higgs $μ^+μ^-\to μ^+μ^- H \to μ^+μ^- NN$ and without heavy Higgs $μ^+μ^-\to μ^+μ^- NN$, followed by $N\to μ^\pm jj$, where the two jets from $W$ boson decay are treated as one fat-jet $J$.

We assess the tension between theoretical predictions and the values quoted by the Particle Data Group (PDG) for the partial decay width and branching fraction associated with the radiative charmonium decay $J/ψ\toγη_c$. A profile scan over the most recent PDG data depending on the branching fraction $\mathcal{B}(J/ψ\toγη_c)$ suggests that the correlation between measured branching fractions is compatible with lattice QCD determinations of the partial decay widths $Γ(J/ψ\toγη_c)$ and $Γ(η_c\toγγ)$. We propose a theoretically grounded photon line shape for the radiative decay spectrum and a prescription for the extraction of (product) branching fractions involving the magnetic dipole (M1) transition $J/ψ\toγη_c$. This approach obviates the need to modify the photon energy spectrum line shape using empirical damping functions, as done in the most recent experimental extractions of $\mathcal{B}(J/ψ\toγη_c)$ from the photon line shape, thereby eliminating an inherent ambiguity in the determination of the derived observables.

We present a study of charge sharing and electronic cross-talk in second-generation Large-Area Picosecond Photodetectors (LAPPD Gen 2). The LAPPD is a vacuum-based device consisting of a photocathode, two microchannel plates, and a resistive anode that capacitively couples to an 8 $\times$ 8 pixelated readout board (25.4 mm $\times$ 25.4 mm pixel area). Using a picosecond pulsed laser, we measure signal distributions across the resistive anode and quantify coupling between target and neighboring pixels. We further examine the relationship between dark-count rate and LAPPD voltage settings, identifying decay behavior characterized by fast, intermediate, and slow relaxation timescales. We additionally observe the LAPPD behaving as a resonant cavity by injecting electrical pulses into the readout board. To further interpret observed signals, we develop a pulse-classification method and identify additional features at approximately 60 ns and 110 ns. Finally, we implement a first-principles Monte Carlo simulation to model the radial and temporal distributions of observed signals, including contributions from electron backscatter and potential ion afterpulsing. The simulation shows reasonable agreement with the experimentally derived pulse classifications.

We revisit flavor oscillations in vacuum in terms of the propagation time of intermediate states. In the limit of a long propagation time (or distance), degenerate intermediate states exhibit oscillatory behavior, as described by the Jacob--Sachs (or Grimus--Stockinger) theorem within wave-packet quantum field theory. By explicitly evaluating the relevant integrals using the saddle-point method, we derive an extended expression for the flavor-changing amplitude that remains valid even for shorter propagation times. We show that oscillations occur only when the propagation time exceeds a threshold set by the energy uncertainty of the external wave packets and by the decay width of the propagating particle. For shorter propagation, the intermediate particle behaves as a purely virtual state, in the sense that it cannot propagate over a macroscopic distance. Although a direct experimental test of the transition from virtual to real propagation is challenging, since it typically occurs at microscopic scales, our result implies that the Jacob--Sachs theorem holds to higher accuracy than previously expected, even at short propagation times. Our formalism applies not only to neutrinos but also to other propagating particles, and future improvements in energy resolution may make this threshold observable.

A variety of experiments are operating or planned to search for displaced decays of light long-lived dark sector particles. In case such a state is discovered, the next step is determining its quantum numbers. We identify an angular observable, reconstructible solely from the decay products' four-momenta, that exhibits an anisotropic distribution for vector bosons from light meson decays and an isotropic distribution for scalars. We demonstrate that searches at DUNE, SHiP and FASER2 will be able to identify the mediator spin in sizable regions of yet unconstrained parameter space.

The first evidence of electroweak (EW) production of pairs of Z bosons in association with two jets (jj) in the final state ZZjj $\to$ $\ell\ellνν$jj, where $\ell$ = e, $μ$, is reported by the CMS experiment. The analysis is based on a data sample of proton-proton (pp) collisions at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events are selected by requiring exactly two leptons of same flavor and opposite charge, large missing transverse momentum, and two jets with a large rapidity separation and large invariant mass. The EW production cross section in a fiducial volume is $σ_{\mathrm{EW}}$(pp $\to$ ZZjj $\to$ $\ell\ellνν$jj) = 0.37$^{+0.14}_{-0.12}$ (stat)$^{+0.06}_{-0.06}$ (syst) fb, in agreement with the standard model prediction of 0.39 $\pm$ 0.06 fb. The observed (expected) significance of the signal is 3.1 (2.8) standard deviations. Limits on anomalous quartic gauge couplings are derived in terms of dimension-8 effective field theory operators. A combination with the previously reported result from the ZZ decay channel with four charged leptons yields an observed (expected) significance of 5.0 (4.5) standard deviations for the EW production of Z boson pairs.

Charged-particle tracking -- reconstructing trajectories from sparse detector measurements -- is a fundamental high-energy-physics inference problem and a canonical example of learning under extreme combinatorial ambiguity. At the High-Luminosity Large Hadron Collider (HL-LHC), tracking must remain accurate and efficient despite unprecedented collision densities. Graph neural networks perform strongly, but incur substantial costs from graph construction and processing, while transformer-based approaches rely on auxiliary stages that prevent end-to-end optimization. To address this, we present HEPTv2, an end-to-end point-transformer architecture that reconstructs tracks from detector hits in one trainable pipeline. HEPTv2 combines a locality-aware point encoder with a track decoder that predicts complete trajectories without graph-building, clustering, or filtering. The encoder uses locality-sensitive hashing in detector coordinate space to preserve tracking-relevant geometry while enabling efficient local attention. The decoder resolves ambiguities through sectorized decoding and direct hit-to-track prediction under joint encoder-decoder supervision, allowing the full pipeline to be optimized end-to-end. On TrackML, HEPTv2 achieves 98.6% double-majority tracking efficiency at a 0.8% fake rate, while requiring only $\sim$15~ms inference time and 0.4~GB peak memory per event on a NVIDIA A100 GPU. Latency and memory scale approximately linearly for events with up to $5\times10^5$ hits. HEPTv2 establishes a new state of the art in the accuracy-latency trade-off, improving efficiency by 4.5% over the strongest prior transformer and by 1.1--2.2% over optimized graph-based pipelines, while reducing latency by factors of 7 and 38--52, respectively. These results show end-to-end transformers can deliver the accuracy and efficiency required for real-time particle reconstruction at the HL-LHC.

We study resonant heterodyne up-conversion in the RADES-BabyIAXO haloscope as a method to search for low-mass dark matter axions using microwave cavities. Starting from axion electrodynamics, we derive the axion-induced source term and the power extracted through a readout mode, explicitly accounting for the finite axion linewidth. This leads to effective quality factors that determine the pump-axion mixing, detection bandwidth, and detected signal power. We extend the BI-RME 3D full-wave formulation to heterodyne axion detection in a realistic two-port cavity, including pump leakage into the readout channel. Applying the formalism to the largest RADES-BabyIAXO cavity identifies the $\mathrm{quasi\textrm{-}TE}_{011}-\mathrm{quasi\textrm{-}TM}_{010}$ mode pair as a favorable configuration, enabling sensitivity to axion frequencies between 0.9 and 34.6 MHz. Analytical and full-wave predictions show excellent agreement at resonance, while the full-wave model provides a more accurate description off resonance and allows a precise characterization of the pump leakage. We also derive the optimal port couplings that maximize the scanning rate. Sensitivity projections for cryogenic copper and superconducting niobium cavities indicate that, under thermal-noise-limited conditions and assuming sufficient pump-leakage rejection, the experiment could probe axion-photon couplings down to $10^{-15}\,\mathrm{GeV}^{-1}$ at 90% confidence level, representing a significant improvement over previous heterodyne-based searches.

Neural scaling laws describe how model performance improves as a power law in compute, model size, and dataset size. While well-established for large language models, these relationships are emerging for large models in particle physics. As with language, empirical studies show that the performance scales as a power law. However, unlike natural language or image domains, fundamental physics has high-fidelity simulators that produce synthetic data cheaply. This favors scaling regimes where additional data is cheaper than additional parameters, and allows the pretraining dataset itself to be engineered to influence the scaling. For the task of classifying hadronic jets produced in collisions of high-energy particle beams, we show that the scaling behavior can be engineered towards requiring more data rather than larger models by inclusion of pretraining data which is more diverse and better aligned with the downstream classification task.

In this proceedings, we will describe the physics program of the ESSnuSBplus, phase-I of the ESSnuSB project. ESSnuSB is a future long-baseline neutrino oscillation experiment in Europe which aims to measure $δ_{\rm CP}$ at the second oscillation maximum with with unprecedented precision. Apart from studying the beam based physics, the large far detector is also capable of studying various other physics cases involving solar, atmopsheric and supernova neutrinos. Under the ESSnuSBplus project, there will be a low energy monitored beam and a low energy nuSTORM facility for the measurement of cross-section.

Given a fixed past-directed timelike vector field, does there exist a time function whose gradient is optimally aligned with it? We address this question by introducing a functional that, on the one hand, captures the misalignment between the timelike vector field and the gradients of suitable Sobolev functions, and, on the other hand, penalizes null gradients. Our analysis focuses on compact subsets of smooth stably causal spacetimes. More precisely, we prove that, under suitable assumptions on the Sobolev index and the strength of the null gradient penalization, there exists a unique smooth temporal function which minimizes the considered functional. We refer to this minimizer as the \emph{alignment time function}. Furthermore, several useful properties of the alignment time function are established: there exists a canonical procedure to improve its steepness, it is stable under $C^{p}$ convergence of the underlying metrics and vector fields and it inherits the symmetries shared by the metric and the given vector field.

The black hole information paradox challenges us to do something that is seemingly impossible: find a violation of the semiclassical approximation in a region where all curvatures are low. The vecro hypothesis proposes a structure of the gravitational vacuum that can accomplish this task. In this article we explain the hypothesis, and give a lattice model to describe the essence of its idea. The Hamiltonian of the model is completely local, but the vacuum exhibits correlations among planck scale fluctuations which fall off relatively slowly with distance. These extended-scale correlations are able to `feel around' the region where a closed trapped surface is about to form, and to react by nucleating fuzzball structure that destroys semiclassical spacetime.

We demonstrate that, for a large black hole of radius $a$, Hawking radiation terminates around the scrambling time $u_{\text{scr}} \equiv 2a \log(a/\ell)$ due to the nonlocal, exponential suppression of trans-Planckian interactions inherent in string field theory (SFT). Modifying a massless scalar field's interaction with a dynamical black hole background via the smearing operator $e^{\ell^2\Box}$ (where $\ell$ denotes the string length scale), we calculate the time-dependent number expectation value $\langle \hat{N}(u) \rangle$ of outgoing Hawking particles at retarded time $u$. While the standard Planck spectrum at the Hawking temperature is reproduced at early times ($u \ll u_{\text{scr}}$), the particle number approaches zero shortly after the scrambling time. This early shutoff reflects the property that the collapsing shell becomes effectively invisible to trans-Planckian modes, offering an alternative resolution to the black hole information paradox via a macroscopic remnant.

In energy-momentum squared gravity (EMSG), the spacetime inside a neutron star is sourced by effective thermodynamic variables that need not coincide with the physical fluid pressure and energy density. It is therefore an open question whether the trace anomaly of dense matter -- the QCD measure of how strongly conformal symmetry is broken -- still organizes interior profiles and curvature in the same way it does in general relativity (GR). We adopt a clear matter-geometry separation: the trace anomaly is computed from the fluid sector alone, while spacetime curvature scalars are built from the variables that actually source the modified Tolman-Oppenheimer-Volkoff equations. For five relativistic mean-field equations of state, the radial trace-anomaly profiles increase monotonically from core to surface in all accepted EMSG models, as in GR, but split systematically with the EMSG coupling strength; the splitting grows with stellar compactness. Despite this deformation, curvature invariants still fall onto organized bands when plotted against the trace anomaly, extending the GR thermodynamic-geometric correspondence. The Ricci contraction shows the tightest organization, whereas the Ricci scalar remains the most equation-of-state sensitive. EMSG effects are modest for observationally accessible stars but largest in stiff, ultracompact configurations, indicating that the trace anomaly remains a useful thermodynamic label for interior geometry even when gravity couples nonlinearly to matter.

We show that higher-curvature Lovelock terms do not restore local cosmic censorship in spherical dust collapse, but instead promote the local visibility of central shell-focusing singularities. On the collapse branch with positive highest-order Lovelock coefficient \(c_N\), the highest nonvanishing Lovelock order \(N\) controls both the near-singularity collapse and the formation of trapped surfaces. In noncritical dimensions, \(D-1-2N>0\), the apparent-horizon curve approaches the singularity curve with trapping exponent \(β_N=(D-1)/(D-1-2N)\). Comparing this scale with the first nonvanishing correction \(r^\ell\) to the singularity curve gives the local-visibility condition \(\ell<β_N\), provided the singularity curve opens outward. Thus increasing \(N\) enlarges the class of inhomogeneous initial data producing outgoing radial null rays from the central singularity. In the critical odd-dimensional branch, \(D=2N+1\), no apparent horizon forms sufficiently close to the center, so any outward opening of the singularity curve gives local visibility. The locally visible singularities are Królak-strong along the emerging null rays, with Tipler strength reached at threshold. For bound and unbound collapse, the noncritical exponents are unchanged: the energy function modifies the opening of the singularity curve, while in the critical branch it enters the leading terminal collapse velocity.

The explicit formulas for the spherical solutions of the Dirac equation in the expanding universe are given. The initial value of the solution can be, in particular, a wave function of the hydrogen-like atom or a spherical wave in the Minkowski space, that then propagates in the Friedmann-Lemaître-Robertson-Walker space-time, which is expanding with the de~Sitter scale

In PRL 129, 110401 it was shown that it is theoretically possible to have operationally detectable causal loops without violating the principle of no superluminal signalling (NSS) in (1+1)-Minkowski spacetime. Whether or not such causal loops are also possible in $d > 1$ spatial dimensions, has remained a key open question. We resolve this question by showing that in a wide class of "conical" spacetimes, including Minkowski with d > 1, NSS does rule out all operationally detectable causal loops, in classical, quantum and post-quantum theories. This establishes that the relationship between the relativistic principles of NSS and no causal loops depends inherently on the geometry of spacetime.

Born-Infeld New Massive Gravity (BINMG) completes New Massive Gravity to all orders in curvature through the determinant of the metric shifted by the Einstein tensor. We recast it with an independent auxiliary metric $q_{μν}$, whose algebraic equation of motion $q_{μν}=g_{μν}+\fracσ{m^2}G_{μν}(g)$ recovers the determinant action exactly on the regular branch and resums the infinite curvature series into a single relation. In the densitized variable $P^{μν}=\sqrt{-q}\,q^{μν}$ the three-dimensional action is polynomial, with all derivative dependence carried by the coupling $P^{μν}G_{μν}(g)$. The formulation makes known properties follow with substantially less algebra: the unique vacuum follows in one line, and the quadratic action yields a single Pauli-Fierz massive spin-2 field with the Fierz-Pauli tuning generated rather than imposed. On locally AdS backgrounds the conserved charges, BTZ mass and angular momentum, central charge, and entropy reduce to the Einstein results times a common factor. The formulation also isolates the nonlinear degree-of-freedom problem in the right variables, leaving the full Dirac count to separate work.

We study regular black hole solutions sourced by an anisotropic energy momentum tensor. It is well known that the geometry of the interior of a spherically symmetric regular black hole approaches the dS metric. Having decomposed the energy momentum tensor into its isotropic and anisotropic components, we assume a hydrodynamic equation of state, $P= P(ρ)$, for the pressure, and look for spherically symmetric, regular black hole solutions. We consider different forms of $ P(ρ)$ which yield the previously known regular black hole solutions, as well as various new metrics. We show that the profile of $ P(ρ)$ has a root and a maximum as it approaches $0^+$ at large distances. Consequently, the square of the sound speed of perturbations, $c_s^2$, changes sign at the point where $P$ reaches its maximum, indicating a potential hydrodynamic instability. In addition, imposing the subluminal bound on $c_s$ puts strong constraints on the model parameters, excluding models in which the energy density has an exponential fall off. We establish a universal hierarchy among the relative positions at which the strong energy condition is violated, at which $P$ has its root, and at which $P$ attains its maximum.

In Plebanski's formulation the coupling of matter is less direct than in the metric formulation since the energy-momentum tensor $T_{μν}$ is symmetric, while the Plebanski variables are naturally valued in the self-dual/anti-self-dual Hodge decomposition of 2-forms. An explicit construction of the Plebanski matter source $T^i$ is obtained by lifting the trace-free energy-momentum tensor $\hat T_{μν}$ into the $(1,1)$ component of the algebraic curvature space using the Kulkarni-Nomizu product, and then extracting its chiral components. This construction reproduces the definition for $T^i$ in terms of the self-dual basis $Σ^i$ and $\hat T_{μν}$ introduced by Krasnov. We also verify that the matter-coupled chiral field equations imply the usual conservation law $\nabla_μT^{μν}=0$ through the chiral Bianchi identity $d^A F^i=0$. As an application, the construction is applied to a spherically symmetric electromagnetic stress-energy tensor, where the anti-self-dual part of the matter-coupled Plebanski field equations yields the Reissner-Nordström-de Sitter solution. The result gives a systematic prescription for translating metric matter sources into the anti-self-dual source terms required by the Plebanski field equations.

Cubic Galileon cosmological models provide a well-motivated framework for investigating late-time cosmic acceleration beyond the standard $Λ$CDM paradigm. In this work, we study observational constraints on cubic Galileon models within the teleparallel gravity framework, where deviations from the standard teleparallel equivalent of general relativity are encoded through the model parameter $b_1$. We consider two scalar-field potentials, namely quadratic and exponential potentials, and analyze four representative scenarios: quadratic and exponential potentials with $b_1$ treated as a free parameter, together with the corresponding cases in which $b_1=2$ is fixed. Using the $\text{Pantheon}^+$ Type Ia supernova sample, cosmic chronometer measurements, SH0ES information, and baryon acoustic oscillation data, we constrain the cosmological and model parameters and compare the observational viability of the different scenarios. We find that the considered teleparallel cubic Galileon models can accommodate the late-time expansion history, although the statistical preference depends on the choice of potential and on whether $b_1$ is fixed or varied. In particular, the fixed-$b_1$ model with a quadratic potential provides the most competitive fit among the Galileon scenarios when BAO data are included, showing a lower $χ^2_{\min}$ than $Λ$CDM and comparable support according to the AIC criterion. However, the BIC criterion continues to favor the minimal $Λ$CDM model because of the larger parameter space of the extended models. These results suggest that teleparallel cubic Galileon cosmologies remain phenomenologically viable, while a stronger claim regarding the Hubble tension requires further consistency tests.

We study static, spherically symmetric stellar configurations in an extended class of Energy--Momentum Squared Gravity using the covariant \(1+1+2\) semi-tetrad formalism. For perfect physical fluids, we show that the nonlinear matter corrections can be reinterpreted as an effective perfect fluid, so that the stellar equilibrium equations retain the standard Tolman--Oppenheimer--Volkoff form when written in terms of effective variables. The resulting covariant structure equations are formulated in both metric and dimensionless variables and, whenever an effective closure relation exists, reduce to an autonomous planar dynamical system. This provides a global qualitative description of the stellar phase space in terms of finite and asymptotic critical points. Specializing to linear physical equations of state, we recover the general relativistic benchmark and identify sectors that are exactly, asymptotically, or piecewise equivalent to general relativity, as well as sectors -- particularly dust configurations -- for which the planar reduction breaks down and the full three-dimensional covariant flow must be considered. We further recover the standard metric Tolman--Oppenheimer--Volkoff equation in terms of effective variables and show that, although the exterior spacetime remains Schwarzschild, the natural matching condition at the stellar surface is \(p_{\rm eff}(R)=0\), which need not coincide with \(p(R)=0\) for self-bound matter.

We extend the analysis of photon surfaces in spherical dust collapse to the general, non-marginally bound case, i.e.\ allowing the \textit{energy function} $k(x)$ of the Lema\^ıtre--Tolman--Bondi (LTB) model to be non-zero. Starting from the dynamical-systems formulation developed in our previous work for the marginally bound case (arXiv:2509.01368), we derive the photon surface equations for the LTB metric with $k(x)\neq 0$, and we recast the geometric condition for a timelike hypersurface to be a photon surface as a non-autonomous first-order dynamical system. Even though the LTB evolution equation does not integrate in closed form when $k(x)\neq 0$, the implicit solutions available in the literature, together with comparison theorems for ordinary differential equations, are sufficient to show that the only physically acceptable extension of the exterior photon sphere $r=3M$ into the collapsing dust cloud is a null hypersurface, generated by outgoing radial null geodesics. Combining this fact with the known results on the causal structure of the general LTB model, we then establish that the photon surface reaches the central singularity if and only if the singularity is naked, thereby extending to the general case the picture already known in the marginally bound regime. The structural dichotomy between the naked and covered end states is also discussed in connection with possible observational signatures in the early-time evolution of black-hole shadows.

We investigate the impact of higher-curvature corrections on photon propagation within an effective field theory framework and explore their observational consequences in strong gravitational fields. In particular, we consider polarization-dependent modifications to photon trajectories induced by higher-order curvature terms and analyze their effects in static and spherically symmetric spacetimes, focusing on Schwarzschild and Reissner-Nordström backgrounds. Using the geometrical optics approximation, we derive the effective metric governing photon propagation and study the resulting shifts in the photon sphere. Based on this modified propagation, we compute the quasinormal modes in the eikonal limit and examine their dependence on the polarization modes. We further analyze gravitational lensing observables, focusing on the deflection angle, incorporating the polarization-dependent corrections. Our results clarify how contributions from beyond-general-relativity effects manifest in both quasinormal mode spectra and strong gravitational lensing observables. These findings further suggest the possibility of placing meaningful constraints on effective field theories.

We study a $q$-deformed extension of Brans-Dicke gravity in a spatially flat Friedmann-Lemaître-Robertson-Walker space-time. The deformation enters through a coupling function that modifies the effective gravitational strength and leads to generalized Friedmann equations. In the matter-free sector, we obtain exact analytic solutions for the scale factor and the Brans-Dicke scalar field, and recast the scalar contribution as an effective fluid. We show that the corresponding equation-of-state parameter and the deceleration parameter are constants and depend only on the Brans-Dicke coupling $ω$ and the deformation function, allowing the scalar sector to mimic radiation-, matter-, or dark-energy-like behavior for a restricted region of parameter space.

We investigate top-down derivations of effective descriptions for radiation from gravitational systems such as binaries. With a specified cutoff prescription, one can derive worldline effective field theories, but the cutoff dependence also complicates their description. We investigate a related effective approach, based on parameterizing dynamics in terms of an action on the boundaries of cavities encompassing individual bodies. We give examples of such cavity descriptions for black holes and for simple models for modifications of their behavior. We also show how cavity effective descriptions connect to observable quantities -- detailed wave profiles, and importantly, accumulated phase shift of emitted signals. A primary motivation is to have a systematic approach to inferring effects of modification of classical black hole behavior, such as those motivated by the need for black hole evolution to be consistent with quantum mechanics, or by other models for new BH behavior, on gravitational wave signals; the latter phase shifts have in particular been argued to provide sensitivity to small new effects from the inspiral phase. To illustrate basic principles and methods, this paper largely focuses on examples with scalar radiation, but we outline extension of the analysis to gravitational wave contexts.

We present for the first time the exact solution of the massive Klein-Gordon equation in the Schwarzschild star (perfect-fluid, uniform-density, spherically-symmetric star), including the non-minimal curvature-scalar coupling. The solution is expressed in terms of the general Heun function. A geometry-induced algebraic coordinate transformation reveals a hidden Fuchsian structure that underlies the exact solvability. Known leading- and next-to-leading-order results are recovered in the low-compactness limit. In the Buchdahl limit, we derive a regularity condition for static modes and describe analytically the divergence in amplitude and oscillation wave vector of dynamic modes as they approach the pressure singularity at the center of the star.

Topological codes form one of the most important classes of stabilizer codes. Most existing algebraic constructions and analyses of topological codes assume translation invariance. Here we show that topological codes can arise in more general settings by incorporating point group operations. The central construction is a class of Calderbank-Shor-Steane (CSS) codes called space-group codes, whose check operators are built from group-algebra templates over space groups that combine translations with point-group operations. We develop methods for analyzing topological properties of space-group codes using ring-modules and their invariant theory. At first glance, space-group codes might appear to complicate practical implementation; however, we find that they can exhibit greater locality than previous codes based purely on translations. Our framework thus extends the landscape of topological codes and opens up a broader design space for the co-design of topological codes with quantum computing platforms.

Navigating the vast space of synthetically accessible molecules demands surrogate models that are interpretable and capable of handling multiple competing objectives at the same time. Deep learning approaches struggle to satisfy them under the computational constraints of quantum-level chemistry. Here, we introduce a modular pipeline that combines interpretable linear meta-learning models and adaptive-confidence uncertainty quantification into an Efficient Global Optimization (EGO) framework for multi-objective molecular discovery. For the first time, linear meta-learning is deployed in a multi-objective chemical search setting: by training across chemical objectives and cheap auxiliary properties, the meta-learned surrogates acquire transferable chemical knowledge that adapts rapidly to new objectives from limited data. Evaluated empirically on a real large scale search for spin-crossover metal-organic complexes, the baseline performs 78% worse in Pareto sense than the meta-learning alternative. We also address the calibration challenges inherent to active search. Since optimal candidates typically lie precisely in the distributional tails, standard uncertainty estimates fail. We introduce an adaptive confidence-tuning algorithm that dynamically recalibrates the exploration-exploitation trade-off as the molecular search evolves. Empirically, dynamic confidence tuning further dominates over 50% of the statically calibrated front.

A defining feature of chirality is the distinction between a system and its mirror image. Despite extensive experimental observations of chiral phases and theoretical advances, a quantum-information theoretic characterization of chirality based solely on the entanglement structure of many-body quantum states remains elusive. Here, we introduce the notion of many-body chirality by formulating it as an obstruction to transforming a quantum state into its complex conjugate through finite-depth local operations. We rigorously establish many-body chirality for stabilizer realizations of $\mathbb{Z}_d^{(k)}$ anyon theories, proving that complex conjugation can be implemented by local quantum channels if and only if the underlying anyon data are mirror invariant. This reveals forms of chirality that evade conventional diagnostics, including examples with vanishing modular commutator, vanishing chiral central charge, and commuting-projector realizations. We further show that this obstruction is intrinsically four-partite, while invisible to tripartite entanglement structure. Finally, we prove that $\mathbb{Z}_d^{(k)}$ states with $d>2$ possess intrinsic many-body imaginarity: their complex phase structure cannot be removed by finite-depth local unitaries. Remarkably, this includes states that are not many-body chiral.