We show that boson correlations from quantum states with a Glauber-Sudarshan representation of their density matrix which provides a well-behaved probability distribution -- including coherent states, thermal states, and all states that can be deemed classical -- are a manifestation of the Simpson paradox: they are spurious correlations from statistical (ensemble) averages over uncorrelated measurements made in varying geometries, due to a process of symmetry-breaking as a confounding factor. Bosonic correlations encoded by the wavefunction appear to be formed in the geometry assumed, which however is not that of the statistical ensemble but varies from realization to realization. This calls to distinguish between quantum and statistical averages and sheds new understandings on the fundamental problems of nonclassicality and quantum advantage.

We review recent progress in string model building in both early and late time cosmology. We describe the main theoretical and phenomenological features of an entire class of inflationary models where inflation is driven by a type IIB Kaehler modulus which enjoys an effective and approximate shift symmetry. We illustrate how reheating can occur via the perturbative decay of the modulus into visible and hidden sector degrees of freedom, paying particular attention to the associated production of axionic dark radiation. We quickly discuss the status of de Sitter vacua versus quintessence model building in string theory, analysing the level of control of these constructions and the main challenges faced by models of dynamical dark energy. We finally present a working model of axion hilltop quintessence in string theory, stressing the importance of initial conditions.

Aziz and Howl argued that a classical gravitational field can generate quantum entanglement through a quantum-field-theoretic channel mediated by virtual matter propagation. However, their claimed channel is more naturally and accurately understood as semiclassical wavepacket motion in an external gravitational field, rather than as a distinctively quantum-field-theoretic entangling effect. Moreover, the result of their perturbative computation is incorrectly magnified: they selected a discontinuous wavefunction with infinite kinetic energy as the initial state and simultaneously treated it as stationary. Once a correct treatment using Gaussian wavepacket is adapted, the resulting effect will be negligibly small.

Engineering large-scale quantum computers which simultaneously provide high-fidelity quantum operations, low memory errors, low crosstalk, and reasonable resource usage remains an outstanding challenge across quantum computing platforms. In trapped ions, progress has largely focused on alkaline-earth and ytterbium ions, whose simple electronic structures facilitate control over their internal state. Here we investigate singly-ionized yttrium ($^{89}\mathrm{Y}^+$), a two-valence-electron ion whose ground-state manifold hosts a nuclear-spin qubit and which also features a variety of low-lying metastable manifolds, for applications in quantum information processing. Because experimental data are limited, we perform high-resolution laser-induced fluorescence spectroscopy to measure the hyperfine structure of several low-lying levels, and carry out comprehensive electronic structure calculations to determine lifetimes, transition matrix elements, and hyperfine coefficients for manifolds addressable with visible, near-visible, or infrared wavelengths. Using these results, we analyze schemes for qubit storage, initialization, readout, leakage mitigation, and single- and two-qubit gates. These results position $^{89}\mathrm{Y}^+$ as a uniquely capable next-generation trapped-ion qubit, combining field-insensitive nuclear-spin or clock-qubit storage with spectrally isolated transitions for operations.

We present the most comprehensive set of empirical optical strong-line metallicity calibrations to date, based on the DEep Spectra of Ionised REgions Database (DESIRED), the largest compilation of HII regions and galaxies with direct electron-temperature determinations assembled to date. We construct a high-quality calibration sample of 2392 spectra$-$1029 extragalactic HII regions, 1296 local star-forming galaxies, and 67 high-redshift ($z > 2$) galaxies$-$drawn from 201 independent literature references and spanning $12+\log({\rm O/H}) \in [6.79, 9.07]$. Physical conditions and chemical abundances are derived homogeneously using up-to-date atomic data. We derive 27 strong-line calibrations covering oxygen-, nitrogen-, sulphur-, argon-, and neon-based line ratios, including 4 previously uncalibrated diagnostics, with reported validity ranges and intrinsic dispersions (typically $\sim0.15-0.35$ dex). For the first time in a systematic calibration framework, all relations are presented for both the homogeneous temperature case ($t^2 = 0$) and a scenario including temperature inhomogeneities ($t^2 > 0$), thereby reconciling abundances from recombination lines (RLs) and collisionally excited lines (CELs) and directly tackling the abundance discrepancy problem. A comparison with previous calibrations shows that the DESIRED relations span the broadest validity intervals while remaining anchored to the empirical data. Crucially, recently proposed JWST-based high-redshift calibrations are consistent with our relations within the intrinsic scatter, demonstrating that the diverse composition of the DESIRED sample naturally encompasses the ionisation conditions found at high redshift. These results indicate that sample diversity, rather than redshift-specific recalibration, is key to reliable abundance determinations across cosmic time.

We provide a method for parallelizing the branch-and-bound with isomorphism pruning algorithm developed by Margot [Symmetric ILP: Coloring and small integers, Discrete Optimization (4) (2007), 40-62]. We apply our method to classify orthogonal arrays. For classifying all non-OD- equivalent OA(128, 9, 2, 4) and OA(144, 9, 2, 4) our method results in linear speedups. Finally, our method enables classifying all non-OD-equivalent OA(192, k, 2, 4) for k = 9, 10, 11 for the first time.

Accurate electrical amplification is essential in molecular electronics for measuring conductance through atomic and molecular junctions, where currents often span several orders of magnitude. In this work, we present a systematic design and comparative analysis of four current-to-voltage ($I\text{--}V$) amplifier architectures: single-stage linear, series-linear, logarithmic, and multi-stage cascaded, specifically optimized for break junction (BJ) techniques, including scanning tunneling microscopy (STM-BJ) and mechanically controllable break junctions (MCBJ). Each configuration is evaluated based on sensitivity, noise performance, and dynamic range. Our results characterize the trade-offs between circuit complexity and noise, providing a robust framework and practical guidelines for selecting amplification schemes in quantum transport experiments.

We study the impact of radiation on quantum systems defined by the spins of elementary fermion-antifermion pairs produced at colliders. We present predictions for several processes, showing that energetic final-state radiation can induce decoherence and significantly reduce the entanglement of quantum systems formed by elementary fermion pairs. We investigate the feasibility of observing this effect experimentally in exclusive samples with energetic radiation. A statistically significant signal can be obtained with current data in associated $pp \rightarrow t\bar{t}(g)$ production at the LHC and in $e^+e^- \rightarrow τ^{+}τ^{-}(γ)$ production at Belle 2. Future electron-positron colliders operated at the $Z$ pole or well above the $t\bar{t}$ production threshold will extend these prospects further.

Freshwater scarcity demands desalination technologies that are efficient, scalable, and sustainable. Capacitive deionisation (CDI) is promising but remains limited by inefficient ion adsorption and poor charge utilisation. Here, we show that suitably chosen polyampholytic block copolymer grafting can substantially enhance CDI performance, via a combination of dipolar response and steric effects. Using mean-field classical density functional theory and grand-canonical Monte Carlo simulations, we demonstrate that such polymer grafted electrodes enable strongly improved desalination performance, without altering the pore architecture. Even an electrode grafting by simple neutral polymers can generate an improvement, although a suitably designed block polymer architecture offers an additional performance gain. These results establish interfacial block copolymer grafting as a powerful route toward high-performance, membrane-free desalination.

The cold-classical Kuiper Belt Object 486958 Arrokoth is a contact binary composed of two flattened lobes, Weeyo and Wenu, closely aligned along their principal axes, despite each lobe having a highly irregular shape. The object's smooth and relatively undamaged structure suggests the observed bilobate shape results from a gentle, low-velocity merger between the lobes. The existing hypotheses to explain such a merger include orbital energy dissipation from the protosolar nebula gas drag and Lidov-Kozai (LK) oscillations originating from an initially ultra-wide binary. However, what is missing is how mutual dynamics due to the lobes' shape irregularities impact their final orientations at the time of the soft merger. Here, we show that none of the proposed orbital evolution scenarios is sufficient to reproduce the contact along the lobes' longest principal axes. Implementing the full two-body problem method using finite element modeling, we numerically quantify the complex mutual interactions between Weeyo and Wenu, before the soft merger under the reported geophysical constraints and orbital configurations. All simulations demonstrate that the rotational states of both lobes become desynchronized shortly after their close approach, eventually leading to substantial misalignment along their principal axes. We also find that the lobes' mutual gravitational torque, destabilizing their aligned orientations, is several orders of magnitude higher than gas-driven torque, suggesting that gas drag plays a negligible role in stabilizing their orientations. The present study suggests the necessity of an additional process reconfiguring Arrokoth's shape after the merging process, possibly due to the Sky-forming impact.

Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant practical challenges, such as the subjective identification of scaling regions (crossovers) and the disambiguation of the physical origins of multifractality. We introduce MF-toolkit, a high-performance, parallelized Python library designed to address these challenges. It integrates three key innovations: (1) fully automatic crossover detection algorithms (CDV-A and SPIC), which remove operator bias and enhance reproducibility; (2) a built-in implementation of the Iterative Amplitude Adjusted Fourier Transform (IAAFT) for generating surrogate data, enabling the robust identification of the source of multifractality; and (3) a comprehensive suite for generating synthetic time series for rigorous validation. We demonstrate the rigor and utility of MF-toolkit through its application to characterize the multifractal properties of non-stationary noise in gravitational wave (LIGO) data. The MF-toolkit library offers a robust, efficient, and user-friendly tool for advanced time series analysis, facilitating more rigorous and reproducible research across physics and other data-intensive fields.

The study of spanning trees and related structures is central in graph theory, closely connected to understanding functions between finite sets. This paper generalizes the established relationship between rooted trees and eventually constant endomorphisms to a wider context including $k$-tuples of functions among $k$ disjoint vertex sets. We derive a weighted count of eventually constant $k$-tuples, which are characterized by their stabilization to constancy upon iterated composition. This construction is the set-theoretic analogue of the nilpotent cone and offers new insight into the combinatorial structure of cyclic digraphs. By identifying these $k$-tuples with their induced digraphs, we construct explicit formulas for their generating polynomials and analyze the cardinality of the set of eventually constant $k$-tuples. These polynomials are multisymmetric in $k$ sets of variables and can be re-expressed as the character of a representation of the product of general linear groups. We extend the ideas to the more general structures of eventually $N$-cyclic and $λ$-cyclic $k$-tuples, which we define and provide similar theorems for their generating functions and cardinality.

A clustering functional block implemented in field-programable-gate-array (FPGA) for time projection chambers (TPC) operating with predictable time regardless the complexity of the event is described in this paper. The clustering functional block reorganizes input data and the hits data belonging to the same clusters are output together for further process in the later stages. The clustering operation consists of two phases, data filling phase and data outputting phase, and the later uses the same number of clock cycles as the data filling phase. The clustering block can accommodate events with arbitrary number of clusters and number of hits per cluster as long as the total number of hits is within a predesigned limit. The operation time is exactly twice of the data filling time with no residual O(n2) term. The clustering block has been implemented with operating frequency of 200 MHz in a low-cost FPGA evaluation module and test results confirm the expected performance.

We identify a universal finite-$N$ structure underlying Wilson loop expectations in lattice Yang-Mills, in any dimension $d\geq 2$, for gauge group $\mathrm{U}(N)$, and for arbitrary smooth central plaquette actions. The starting point is a state-sum expansion in plaquette labels by irreducible representations, in which each term factorizes into an action-dependent spectral weight and an action-independent topological coefficient. We then analyze these coefficients in three exact ways: as a gauge/string expansion over decorated spanning surfaces, as a local spin-foam/channel model on the dual incidence graph, and as a universal finite-$N$ master loop equation that closes on the coefficient side. As a consequence, several recent Wilson-action results are recovered as specializations of our broader action-agnostic framework.

Two-photon absorption (TPA) enables three-dimensional characterisation of silicon detectors by generating charge carriers within a confined volume around a focused laser spot. In combination with pixelated readout systems, TPA measurements provide access to spatially resolved timing observables relevant for electric field reconstruction. However, the interpretation of TPA data in segmented detectors is non-trivial: a single excitation produces multi-pixel clusters within the intrinsic time resolution of the readout, and in many implementations no external synchronisation between laser pulses and detector data is available. In this work, we present a reconstruction framework for event-level voxelisation of TPA scans using Timepix3, operating on continuous, unsynchronised data. The method introduces a pixel-overlap-based definition of TPA events and a cluster-level timing estimator based on the highest deposited charge within a region of interest. This approach enables blind reconstruction of dwell structure and stable assignment of voxel timing without external triggers. We demonstrate that commonly used alternatives, such as centroid-based selection or earliest-hit timing, introduce systematic spatial biases in clustered events. The proposed framework provides a robust and general method for reconstructing voxel-resolved timing information in segmented detectors, and is directly applicable to TPA-based studies of electric field distributions and charge transport in silicon sensors.

Saturn's moon Titan is a prime destination for investigating prebiotic chemistry beyond Earth, particularly at impact crater sites where transient liquid water may have enabled aqueous reactions between organic molecules. Selk crater represents one such environment and is a primary target of NASA's Dragonfly mission. Here, we present a thermodynamic assessment of nucleobases, ribose, and fatty acids formed from simple atmospheric precursors (HCN and C2H2) within a Selk-sized aqueous melt pool across varying ammonia (NH3) abundances. We find that ammonia acts as a chemical gatekeeper for molecular accessibility. In NH3-free systems, accessibility is restricted to adenine and butanoic acid. Once >=1% NH3 is introduced, all investigated molecular classes become thermodynamically accessible. Distinct molecular classes have different NH3 sensitivities: nucleobases, ribose, and C2-C6 fatty acids yield peaks at 1% NH3, and C7-C12 fatty acids yield peaks at 2% NH3. The modeled preference for pyrimidines vs. purines and monotonic decline of fatty acid abundance with chain length qualitatively mirror patterns observed in carbonaceous meteorites and returned asteroid samples. We show how molecular distributions and cross-class correlations may provide indirect constraints on Selk's past aqueous environment, help constrain past ammonia availability, and distinguish abiotic production from potential anomalies. By coupling thermodynamic predictions with an assessment of Dragonfly's mass spectrometer (DraMS) capabilities, we posit concrete, testable predictions for evaluating Selk's prebiotic potential in situ.

In order to predict the long-term effects of irradiation on the material properties of tungsten, a continuum approach to simulating the interactions of dislocation loops, which arise from radiation damage, is proposed. Continuum models of the displacement, strain and stress fields produced by dislocation loops exhibit unphysical singularities near the defect core, but are thought to accurately capture atomistic displacements in the far-field. A linear elastic model of nanoscale dislocation loops in tungsten is developed, and the model is verified using atomistic simulations to ensure that the model is informed by lower-length scale phenomena such that the physics of the problem is correctly captured. We discuss the model and its advantages, and show that predictions produced by atomistic simulations do indeed agree well with the far-field behaviour of the continuum model when dislocation loops are far from material boundaries. In particular, we robustly demonstrate that the decay rate of atomistic results and continuum results coincide with one another, and show that the results converge as the size of the atomistic simulations approach the far-field limit.

We present results from two test beam campaigns that investigate the performance of straw tube detectors as potential candidates for an FCC-ee straw tracker. These studies were carried out at CERN using 150 GeV muon beams. Dedicated algorithms were developed to determine both single tube spatial resolution for the primary coordinate in the $r-ϕ$ plane and spatial resolution for the secondary coordinate along the tube direction within a straw chamber. Detection efficiency was also evaluated as a function of the extrapolated hit position for each tube. Both datasets showed consistent results for spatial resolutions and efficiency. Our findings will help establish benchmark performance metrics and provide valuable insight for future design, optimization, and construction of straw chambers for high-precision tracking applications.

We present the latest physics results from the FASER experiment at the LHC. Using $pp$ collision data at $\sqrt{s} = 13.6$ TeV collected during LHC Run 3, FASER reports new results on four fronts: a search for dark photons with an improved analysis strategy using $177~fb^{-1}$ of data, yielding world-leading exclusion limits; neutrino cross section measurements and the first search for charm hadron production in neutrino interactions, both using the FASER$ν$ emulsion detector with a 681 kg tungsten target and $9.5~fb^{-1}$ of 2022 data; the first observation of $ν_e$ in the FASER electronic detector at $5.5σ$ using $176.8~fb^{-1}$ of data; and the first double-differential measurement of $ν_μ$ interactions as a function of energy and rapidity with $186~fb^{-1}$ of data.

Holographic displays are widely regarded as the "ultimate" display technology, promising immersive 3D visuals with natural depth cues, continuous parallax, and perceptual realism. Realizing this potential, however, has remained elusive due to persistent image quality limitations -- most notably speckle noise, a byproduct of the random interference inherent to coherent light. This is typically further exacerbated by the hologram's phase randomness required for maintaining uniform energy distribution across the eyebox. While speckle suppression techniques like temporal multiplexing or smooth-phase heuristics exist, they often necessitate high-speed hardware and introduce visual artifacts, hindering their practical adoption. We introduce Ellipsography, a single-shot holography technique that achieves near-limit speckle suppression, reaching the image fidelity equivalent to averaging a million conventional scalar holograms -- in a single frame in simulation. By jointly modulating the phase and polarization of light, we structure optical interference and suppress speckle at its source. We present a full pipeline including a vectorial wave model, an end-to-end hologram synthesis algorithm, and a functional prototype display. Our experiments demonstrate substantial improvements in visual clarity, depth continuity, and focus cues over current state-of-the-art methods, achieving high-quality reconstructions approaching 30dB PSNR on a real holographic display for the first time -- a 10dB improvement over the best existing techniques. By pushing holographic reconstruction closer to the perceptual quality expected of modern displays, Ellipsography sets a new benchmark for practical, high-fidelity, speckle-free holography.

We show that jets of initial data can be approximated up to arbitrary order by finite-gap solutions for classes of so-called BKM systems of PDEs introduced by Bolsinov--Konyaev--Matveev, which include classical PDEs such as KdV, Kaup--Boussinesq and Camassa--Holm. Finite-gap solutions are obtained via a finite-reduction map, defined algebraically, which sends solutions of a Stäckel system to solutions of the BKM PDE. For the classes containing KdV and Kaup--Boussinesq we obtain full jet-surjectivity via a triangular structure, whereas for the class containing Camassa--Holm we establish jet-surjectivity on an open set of initial data over $\mathbb{R}$ and a Zariski-open (dense) set over $\mathbb{C}$.

In recent years, with the advancement of frontier AI, we have observed certain dynamics in open-sourcing and closed-sourcing decisions. We propose a game-theoretic model to analyze these dynamics in the current landscape of the AI race. Our model builds on an R&D race framework under a winner-takes-all setting, and it accounts for the cases where the players' actions can be either discrete or continuous (i.e., partial open-sourcing, such as open weights). We show that determining the existence of a discrete pure non-trivial Nash equilibrium is NP-hard in general but that we can transform the discrete Nash existence computation into a MIP (Mixed-Integer Programming) problem, making it tractable for small instances using a standard MIP solver. Next, we show the existence and tractability of pure Nash equilibria in the continuous version of our problem, leveraging standard convex analysis results, and constructing an equivalent MIP formulation. Throughout this work, we leverage both our main technical results as well as surrounding technical analysis, to derive socially relevant insights that we believe can serve both to understand already existing decisions and dynamics and to potentially inform new policies.

Solar-System constraints on a general scalar-tensor theory with generic non-minimal coupling function, non-canonical kinetic function, and scalar potential, are investigated in both the metric and Palatini formalisms. A unified post-Newtonian treatment is developed, yielding analytical expressions for the effective scalar mass, the effective gravitational coupling, and the parametrised post-Newtonian parameters $γ$ and $β$. The results show explicitly how the choice of variational principle affects the weak-field phenomenology. Comparison with Solar-System observations, primarily the Cassini bound on $γ$, indicates that the observational impact of the formalism is strongly model dependent. Generic non-minimally coupled scalar fields may satisfy significantly weaker local bounds in the Palatini case because of stronger Yukawa suppression, whereas in Brans-Dicke gravity the differences are typically small and become appreciable only in restricted regions of parameter space. For the point-particle source considered here, Palatini $f(\hat{R})$ gravity reproduces the general-relativistic exterior post-Newtonian limit, unlike metric $f(R)$ gravity.

We construct cubic scalar field theory on $λ$-Minkowski space by combining the Batalin-Vilkovisky formalism with harmonic analysis, and produce two inequivalent noncommutative quantum field theories. The braided theory is based on a braided $L_\infty$-algebra whereby covariance dictates a spectral decomposition into cylindrical Bessel functions that diagonalise the angular Drinfel'd twist; in this theory we find the usual logarithmic ultraviolet divergences and confirm the absence of UV/IR mixing. The standard noncommutative theory is based on a classical $L_\infty$-algebra; in this theory we relate the spectral decompositions into plane wave and cylindrical harmonic eigenmodes of the Klein-Gordan operator, we verify the planar equivalence theorem, and we demonstrate a periodic form of UV/IR mixing in which non-planar correlators are generically ultraviolet finite but become non-analytic on an infinite lattice of exceptional momenta.

Ceres, the dwarf planet in the main asteroid belt, hosts heavily cratered surfaces where craters are continuously eroded mainly due to impact bombardment with a limited influence by non-impact processes. Over continuous bombardment, such regions experience both crater production and erasure, eventually ceasing the crater population growth. This end-state, known as crater equilibrium, provides key information to constrain the mechanisms of crater degradation. The present study applies a recently extended crater equilibrium model to the crater equilibrium features and constrains the conditions for crater degradation on Ceres. We select eight heavily cratered sites as our test locations across four quadrangles (two sites per quadrangle) and collect crater counts using Dawn Framing Camera imagery. All sites exhibit cumulative size-frequency distributions (CSFD) with slopes slightly shallower than a power law of -2 at diameters below a few kilometers, strongly suggesting that the tested sites are at crater equilibrium. Our results show that the crater equilibrium state on Ceres resembles that on the Moon but is denser. Performing model fitting with crater counting data under negligible ejecta blanketing for crater erasure, we further show that crater degradation per single crater production on Ceres is comparable to or higher than that on the Moon. Combining this finding and the impact flux on Ceres, which is orders of magnitude higher than that on the Moon, suggests that crater degradation is much more elevated on Ceres than on the Moon, despite its denser crater population.

With a steady increase in the inverter technology integration to the grid, frequency response of the large inter-connection system becomes more unpredictable. This leads to a significant change in the boundaries of the coherent region, which highly depends on the changing disturbance locations and operating conditions. While most of the existing coherency identification is based on a single large generator outage, it is important to identify these boundaries in view of wide range of disturbances. With large amount of inverters in the system, there is increase in the dynamic interactions of the various grid components leading to a need for such boundary identification. This paper presents the multi-view consensus algorithm to identify coherency in the case of variable grid operating conditions and wide range of disturbances. The proposed approach is demonstrated by identifying the coherent regions in the miniWECC 240 bus test system.

We show that the covariance matrix of the treatment effect estimates in a network meta-analysis can be obtained without matrix inversion using a geometric series of diffusion matrices. This property extends to the hat matrix and provides a connection between parameter estimation in regression analysis and random walks on the network graph. We also provide a number of visualization tools implemented in R.

For time series with long-range temporal dependence, inference for covariance and precision matrices is non-trivial. We propose a Berry-Esseen type Gaussian approximation result that gives a finite-sample bound for the Kolmogorov distance between the infinity norms of the estimation error of sample covariance matrix and the corresponding Gaussian approximation. The method utilizes martingale and m-dependent approximation and relies on constructing triadic blocks. We also establish a bootstrapping result with block sampling method, which preserves validity despite strong temporal dependence. Our results on covariance allow ultra-high-dimensional settings where the dimension of time series can grow sub-exponentially with sample size. Similar results can be built for precision matrix under low-dimensional settings. No assumption is required on the structure of covariance and precision matrices.

Angular correlations in Higgs decays to electroweak gauge bosons, $h \to ZZ^*, WW^*$, provide a powerful probe of both new physics effects and quantum information observables. We present a systematic study of semi-leptonic decays $h \to V V^* \to \ell^+\ell^- q\bar{q}$ and $\ell^\pm ν_\ell q\bar{q}'$, including finite final state fermion masses, NLO QCD, and NLO electroweak corrections. We show that finite final state quark masses can induce effects that go beyond the two-qutrit description in more inclusive regimes, while remaining controllable with suitable kinematic selections. QCD corrections lead to modest percent-level shifts, whereas electroweak corrections can significantly modify the angular structure, particularly in the $h\to ZZ^*$ channels. We assess the impact of these effects on the reconstructed density matrix and entanglement measures, finding that, while they modify the angular observables, semi-leptonic channels retain an effective two-qutrit description.

Let $(X,Δ)$ be a smooth complex projective simple normal crossing pair of dimension $n\geq 3$ endowed with an everywhere nondegenerate logarithmic conformal tensor. If $K_X+Δ$ is not nef, then precisely one of the following mutually exclusive alternatives occurs: either $Δ=\varnothing$ and $X\simeq Q^n$; or $X\simeq \mathbb{P}^n$ and $Δ$ is a hyperplane; or $n=2m$ is even and $(X,Δ)$ admits a rational maximal isotropic fibration whose geometric generic fibre is the log pair $(\mathbb{P}^m,H)$. If $K_X+Δ\equiv 0$, then, under a Bochner extension principle and an irreducibility assumption on the restricted holonomy of a complete Ricci-flat Kähler metric on $M:=X\setminus Δ$, the existence of a logarithmic conformal tensor with trivial conformal line bundle forces $M$ to be semi-abelian and $(X,Δ)$ to be its toroidal compactification.