Papers

The design and control of wave scattering, that is, of the reflection and transmission parameters of a device, is of ubiquitous importance. These parameters generally change with varying frequency, though certain frequency-independent linear relations may exist between them. Reciprocity and geometric symmetry (reflections, rotations, etc.) are classic and well-known examples that are present in many devices and significantly ease their design. In this work, we go beyond these and introduce a new class of relations that cannot be induced by reciprocity or geometric symmetry. Choosing networks of waveguides as our workhorse, we discuss the conditions and consequences of such novel behaviour and showcase suitable example setups. We further experimentally test our predictions using coaxial cables and find excellent agreement in the broad frequency range between 0 and 1 GHz. Our work not only deepens the theoretical understanding of waveguide network dynamics, but also opens new avenues for applications in broadband signal processing, quantum information, and integrated photonics.

A looped transformer performs inference by iterating a weight-tied map, making its computation a dynamical process whose cost is set by the resulting inference dynamics. Here we show that networks with identical architecture and objective, trained to identical accuracy, nevertheless realize distinct dynamical phases depending strongly on initialization, and that the bifurcation defining each phase determines how test-time compute scales. The phases are distinguished by their bifurcation mechanisms, including a saddle-node fold and a Neimark-Sacker-type transition to bounded nonstationary motion. In the fold phase, a one-dimensional normal-form reduction predicts both the relaxation-time and spectral-gap amplitudes from local derivatives of the trained map, yielding the parameter-free relation $\tau(\varepsilon)[1-\lambda_{\max}(-\varepsilon)]\to\pi$. Composed with a regular distribution of problem difficulty, the same critical slowing down produces the workload-level tail $P(\tau>N)\sim N^{-2}$. In the Neimark–Sacker phase, the fold scaling law disappears rather than merely changing its prefactor. Thus, test-time compute is not determined by architecture alone. It is governed by the dynamical phase of the solution found by training.

In the 170 years since its discovery, U Gem has been intensively studied as the prototypical cataclysmic binary star. Its massive white dwarf (WD) (~ 1.2 Msun) is cannibalizing its ~ 0.42 Msun red dwarf companion. The WD's resulting accreted hydrogen-rich envelope has previously undergone thermonuclear runaways seen as nova eruptions. These weekslong transient events brighten U Gem to m ~ -3 and eject the accreted envelope (~ 0.00001 Msun) at thousands of km/s. Ultraviolet observations show that the accreted envelope of U Gem's WD is greatly enhanced in nitrogen and depleted in carbon relative to solar composition, and that the WD's effective temperature is much hotter than that of most cataclysmic binary WDs. These suggest that U Gem underwent a classical nova eruption quite recently and should therefore still be surrounded by the ejecta of that event. Modeling of U Gem predicts a nova event ~ 1000 years ago, and the existence of two concentric shells, each of order 1 degree in size, surrounding U Gem. We obtained deep narrowband H-alpha imaging of U Gem with the Condor Array Telescope. The two concentric H-alpha-bright shells that we find, centered on U Gem, may be the first-ever predicted old nova ejecta. A transient "guest star" in the asterism Shuiwei, recorded by Chinese imperial astrologers in November 829 CE is consistent with the timing and location of U Gem's last predicted nova eruption, but the transient's absence in Japanese and Korean records weighs against this suggestion.

We study the weak coupling of two identical two-level atoms to a four-dimensional massless conformally coupled scalar field and compare three settings with the same local temperature but different physical origins: comoving atoms in the Bunch–Davies vacuum of de Sitter spacetime, transversely separated uniformly accelerated atoms in the Minkowski vacuum, and static atoms in a Minkowski thermal bath. We first derive the two-atom cross spectra in the three settings and then obtain the single-atom local spectra uniformly from the zero-separation limit. When $a=H$ and $\beta=2\pi/H$, the complete local Wightman kernels and local spectra are identical in all three cases. At finite separation, a genuine thermal bath produces a $\sinc(\Omega L)$ spatial factor, whereas de Sitter spacetime and the transversely accelerated vacuum produce a hyperbolic geometric factor. In the long-distance limit, the cross correlations in de Sitter spacetime and the transversely accelerated vacuum decay as $L^{-2}$, whereas those in the Minkowski thermal bath decay only as $L^{-1}$. The de Sitter and transversely accelerated vacuum cross spectra coincide when $a=H$ and the separations are instantaneously matched. For a fixed experimental setup, the physical separation between the two comoving atoms in de Sitter space evolves with cosmic expansion, whereas the pulled-back cross correlations in the uniformly accelerated and thermal Minkowski configurations are stationary.

We investigate random recursive simplicial complexes growing by adding, at each step, a vertex together with a simplex formed by joining the new vertex with a randomly chosen existing simplex. We also add all faces of the new simplex to ensure that the resulting object remains a simplicial complex. If the choice of an existing simplex is uniform among simplices of dimension $<m$, the number $S_d$ of simplices of any admissible dimension $d\leq m$ is an asymptotically self-averaging random variable. This feature allows us to determine the asymptotic growth law of the average of $S_d$ when the number of vertices diverges. We also probe the degree distribution, examine the probabilities of various extreme outcomes, and analyze the characteristics of the first vertex.

Detector lag, also referred to as afterglow, is a source of image degradation in flat-panel x-ray detectors, producing temporal artefacts that reduce image quality and quantitative accuracy. In this work, we present a robust and repeatable experimental framework for characterising long-term detector lag (from minutes to hours) under controlled step-up and step-down exposure transitions of particular relevance to tomography. The measured transition curves from an amorphous silicon detector with a CsI:Ti scintillator exhibit unexpected behaviour, with the detector response temporarily overshooting its final equilibrium intensity following step-up transitions, rather than exhibiting the gradual monotonic rise and decay typically expected. These curves were well fitted by multi-exponential functions, providing initial estimates for the depth of the charge traps in the scintillator. These parameters were incorporated into a proposed multi-trap rate equation model that reproduces the overall observed behaviour of both step-up and step-down transitions, including the overshoot that is not captured by previous models. Although discrepancies remain between the model and observation, this work establishes a reproducible methodology for detector lag characterisation and presents an improved physical model that offers greater insight into the mechanisms governing detector lag.

MnF$_2$, the textbook two-sublattice antiferromagnet, has reemerged as a prototypical altermagnet, yet the sublattice-odd exchange that defines this identity remains under active debate: it enters the magnon splitting only in quadrature with the dipole–dipole interaction, its magnitude suppressed and its sign erased. An overdetermined first-principles total-energy mapping resolves this scale as a seventh-neighbor imbalance $\delta{J_7}\simeq+8~\mu$eV. The resulting Hamiltonian, with the dipole–dipole interaction included explicitly, reproduces the low-energy gap and the visible finite-momentum splitting. A longitudinal field $B\parallel c$ then acts as a linear amplifier of the hidden scale, opening two signed, field-linear readouts. The first is the compensation field $B^\ast(\mathbf Q)$, the position of minimum splitting, which is equal and opposite at the rotation-related partner momenta: a shift from zero field is itself evidence of a finite imbalance, its side gives the sign, and its magnitude, $|B^\ast|\simeq0.34$~T here, gives the scale. The second is the fixed-field contrast of the partner splittings, $\simeq0.14$~meV at $1$~T, six times the zero-field excess: a sign check from just two spectra. Both readouts survive a $0.12$~meV energy resolution, and the construction carries over to any easy-axis collinear altermagnet, bringing $\mu$eV altermagnetic exchange within present instrumental reach.

CePdAl is a heavy-fermion compound with a quasi-kagome structure, where geometrical frustration competes with the Kondo effect. Using a high-sensitivity magnetometer, we observe clear first-order metamagnetic transitions without magnetization plateaus in CePdAl at 80 mK, indicating a lifting of frustration through the suppression of the Kondo effect and spin flips of ordered moments under fields. An anomaly in the nonlinear magnetic susceptibility at 4.3 T suggests nondipolar correlations in the polarized paramagnetic state. Furthermore, we found no evidence of non-Fermi-liquid behavior in the high-field region, where the antiferromagnetic order is completely suppressed. These findings establish the essential thermodynamic constraints for understanding the field-induced spin-liquid state in CePdAl.

We present a general approach for calculating new electron-electron interactions with atomic structure theory, include dominant many-body effects, and extract bounds for parity-odd cases. The procedure is valid for any mediator mass and improves previous calculations by including many-body corrections to the new interaction through the time-dependent Hartree-Fock method. Bounds on coupling strengths are then extracted for scalar-pseudoscalar and vector-axial vector interactions by comparison with experimental atomic electric dipole moments and parity non-conserving (PNC) transitions respectively. In the latter case, our calculations rule out any coupling-mass ratio |g^e_V g^e_A|/m_X^2 greater than 10^-11 MeV^-2 above m_X ~ 10 MeV, covering a previously unconstrained mass region. We also report an updated calculation of the regular (Standard Model) electron-electron Z^0 exchange contribution to the 6s-7s PNC transition amplitude E_PNC in cesium.

Accurate background intensity estimation is crucial for precise astrometric measurements in astronomical imaging, particularly in complex scenarios such as those encountered in Cassini Imaging Science Subsystem (ISS) observations of Saturn's ring system. Traditional methods, like polynomial fitting and statistical method, often fail in non-uniform conditions, such as those caused by Saturn's rings or scattered light, due to mismatched assumptions and reliance on prior knowledge. This results in biased estimates and poor generalizability. We propose a deep learning framework based on Denoising Diffusion Probabilistic Model (DDPM) to address these challenges. By learning noise patterns and iteratively reconstructing backgrounds, DDPM improve background intensity estimation in ring-gap regions of ISS images by up to 62% relative to polynomial fitting. Additionally, When applied to centroiding of unresolved satellites in ring-gap, DDPM-based background estimation enhances positional precision by about 14% in the line direction and 15% in the sample direction. The framework autonomously captures spatial correlations, requires no manual parameter tuning, and generalizes across diverse backgrounds. These characteristics make it a promising, assumption-light solution for background estimation tasks in astrometry, photometry, and source detection, with potential applications to exoplanet transit imaging, deep-field surveys, and future missions.

We show that edge states in fractional quantum Hall effect samples can be selectively probed and excited with sub-terahertz optical spectroscopy. Using the composite fermion (CF) mean-field framework, which maps the strongly correlated fractional quantum Hall problem onto an effective integer quantum Hall problem, we calculate the absorbance spectrum for the Jain sequence of filling fractions including both bulk and edge states. The CF edge-state absorption peaks appear in the millimeter-wave to sub-terahertz range, e.g., 60-500 GHz at B = 10 T in GaAs, i.e. they are blueshifted with respect to the bulk CF cyclotron frequency but are well below the integer quantum Hall cyclotron frequency scale at the same magnetic fields. The number of resolved peaks in each series of the absorption spectrum counts the filled Lambda-levels and fingerprints the fraction. Inversion symmetry breaking near the edge activates optical transitions forbidden in the bulk and enables second-order nonlinear processes in electric-dipole approximation. The absolute frequency scale of the spectrum is set by the CF effective mass, which is generated entirely by electron-electron interactions, so the absorption spectrum provides a direct optical probe of this interaction-induced mass.

In swollen elastomers, elasticity can arrest macroscopic demixing between the polymer network and the solvent, producing stable domains of finite size. While previous theories have focused on isotropically swollen elastomers, anisotropy strongly influences the phase behavior of many related systems, such as gels and crosslinked polymer blends. Building on the approach developed in Part I of this two-part paper, we investigate the effects of two experimentally induced sources of anisotropy: uniaxial swelling and stiffness gradients. We show that uniaxial swelling can lead to the formation of stable lamellar microphases and modify phase behavior, while stiffness gradients can cause spatial variations in the characteristic microphase size.

The Two-Point Correlation Function can be used to demonstrate the existence of substructure within a dataset, but typical implementations do not track the individual points which contribute to each specific substructure. In this paper, we develop an algorithm that traces a two-point correlation signal back to the contributions of each data point, allowing for structure to be visualized in novel ways. Using this tool, we find substantial evidence for pervasive spatial clustering in the Milky Way and reveal complex undulations that warp the previously discovered vertical density waves. We also explore the “clumping" of stars in the thick disk and near-halo regions and discuss the possibility of dating the structure.

We propose a new early dark energy with a potential that has an inverse power-law asymptotic tail to alleviate the Hubble tension. Fitting this model to the datasets of CMB+BAO+SN+H0DN, one obtains a 68$\%$ confidence-level value of $H_0\sim 70.20^{+0.60}_{-0.47}$ km s$^{-1}$Mpc$^{-1}$ and a best-fit value of $H_0\sim 70.56$ km s$^{-1}$Mpc$^{-1}$ for index $n=10$. We show that this model can be tested by future data of CMB and matter power spectra. Finally, we briefly discuss fine-tuning problems related to this model.

Spontaneous parametric down-conversion (SPDC) is one of the most widely used sources of polarization-entangled photon pairs, and understanding the generated biphoton state is essential for realizing high-brightness and high-purity entangled-photon sources. In particular, Type-II SPDC produces a biphoton wavefunction with a complex coupling between the spatial and polarization degrees of freedom owing to birefringence. In this study, we calculate the real-space distribution of the two-photon polarization state from the biphoton wavefunction of Type-II SPDC generated in a e̱ta}-barium borate (BBO) crystal. By identifying the spatial correlation direction between polarization and real-space coordinates, we designed aperture shapes that restrict the collection along this correlation direction. Through both numerical simulations and experiments, we demonstrate that such correlation-aligned apertures simultaneously achieve higher entanglement purity and improved photon collection efficiency. These results establish a practical design principle for optimizing aperture geometries based on the real-space biphoton wavefunction, providing a new approach to realizing high-purity and high-brightness SPDC entangled-photon sources.

The temperature-dependent band gap of solids is usually computed from the perturbative Allen-Heine-Cardona (AHC) electron-phonon self-energy evaluated on-shell. Extending AHC to arbitrary frequency $\omega$ to determine the full spectral function via the Dyson equation is known to fail, misplacing satellites and yielding no broadening at band extrema, while non-perturbative supercell (SC) methods have focused on eigenvalue averages rather than lineshapes, and approaches based on special displacements cannot describe the full lineshape, or the lineshift at degenerate bands. Here we use a non-perturbative Green's function method (NPG), stochastically sampling distorted SC configurations, from which the spectral function, including lineshift, linewidth, and asymmetry, follows directly, and we recover finite spectral weight at the renormalized band extrema. We prove that the perturbative self-energy, computed to any order with the bare propagator and introduced into the Dyson equation, has an imaginary part that vanishes within the bare gap, giving incorrect spectral functions: self-consistency of the propagator is essential to broaden the band edges. NPG satisfies this property by construction, and contains all non-bubble diagrams. We also give a simple explanation of why SC methods converge with much smaller SCs than the corresponding $\mathbf{q}$-grids required by perturbation theory. For the band gap shift itself, the NPG and on-shell AHC results are found to be comparable, demonstrating that higher-order terms do not significantly alter the resulting renormalization in diamond. When it comes to the spectral function though, our results show that going beyond bare perturbation theory is not merely more accurate, but necessary, and NPG provides a robust framework to capture spectral broadening and higher-order effects from first principles.

Forecast-error growth has been studied through complementary approaches: scalar models describe the evolution of bulk error, whereas spectral theories follow decorrelation and error transfer across scales. Their connection matters when a fitted growth curve is used to infer a physical mechanism or a limit of predictability. We establish a conditional link between these approaches. Within a bilinear spectral exchange model, assume a stationary reference spectrum and a remainder that vanishes on the proposed common-shape evolution. For a common initial decorrelation fraction strictly between zero and one, the spectral shape is preserved and its amplitude grows logistically exactly when every participating scale shares one positive growth coefficient. The converse inference fails: a logistic aggregate need not imply proportional decorrelation or a common coefficient. An exact two-shell construction demonstrates this failure with identical aggregate curves and different spectral dynamics. For heterogeneous amplitudes, an exact averaging identity separates the contributions of growth-rate mismatch, shape variance, rate–shape covariance, evolving spectral weights, and residual tendencies. A finite-time bound relates their combined effect to departure from a reference logistic curve. Forced surface-quasigeostrophic simulations illustrate how similar retrospective agreement with a logistic reference can coexist with heterogeneous effective shell rates and substantial instantaneous tendency discrepancies. Thus a scalar growth curve alone cannot identify how uncertainty is distributed across scales or justify interpreting a fitted rate as a common spectral growth coefficient. The framework specifies the additional spectral and budget evidence needed to give scalar predictability models that interpretation.

Confining optical fields to molecular dimensions is a central objective in nanophotonics and molecular quantum optics. Here, we report strong coupling of the Mo Mo stretching vibration to a locally confined Raman scattering field in quadruply bonded dimolybdenum complexes. Under ambient, cavity-free conditions, the dimolybdenum formamidinate complexes Mo2(DAniF)4 and Mo2(DTolF)4 exhibit Rabi-type splitting, Mollow-type sidebands, and higher-order Raman features centered near the Mo Mo stretching frequency of 400 cm-1, indicating formation of dressed vibration field states. The sideband displacements from the resonance follow the photon-number-dependent relation {\Omega}n={\Omega}{\nu}n, consistent with Jaynes Cummings-type coupling, while strongly displaced Raman features are assigned to leapfrog transitions within the same dressed-state ladder. In contrast, the less polarizable Mo2(O2CCH3)4 complex exhibits essentially a single Mo Mo stretching band. Reanalysis of reported resonance Raman spectra of an alkynyl Mo2 complex further supports this coupling framework. These results suggest that the Mo2 unit simultaneously serves as the Raman active oscillator and the molecular resonator that supports, confines, and enhances the locally generated scattering field, providing spectroscopic evidence for vibration field coupling and optical-field confinement within a chemically defined metal metal bond.

The asymptotic properties, with vanishing viscosity, of inertial turbulence in Newtonian fluids have been of intense scrutiny over the years. Much less is known about elastic turbulence - a distinct spatio-temporally chaotic state exhibited by viscoelastic fluids. In this work, using direct numerical simulations of turbulence in a triperiodic box, we show that elastic turbulence achieves an ultimate state with increasing polymer relaxation time, i.e., the Deborah number, for two different constitutive models (Oldroyd-B and FENE-P). In the limiting state, various bulk quantities - the fluid dissipation, the polymeric energy transfer, as well as the elastic stresses - are shown to become independent of the polymer relaxation time scale, notwithstanding the microstructure deformation scales distinctly depending on the model.

In this paper we derive the time-dependent correlation functions of the renormalized Hartree NLS equation on the torus $\mathbb T^d$, $d=2,3$, from the corresponding bosonic many-body Gibbs dynamics. In contrast with the 1D problem studied earlier by Fröhlich, Knowles, Schlein and Sohinger, in higher dimensions the scaled quantum particle number is not uniformly bounded and the relevant classical fields require Wick renormalization. Our proof combines convergence of the quantum generators in weighted Hilbert spaces with uniqueness for positive solutions of the limiting Liouville equation that are dominated by the Gibbs measure.

Non-relativistic objective collapse theories have been remarkably successful in addressing the conceptual problems of standard quantum mechanics. Despite substantial efforts, the project of extending them to the relativistic domain remains burdened by significant conceptual objections and technical challenges, often taken to cast doubt on the viability of the program as a whole. On the conceptual side, relativistic collapse theories have been claimed to face challenges involving tension between instantaneous collapse and relativity, frame-dependence of property values and probabilities, the possibility of superluminal signaling and the failure of narratability. On the technical side, persistent infinities, difficulties in constructing fully covariant frameworks and the apparent need for non-standard fields have hindered the development of workable models. In this paper, we offer a systematic rebuttal of the conceptual objections and provide a structured account of the remaining technical challenges. We conclude that relativistic collapse theories do provide a promising route toward a fully relativistic quantum framework that overcomes the conceptual limitations of standard quantum theory.

We study short-horizon neonatal seizure prediction on Helsinki-style (HUH) preprocessed EEG feature tables using quantum-inspired reservoir computing. Under strict subject-wise cross-validation on imbalanced preictal–interictal windows, we test whether reservoir constructions shaped after (i) gate-based qubit dynamics and (ii) continuous-variable (bosonic/photonic) dynamics provide a practical sequence encoder relative to strong classical baselines. Both reservoirs are executed here purely in classical simulation on a single GPU; accordingly, we do not claim quantum advantage, but rather evaluate whether quantum-shaped dynamics act as useful, low-footprint random feature maps with a trained linear readout. We compare against Random Forests and RBF–SVMs, and report AUROC, AUPRC, per-subject AUPRC, expected calibration error, and stratified bootstrap confidence intervals. Across our experiments, the CV/bosonic reservoir is consistently competitive and can improve AUPRC over the baselines, while the gate-style reservoir is more sensitive to hyperparameters. These results suggest that quantum-inspired, photonics-motivated reservoirs can be practical sequence encoders for neonatal EEG feature tables under conservative subject-wise evaluation.

We present a focused and reproducible study of multi-horizon forecasting on the Lomnicky Stit neutron monitor (LMKS) time series. Our evaluation suite covers simple seasonal baselines, modern deep sequence models, and functional and quantum-inspired architectures, including Seasonal Naive, Long Short-Term Memory (LSTM), Temporal Convolutional Network (TCN), N-BEATS, Kolmogorov-Arnold Networks (KAN), and two quantum-inspired variants, QiLSTM and QiKAN. We describe the dataset characteristics, diagnostic analysis, preprocessing pipeline, and training procedures, and report aggregate point-forecast performance using mean absolute error (MAE) and root mean squared error (RMSE) for all evaluated models. Our quick-run results indicate that the quantum-inspired KAN variant, QiKAN, achieves the lowest aggregate forecasting error among the evaluated configurations, while the simple Seasonal Naive baseline remains remarkably competitive. These results suggest that, for highly periodic scientific monitoring time series, models incorporating strong seasonal or low-dimensional functional priors can match or outperform substantially more complex sequence architectures. The findings motivate further investigation of parsimonious and decomposable function approximators for forecasting periodic scientific signals.

Quantum reservoir computing (QRC) uses fixed quantum dynamics to encode a time series and trains only a classical readout, but a benchmark capacity alone does not reveal whether task information is lost in the reservoir, the measurement, feature compression, or finite sampling. We introduce task-resolved Fisher spectroscopy, in which prediction targets define orthonormal score coordinates on the stationary distribution of input histories. Reweighting labeled histories along these scores generates an exactly affine family of reservoir states and measurement outcomes. In the same coordinates, we obtain a many-body Fisher-information hierarchy relating the state quantum Fisher information, the Fisher information of the complete measurement record, and moment matrices retained through many-body order $r$. The quadratic form of each moment matrix is exactly the stationary capacity of the optimal linear readout, while a finite-measurement extension predicts the approach from one-shot records to ideal expectation-value features. The measurement-level quantities require only stationary labeled records and measured outcome strings, not an input model or quantum-state tomography. In a five-spin open reservoir, interactions route fourth-order temporal information into higher-body correlations, so low-order compression can incur orders-of-magnitude sampling overhead even when a conventional parity target remains accessible. For correlated inputs and outputs, record-defined task scores predict held-out capacities, the required feature order, and measurement-budget dependence; optimizing the local measurement axis recovers otherwise hidden task information. The framework connects benchmark performance to experimentally actionable diagnoses of reservoir encoding, measurement choice, classical representation, and shot allocation.

We study graded arrays of highly dispersive subwavelength resonators through their volume-potential matrix reduction. The reduction gives a finite-dimensional nonlinear resonance problem whose diagonal entries encode the local dispersive response and whose off-diagonal entries encode volume-mediated coupling between distinct resonators. We show that monotone material grading turns this matrix into an analytically controllable frequency sorter. When graded detuning dominates coupling in the reduced characteristic matrix, the characteristic vectors localize near individual resonators; under an explicit half-lattice-site localization condition, this localization becomes a monotone frequency-position map. We also prove a constructive inverse-design statement: prescribed monotone target frequencies can be realized by choosing the local dispersive parameters, with robustness under sufficiently small grading errors. Numerical experiments, whose parameters and algorithms are recorded in an appendix, illustrate localized resonances, designed frequency-position maps, disorder stability, spacing dependence, and a resolved physical Lippmann-Schwinger validation beyond the leading logarithmic quadrature model.

Three-dimensional Einstein gravity and Chern-Simons-Higgs matter both admit Chern-Simons descriptions, but their holonomies encode different physics. We prove that charge conjugation reverses the vortex winding $n\to-n$ while leaving the metric and the gravitational connections pointwise unchanged, so every closed gravitational holonomy character, the BTZ charges, the Bañados data and the leading geometric mixed-state hierarchy are exactly even in $n$. On a fixed marked Euclidean replica filling the same change of variables gives $Z_q[n;\mathcal J_+]=Z_q[-n;\mathcal J_+]$, so the uncharged Rényi hierarchy, the Faulkner-Lewkowycz-Maldacena one-loop correction, the renormalized generalized entropy and the quantum extremal surfaces coincide for the two orientations. The complementary sector is fixed exactly: with an Aharonov-Bohm angle $\mu$ conjugate to the entangling-region charge, $Z_q[n;\mu]=Z_q[-n;-\mu]$, so the symmetry-resolved spectrum obeys $\mathcal Z_q(\mathcal Q;n)=\mathcal Z_q(-\mathcal Q;-n)$ and every odd charged cumulant reverses with the winding. The orientation is therefore stored entirely in the charge asymmetry of the entanglement spectrum, and is read at topological order by a linked charged matter line. The pair is a bulk logical qubit on which the neutral gravitational-replica algebra acts as a multiple of the identity. Exact BTZ cross sections show that the purification plateau and the entanglement wedge disconnection transition are orientation blind, the latter closing with the cutoff-independent jump $(c/3)\log(1+\sqrt2)$. Numerical Bogomolny solutions verify odd flux and even energy and spin; used as linearized charge-matching data they give the even asymptotic shifts $\delta\widehat M=16\pi Gv^2|n|$ and $|\delta\widehat j|=16\pi Gv^2n^2/(mL)$ and, conditionally, a finite continuous winding envelope.

Complex hypergraphs (chygraphs) contain graphs, hypergraphs, multiplex and interacting networks as special cases, and the percolation threshold of all of them follows from one symbolic calculation: the spectrum of a tensor $A$ built from four matrices of first moments. That calculation stops at the threshold. Here I show that $A$ is the Jacobian, at its trivial fixed point, of a non-linear self-consistency map whose non-trivial fixed point is the giant component fraction, so threshold and order parameter are two orders of one object on one index set. Carrying the expansion one order further gives the critical amplitude $B$ in $S=B\Lambda+O(\Lambda^2)$ in closed form, and exposes a hierarchy: first moments fix the threshold, second moments the amplitude, and only the generating functions themselves the order parameter away from it. Dropping the assumption that a complex's participation in different layers is independent generalises the tensor again, replacing unconditional first moments by inclusion-biased second moments: distributions with identical marginals have different thresholds and different order parameters. Six constructions from the literature are then solved by substitution, among them AND- against OR-logic hypergraph percolation, which share a chygraph and differ in one generating function, and SIR epidemics with two levels of mixing, whose household reproduction number falls out of the tensor. A reported failure of mean-field theory on strongly clustered graphs is shown to be a failure of applying it to the wrong object: mapped onto the treelike backbone rather than the clustered graph, the same calculation reproduces the exact threshold, order parameter and critical exponents. Everything is implemented in one class, in which a chygraph is specified once by its generating functions and then returns all three, and validated against Monte Carlo simulation.

Impact craters relax over long timescales, and this process is commonly described by a diffusion model. The diffusion coefficient determines the relaxation rate, and it has been estimated from observed crater shapes. This coefficient, however, represents the combined effect of several physical mechanisms. Its physical basis has not been revealed yet. In this study, we isolate the contribution of seismic vibration in a controlled experiment. Using a quasi-two-dimensional setup, we first confirm that a linear diffusion equation reproduces the crater relaxation. We then measure the diffusion coefficient and obtain the scaling form through systematic experiments. We find that the diffusion coefficient is proportional to the crater diameter. This dependence is not expected for simple diffusion. We interpret this dependence as arising because the thickness of the vibro-fluidized granular layer scales with the crater depth. This scaling relation is the main result of this study. We then apply it to the Moon with a parameterized model of impact-driven seismic spreading in the regolith layer. Integrating over the impact flux yields a macroscopic coefficient nearly proportional to crater diameter for shallow-layer-like spreading. Its magnitude depends on uncertain model parameters but is consistent with observations for plausible values. These results indicate that vibration is a physically plausible contributor to crater relaxation on the Moon.

QBists insist that theirs is a realist position while denying that the quantum formalism represents a mind-independent world. The insistence is hard to place. The realism debate is throughout a dispute about represented content, so a theory that denies standing in the representation relation appears not to take up a position within that debate at all. This paper examines the most developed attempt to make good on the QBist claim–David Glick's perspectival normative realism–and argues that it fails instructively. Glick seeks the ground of the Born rule's objectivity among states of affairs and construes an agent's perspective as a location within an already-constituted world; finding no state of affairs fit to bind every agent at once, he must book the ground as brute. Phenomenology supplies the third thing his picture lacks. A horizon is not a position within the world but the condition under which a world is given. Read as an agent's weighting–her curvature–of such a horizon, the quantum state is neither a defective description nor a brute posit, and the Born rule articulates the invariant lawfulness by which any sense confers a curvature at all.

Quantum oracles act as reversible black-box operators that encode classical Boolean functions into quantum states, enabling efficient function evaluation in quantum superposition. The resource efficiency of oracle implementation is critical to the performance of numerous quantum algorithms. Most state-of-the-art oracle synthesis approaches rely on compact Boolean function representations such as exclusive-sum-of-products (ESOP), yet still suffer from excessive $T$-count and $CX$-count for large-scale functions. In this paper, we propose a novel compact representation named X-Map decision diagram (XMDD) for Boolean functions, which integrates local invertible maps and complement edges to achieve higher compression efficiency. Based on XMDD, we further develop an optimized quantum oracle synthesis algorithm. Extensive experimental results demonstrate that, for Boolean functions with more than seven input variables, our method outperforms the state-of-the-art ESOP-based approach and Qiskit in nearly all test cases, achieving simultaneous reduction in both $T$-count and $CX$-count without an obvious trade-off. Moreover, we show that the performance can be further boosted by employing more optimal variable orderings. The proposed XMDD-based framework provides a scalable and resource-efficient solution for practical oracle synthesis in near-term and fault-tolerant quantum computing.