Papers

We show that, for stationary geometries whose linearized fluctuation equations separate into radial and angular Heun equations, a pair of diffeomorphisms projects the full problem onto two coupled, isospectral Gauss hypergeometric problems in complementary spacetime regions. This projection requires Robin boundary conditions to be imposed at the intersection between the complementary regions, which are uniquely fixed by requiring the two diffeomorphisms to match there. The method provides an independent derivation of recent results obtained from the correspondence between Heun connection coefficients and instanton partition functions in the Nekrasov-Shatashvili limit. As an application, we identify a subset of modes in Kerr-de Sitter and Kerr-anti-de Sitter black holes that, in the near-extremal limit, continuously reduce to a basis of the Schwarzian/Jackiw-Teitelboim functional space of gravitational fluctuations.

Determination of the stress-free reference lattice spacing, $d_0$, is a central and often underestimated difficulty in diffraction-based strain measurement. Although commonly treated as a material constant, $d_0$ often varies with position and measurement direction as a result of composition, phase, texture and residual stress at the sub-bulk scale. While direct measurement of $d_0$ from coupons is usually preferable, this is sometimes impractical or even impossible. This paper reviews the $d_0$ problem in general and develops a hierarchy of non-destructive alternatives based on mechanical equilibrium. This ranges from established techniques based on force-balance, to the application of boundary conditions and finally an approach based on point-wise equilibrium within a sample, implemented through eigenstrain analysis. In all cases, examples are provided in the form of real samples including an additively manufactured Inconel cube, ancient Roman bronze medical probes and an ancient bronze dagger of purported Persian origin. These latter examples demonstrate that equilibrium can provide a practical physical constraint for estimating $d_0$ when destructive reference measurements are entirely inappropriate.

Renewed interest in lunar exploration is creating a growing population of poorly tracked cislunar objects, some of which will ultimately impact the Moon$^{1}$. The ultimate fate of rocket upper stages or failed mission payloads is often unknown and unplanned. Determining the origin and physical properties of such objects will become increasingly important as sustained lunar exploration places humans and infrastructure on the surface$^{2;3;4;5}$. Here we present a ground-based physical and dynamical characterization of 2025-010D, a Falcon 9 upper stage predicted to impact the lunar farside on 2026 August 05. Backward propagation of its orbit independently links the object to the “Ghost Riders in the Sky” launch, while visible and near-infrared spectroscopy distinguishes it from natural objects and reveals absorption bands consistent with spacecraft thermal control materials. Photometric lightcurves confirm its elongated shape and reveal an unexpected change of more than 8 s in its $\sim$7 min rotation period during observations. We predict an impact between Bell and Einstein craters at $\sim$2.4 km s$^{-1}$, producing a crater $\sim$40 m in diameter. Since its provenance is independently known, 2025-010D provides a benchmark for identifying and characterizing future cislunar objects of uncertain origin.

Strongly regular graphs, hereafter SRGs, are highly structured combinatorial objects of central interest in algebraic graph theory and quantum information, whose explicit construction becomes rapidly intractable as the number of vertices grows; Conway's still unresolved $99$-graph problem is an emblematic example. The matrix equation defining SRGs is quadratic in the binary edge variables, so the natural penalty enforcing it, a sum of squared residuals, is quartic and lies outside quadratic unconstrained binary optimization, known as QUBO. We prove a considerably stronger obstruction, namely that no quadratic function of the edge variables has the labeled SRGs as its exact set of global minimizers, except for three degenerate families given by the perfect matchings, the cocktail-party graphs and the pentagon. In particular, we formally establish that the $99$-vertex graph of Conway's problem cannot be obtained from any QUBO over the edge variables without auxiliary variables. Guided by this theorem we develop two complementary algorithms. The first operates within pure QUBO, solves the degenerate families exactly, and beyond them works as a generate–prune–verify pipeline whose output is a reduced set of candidates certified by a polynomial-time classical test. The second solves the full problem by quadratizing this quartic penalty through Rosenberg auxiliary variables, whose number grows as $\Theta(N^3)$ with the number of vertices $N$. We test the pure-QUBO route under simulated annealing on all feasible families with at most $18$ vertices and the auxiliary-variable route on representative targets up to $16$ vertices, and tabulate the algebraically feasible parameter sets for graphs with at most $49$ vertices.

Two quantum states may relax toward the same steady state, yet the one that starts farther away can overtake the closer one. This is the quantum Mpemba effect. The same pair can reverse order more than once, but these crossings may depend on the divergence used to compare them. We ask which crossings persist for every normalized operator-convex Petz divergence. Because each such divergence is a positive average of one-parameter $\chi^2$ kernels, the problem reduces to the sign of one profile across the full kernel range. Alternating sign margins guarantee repeated family-wide reversals, while finite dimension yields a polynomial positivity test. A simple real slow mode fixes the common late-time order; near stationarity, coherence between unequal-eigenvalue sectors makes the order divergence dependent. In a trapped-ion qutrit ideal model, the reported preparation shows divergence-selective crossings. A nearby preparation is a candidate for at least two family-wide reversals.

Grover search, amplitude amplification, and quantum counting all rely on the same reusable subroutine, a phase oracle, whose construction the algorithms literature takes as given: the classical predicate is assumed to be already encoded as a correct, resource-bounded circuit. We turn this assumption into a measured capability. QEncodeBench tasks large language models (LLMs) with encoding classical constraint problems as phase oracles and scores the generated circuits with an adversarially self-validated verifier that decides full solution-set equivalence up to a global phase, with ancillas restored and resource budgets enforced. Sampled basis-state tests, we show, systematically overestimate this ability. Measured this way, models separate sharply: code models without a reasoning mode solve essentially nothing, and enabling native reasoning on identical weights improves accuracy by an order of magnitude. The failures are overwhelmingly semantic rather than syntactic. Two architectures, a unit-verified constraint agent and a neuro-symbolic compilation pipeline, close most of the remaining gap by delegating correctness-critical composition to deterministic procedures. Ablations quantify the contribution of each component, and resource gating exposes an architecture-dependent trade-off between circuit width and depth. Finally, controlled difficulty escalation reveals architecture-specific responses to difficulty structure: different difficulty axes degrade different methods, while the neuro-symbolic pipeline passes every evaluated instance. Code and data are available at https://github.com/chexujun/QEncodeBench.

Borrowed from non-equilibrium statistical mechanics, the generalized Langevin equation (GLE) is imported as a framework for stochastic volatility to address the structural limitations of fractional Brownian motion (fBm), the standard engine of rough volatility. The fBm forces a single parameter to set two logically independent properties at once: how volatility scales and how it remembers. The GLE separates them using a memory kernel $K$, a potential $U$, and a noise covariance $C$. Memory becomes a measurable object, and an asymmetric potential supplies a lever on variance skew that the price-variance correlation cannot reach. Physical-measure tests on public datasets decisively reject two constrained corners of the class, a memoryless leverage effect and time-reversal symmetry, while the central rough scaling constraint is left identification-limited rather than refuted. The paper reports these limits honestly, and validation on industry-grade data remains a valuable direction. The risk-neutral construction and the joint SPX–VIX calibration will be developed in a companion paper.

Information distance and circuit complexity are both obtained by minimizing lengths, but they minimize over different objects. We make this distinction explicit for faithful one-mode Gaussian states. First, invariant-form uniqueness implies that no positive-definite quadratic gate cost can be invariant under the full adjoint action of the noncompact symplectic group; a positive Cartan majorant necessarily introduces additional reference data. The Uhlmann purification quotient realizes the Bures metric, and the radial covariance direction requires a system-ancilla coupling because system-only Gaussian unitaries preserve the Williamson eigenvalue. We then minimize fixed right-invariant quadratic norms on the minimal two-mode Gaussian gate algebra \(\mathfrak{sp}(4,\mathbb R)\). For the unweighted Frobenius norm, the quotient coefficients for radial and traceless covariance tangents are $G_0=[\hbar^2(u-1)]^{-1}$ and $G_2=[\hbar^2(3u-1)]^{-1}$, where $u=(2\nu/\hbar)^2$. Their ratio does not equal the Bures ratio. The radial coefficient, however, reproduces the Bures value exactly at every $u$; the mismatch is confined to the traceless sector. More generally, a constant block-diagonal two-weight schedule gives $G_0/G_2=1+2(\beta/\alpha)u/(u-1)$; matching Bures throughout the isotropic family would require the state-dependent relation $\beta/\alpha=1/u$. At the Bures-Fisher determinant crossing \(u=\varphi\), pointwise matching is possible only by inserting $\beta/\alpha=\varphi^{-1}$. Thus the Bures purification quotient is an exact state-geometric cost, but it is neither an unweighted symplectic gate cost nor a member of this fixed two-weight Nielsen family. The existence of a more general fixed positive gate norm realizing the quotient remains open.

Early-warning signals are usually computed from one or a few observables, although the underlying dynamics are high dimensional. Projection creates a structural ambiguity: the same scalar record may reflect spectral loss of stability, hidden-state memory, nonnormal amplification, a turning point of a physical balance, or a combination of these. We develop a unified operator theory that makes these alternatives explicit. For a resolved-hidden block linearization we derive exact Volterra reductions, finite and diffusive Markovian liftings, and a Schur-resolvent factorization of the stability problem, distinguishing three notions of memory: realized pathwise, structural Schur return, and finite-horizon projected. A covariance theorem gives sufficient conditions for a scalar to inherit critical slowing down from a real multiplier approaching the unit circle: spectral separation, bounded eigenvector conditioning, observability of the critical mode, stochastic excitation of that mode, and quasi-stationary forcing. We then prove failure mechanisms: a critical mode can be invisible or unexcited; an oscillatory crossing need not raise lag-one correlation; a nonnormal family can produce diverging scalar variance with a fixed stable spectrum; a physics-based turning point need not coincide with a spectral boundary; and finite-horizon data cannot identify long memory uniquely. The theory is illustrated with a 4400-year CESM AMOC hysteresis experiment. EOF1 alone detects altered susceptibility, but EOF1-EOF2 is the smallest resolved space revealing changed Schur return and projected memory after recovery; F_ovS reaches its minimum 26 years before collapse while the modal margin does not decrease toward zero: the two diagnostics probe complementary mechanisms. The application is mechanistic and single-trajectory; no validated early-warning signal is claimed.

We study the recently developed theory of quantum convolution for discrete-variable quantum systems. We classify the discrete quantum convolutional channels generated by an invertible $2\times2$ coupling matrix and a fixed environmental state according to which entries of the coupling ma- trix vanish. Under role-preserving basis relabelings, matrices with all four entries nonzero form $d-2$ canonical cross-ratio classes, whereas matrices with exactly one vanishing entry split into four inequivalent branches. We determine the optimized one-shot Holevo information and the classical, quantum, and private capacities for all four one-entry-vanishing branches. If a diago- nal entry vanishes, the channel is an entanglement-breaking measure-and-prepare orbit channel: its classical capacity equals a relative entropy coherence of the environmental state, whereas its quantum and private capacities vanish. If an off-diagonal entry vanishes, the channel is a degradable generalized-dephasing channel: one complete orthonormal basis is transmitted without error, whereas the quantum and private capacities are determined by the entropy deficit of the environ-ental state after dephasing in the conjugate basis. Thus, the position of a single vanishing entry selects two qualitatively different communication regimes. When all four entries are nonzero, the channels are irreducibly Weyl covariant, reducing the classical-capacity problem to a regularized minimum-output-entropy problem. For the unique fully nonzero coupling class in the single-qutrit case, we further derive an exact Holevo formula for a depolarized one-parameter family and identify its entanglement-breaking threshold.

A new kinetic equation and Lagrangian of a massive and charged spin-one vector boson is outlined in this paper. Those quantities are derived by exploiting directly the Lorentz group generators including the boson spin. Thereby, the chiral symmetry of the Lorentz transformation is guiding the algebraic calculations. Two associated 4\,x\,4 spin and helicity matrices can be defined, the sum of which give the rotation operator that yields in the presence of an electromagnetic field the boson-spin coupling to the magnetic field. The four polarization vectors of the boson field are calculated and discussed. Moreover, the current density is derived and used to reveal the bosonic nature of the kinetic equations. The energetic stability of the vector boson quantum field is shown. A Pauli equation for the vector boson is derived.

We present a derivation showing that classical spacetime geometry is a gravitational condensate within the Unified Standard Model with Emergent Gravity–Effective Field Theory (USMEG-EFT): the background metric $\barg_{\mu\nu}$ is the vacuum expectation value of the quantum metric operator, existing as an ordered phase below the gravitational breakdown scale $\Lgrav \sim 10^{18}$\,GeV. The condensed phase is characterized by a nondegenerate metric expectation value, a diffeomorphism-invariant criterion whose controlled realization is confined to scales below $\Lgrav$. Three convergent quantum-field-theoretic analyses within the framework, namely canonical covariance breakdown \cite{Chishtie23}, one-loop renormalization group analysis \cite{Chishtie25CJP}, and conditional BRST closure \cite{ChishtieSymmetry26}, identify this scale as the boundary of the controlled geometric description. We show that the condensate order parameter, defined via the Legendre transform of the Lagrange multiplier path integral \cite{BrandtFrenkelMcKeon20,McKeonBrandt25}, satisfies a quantum-corrected saddle-point equation whose one-loop correction grows to the size of the tree term at $\Lgrav$, beyond which the framework supplies no controlled nondegenerate solution; we interpret this boundary as the onset of condensate dissolution. Because the Lagrange multiplier constraint acts on virtual graviton fluctuations and terminates the gravitational sector exactly at one loop, this boundary arises from a finite, closed set of quantum corrections, in contrast to the gradual failure of the derivative expansion in the standard effective field theory treatment of general relativity \cite{Donoghue94}. This mechanism is fundamentally distinct from, and resolves known inconsistencies of, Verlinde's entropic gravity programme.

Fast and nonuniform translocation through solid-state nanopores limits both the detection of small molecular labels and their precise localization along molecular carriers. In this work we report the detection and localization performance of nucleotide-based molecular labels along double-stranded DNA scaffolds using solid-state nanopores in thin planar membranes. For small labels that are challenging to resolve individually, we introduce an anchoring strategy where readily detectable bulky labels serve as reference points to align multiple translocation events, enabling population-based detection and localization of smaller molecular features. The measured anchor positions constrain a probabilistic model of translocation velocity, identifying the most probable velocity profile for each event and enabling nonlinear trace "unwarping" for improved multi-event alignment. A complementary window-based evidence aggregation procedure accumulates weak but consistent label signatures across events, enabling detection of features that are individually masked by noise. These approaches enable robust recovery of single-dumbbell labels (DB1) on the order of 28 nucleotides and reduce mean localization errors to as low as 10 base pairs for DB3 labels and 40 base pairs for DB1 labels when averaging over multiple events. Stronger fractional DNA-associated current blockades, used as proxy for smaller pore geometries, are additionally associated with improved detection and lower localization error across membrane-based nanopore fabrication techniques. Overall, anchor-guided alignment provides a route to higher-density molecular information readout without compromising throughput via controlled translocation approaches.

Compound drought-to-extreme-precipitation (CDEP) events are recognized in climate science as a growing driver of extreme impact, but whether this recognition carries over into real-world early warning and post-event documentation is unknown, so a meteorologically real CDEP event may pass with neither advance warning nor any later record. Here we present CDEP Agent, an auditable LLM-agent framework that tests this mismatch directly by linking CDEP candidates detected from meteorological reanalysis to real-world hazard and impact evidence across sources with different spatial scales, temporal resolutions, and reporting conventions. Using California as a case study, we identify 408 candidate CDEP events from ERA5 observations during 2021-2025 and evaluate each against the U.S. Drought Monitor, NOAA Storm Events, and public webpages along five dimensions: antecedent drought, extreme rainfall, local impact, hazard-impact attribution, and explicit drought-to-rainfall linkage. Only 34.3% of candidates are corroborated on both hazard components, and just 1.5% are ever explicitly linked to their antecedent drought, indicating that most meteorologically detected CDEP events go undocumented and their compound nature almost never enters the record at all. Our framework gives climate scientists a way to test physical event definitions against what actually gets documented, and gives social scientists, economists, and disaster-response agencies a provenance-linked evidence base for compound events that current warning and reporting systems largely fail to capture.

This paper presents the systematic fabrication and characterization of cryogenic thermometers based on neutron transmutation-doped germanium (NTD-Ge). High-purity (10N) germanium samples were irradiated by thermal neutrons with different fluences at the China Advanced Research Reactor (CARR). After irradiation and a six-month cooling-down period, positron annihilation lifetime spectroscopy and temperature-dependent Hall effect measurements were performed to characterize irradiation-induced defects and carrier concentrations in the NTD-Ge samples. Utilizing standard semiconductor fabrication techniques, point electrodes were deposited onto the processed samples to fabricate functional NTD-Ge cryogenic thermometers. The low-temperature resistance performance of the devices was characterized down to 20 mK on a millikelvin range cryogenic test platform. The measured temperature dependence of resistance follows Mott's law, showing excellent agreement across the full measured range. The extracted T0 is consistent with expectations. These results collectively verified both the applicability of the thermometers in cryogenic system and the reliability of the fabrication procedure.

18F-fluorodeoxyglucose ([18F]FDG) positron emission tomography (PET), combined with compartmental modeling, is a powerful non-invasive imaging method for assessing cellular metabolism. However, classical two- and three-tissue compartment models assume homogeneous [18F]FDG distribution within the tissue, which needs justification, and the definition and interpretation of rate constants across these models is not always consistent. To address these issues, we develop a finite difference solver to simulate [18F]FDG transport and metabolism within a 1 mm3 tissue volume, representing the smallest volume resolvable by PET. Our simulations reveal sub-millimeter heterogeneity in [18F]FDG distribution and show that the measured PET signal is dependent not only on cellular metabolic activity but also on interstitial [18F]FDG diffusivity, vascular permeability, and vascular architecture. We further demonstrate that our finite-difference simulation reduces to a three-tissue compartment model when interstitial [18F]FDG concentration is homogeneous. Furthermore, this simplified model itself reduces to the two-tissue compartment model when vascular permeability is sufficiently high. This work quantitatively links vascular permeability, vascular architecture, cellular uptake kinetics, [18F]FDG diffusivity, and acquisition time. It also unifies the two- and three-tissue compartment models and identifies their applicable regimes. These findings deepen our understanding of [18F]FDG transport kinetics and enhance the interpretability of dynamic [18F]FDG-PET imaging.

AI weather models are often reported to underestimate extremes, but most evidence concerns deterministic regression models verified against reanalysis. We evaluate twelve physical and AI forecast models against ECMWF IFS using ten months of European station observations. The evaluation covers 10 m wind, 2 m temperature, solar radiation, and precipitation within regimes defined from a fixed ERA5 1991-2020 climatology. We find no uniform AI-specific deficit in the tails. Several AI models remain more accurate than IFS under extreme conditions, while others deteriorate markedly; comparable variation occurs among physical models. Every model nevertheless exhibits a common conditional-error pattern, overpredicting low observations and underpredicting high observations. Attenuation of extreme values therefore does not imply a uniform loss of relative skill: tail performance depends on the model, variable, and evaluation setting rather than on whether the forecast is produced by AI or physical numerical modelling.

We develop a mechanically faithful reduced model for a two-dimensional topological phononic crystal composed of rigid square masses connected by slender elastic ligaments. Exploiting Euler Bernoulli beam theory, we derive a Hermitian 12 degree of freedom dynamical matrix that retains in-plane translations, rotations, and ligament eccentricity. This reduction captures effects that are absent from scalar mass spring SSH models while remaining computationally much more tractable and more easily interpretable than full finite element simulations. Dimerizing the ligament widths produces a mechanical 2D SSH lattice with a full band gap and a quantized bulk polarization. The sign of the dimerization controls the transition from trivial to non trivial phases, while ligament eccentricity provides an additional purely geometric mechanism for changing the topology. Ribbon and finite cell calculations predict in gap edge and corner modes, quantified by localization measures and confirmed by finite element simulations. Measurements on 3D printed samples show an evanescent response in the trivial structure and enhanced boundary/corner response in the non trivial structure within the predicted gap. The results provide a validated route for designing topological elastic metamaterials using a continuum informed discrete model rather than either idealized mass spring networks or brute force numerical optimization.

A precise characterization of the QCD phase transition remains a fundamental open problem, primarily due to the intrinsically non-perturbative nature of the dynamics that govern the breakdown of We quantify the logarithmic thermal variation of the normalized enthalpy density in finite-temperature Quantum Chromodynamics using a dimensionless response thermal function, $\mathcal{H}(T)$. We establish an exact identity that links $\mathcal{H}(T)$ to the speed of sound, $c_s^2(T)$. Using continuum-extrapolated lattice Quantum Chromodynamics, Monte Carlo uncertainty propagation, and cubic spline interpolation, we extract a stable peak at $T_{\text{peak}} \approx 153.6\text{ MeV}$ ($\mathcal{H}_{\text{peak}} \approx 6.24$), which remains robust under changes in the smoothing parameter $s$. By contrast, $\mathcal{H}(T) = 0$ for the MIT Bag Model despite its non-vanishing trace anomaly. We highlight $\mathcal{H}(T)$ as an effective diagnostic of the QCD crossover and discuss its limitations for universal critical scaling at zero chemical potential.

Quantum programs are difficult to validate: circuits are typically expressed as imperative gate sequences with limited inspectability, execution modalities must be selected manually, and outputs are inherently probabilistic. These challenges are compounded when programs must be portable across backend frameworks with differing internal conventions. We present a quantum domain-specific language (QDSL) that addresses these problems through three mechanisms: (i) intent-execution separation, where algorithmic constructs such as preparation, superposition, entanglement, and measurement are represented as inspectable objects compiled into backend-specific circuits only after pre-execution Intermediate Representation (IR) validation; (ii) first-class IR introspection, exposing circuit width, wire mapping, operation order, and measurement intent for developer inspection prior to execution; and (iii) assertion-guided modality inference, where the engine examines declared verification properties to automatically select sampling, statevector, or dual execution without user intervention. Results are logged in structured form to support reproducible regression testing. We evaluate our prototype on benchmark circuits spanning entanglement, oracle-based, structured-transform, and variational examples. In fault-injection experiments on Bell and 3-qubit GHZ circuits, a total-variation-distance detector identifies the injected faults across all evaluated shot budgets (True Positive Rate 1.0), with observed false positives (False Positive Rate 2.7-3.8%) only at 128 shots. Differential testing demonstrates numerical agreement across PennyLane and Qiskit compilation targets for the evaluated constructs after endianness canonicalization. IR generation costs are sub-millisecond.

Whether negative-partial-transpose entanglement can remain undistillable is a longstanding problem in quantum information theory. We analyze the first unresolved three-copy Werner endpoint using a sharp dimension-free inequality for complementary partial traces and an optimal exterior-square inequality for orthonormal tripartite vectors. The latter identifies local SWAP- parity statistics with metric data of a decomposable Plucker bivector. Together these inequalities prove endpoint nonnegativity for every positive semidefinite rank-two coefficient operator and for the complete normal rank-two sector in arbitrary finite local dimensions. For genuinely nonnormal operators, an exact crossed-Gram criterion proves nonnegativity when one local outpu-input support overlap is at most two, including every system with a qubit-sized factor, and when either support plane contains a product ray. Explicit anti-state and rank-boundary families establish optimality of the constants and the rank restriction.

Accelerating scientific discovery is among the most consequential applications of AI, and computational biomolecular simulation stands out as a particularly promising target within this broader effort. Coding agents promise to automate significant portions of this workflow, yet their reliability on realistic molecular dynamics (MD) tasks remains poorly characterized. To address this issue, we introduce MDArena, a benchmark of 50 containerized tasks drawn from active biomolecular simulation projects, spanning 29 molecular systems and 14 broad research protocols, including trajectory analysis, complex system preparation, free-energy protocols, and enhanced sampling. We evaluate six model/harness configurations spanning Codex and OpenCode. Among the evaluated configurations, Codex GPT-5.5 at extra-high reasoning effort performs best, reaching 24/50 Strict-Pass@1 successes (48%), followed by Codex GPT-5.5 Medium with 21/50, and OpenCode Gemini Flash 3.5 with 20/50. Average correctness and process rewards are substantially higher than strict success rates across all configurations, indicating that agents frequently make meaningful partial progress but fail on the fine-grained details required for reproducible scientific workflows. Hard tasks remain largely unsolved, particularly membrane-protein system preparation and alchemical free-energy setup, both unsolved or near-unsolved by every evaluated configuration. MDArena thus exposes a substantial gap between the usefulness of coding agents as supervised assistants and their reliability as autonomous MD researchers, while providing a reproducible and extensible platform for tracking progress toward closing it.

We present SU3HOB-ladder, a Fortran 2008 package computing the general Talmi-Moshinsky harmonic-oscillator transformation brackets for an arbitrary mass-ratio parameter d in the SU(3) basis. The bracket reduces to a single sum over Wigner d-functions of the reflection-containing Talmi-Moshinsky matrix, weighted by products of SU(3) > SO(3) isofactors of the chain U(6) > U(3)xU(2); the isofactors are d-independent, so they are built once per block (E,L) and reused for every d. We obtain them from the U(2) pseudo-spin generators of that same chain: because the U(3) and U(2) labels inside [E] of U(6) are complementary, the highest-weight states are the null space of the raising operator J_+ = a^dag(1).a(2) and the remaining members of each multiplet follow by lowering, so that no SU(3) recoupling machinery, K-matrix or outer-multiplicity resolution is required at any point. We compare this construction with two alternatives that produce the same brackets - the same scheme with isofactors taken from the vector-coherent-state library Su3cgvcs, and the classical Talmi-Moshinsky sum of Kamuntavicius et al. - over every block up to E=50. Evaluating the classical sum with its factorials in logarithmic form rather than as tabulated binomials removes the range limit that otherwise caps it near E ~ 12, and makes it an absolute check on the bracket values over the whole range where its cost is bearable. Against that check the two routes agree to within a factor of a few at every shell, while the ladder construction is faster by three orders of magnitude; it is also the only one of the three usable over the whole range, retaining max|HOB.HOB^T - I| <~ 2x10^-6 at E=50, where the library route has become unusable and the classical route is prohibitively slow.

Conformer assignment is meaningful only when the measurement can distinguish the candidate structures. We formulate conformer spectroscopy as a measurement-model-dependent identifiability problem in which each modality defines an observation law with explicit experimental and theoretical uncertainty. Equality of observation laws defines exact classes that refine as modalities are added, whereas finite-resolution ambiguity is non-transitive and is represented by a Bayes-error graph. We also give rank and constrained-Fisher criteria for population recovery from unnormalized additive spectra. The framework is applied to audited B3LYP-D3(BJ)/def2-TZVP ensembles of 1,2-difluoroethane, ethylene glycol, and n-pentane. Under the declared shared-covariance working model, IR separates all non-mirror pairs, leaving only mirror pairs that are exactly degenerate under the achiral observation maps. This within-method result does not imply general IR sufficiency: in a six-case PBE0-to-B3LYP diagnostic, fixed calibration recovers one intended representative, whereas scale-and-shift profiling with a conservative cross-method covariance recovers five representatives and all six achiral classes. Under a combined stress-test covariance, n-pentane develops one non-mirror quotient ambiguity. Three individual Raman windows remove it, while no tested IR window does. Mirror-collapsed class populations remain identifiable and well conditioned under the calibrated-scale working model, whereas separate mirror-partner populations are exactly unidentifiable from achiral additive spectra.

Read noise in infrared sensor arrays remains a major obstacle for ground- and space-based astronomy. It has long been recognized that the upcoming extremely large telescopes cannot meet their full potential unless read noise is significantly improved, and it is also a prohibitive constraint on the Habitable Worlds Observatory, a space telescope with the goal of detection and characterization of nearby Earth-like exoplanets. The main strategy for lowering read noise is averaging through multiple non-destructive reads. However, this typically results in less noise reduction than the 1/$\sqrt{N}$ scaling predicted by theory. In this work, we show the poor averaging behavior can largely be explained by readout glow, photon emission from the sensor electronics that generates photoelectrons in the pixels during readout. Because glow accumulates with reads rather than averaging, this imposes a fundamental noise floor of \sigma_min ~ 1.5 sigma_RN^(1/2)G^(1/4). This limits averaging in HxRG-like sensors to about 2-3 e- of noise, and linear-mode avalanche photodiodes (LmAPDs) to about 0.5 e-. We present laboratory data using both sensor architectures, with the LmAPD following the predicted noise value to within 0.1 e- over two decades of averaging.

Thermospheric mass density governs aerodynamic drag in low Earth orbit and is a primary source of uncertainty in orbit prediction and conjunction assessment, particularly during geomagnetic disturbances. We present AETHER-P3 (Accelerometer-driven Estimation of THERmospheric density-A Physics-Informed Probabilistic Prediction Platform), a machine-learning-based global thermospheric density forecasting model that provides multi-step forecasts up to 6 hr ahead using a 3-hr input window, with predictive uncertainty estimates. AETHER-P3 formulates thermospheric density forecasting as a sequence-to-sequence regression task conditioned on recent space weather evolution and a user-specified sequence of future times and locations. To enhance physical consistency and generalization, AETHER-P3 incorporates JB2008 and NRLMSISE-00 density estimates evaluated at future locations, along with solar, geomagnetic, and solar-wind drivers. The network employs dual recurrent encoders and an evidential Normal-Gamma output head to jointly estimate forecast mean and uncertainty. The model is evaluated using independent satellite test cases spanning quiet, moderate, and extreme geomagnetic conditions. During quiet periods, AETHER-P3 achieves high forecast skill (R=0.95). Under moderate activity, strong skill is retained (R=0.93), with reduced physical-domain errors than empirical baseline models. During extreme storm conditions, deterministic forecast skill degrades as expected yet remains robust (R=0.89-0.90). Predictive uncertainty remains well calibrated across all regimes. These results establish AETHER-P3 as a practical, low-latency, uncertainty-aware capability for thermospheric density forecasting that supports orbit prediction, drag-risk assessment, and operational decision-making over its validated altitude range of approximately 300-520 km, with highest confidence in the data-rich 400-520 km region.

A promising new architecture for extreme-precision radial velocity (EPRV) spectrographs, hunting for small-amplitude stellar Doppler shifts induced by orbiting planets, is to build diffraction-limited instruments by using single-mode fibers fed by an adaptive optics system. However, the target stars are partially resolved when observing at the diffraction limit, and the resulting RVs are expected to be affected by differential limb coupling (DLC), an effect where the red- and blue-shifted sides of the stellar disk are coupled unequally into the spectrograph, producing an RV error term on the order of m/s for nearby EPRV target stars for the upcoming HISPEC spectrograph for Keck II. We present our efforts to directly measure the RV shifts resulting from DLC for the first time, using the diffraction-limited spectrograph PARVI, in order to verify the expected behavior of DLC and subsequently develop mitigation strategies for HISPEC and other future instruments. We outline an observing strategy designed to produce DLC-induced RV shifts of hundreds of m/s, and describe the execution of this experiment with PARVI. We use these data to characterize the PARVI tip-tilt guide camera and its performance, and have begun analysis of the derived RVs, though this investigation has proven complicated since the RVs are deeply entangled with other instrumental and algorithmic effects.

The finite transverse granularity of a segmented electromagnetic calorimeter fundamentally limits the precision with which the observables of a shower can be reconstructed, among them its position, its lateral profile, and the direction of the incident particle. We show that a substantial fraction of the information suppressed by the segmentation can be inferred under physical constraints, and that it propagates to downstream physics quantities. The reconstruction is cast as an inverse problem and solved with a generative model constrained by the low-order spatial moments of the shower, driving the solution toward physically consistent energy distributions rather than image similarity alone. Using the undoped CsI calorimeter of the KOTO experiment as a reference system, the reconstruction reduces the per-event residual of these moments with respect to the truth-level reference by roughly 40-62% in a representative 1 GeV bin. The inferred morphology also generalizes beyond the training objective: on a $K_{L}\to\pi^{0}\nu\bar\nu$ Monte Carlo sample it improves the reconstruction of the photon incident angle, a quantity never used during training, and of the $\pi^{0}$ decay vertex. These results indicate that finite segmentation is better viewed as a limit on what a calorimeter measures directly than as an absolute limit on the physics information it retains, with the recoverable fraction depending on the observable and growing with the shower energy.

We study the stochastic dynamics of a rotating Brownian particle in a non-Markovian fluid. Experimentally, we find that rotation enhances the long-time diffusivity of the particle and generates time-antisymmetric cross-correlations between orthogonal displacement components in the plane perpendicular to the rotation axis. To rationalize these observations, we introduce a minimal linear model in which a tracer is coupled to a slow bath degree of freedom and rotation enters through an advective coupling. Eliminating the bath variable yields a generalized Langevin equation with a non-reciprocal memory kernel. This kernel rotates in time, forming a logarithmic spiral, and it obeys Onsager-Casimir symmetry under reversal of the rotation vector, and the corresponding fluctuation-response relation. From the latter we obtain a geometric construction that links two-time cross-correlations to the transverse response of the particle in bulk. Unlike the ordinary Einstein relation, this relation involves the antisymmetric sector of the response. Our experiments and theory are in qualitative agreement, establishing rotating colloids in viscoelastic fluids as a minimal realization of Onsager-Casimir symmetry in time-nonlocal stochastic dynamics

We investigate the linear dynamics of non-axisymmetric perturbations in Keplerian discs subject to a weak uniform vertical magnetic field in the shearing box approximation. Perturbations are decomposed into shearing waves and evolved by numerically integrating the linearized ideal MHD equations. The disc flow supports three basic perturbation modes: two incompressible modes – a magnetic mode that exhibits magnetorotational instability (MRI) and inertia-magnetic wave – and a compressible spiral density wave. The magnetic mode and inertia-magnetic wave have a low frequency of the order of Alfvén and orbital frequencies, respectively, while density wave has a high frequency. We introduce mode eigenfunctions and governing modal equations to analyse the dynamics of individual modes and their interaction. For non-axisymmetric modes, the modal equations are coupled due to the shear of the disc's Keplerian rotation, giving rise to a new shear-induced linear mode coupling process, which is rooted in the non-self-adjoint nature of shear flows. We focus on the generation of density waves by the dominant MRI-unstable magnetic mode. We show that initially imposed magnetic mode undergoes MRI growth and abruptly excites density waves when its radial wavenumber crosses zero. This density wave–MRI coupling is most efficient when the azimuthal and vertical wavelengths of perturbations are comparable to the disc scale height. Since density waves are compressible, whereas MRI is incompressible, this wave excitation process can also be regarded as a linear mechanism generating compressible motions via MRI-driven incompressible ones. Its implications for compressible non-zero net vertical field MRI turbulence are also discussed.