We study the problem of computing competitive equilibria in the Arctic product-mix auction, originally developed for the Icelandic government for exchanging blocked financial accounts, and more recently proposed by IMF staff for sovereign debt restructuring. From the buyers' perspective, the Arctic auction is equivalent to the quasi-linear Fisher market. However, unlike the standard Fisher model, the seller can express rich supply preferences through explicit supply-side costs and constraints. Despite extensive algorithmic literature on Fisher markets, the seller side has not received much attention, and no polynomial-time algorithm was previously known for computing competitive equilibrium when sellers face nontrivial costs. We examine the natural and expressive regime of separable, stepwise-increasing marginal costs that underlie the above-stated applications. Using polyhedral theory techniques, we first show that rational inputs lead to rational-valued competitive equilibria. Motivated by this result, we develop the first polynomial-time algorithm for this setting based on a non-trivial extension of classic primal-dual balanced-flow techniques for linear Fisher markets. Our work provides a robust computational foundation for auctions with sophisticated preferences, paving the way for flexible and institutionally feasible market designs in global finance.

Stellar streams are a promising way to gravitationally detect low-mass substructure, since their low dynamical temperature makes them retain the imprint of weak gravitational perturbations. We develop a fast, differentiable forward model for perturbed stellar streams in the diffusion regime, where the stream is heated by many small velocity kicks rather than by a few strong encounters. The substructure population enters only through its power spectrum, so the computational cost is insensitive to the number of perturbers, and alternative dark matter models and/or baryonic perturbers can be explored by changing this single input. We validate the simulations against analytical predictions, then forecast the sensitivity of a GD-1-like stream to the substructure power spectrum, adding to the stream density the full kinematics, both proper motions and the radial velocity. Kinematic information tightens the constraints by a factor of $\sim 3$-$5$ relative to density alone, improving the precision on the dark matter free-streaming cutoff scale from $\sim 1.2$ dex to $\sim 0.25$ dex at a fiducial value of $M_{\rm hm} = 10^6 M_\odot$ for a $5$ Gyr stream. A single well-measured stream could thus constrain dark matter competitively with current limits from strong lensing and satellite counts.

Uniaxial stress is a promising method to tune magnetic frustration, allowing its effects to be studied in a precise way. In this work, uniaxial stress is applied to the triangular-lattice antiferromagnet PdCrO2. The Cr-Cr magnetic interaction is very sensitive to interatomic separation, so laboratory-achievable stress can induce substantial changes in magnetic structure. Results from three types of measurement are presented: X-ray diffraction, the stress-strain relationship, and neutron diffraction. The combined data show that the elastic moduli of PdCrO2 are strongly affected by stress-induced changes in magnetic structure. A new, first-order stress-induced magnetic transition is observed, at which the lattice constant shrinks by 0.21%. The lattice stiffens dramatically across this transition: the Young's modulus increases by about 80 GPa, and the Poisson ratio falls from about 1 to about 0.4. This stiffening indicates that the magnetic order "locks," that is, becomes insensitive to lattice strain. This locking might occur because the new stress-induced magnetic order nests the Fermi surface of the Pd sheets. Other frustrated magnets, including candidate spin liquids, may show similarly strong coupling between magnetic and elastic degrees of freedom.

Cataclysmic variable stars (CVs) evolve toward shorter orbital periods ($P_{\rm orb}$) until they reach a minimum $P_{\rm orb}$ near $P_{\rm orb}\sim80$ min. Beyond this point, the donor star becomes out of thermal equilibrium or increasingly degenerate, causing the system to "bounce back" to longer $P_{\rm orb}$ values. Such highly evolved systems are known as period-bouncers. Although 40-80\% of all CVs are expected to have reached this stage, period-bouncers come up for only 3-25\% of the observed CV population. This is likely a consequence of their intrinsic faintness associated with lower mass-transfer rates. Establishing new diagnostics to unveil this missing population is therefore crucial. Two samples of non-magnetic CVs with public SDSS optical spectra were constructed: one of short-period pre-bounce CVs and another of period-bounce CVs. For systems showing Balmer absorption from the white dwarf (WD), hydrogen-dominated atmosphere models were fitted and subtracted to correct for the WD component. H$α$, H$β$, and H$γ$ fluxes were measured. We then investigated statistical relations between the Balmer decrements, the H$β$ line luminosity, and $P_{\rm orb}$, and compared the measured Balmer decrements with theoretical predictions from accretion disc models. Short-period pre-bounce CVs show flat Balmer decrements, that is Balmer line ratios close to unity. In contrast, systems near and beyond the period minimum exhibit progressively steeper decrements (H$α$/H$β$>1 and H$γ$/H$β$<1). This behaviour is attributed to their lower mass accretion rates, as inferred from the H$β$ line luminosity. We fitted a linear logistic regression model to the diagram of H$γ$/H$β$ versus H$α$/H$β$. We establish that this diagnostic diagram effectively separates period-bouncers from pre-bounce CVs.

We present analytical model for peristaltic transport within compressible, ideal magnetohydrodynamics (MHD). By employing small-amplitude perturbation expansion, under thin-tube long-wavelength approximation with a uniform axial background magnetic field, we study non-linear coupling between thermodynamic pressure variations and Maxwell's magnetic tension stresses. The resulting net time-averaged volumetric flow rate $\langle Q \rangle$ is calculated. When applied to solar chromospheric spicules under equipartition constraints ($β\sim 1$), where sound speed matches the Alfv{é}n speed, we find $\langle Q \rangle = 4ε^2/(M^2-1)$. Because the denominator remains positive across all operational supersonic Mach numbers ($M \approx 2\text{--}10$), upward-propagating mechanical disturbances drive a highly directional, collimated upward flow which we interpret as a spicule. Estimates show that for observationally realistic magnetosonic waves with amplitudes of $\approx 10\%$, the peristaltic mechanism generates a localized mass flux $\approx 100$ times that of solar wind. We propose an explicit observational signature of this mechanism, wherein the launch of individual spicular jets is directly preceded by magnetosonic wave trains detectable as localized intensity modulations. Beyond solar chromospheric application, the model may be applicable to traveling magnetic field pinches in laboratory plasma devices and astrophysical mass-loading processes in stellar winds and inner regions of magnetized accretion disks.

This paper proposes a synthetic control (SC) framework for the estimation of conditional distributional treatment effects. Identification rests on a parallel trends condition formulated in the parameter space of the semiparametric distribution regression (DR) model, which keeps the counterfactual conditional distribution within the model class. The weights solve a least-squares problem subject to an adding-up constraint, yielding a closed-form estimator. We derive the asymptotic distribution of the counterfactual estimator, with DR estimation error and weight estimation error contributing at the same rate to the asymptotic variance. Moreover, we propose a supremum test for the null of no treatment effect, whose limit is the supremum of a Gaussian process. Simulations illustrate that conditioning on covariates can reveal effects being difficult to detect from the unconditional distribution alone. An application to the 1992 New Jersey minimum wage increase using CPS data finds effects concentrated in the minimum-wage corridor for low-education, low-experience workers.

We compare phase-only control with phase-and-amplitude control when designing shaped pulses using the GRAPE algorithm, and explain why phase-only control has significant advantages. Trotterisation can be used to simulate amplitude modulation with phase modulation, indicating that the two approaches are fundamentally equivalent. Pulses designed by either method can be interconverted, but phase-only optimization is faster and simpler. The resulting pulses can then be converted into phase-and-amplitude form for more robust implementation if desired.

High harmonic generation (HHG) is a sensitive probe for investigating electronic structures and dynamics of materials and a source for attosecond pulses. In particular, HHG with terahertz (THz) light can enable probing of nonlinear responses in correlated materials arising from low-energy many-body interactions. However, THz HHG studies have so far largely focused on topological materials and superconductors, leaving out other potential material systems which could also become efficient THz HHG sources. Here, we report THz third harmonic generation (THG) in rare-earth nickelates -- a prototype material for exploring the Mott insulator-metal transition and related technological applications. We find that the THG amplitude is highly sensitive to the strengths of electronic and magnetic phases of nickelates. In films with sharp phase-transitions, the local maximum and minimum in the temperature-dependent THG amplitude coincide with insulator-metal and magnetic transition temperatures, respectively. While in films with weaker transitions, these features shift toward lower temperatures or even monotonous THG enhancement is observed down to low temperatures. We developed a generalized theory for THz harmonic generation in negative charge-transfer insulators and outlined strategies to enhance the THz nonlinearities further. Our study broadens the scope of THz HHG studies and related applications to strongly correlated materials.

The structure and dynamics of neutron stars can be used to probe the physics of extreme matter at nuclear densities and beyond. Nucleonic matter up to ~2-3 times nuclear saturation density is well-studied by nuclear experiments and theoretical modelling. Matter beyond these densities may contain non-nucleonic degrees of freedom that determine the structure of the neutron star inner core and influence bulk observables like stellar radius. Neutron star radius is a key parameter for constraining the core equation of state, but is not a direct gravitational-wave observable during neutron star mergers. Here we show that, if nucleonic physics is well constrained at low densities, the frequency of the asteroseismic crust-core interface mode in a neutron star can be used to infer its radius to within 5-10%, in a way which is notably insensitive to the details of the inner core. This frequency can be measured through multimessenger coincident timing of resonant shattering flares, or direct observation of dynamical tidal resonance with next-generation gravitational-wave detectors. We show that improved constraints on low-density nucleonic physics by nuclear experimental and theoretical efforts will substantially improve such a radius measurement, leveraging low-density efforts for an improved understanding of physics at higher densities.

Strict Priority (SP) scheduling is widely used at switch egress to provide low-latency service to high-priority (HP) traffic. Existing deterministic and stochastic latency models typically account for scheduler behavior and packet transmission, but omit a common switch implementation detail: the transmit ring (TXR) between the scheduler and the physical port. Because the switch must prepare the next packet before the current transmission completes, packets already placed in the TXR can further delay HP packets. This changes both the worst-case delay and the per-hop delay distribution of HP packets. This paper identifies this modeling gap, extends standard SP latency models to include the TXR, and validates the revised model through measurements on multiple switches. It also provides a measurement method for estimating the TXR size, a parameter that is often not reported in switch datasheets. The resulting model provides a closer representation of switch behavior for systems that use SP scheduling and require either delay bounds or delay distributions.

Modulated circulant matrices form a special class of N-parametric circulant matrices, recently introduced in the literature, with a structured spectral decomposition based on a Vandermonde type basis. Motivated by this definition, in this work we define the Modulated Quantum Fourier Transform (MQFT), a quantum primitive tailored to this matrix family.

We present a spatially resolved analysis of the stellar populations in the inner kiloparsec of NGC 3884, 3C 293, and CGCG 012-070. Using near-infrared spectroscopy, we reconstruct their star formation histories (SFHs) by comparing the M13, XSL, and FSPS stellar population synthesis models. The stellar light is dominated by intermediate-age to old populations (t >= 1 Gyr) with super-solar metallicities (Z >= 1 Z_sun). All models clearly indicate recent star formation (rejuvenation) in these AGN hosts, with young to intermediate-age populations contributing significantly in the nuclear regions. The SFHs from M13 and XSL broadly agree in showing coexisting old and young components, whereas FSPS favours a larger fraction of very young (t < 50 Myr) stars. Moreover, XSL- and FSPS-based SFHs are generally more irregular and "bumpy," while M13 yields smoother, more continuous SFHs. In NGC 3884 and 3C 293, stars with 0.2 < t <= 0.7 Gyr form a ring-like structure around the nucleus. The nuclear spectra further require non-stellar components: a featureless power-law continuum (FC) and hot dust emission (HD). In 3C 293, the FC component appears in two spatially separated regions, possibly indicating a dual active galactic nucleus, though a heavily reddened starburst origin for the secondary component cannot be excluded. Nearly all fits show a central drop in stellar metallicity, consistent with inflow of metal-poor gas that fuels recent accretion and AGN activity. Radial profiles show that HD and FC contributions decrease with radius, while younger stellar populations become more prominent outward. Together, these results support a feeding-feedback scenario in which gas inflows trigger circumnuclear star formation and, via stellar mass loss, help sustain ongoing AGN activity. .

In this paper, we resolve the question of whether the Neumann problem for the parabolic PDE $-\partial_tu + \mathrm{div}(A\nabla u)=0$ on a Lipschitz cylinder $\mathcal O\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumption that the matrix $A$ is elliptic with bounded and measurable coefficients that satisfy a natural Carleson condition (a parabolic analog of the so-called DKP-condition). We prove that for any $1<p<\infty$ the Neumann problem is solvable under the assumption that both the Carleson norm of coefficients and the Lipschitz constant of the domain are sufficiently small (with dependence on $p$). The question of what happens in the "large Carleson norm/large Lipschitz constant" regime remains open, and even for elliptic PDEs this question has only been resolved in two dimensions. This paper complements results from our recent manuscript (by the same authors) in which the parabolic regularity problem has been fully resolved in both the small and large Carleson norm regime. Previously, the Dirichlet problem had been resolved under the same conditions by various authors.

Controlling product selectivity in plasmonic catalysis, particularly in CO2 reduction (CO2R), remains a central unsolved challenge with direct implications for light-driven fuel and chemical synthesis. Here, we deploy quantitative operando scanning photoelectrochemical microscopy (photo-SECM) to provide a direct demonstration that tuning photon energy switches CO2R selectivity through an electronically driven pathway. On plasmonic Au/p-GaN photocathodes, interband excitation (460-560 nm) drives selective CO production while intraband excitation (640-800 nm) favors H2 evolution. By maintaining constant absorbed power across wavelengths and confirming linear power dependence, we isolate the role of hot-carrier energy from photonic and photothermal contributions. Density functional theory calculations reveal that higher-energy interband excitation progressively increases the overlap between hot-electron-accessible states and the CO-producing intermediate, selectively promoting CO over formate, in excellent agreement with experiment. We further show that selectivity is geometrically gated by hot-carrier transport: sub-100 nm nanostructures sustain CO2R activity, while ~300 nm nanodisks suffer transport losses that suppress it, consistent with ab initio hot-carrier transport calculations. Together, these results establish photon energy, carrier transport, and nanostructure geometry as coupled design parameters for plasmonic CO2R selectivity, resolve a longstanding debate on the origin of plasmon-driven selectivity effects, and position photo-SECM as a broadly applicable operando platform for photo(electro)catalysis.

Inspired by the concept of a generalized materials genome, we introduce the notions of lattice gene and lattice genome for crystalline materials. A lattice gene is a compact representation of the local crystalline structure obtained by encoding the Kikuchi diffraction patterns with a variational autoencoder. We show that this representation satisfies key criteria for a materials gene: compactness, experimental accessibility, existence of a distance metric reflecting structural similarity, and sufficient information content for reconstructing the original diffraction patterns. The lattice genome is the spatially resolved collection of lattice genes across a representative area mapped by electron backscatter diffraction (EBSD), which captures mesoscale heterogeneity that ultimately controls properties. We demonstrate three applications of the lattice genome: (i) latent component maps that visualize grain-scale and intra-grain heterogeneities, (ii) domain segmentation based on distance and angle metrics in the latent space, and (iii) kernel and domain latent vector spreads that quantify intragranular heterogeneity as high-dimensional analogs of kernel average misorientation and grain orientation spread. All three tools are validated on microstructures of additively manufactured and wrought Ni-base superalloys in as-built and recrystallized conditions.

This paper investigates Polynomial Differential Variational Inequalities (PDVIs), a class of non-smooth dynamical systems in which an ordinary differential equation is coupled with a time-dependent variational inequality (VI) defined by polynomials. As a foundation for polynomial differential variational inequalities, we investigate the parametric polynomial variational inequality and establish that, under mild assumptions, its parameter space admits a stratification into finitely many disjoint semi-algebraic regions, each corresponding to a qualitatively distinct solution structure. Furthermore, we establish the existence of maximal regular solutions to the PDVI for almost every initial condition in the parametric feasible set, where each solution has finitely many switches and evolves according to continuous semi-algebraic selection laws between switching times. Leveraging the structured partition of the parameter space, in which region boundaries correspond to discontinuities in the solution map of the parametric VI, we propose the structure-aware SOS-PDVIRK4 algorithm to handle solution multiplicity and structural transitions. This method integrates a fourth-order Runge--Kutta integrator with the Moment--SOS hierarchy and features a novel hybrid strategy that is explicitly guided by the underlying parameter space geometry. The efficacy of our structure-aware framework is demonstrated through numerical experiments on a constrained cyber-physical control system. Our numerical experiments demonstrate that, from identical initial states but different initial controls, trajectories can diverge significantly, revealing the discontinuous structure of the solution map of the parametric polynomial VI. The experiments also include numerical convergence studies and highlight the potential of our algorithm to explore the long-term behavior of PDVI systems.

Ray tracing enables 3D Gaussian fields to serve as a representation for physically based light transport. Faithful inverse rendering requires forward rendering and backward optimization to be defined within a consistent light-transport pipeline. Existing inverse rendering methods estimate G-buffers via splatting and optimize materials in screen space, tying the recovered properties to a rasterization-based pipeline. This pipeline mismatch, together with simplified rendering equations that neglect indirect illumination, often leads to inconsistent shading, visible artifacts, and inaccurate material-lighting estimation under path-traced rendering. Therefore, we propose a splatting-free path-traced inverse rendering framework for 3D Gaussian fields, where forward light transport and backward gradient propagation are defined within a unified ray-tracing pipeline. Our key idea is to define a path-space equivalent interaction model for overlapping Gaussian primitives, under which Monte-Carlo-based path tracing is unbiased for the induced light-transport integral, while pathwise gradients are replayed over the same ray-traced interactions rather than splatting-derived screen-space buffers. The framework optimizes materials and a compact Spherical-Gaussian environment under the full rendering equation with ray-traced visibility and multi-bounce light transport. Extensive experiments demonstrate competitive material inversion and improved path-traced rendering quality, producing more plausible shadows, reflections, and relighting results under global illumination.

The recent detection of Galactic neutrinos by the IceCube Observatory constitutes a remarkable achievement for neutrino astrophysics. By means of model dependent analyses based on spatial and spectral templates, a purely diffuse neutrino flux was measured in which no individual source was resolved. We present here a novel theoretical computation about the expected neutrino emission from the Galactic Plane that, differently from previous models, includes both the contributions from cosmic-ray (CR) sea and hadronic sources, represented by star clusters and supernova remnants therein, which are to date believed to be the dominant sources of Galactic CR protons. For the modelling of sources, diffusive particle acceleration is considered at both the collective wind termination shock blown by member stars and at the supernova shocks. The predicted flux of very-high energy neutrinos from individual star clusters is found to be marginally detectable even by cubic kilometer scale detectors, such that their cumulative contribution is expected to appear as an unresolved diffuse component, on top of that guaranteed by the CR sea interacting with the gas along the Plane. The overall neutrino production of the Milky Way star cluster population is computed, based on multiple synthetic realizations of the cluster population reproducing local stellar observations. As a result, we obtain novel neutrino template maps and provide them to the community, to be tested in future neutrino analyses in order to constrain the role of star clusters for extreme CR acceleration and neutrino production. The normalization of our models is consistent with the IceCube best-fit of existing Galactic templates, suggesting that the unresolved contribution from cluster emission may be non-negligible.

The river-crossing problem, also known as Zermelo's navigation problem, is a classic example of an optimization problem with practical relevance and a scalable degree of complexity. It asks for the optimal trajectory of a vessel moving through a water flow field and provides a setting in which physics, variational methods, and optimization are naturally intertwined. We state a version of Zermelo's problem and then solve it as formulate it as an adiabatic quantum-computing problem using quantum trits, or qutrits for short. The construction includes a penalty term that enforces the prescribed boundary conditions and an exploration term that allows the system to move through intermediate configurations toward the optimal feasible path. In the adiabatic description, the evolution proceeds through a sequence of avoided crossings, so that the resulting fidelity can be estimated using the Landau-Zener formula. Remarkably, the regime in which this approximation is valid also provides a deterministic way to identify the correct solution with computational effort that scales only quadratically with the problem size. Thus, a quantum formulation initially motivated by the apparent exponential complexity of the problem reveals an underlying classical structure that can be exploited efficiently. Our approach also provides a pedagogical illustration of how a real-world optimization problem can be cast into a quantum-annealing framework and then analyzed using the Schrödinger equation, avoided crossings, and Landau-Zener theory.

Covering codes in finite Hamming spaces ask for small sets of words whose Hamming balls cover the whole space. This paper presents a Lean 4 formalization of the elementary theory of q-ary covering codes, centered on certificate predicates for upper bounds, lower bounds, and exact covering numbers $K_q(n,r)$. The formalization proves the q-ary Hamming-ball volume formula, the sphere-covering lower bound, elementary exact cases, product and relation rules, and selected small exact certificates. It also demonstrates an end-to-end workflow for checking explicit upper bounds transcribed from van Laarhoven et al. (1989). The accompanying database is proof-carrying: stored bounds have traces that replay to Lean proofs of the corresponding upper- or lower-bound predicates. The contribution is not new record bounds or a reproduction of known tables, but a reusable, auditable foundation for machine-checked covering-code certificates.

The controlled generation of quantum entanglement from separable states remains a central challenge in quantum information science. Here, we investigate entanglement generation using two related control paradigms: coherent path superposition of local unitary operations and stochastic implementations of Pauli channels under coherent control. We show that entangled states belonging to the Bell, GHZ and W classes, can be deterministically generated from fully separable inputs by coherently superposing alternative sets of local unitary transformations. Conditions on the local operators for entanglement generation are derived, and the resulting states are shown to be locally unitary equivalent to standard multipartite entangled states. We further extend the analysis to noisy scenarios, where separable mixed states evolve through pairs of Pauli channels arranged in path-superposition and indefinite causal order configurations. Closed-form expressions for the output states are obtained, and entanglement is quantified using concurrence. By exploring representative channel families across their parameter space, we identify regimes where stochastic entanglement emerges, determine the associated success probabilities, and characterize trade-offs between entanglement and purity.

The deep integration of Artificial Intelligence (AI) into elementary mathematics education necessitates a conceptual tool capable of explaining students' cognitive transition from disciplinary knowledge to AI understanding. This study proposes a novel core concept, "Awareness of Technological Isomorphism, " defined as a student's metacognitive realization that their own mathematical cognitive operations (e.g., observing trends, inducing patterns, and making predictions) share an underlying logical structure with AI technical operations (e.g., pattern recognition and predictive modeling). This awareness, in turn, facilitates cognitive transfer from disciplinary mathematics to AI comprehension. Underpinned by transfer learning and metacognitive theories, this study clarifies the distinct essence of this concept from traditional "computational thinking." We demonstrate the explanatory power of this framework in two ways: elucidating the mechanism of students' cognitive leap from mathematics to AI, and guiding instructors to identify "isomorphic interfaces" within disciplinary curricula. On this basis, a three-stage pedagogical pathway--spanning "Perception, Comprehension, and Creation"--is constructed alongside a corresponding evaluation rubric. This framework is empirically validated through a case study based on the "Compound Line Graph" lesson from a fifth-grade mathematics textbook in China, offering a highly replicable operational framework for the deep convergence of disciplinary instruction and AI literacy education.

Here we present ARTGEL, an actively regulated-temperature gel electrophoresis platform designed for long-duration experiments under independently controlled thermal and electrical conditions. ARTGEL combines thermoelectric regulation of the gel temperature, a large heated and circulated buffer reservoir, and an automated electrode-wiping mechanism that stabilizes the voltage across the gel during runs exceeding 24 h. The platform was developed to address a limitation of conventional electrophoretic mobility shift assays, which are commonly used to analyze reversible biomolecular association but usually aim to suppress reaction during electrophoresis by dilution, competitors, or reduced temperature so that the gel reports a pre-equilibrated bulk solution. For temperature-sensitive systems, these strategies can alter the chemical state during loading and migration and obscure whether the measured band pattern reflects the original bulk sample or a re-equilibrated state inside the porous gel. Rather than attempting to quench reactions, ARTGEL enables electrophoresis to be performed at the same temperature as complementary bulk measurements, so that reversible association can be quantified directly in the gel and compared with matched measurements in solution. Using DNA origami assemblies, we show that ARTGEL preserves distinct temperature-dependent association states, resolves reaction-dependent distortions of migrating bands, and supports extraction of in-gel kinetic and thermodynamic parameters from reaction-diffusion-advection modeling.

Semileptonic heavy-baryon decays provide a sensitive probe of the helicity structure underlying possible lepton-flavor universality violation in $b\to c\,τ\barν_τ$ transitions. We perform an effective-field-theory analysis of $Λ_b\toΛ_cτ\barν_τ$ and related baryonic modes using lattice-QCD helicity form factors with full covariance propagation. Propagating meson-compatible EFT solutions into the baryonic observable space$(R_{Λ_c},\,P_τ,\,A_{\rm FB})$, we show that tau polarization provides the leading source of sensitivity for lifting EFT degeneracies that remain unresolved in current measurements of $R(D)$ and $R(D^\ast)$. Vector-like and tensor-like solutions remain clustered near theStandard-Model prediction, whereas scalar-containing directions produce large polarization displacements and characteristic low-$q^2$ deformations of the normalized differential spectrum. A covariance-aware analysis demonstrates that baryonic polarization and differential observables provide complementary and independent information on the Lorentz structure of semileptonic new physics. $P_τ(Λ_b\toΛ_cτ\barν_τ)$ and the low-$q^2$ spectrum as particularly powerful probes for future tests of semitauonic flavor anomalies at LHCb and future flavor facilities.

Movies are long-form audiovisual works, yet recommender benchmarks often rely on trailers, thumbnails, or metadata. These sources differ in semantics and scalability: full movies preserve consumption-level evidence, trailers concentrate promotional highlights, and thumbnails provide sparse but catalog-scale visual signals. We present Popcorn, a configurable benchmark for visual evidence in multimodal movie recommendation, combining title-aligned full-movie/trailer embeddings with MovieLens-linked thumbnail features encoded by modern visual and vision-language models. Popcorn standardizes modality assembly, fusion, splitting, evaluation, and LLM-augmented metadata through a single configuration contract. Experiments show that thumbnail VLMs provide strong, scalable item-side evidence, while controlled trailer/full-movie comparisons show that visual evidence sources are not interchangeable: the choice of source and fusion strategy affects ranking accuracy, coverage, diversity, and calibration. The framework is available at https://github.com/RecSys-lab/Popcorn.

Bayesian inverse problems constrained by state equations are often sampled in a full parameter-state space by penalising the residual, rather than in a reduced space where the state is eliminated. We show that these formulations are not automatically equivalent as posterior measures. For finite-dimensional discretisations of equality-constrained inverse problems, assume the state equation \(c(θ,u)=0\) has a unique solution \(u=G(θ)\) and nonsingular state Jacobian \(\D_u c\). The reduced posterior, its graph lift, and the zero-noise residual posterior are then distinct. A local change of variables shows that an uncorrected Gaussian residual penalty converges, after marginalisation over \(u\), to the reduced density multiplied by \(\abs{\det \D_u c(θ,G(θ))}^{-1}\). Thus algebraically equivalent residuals can define the same feasible set but different limiting posteriors. We derive determinant corrections for unweighted, weighted, and rescaled residual penalties that have the graph-lifted reduced posterior as their hard-constraint limit. The result separates feasibility from posterior calibration: driving the residual to zero is not sufficient for exact sampling of the graph-lifted reduced posterior unless the sampling or correction step targets the corresponding corrected density.

Provenance trees are append-only directed acyclic graphs of artifact registrations anchored on a public blockchain, recently introduced as the data substrate of operator-gated provenance infrastructure. Their defining data-structural pattern is a parent-hash directed acyclic graph (PHDAG), in which each append performs a constant number of storage writes to previously-untouched slots. This pattern has not previously been isolated as a standalone primitive, formally bounded with explicit constants, or benchmarked against the standard alternative, the incremental Merkle tree (IMT). We formalize PHDAG append as O(1) in gas cost, independent of registry size and tree depth, and develop a stochastic cost model for IMT in which per-insert cost is a random variable over the leaf index, deriving closed-form expressions for its mean and variance. We validate both analyses empirically on Base Sepolia across tree depths 1 to 25. PHDAG is observed to be depth-invariant at 76,276 gas (standard deviation about 6 gas), while IMT cost grows linearly with depth. The crossover below which IMT is cheaper falls far beneath the depths of every production registry surveyed. We further establish trustless registry reconstruction from public event logs in linear time with no off-chain dependency.

We revisit quantum field theory in curved spacetime (QFTCS) as a semi-classical framework for quantum matter on classical geometries, emphasizing its limitations, including vacuum ambiguity and background dependence. We briefly review major approaches to quantum gravity (QG), including Loop Quantum Gravity (LQG), string theory, and asymptotic safety, highlighting their conceptual challenges. Motivated by these issues, we outline a teleparallel framework based on coframe and spin-connection variables, where gravity is encoded in torsion rather than curvature. This framework naturally incorporates local Lorentz symmetry and fermionic couplings while displaying a gauge-like structure. We argue that the coframe/spin-connection pair provides an alternative and geometrically refined description of gravitational variables, which may serve as a useful starting point for future investigations of QG. The purpose of this work is not to provide a complete quantization of teleparallel gravity but to identify the geometric and conceptual ingredients that such a formulation would require.

We study the distribution of rational points in $\mathbb{R}^n$, with denominators restricted to the interval $[Q-Δ, Q]$, and $Q,Δ\to\infty$ such that $Δ/Q\to 0$. Previous results in the literature, due to Hall and others, were limited to Farey sequences, where the window size $Δ$ is of the same order as $Q$. We prove the convergence of fine-scale statistics in a range of scaling limits and express the limit laws in terms of natural probability measures on the space of affine lattices. The key technical ingredient of our approach is an equidistribution theorem for slowly expanding horospheres, with some new exotic limit measures. Our techniques furthermore allow us to answer a recent question by Anderson, Boca, Cobeli and Zaharescu concerning the directional statistics of lattice points.

The model of interactive oracle proofs (IOP) generalizes the notion of probabilistically checkable proof (PCP), in which a static proof is verified probabilistically by querying a small number of bits, to the interactive setting: a polynomial-time verifier interacts with an unbounded prover, but is restricted to only reading a small number of bits, in total, from the messages sent by the prover. IOPs provide a relaxed setting in which to study local probabilistic verification. They have proved instrumental in devising efficient methods for verification through subsequent compilation into non-interactive or succinct protocols. We study a quantum analogue of interactive oracle proofs (qIOP) in which the verifier and communication are both allowed to be quantum; yet the verifier is restricted to perform measurements only on a small number of qubits received from the prover. Our main result is a qIOP for any language in QMA, in which the total communication is polynomial but the verifier only reads a polylogarithmic number of qubits in total. The protocol has completeness parameter exponentially close to $1$ and soundness bounded away from $1$ by a constant. In the absence of a quantum PCP theorem, this provides the first information-theoretically sound local and robust characterization of QMA, albeit interactive. Our protocol combines the use of a quantum locally testable code (LTC) with classical techniques, notably probabilistically checkable proofs of proximity (PCPP). We avoid the necessity for complex multi-qubit tests employed in other settings by leveraging the local indistinguishability property of the quantum LTC.