Primordial non-Gaussianity (PNG) is a powerful probe of the origin of cosmic structure. Stage-IV surveys like \Euclid will measure galaxy $2$- and $3$-point clustering at high signal-to-noise, whose exploitation requires robust joint analysis. We prepare for Euclid's spectroscopic sample by validating a redshift-space power-spectrum and bispectrum pipeline (one-loop $P_\ell$, tree-level $B_\ell$) on Euclid-like mocks from Abacus-PNG $N$-body simulations with Gaussian and local-PNG initial conditions, using a halo occupation distribution (HOD) tuned to Euclid Flagship 2. We stress-test analysis choices -- PNG-bias parametrisation, priors, and scale cuts -- and perform null tests without PNG. In a `prior-agnostic setup', detection of the dominant PNG term $\propto f_{\rm NL} \, b_ϕ$ in single redshift bins is difficult; nevertheless, the bispectrum provides constraints on other PNG combinations that partially lift degeneracies. We propose a physically motivated prior on $b_ϕ$ that yields unbiased $f_{\rm NL}$ while accounting for theory uncertainty, and determine scale cuts that give unbiased $Λ$CDM and $f_{\rm NL}$. With $V_{\rm eff}=16\,h^{-3}\,{\rm Gpc}^3$ across four snapshots ($0.8\le z\le1.7$), our likelihood analyses recover $<1σ$ bias in $f_{\rm NL}$ and $Λ$CDM. At fixed cuts, $B_\ell$ alone reduces $σ({f_{\rm NL}})$ by $\sim29$--$46\%$ relative to $P_\ell$, and joint power spectrum-bispectrum analysis tightens a further $\sim8$--$13\%$; the cumulative gain from $z=0.8$ to $1.7$ is $\sim2.3$ for the joint case. The bispectrum quadrupole is key. Our strongest results are at $z=1.7$: $1.9σ$ for $f_{\rm NL} \, b_ϕ$ (prior-agnostic) and $2.35σ$ for $f_{\rm NL}$ (prior-based). Joint analyses thus offer strong prospects for testing multi-field inflation, pending end-to-end validation in the full Euclid geometry with observational systematics.

Verifying LLM-generated systems code is hard: bugs are prevalent, formal specifications are missing, and safety contracts are encoded implicitly at call sites rather than enforced at function boundaries. We propose agentic model checking, a paradigm that couples LLM agents with a bounded model checking backend under the principle agents propose, solvers verify: agents handle tasks requiring semantic judgment (spec inference, check selection, counterexample classification, refinement proposal) while BMC discharges every soundness-relevant decision. The paradigm rests on three commitments. Specifications are inferred top-down from caller context in a restricted DSL that translates deterministically into the backend's assume/assert primitives, with optional functional-correctness clauses lifting verification from panic-freeness to behavioural faithfulness. Verification is compositional: each function is checked in isolation against its spec with callees replaced by postcondition-constrained stubs, so per-query cost scales with a single function's state space and refinements propagate automatically to callers. Counterexamples are not bug reports: they pass through a validation pipeline (reachability, callee feasibility, dynamic replay, realism audit) that distinguishes active in-tree crashes from latent public-API failures, while modelling artifacts drive a refinement loop rather than being suppressed. We instantiate the approach in BMC-Agent and evaluate it on LLM-generated kernel and compiler code in C and Rust alongside mature OSS-Fuzz-hardened libraries, confirming real defects, producing bounded clean verifications on heavily-fuzzed surfaces, and establishing functional equivalence on selected algorithmic functions.

Transparent conducting oxides near their epsilon-near-zero frequency exhibit near-unity ultrafast modulations of the refractive index which have enabled the field of time-varying metamaterials, yet the underlying carrier dynamics at high driving fluences remain poorly understood. Here, we report ultrafast modulations in the reflectivity and transmissivity of indium tin oxide, and a non-monotonic oscillatory behavior. This is especially evident in the time evolution of the complex Fresnel coefficients retrieved directly from pump-probe spectrograms using a optical gating technique, GRUMPY FROG. The dynamics of the retrieved plasma frequency and damping coefficient are well captured by an extended two-temperature model incorporating a competing nonlinear interband process: at high fluences, Auger-type scattering of hot conduction electrons promotes valence band carriers, increasing the plasma frequency while accelerating hot-electron cooling and raising the damping coefficient. These results clarify the origin of anomalous high-fluence dynamics in indium tin oxide and identify a fluence-tuneable modulation dynamic with direct implications for ultrafast refractive index engineering in time-varying photonic devices and optical switching

Extreme ultraviolet (EUV) lithography is the cornerstone of the fabrication of advanced integrated circuits at the 7-nm node and beyond, but its reliance on multi-element reflective projection optics makes it inaccessible for small-scale research and prototyping. EUV interference lithography (EUV-IL) provides a lensless alternative but is intrinsically restricted to periodic structures. Here we demonstrate EUV holographic lithography (EUV-HL) as a lensless route to arbitrary, non-periodic, curvilinear patterning at the EUV wavelength of 13.5 nm. We introduce an inverse-design framework for computer-generated holograms that captures the dominant physical effects of EUV mask diffraction within a shift-invariant convolution model that is tractable for full mask layouts. Using this framework, we design and fabricate transmissive holographic masks by direct-write electron-beam lithography in hydrogen silsesquioxane, expose them with synchrotron-generated EUV radiation, and print target layouts with critical dimensions down to 40 nm, nearly an order of magnitude finer than the previous state of the art in EUV-HL. The demonstrated combination of sub-50 nm resolution, curvilinear design freedom, and a lensless optical setup establishes EUV-HL as a uniquely flexible tool for nanostructure prototyping at EUV wavelengths, and provides a natural pathway to non-periodic pattern prototyping at beyond-EUV (BEUV) wavelengths, which is currently inaccessible to interference-based methods.

When discretizing symmetric stress tensors in variational problems arising in continuum mechanics, one has to choose how to enforce the symmetry of the stress tensor: (i) strongly by requiring the discrete tensors to be pointwise symmetric or (ii) weakly by introducing a Lagrange multiplier. For $H(\mathrm{div})$-conforming finite element discretizations of Hellinger--Reissner elasticity and velocity--stress formulations of incompressible flow, where symmetry of the Cauchy stress tensor is tied to the conservation of angular momentum, we show that this choice may substantially impact the accuracy of the numerical scheme. Through a series of benchmark problems featuring anisotropic constitutive laws inspired by fiber reinforced material, liquid crystal polymer networks, and polar fluids, we show that schemes enforcing symmetry weakly can yield arbitrarily poor stress approximations -- even for zero-stress configurations. However, schemes enforcing symmetry strongly deliver accurate stress approximations independently of the constitutive law, a property we term material robustness. We present a unifying theory that rigorously explains this behavior.

We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities of a general version of the game are investigated via conjugacy relations between Gamma and Poisson distributions, as well as between negative multinomial and inverted Dirichlet distributions. We show a monotonicity property of the regularized beta function, which implies a monotonicity property of the winning probability. Furthermore, the asymptotic behavior of the game for one or several parameters of the game tending to infinity is analyzed, as well as the probability of being last in the game.

Quasiperiodic systems are an intermediate class of systems between periodic crystals and disordered systems, famously exhibiting metal-insulator transitions (MITs) even in one dimension. While their transport properties have been studied extensively, a systematic analysis of the finite-frequency optical conductivity near the critical point has been lacking. In this work, we carry out a detailed study of the optical conductivity in the paradigmatic Aubry-André model. We find that the zero-temperature low-frequency optical signal is strongly restructured by the quasiperiodic potential, exhibiting an optical gap that closes discontinuously as the system approaches the MIT. Most strikingly, we uncover a mechanism for a strong enhancement of the low-frequency finite temperature optical conductivity at certain resonant frequencies. This enhancement stems from the thermal activation of Pauli-blocked transitions between strongly resonant van Hove singularities. This mechanism provides new insight into finite-frequency transport in quasiperiodic systems and a new pathway for manipulating optical properties near a localization transition. Furthermore, our findings establish the optical response as a powerful, experimentally accessible tool for probing non-trivial quasiperiodicity effects.

We study cosmological collider (CC) signatures generated by right-handed neutrino loops in the setup of inflation combined with neutrino seesaw mechanism. We formulate the inflaton interaction with the right-handed neutrino through a unique dimension-5 operator respecting shift symmetry, which induces an effective chemical potential in the slow-roll background, leading to helicity-dependent right-handed-neutrino production and enhancing the CC signatures. The right-handed neutrino is described by two-component Weyl spinor with Majorana mass term. Using the Schwinger-Keldysh (SK) formalism, we derive a set of seed integrals for fermion propagators of the right-handed Majorana neutrino. With these we compute the factorized nonlocal contributions to the three-point inflaton correlator generated by the right-handed-neutrino triangle loop. We show that the chemical potential can substantially soften the heavy-mass Boltzmann suppression and amplify the oscillatory non-Gaussianity signatures associated with the dominant helicity mode. These provide a systematic framework for analyzing the fermion loop signatures in the cosmological collider physics and demonstrate that the heavy right-handed neutrinos associated with seesaw mechanism may leave observable imprints in the primordial non-Gaussianities.

We introduce the data driven extreme value distribution (DDEVD) estimator, a kernel-based method for estimating extreme value distributions from data. We derive its mean integrated squared error (MISE) in detail, use it to compute the optimal bandwidth and establish stability conditions for the bandwidth optimization procedure.

There is a growing consensus that the exceptional optoelectronic properties of metal halide perovskites (MHPs) are largely due to the peculiar interplay between the inorganic cage lattice, composed of a labile network of corner-sharing metal halide octahedra, and the A-site cationic sublattice. This interaction significantly affects the vibrational spectrum of MHPs (phonon frequencies, linewidths, and lifetimes), resulting from the effects of lattice potential anharmonicity and/or static/dynamic disorder. Raman scattering is a suitable technique to probe phonon interactions in solids, allowing for the in-situ characterization of chemical environments, revealing the nature of lattice vibrations. In this perspective, the available experimental evidence of the aforementioned interplay will be reviewed with special emphasis on understanding Raman signatures depending on whether the coupling is principally mediated by hydrogen bonding or steric hindrance. The controversy about the origin of a strong Raman background, steeply rising towards zero Raman shift and called central peak, will be specifically addressed. This background signal, which is typically observed in the temperature range of stability of cubic and tetragonal phases when the A-site cation dynamics unfold, will be shown to be mostly due to disorder-induced second-order acoustic-phonon Raman scattering. This interpretation receives support from other semiconductor systems with nanoscale structural disorder, where the central Raman peak arises either from the vertical misalignment of Ge quantum dots in multi-stack heterostructures or from the interface roughness exhibited by short-period GaAs/AlAs superlattices. In this way, a unifying picture of phonon interactions in MHPs and how they impact different Raman processes is provided, which is key to interpreting their Raman spectra.

We prove a Serre type vanishing property for the twisted primitive cohomology of a symplectic manifold. It is based on Tseng and Zhou's vanishing property under the symplectic flatness. These vanishing properties emphasizes the necessity of the symplectic flatness when generalizing certain results from the sheaf cohomology in complex geometry to the primitive cohomology in symplectic geometry.

Institutional crossing platforms face a hidden-information problem: investors value trades as portfolios, but liquidity discovery is typically organized around individual securities. We model portfolio crossing as limited-communication preference elicitation over signed portfolio trades. The platform first uses price-directed demand queries to search the portfolio space and then verifies selected packages through value queries; an incumbent verification query records the demand-discovered allocation before further exploration. Final allocations are chosen from elicited reports, so the learning model guides queries but does not determine welfare. The analysis shows why search and verification are complementary. Demand queries locate high-value regions of a nonseparable portfolio space, but they provide only conservative welfare evidence unless selected packages are verified. Value queries provide exact welfare comparisons, but they are ineffective when applied to poorly targeted packages. Market-calibrated experiments using equity panels from the United States, Korea, Japan, and Germany show that demand-only and value-only designs recover only about half of full-information welfare under a limited query budget, whereas the hybrid procedure recovers 88\% and approaches 95\% as communication expands. We then compare exact security-level packages with factor-completed basket packages within the same allocation rule. Security-level packages are the unadjusted-efficiency mode when exact-securities disclosure is inexpensive. Factor-completed baskets become preferable when pretrade message informativeness is costly. The results characterize portfolio crossing as a selective verification problem and identify disclosure-sensitive package representation as a core design choice for hidden liquidity platforms.

Modern experimental designs often face the so-called treatment cardinality constraint, which is the constraint on the number of included factors in each treatment. Experiments with such constraints are commonly encountered in engineering simulation, AI system tuning, and large-scale system verification. This calls for the development of adequate designs to enable statistical efficiency for modeling and analysis within feasible constraints. In this work, we study two-level designs under this $k$-treatment cardinality constraint (TCARD), where the design matrix $\mathbf{X} \in \{0,1\}^{n \times p}$ has constant row sums equal to $k$. Although TCARDs are closely related to balanced incomplete block designs (BIBDs), exact BIBD structure is unavailable for many practical $(n,p,k)$ combinations. This leads to the notion of nearly balanced TCARDs, which we prove minimize the first two components of the generalized word-length pattern. We also show that good projection behavior in this setting is governed by two count-based regularities: balanced factor replications and uniform pairwise concurrences. Motivated by this characterization, we then propose the Balanced Concurrence Deviation ($Φ_{\mathrm{BCD}}$), a model-free objective that jointly penalizes replication imbalance and concurrence dispersion. We further show that this criterion is closely connected to classical optimality principles, including $(M,S)$-optimality, centered $\mathrm{UE}(s^2)$ criterion, and Bayesian $D$-optimality. To construct designs minimizing $Φ_{\mathrm{BCD}}$, we develop a coordinate-exchange (CE) algorithm with efficient incremental updates, together with a simulation-based procedure for calibrating the criterion weights to the intended downstream task. Numerical experiments confirm that the proposed method compares favorably with existing alternatives across a range of problem sizes and constraint strengths.

Theoretical models predict that subgiants within a narrow mass regime can retain detectable lithium enrichment signatures from planetary engulfment. We test this prediction using TOI-5882, selected because it occupies this favorable subgiant parameter space and hosts a massive brown dwarf ($22 \, M_{ \rm J}$, $P=7.1 \,{\rm d}$) companion capable of dynamically perturbing inner planets. We investigate whether: (1) TOI-5882 exhibits lithium enhancement among similar subgiants, (2) planetary material would be deposited in the convective zone, and (3) the required engulfed mass lies within a plausible range for planetary engulfment. Using spectra from the Tillinghast Reflector Echelle Spectrograph, we measured a Li I equivalent width of $75.39 \pm 3.58$ mA and an abundance of A(Li) $=2.49 \pm 0.12$ dex. Comparing these values to a control sample of 61 subgiants from the GALactic Archaeology with HERMES (GALAH) DR4 survey, we find that TOI-5882 ranks in the 98.4th percentile in both metrics, confirming significant lithium enrichment. We evaluate the engulfment scenario by modeling convective zone deposition and estimating the mass required to reproduce the observed enhancement relative to the control sample. We perform an estimate of the engulfed planetary mass incorporating CI chondritic Li abundances, as planets formed via core accretion are enriched in heavy elements and lithium partitions with these metals. This yields a required engulfed mass of $9$-$95\,M_\oplus$--an order of magnitude lower than the $5.6 \, M_{\rm J}$ implied by proto-solar assumptions. TOI-5882's lithium excess can plausibly result from the ingestion of a super-Earth to Neptune-mass planet, motivating further studies to test this scenario.

This paper introduces a systematic method for designing robust linear controllers using output feedback in the presence of operational constraints. The design uses Nagumo's Theorem and the Comparison Lemma to guarantee constraint satisfaction, while incorporating min-norm optimal control principles inspired by Control Barrier Functions. The resulting controller is a continuous piecewise-linear output feedback policy that preserves the closed-loop system's analyzability using linear systems theory. Due to the linear control design, multi-input multi-output (MIMO) robustness margins can be derived with and without active operational constraints. This paper shows that operational constraints on the system's state can be satisfied using an observer-based output feedback control design. Through flight control trade studies, we demonstrate the practical relevance of the framework in safety-critical aircraft control applications.

Distribution networks are transitioning from passive to active systems due to the growing integration of distributed energy resources (DERs). Peer to Peer (P2P) energy trading has emerged as a viable framework that enables local energy exchange among participants, represented here as aggregated microgrids (MGs). Incorporating network constraints is essential to ensure that P2P transactions remain physically feasible and consistent with grid's operating limits. However, existing P2P frameworks still lack advanced predictive mechanisms that allow prosumers to anticipate network feasibility or the distribution system operator (DSO) response during trade formulation. This paper proposes a learning augmented P2P and DSO interface that predicts the DSOs response to the proposed P2P trades, allowing prosumers to self-assess and refine their trading decisions. A supervised transformer based regression model is trained to enable MGs to locally predict the DSOs response without sharing their proposed trades, thereby reducing transaction overhead, alleviating DSO burden, and preserving information privacy. The proposed framework is validated on the modified IEEE 33 bus distribution power system with interconnected microgrids. Case studies are presented to validate the effectiveness of the proposed model in terms of market efficiency, trade acceptance and computational burden.

We investigate a one dimensional flux limited Keller Segel system (FLKS) in which the chemical decay rate is allowed to vary explicitly in time, a feature motivated by enzymatic regulation and environmental variability in chemotactic signalling. Treating the decay rate as an arbitrary function, we carry out a systematic Lie symmetry analysis of the resulting PDE system and employ equivalence transformations to perform a complete group classification, we identify the kernel symmetry algebra admitted for arbitrary decay functions and determine three distinguished cases that extend the symmetry algebra constant decay rates, inverse time (power law) decay, and exponential decay. For each case, we construct an optimal system of subalgebras and derive the corresponding similarity reductions. Finally, we find some explicit solutions for our FLKS model. Our results provide a rigorous mathematical foundation for understanding which temporal decay patterns admit similarity reductions, thereby enabling analytical progress on flux limited chemotaxis models with realistic time varying degradation mechanisms.

We develop a physics-facing version of the persistence/transition-variety framework for scalar-field cosmology, tailored to inflationary dynamics. The guiding idea is that observationally viable inflationary models are often best understood not as single asymptotic phases but as concatenations of persistent regimes separated by universal transition episodes. In this picture, slow roll appears as a robust persistent balance, ultra-slow roll as a bottleneck passage near a nonhyperbolic organising set, and oscillatory post-inflationary behaviour as a recurrent exit sector. Using the exponential model as a reference regime atlas and the massive case as a dynamical realisation of slope drift, we show how such histories may be organised and read geometrically. The resulting framework makes explicit that the relevant regime transitions are organised precisely where hyperbolicity is lost or the spectrum crosses the imaginary axis, and are therefore invisible to a purely hyperbolic or asymptotic treatment.

Model Context Protocol (MCP) has emerged as a standard interface for connecting LLM agents to external tools. Because MCP servers expose privileged operations such as shell execution, network access, and file-system manipulation to agent-driven invocation, implementation flaws in tool handlers can create a direct path from natural-language input to security-sensitive sinks, potentially granting attackers remote code execution or full system compromise. Existing approaches either produce unconfirmed static alerts without dynamic validation, or rely on fixed template libraries that lack code-level guidance and fail to trigger vulnerabilities requiring specific parameter shapes or multi-step taint paths. In this paper, we present VIPER-MCP, the first end-to-end automated vulnerability auditing framework for MCP servers that not only detects taint-style vulnerabilities but also dynamically confirms their exploitability by producing concrete proof-of-concept prompts. VIPER-MCP introduces two novel techniques: (1) an anchor-query pass in a two-pass static analysis strategy that augments standard taint alerts with function-level structural context, resolving file-level static artifacts to specific MCP tool handlers and producing vulnerability-anchored call chains; and (2) a feedback-driven prompt evolution mechanism that employs dual-mutator scheduling that independently corrects tool-selection drift and deepens parameter penetration, together with fitness-scored seed selection to iteratively refine natural-language prompts toward vulnerable sinks. In a large-scale scan of 39,884 real-world open-source MCP server repositories, VIPER-MCP discovered 106 0-day vulnerabilities, all of which were confirmed through end-to-end exploit traces, with 67 CVE IDs assigned to date. We responsibly disclosed all confirmed findings to the affected developers and coordinated CVE assignment where applicable.

Subpicosecond laser excitation of ferromagnetic metals induces strongly nonequilibrium dynamics involving scattering and transport of electrons, phonons, and magnons. Widely used theoretical approaches, such as the three-temperature model and diffusion equations, are ill-suited to capture these processes on ultrafast timescales. Here, we present an ab initio-parameterized microscopic framework that incorporates nonthermal magnon scattering and transport via the quantum Boltzmann equation. We apply this approach to simulate ultrafast laser-induced demagnetization in bcc Fe films. The model predicts an ultrafast spin Seebeck effect, characterized by a strong burst of fast-moving magnonic spin current reaching technologically relevant amplitudes. Furthermore, we identify a superdiffusive transport regime: a crossover from initially ballistic magnon transport to a diffusive regime at later times. To connect our theoretical predictions to experimentally accessible observables, we calculate the magneto-optical Kerr angles resulting from the predicted depth-resolved magnetization profiles. Our framework provides a route to describe ultrafast nonthermal magnon transport beyond diffusive models and will aid in the design and interpretation of time-resolved spin-transport experiments.

Summaries of craters on terrestrial bodies, such as the number and size distribution, are essential for understanding the history of the Solar System. Identifying craters, however, has not been automated and thus relies on expert crater-counters marking static images. Robbins et al. (2014) (hereafter R14) showed that, contrary to previously held assumptions, there exists large variability across expert crater-counters' identified crater lists. How best to combine identified crater lists across multiple experts for the purposes of learning about the Solar System is an open and consequential question. R14 combined identified crater lists via clustering through a modification of the popular DBSCAN clustering method. Their approach did not, however, make use of all the constraining information available nor did it provide an estimate of clustering uncertainty. To address the shortcomings of the DBSCAN method, we present a novel clustering approach that can combine multiple lists of identified objects of interest from the same image. The key innovation is incorporating a dysfunctional family constraint into the Bayesian nonparametric clustering approach, the Chinese restaurant process (CRP), which naturally takes into account information about the crater identifier. The dysfunctional family Chinese restaurant process (DFCRP) provides an estimate of clustering uncertainty. In this work, we provide guidance on hyperparameter specification, present a Gibbs sampler, and perform a simulation study to compare the performance of the DFCRP to the CRP. Finally, we apply the DFCRP to the crater identification problem of R14, comparing results, and also demonstrate the types of analyses that can be performed with posterior draws of cluster assignments.

Strange metallicity, characterized by a linear temperature dependence of the resistivity, is observed in a broad range of correlated materials, including heavy-fermion compounds and cuprate superconductors. It has also recently been reported for the Kagome metal Ni$_3$In, where almost localized and itinerant electronic degrees of freedom coexist as a result of a partially flat band. We investigate the correlated electronic structure and transport properties of Ni$_3$In with dynamical mean field theory (DMFT) calculations performed on a minimal single-band Hubbard model, constructed from compact molecular orbitals. Despite the large band filling, even for moderate Hubbard repulsion, we observe a non-Fermi-liquid like frequency dependence of the self-energy, as well as the formation of local magnetic moments. With increased hole doping, a crossover to a heavy Fermi-liquid regime is found. We interpret these results in terms of an effective model for the partially filled narrow band near $k_z=0$.

The majority of white dwarfs that host periodic transiting planetary debris do so at distances that exceed the rubble-pile Roche limit, in disagreement with canonical formation models that focus on the tidal disruption of minor planets. Here, we quantify the conditions by which rotational fission due to sublimative outgassing ("SYORP" break-up) can occur outside of the Roche sphere in the distance range of 1-5 Roche radii. We use the Many Materials Orbital Sublimation (MaMOS) model to quantify the outgassing properties of three representative types of planetary materials: cores (iron), mantles (forsterite olivine) and comets (water ice), and characterise the resulting spin-up rate analytically by adopting SYORP coefficients in the range of $10^{-5}-10^{-3}$. We then compare this rate to that generated by the radiative YORP effect with YORP coefficients of $10^{-3}-10^{-2}$, and focus on planetesimals with radii of 0.1, 1.0, and 10 km. We find that for white dwarf cooling ages of up to $\sim$ 1 Gyr, sublimative fission of planetesimals and fragments $\lesssim$ 0.1 km in size due to water ice outgassing occur on observable timescales (within 10 yr), regardless if the spin-up is monotonic or stochastic. Further, these timescales are orders of magnitude shorter than the corresponding YORP fission timescales. For drier planetesimals, both iron and forsterite outgassing can be effective at 10-100 Myr cooling ages. Our results do not substantially differ for strengthless rubble piles versus objects with 1 kPa of internal strength. These findings add to growing evidence that gravitationally scattered comets and asteroids do not need to adopt pericentres within a white dwarf's Roche radius to eventually enrich, or pollute, the star with metals.

This paper connects two seemingly different ways of studying knots: quantum group invariants and the dynamics of Morse flows. For fibered knots, we define a two-variable series invariant by counting Morse flow loops in the complement. This dynamical series is conjectured to agree with the BPS $q$-series of the knot complement, which arises from Verma modules for quantum groups and encodes all colored Jones polynomials. We prove this correspondence for all braid-homogeneous knots.

Quantum computing has demonstrated its significant advantage over supercomputing for specific applications and shown promising prospect, such as machine learning, cryptography, finance, etc.. Quantum oracles are very common in many quantum algorithms and oracle resource consumption directly affects algorithm performance. However, existing oracle designs often exhibit high resource overhead and limited compatibility. Moreover, structured description tools and complexity analysis methods are lacked. In this work, we introduces a Hierarchical Recursive Synthesis-Evaluation (HRSE) model, enabling formal description and precise quantum gate complexity analysis of oracles. Based on this model, we propose an Adaptive Space-depth Trade-off (ASDT) algorithm for generating oracle structures under a fixed qubit constraint. We provide a theoretical proof showing that the ASDT algorithm achieves the optimal gate count for a given number of qubits. Experimental results show that the ASDT algorithm reduces the average quantum circuit depth by 53.99% compared with the W-cycle approach, with the number of variables being 10, 15, and 20, respectively.

Relativistic hydrodynamics successfully provides an effective field theory description for the low energy regime of many out-of-equilibrium systems. On the other hand, in this paper we proof that any stand-alone hydrodynamic EFT is inherently acausal and therefore requires the addition of transient UV modes in order to restore causality. This is made possible by the exponential decay of dissipative hydrodynamics in a majority of the lightcone, allowing the possibility of a causal description that still reduces to the hydrodynamic one at late timescales. We then investigate the emergence and possible restrictions of the non-hydrodynamic modes in these causal UV completions.

California's consumer privacy law is widely deemed to be the most protected in the United States, one of the few to expressly regulate third party entities that buy and sell consumer data (data brokers). We offer the first empirical assessment of data broker compliance with the 2018 California Consumer Privacy Act (CCPA) and the 2023 Delete Act, which requires data brokers to register with the state and report consumer rights requests metrics annually. First, we demonstrate that only 9% of 522 registered data brokers were fully compliant with transparency requirements after the Delete Act took effect, although we do identify slight improvements over time. Second, we descriptively characterize wide heterogeneity across data brokers in the volume of consumer rights requests received, with many reporting none. We bring in external business data to explore correlates associated with this variation, a challenge given the general lack of opacity into broker business practices. Third, in an audit of a sample of 250 data brokers' consumers request processes, we find that 43% make it impossible for consumers to exercise all privacy rights and 64% introduce at least one design feature that creates substantial friction into the consumer request process. Last, we show how these deficiencies stem from the decentralization of compliance decisions to brokers themselves, enforcement limitations, and regulatory ambiguity. We articulate reforms that could improve consumer privacy, transparency in broker practices, and compliance with these laws.

Astrometry - the precise measurement of celestial positions and motions - is entering the micro-arcsecond ($μ$as) era at multiple wavelengths, enabling new insights on compact objects across all mass scales. Here we review how high-precision astrometry is advancing our understanding of compact objects - neutron stars (NSs) and black holes (BHs). We provide the context for high precision astrometry before discussing natal kicks and the latest results from Gaia Data Release 3 (DR3). We highlight the evidence for mass-dependent peculiar velocities of accreting binaries, and also reveal a close similarity between NSs and BHs. Next-generation surveys will find recoiling supermassive BHs (SMBHs) in galactic nuclei, exploring how gravitational-wave-induced kicks operate. Exploitation of scientific opportunities on the lunar surface could facilitate much larger collecting areas and astrometric precision in X-rays than currently feasible.

Background and Context: Large Language Models (LLMs) are more accessible and accurate than ever before, raising significant concerns for computing educators. One major concern is students using LLMs to bypass the effort needed to understand concepts and metacognitive strategies essential for success in computer science. Objectives: We contribute a unique approach to assessing and building up student understanding through weekly oral code review assessments. These formative assessments incentivize students to understand their submitted code, regardless of whether or not the code was generated by AI tools. We also use a flipped classroom to provide time for students to learn concepts outside of class and provide ample time for students to schedule code review interviews. Methods: For this paper, we collected data from three semesters. We analyze student exam scores, keystroke logs, and surveys to understand how the new course policies affected student learning, behavior, and attitudes. Findings: Pairwise comparison of exam results reveals a statistically insignificant increase in average scores for Fall 2025 compared to previous semesters. Keystroke logs show a significant increase in characters pasted per total characters input into coding assignments in Fall 2025, pointing towards higher AI usage. Survey results show positive student sentiment towards code reviews at the end of Fall 2025, with nearly all negative feedback being addressable through better scheduling and more rigorous TA training. Implications: Oral code reviews with a flipped classroom appear to be effective at mitigating harms of LLM use while providing space for students to freely experiment with these tools. Our work suggests that students in Fall 2025 still show adequate understanding of material covered in written exams, despite dramatic increases in LLM usage for coding assignments.

We develop a finiteness notion for unbounded chain complexes over a commutative noetherian integral domain $R$ employing the Abel summation method. The algebraic K-theory of such complexes is defined, and shown to be non-trivial. We also exhibit a natural map from the (usual) algebraic K-theory of $R$ into the new K-theory and show that its image contains a canonical infinite cyclic subgroup.