We propose a model of causal persuasion, in which a sender selectively discloses a set of variables together with their true joint distribution and proposes a subjective causal model that binds them. A receiver is persuaded by this model only if the data conclusively identifies the causal link of interest. We characterize when such persuasion succeeds or fails, and how easily it can be achieved. We further show that if the receiver holds a pre-existing subjective model, debunking it is similar to persuading a receiver without one. To establish a true causal link, the sender often needs to disclose only one or two well-chosen variables. But to dispel a perceived link -- to persuade the receiver there is no causal relationship -- every common cause must be disclosed. Our results highlight a fundamental asymmetry in causal persuasion: Establishing causality is often much easier than ruling it out.

In this work, we present a detailed comparison of the SuSAv2 (SuperScaling Approach version 2) and RDWIA (Relativistic Distorted-Wave Impulse Approximation) models with measurements of charged-current neutrino-induced single-pion production from different experiments (T2K, MINERvA and MiniBooNE), studying the differences between the two theoretical descriptions. The neutrino energy range in these experiments spans from hundreds of MeV to roughly 20 GeV, and the nuclear targets are mainly composed of $^{12}$C. The SuSAv2 model uses the single-nucleon inelastic structure functions from the ANL-Osaka DCC model, which allows for a separation of pion production channels, distinguishing between the $π^+$, $π^-$ and $π^0$ final states. In the RDWIA approach, the Hybrid model developed by the Ghent group is used for the description of the boson-pion-nucleon vertex.

In the coming years, the Vera Rubin Observatory's Legacy Survey of Space and Time (Rubin-LSST) and the Nancy Grace Roman Space Telescope's (Roman) High Latitude Time Domain Survey (HLTDS) are expected to discover more than a million Type Ia supernovae (SNe Ia), several orders of magnitude more than current samples and with a tighter control on systematic uncertainties. One of the largest systematic uncertainties in cosmological analyses with SNe Ia is the accuracy of the spectro-photometric model for SNe Ia time series data, which depends on the photometric calibration of the surveys. To quantify the impact of this uncertainty, we analyze simulated Rubin-LSST and HLTDS data, perturb the photometric zero-points and filter mean wavelengths, and propagate these systematics to spectral model recovery, estimated distances, and dark energy figure of merit (FoM) based on the $w_0 w_a$CDM model. Zero-point shifts of 5 mmag and filter mean wavelength shifts of 5 angstrom lead to a $\sim 50\%$ decrease in the FoM relative to a statistical-only case when calibration uncertainties are propagated only through light-curve fitting. The same calibration shifts applied only during model training produce a smaller $\sim 13\%$ degradation. Contrary to previous analyses, calibration uncertainties in light-curve fitting dominate over those from model training. Their effect during light-curve fitting varies smoothly with redshift and is nearly degenerate with cosmology, preventing mitigation through self-calibration. Finally, we show that the FoM dependence on the size of the calibration uncertainties (in the range of expected sizes) is roughly linear.

We solve the Langevin equations for the time evolution of parameters that describe the shape of fissioning system. On each integration step, we calculate the probability of neutron emission and estimate whether a neutron would be emitted or not. If yes, we decrease the excitation energy of the nucleus by the neutron separation energy plus the average energy of the emitted neutron, switch to the layer of potential energy surface with a smaller number of neutrons and continue the process of integration. If the trajectory reaches the scission point, we check how many neutrons were emitted along this trajectory. The pre-scission neutron multiplicity $M_{pre}$ is defined by the ratio of the total number of emitted neutrons to the total number of fission trajectories. Besides $M_{pre}$, the mass distribution of fission fragments, the distribution of emitted neutrons with respect to the fission stage (deformation of system) and the distribution of emitted neutrons with respect to their energies are calculated. The calculated quantities are compared with the available experimental data.

In recent years, computational power and data availability breakthroughs have revolutionized our ability to analyze complex physical systems through the inverse problem approach. Data-driven techniques like system identification and machine learning play an important role in this field, allowing us to gain insights into previously inaccessible phenomena. However, a major hurdle remains: How can meaningful information from partial measurements be extracted? In the aerospace domain, the challenge of state estimation is particularly pronounced due to the limited availability of observational data and the constraints imposed by sensor capabilities for tracking resident space objects (RSOs). To address these limitations, advanced compensation methodologies are required. Currently, range and bearing measurements obtained from radar and optical systems constitute the primary observational tools in the space situational awareness (SSA) community. In this work, we propose a novel framework that integrates a simplified reference dynamics model with a data-driven surrogate measurement model. This fusion process leverages the strengths of both models to estimate complex dynamical behaviors under conditions of partial observability. Extensive numerical experiments were conducted across multiple datasets to validate the proposed framework. The results demonstrate its efficacy in accurately reconstructing system dynamics from incomplete measurement data. Furthermore, to ensure the robustness of the framework, an initial consistency analysis of the surrogate modeling approach is presented. By addressing the current challenges and refining the integration of data-driven techniques with traditional physics-based modeling, this framework aims to advance state estimation methodologies in the aerospace sector.

The quantum instrument (QI) formalism is required to model mid-circuit measurements (MCMs) and the dependence of the post-measurement state on the measurement outcome. Correctly modeling QIs is essential for applications using MCMs, such as adaptive circuits and quantum error correction. Although QIs yield a joint quantum-classical state after measurement, errors in QIs can still be represented by a $d^2 \times d^2$ superoperator (e.g., process or transfer matrix) for each outcome, just as superoperators describe Markovian errors on unitary gates. However, because the joint quantum-classical system has a distinct error model for each outcome, this complicates the usual interpretation of process- or transfer-matrix error models. This Note offers practical guidance on understanding and interpreting QI error models.

We propose a clustered local projection (clustered LP) method to estimate impulse response functions in a class of time-varying models where parameter variation is linked to a low-dimensional matrix of observables. We show that the clustered LP recovers the conditional average response when the driving variables are exogenous and a weighted average of the conditional marginal effects when they are endogenous. We propose an iterative estimation method that first classifies the data using k-means, estimates impulse response functions via GMM, and evaluates differences across clustered LP estimates. Our Monte Carlo simulations illustrate the ability of clustered LP to approximate the conditional average response function. We employ our technique to examine how uncertainty influences the transmission of a contractionary monetary policy shock to the 5- and 10-year U.S. nominal Treasury yields. Our estimation results suggest macroeconomic and monetary policy uncertainty operate through complementary but distinct channels: the former primarily amplifies the risk compensation embedded in the term premium, while the latter governs the speed and persistence with which markets revise their expectations about the future rate path following a monetary policy shock.

Privacy policies are intended to inform users about how software systems collect and handle data, yet they often remain vague or incomplete. This paper presents an empirical study of patterns in log-related statements within privacy policies and their alignment with privacy disclosures observed in Android application logs. We analyzed 1,000 Android apps across multiple categories, generating 86,836,964 log entries. Our findings reveal that while most applications (88.0%) provide privacy policies, only 28.5% explicitly mention logging practices. Among those that reference logging, most clearly describe what information is logged; however, 27.7% of log-related statements remain overly simplistic or vague, offering limited insight into actual data collection. We further observed widespread privacy leakages in application logs, with 67.6% of apps leaking sensitive information not mentioned in their policies. Alarmingly, only 0.4% of applications demonstrated consistent alignment between declared policy contents and actual logged data. These findings highlight that current privacy policies provide incomplete or ambiguous descriptions of logging practices, which frequently do not align with actual logging behaviors.

Superconducting qubits, realized by incorporating Josephson junctions into superconducting circuits, behave as artificial atoms with anharmonic energy spectra and can be precisely controlled and measured using microwave cavities within the framework of circuit quantum electrodynamics (cQED). Since its emergence in the early 2000s, cQED has established superconducting qubits as leading candidates for scalable quantum devices and has enabled the exploration of hybrid quantum systems that integrate disparate physical platformsThis review surveys superconducting hybrid quantum electromechanical systems in which mechanical resonators are coupled to superconducting qubits, with a focus on two widely used qubit platforms: the transmon and the fluxonium. We provide an overview of the underlying coupling mechanisms arising from interactions through the phase and charge degrees of freedom of the qubit, and discuss how these mechanisms give rise to both longitudinal and transverse qubit-mechanical interactions. We further review extensions of electromechanical platforms to electro-optomechanical architectures, in which optical cavities are integrated to enable coherent interfacing between superconducting circuits and optical photons. This review aims to present a unified framework and perspective on qubit-mechanical and qubit-mechanical-optical hybrid systems in superconducting quantum technologies and applications related to sensors.

We study an analogue of the conjugacy growth function in finitely generated groups: the automorphic growth function. This counts the number of automorphic orbits that intersect the ball of radius $n$ in the group. We show that this is not a commensurability invariant, by giving virtually abelian counterexamples. We classify the automorphic growth rate of all virtually abelian groups of rank at most $2$, the Heisenberg group, finite rank free groups and Thompson's groups $T$ and $V$. This last computation allows to conclude that $T$ and $V$ have exponential conjugacy growth.

Fluid antenna system (FAS) becomes a promising paradigm for next-generation wireless networks, which enables position-flexible antenna elements that can dynamically adjust to more favorable channel conditions. However, the optimization of fluid antenna (FA) positions, beamforming, and power allocation in FA-assisted wireless networks is challenging, due to the non-convexity and the lack of base station (BS) coordination. In this paper, we first formulate this challenging optimization problem as a decentralized partially observable Markov decision process, and then propose a multi-agent group relative policy optimization (MAGRPO) algorithm under the centralized training decentralized execution (CTDE) paradigm. Compared with multi-agent proximal policy optimization (MAPPO), MAGRPO replaces the critic network with group relative advantage estimation. This design reduces computational complexity by nearly half under parameter sharing. Furthermore, we derive a variance upper bound of the cumulative reward, which scales with network parameters, e.g., the number of BSs, users, and FAs. Simulation results show that compared with wireless networks with fixed antenna positions, FA-assisted wireless networks achieve multiple-fold sum-rate enhancement. Moreover, the proposed MAGRPO attains sum-rates comparable to those of MAPPO in testing, while reducing training time by $30\% \sim 40\%$.

A rational Diophantine $m$-tuple is a set $\{a_1,\ldots,a_m\}$ of distinct nonzero rational numbers such that $a_i a_j+1$ is a square for all $1\leq i < j\leq m$. Similarly, we may ask when $a_ia_j+1$ is a $k$-th power. Here, we study the case $k=4$ and produce some non-trivial infinite families of such triples. We show that there are infinitely many triples with positive elements for $k=4$. We also briefly consider the $k=6$ (sextic) and $k=8$ (octic) cases, explaining the difficulties in extending the method to higher exponents.

Reliable optical control of valley degrees of freedom in moiré excitons requires that the emitted polarization faithfully reflect the underlying valley state. Here, we show that linearly polarized photoluminescence from WSe2/WS2 moiré excitons is largely insensitive to the excitation polarization and therefore does not arise from valley coherence. Automated polarization-resolved photoluminescence and Raman mapping at cryogenic temperature reveals that the degree of linear polarization correlates strongly with local Raman shifts and moiré-exciton observables, identifying strain as the dominant experimental correlate. Linear-regression analysis further shows that strain-related descriptors provide the best prediction of the observed polarization. Guided by theory, we attribute this behavior to strain-amplified breaking of C3 symmetry in the moiré potential: weak uniaxial strain produces only partial cancellation of locally elliptical emission, yielding a finite far-field degree of linear polarization. These results establish strain as a key control parameter for reliable optical readout in TMD moiré superlattices.

Chemical kinetics is becoming an increasingly vital component of hot Jupiter general circulation models (GCMs). Here we simulate the hot Jupiter WASP-96b using two chemical networks, a reduced chemical network frequently used in the GCM literature (which we refer to as V19) and a more recent effective network making use of tables of net reactions (MiniCHEM), coupled to the same GCM in order to provide a robust benchmark. We find a numerical escape criterion used by the Unified Model chemical kinetics solver to stop integration for the duration of the chemical timestep, independent of the chemical network, results in artificial quenching, overestimating of HCN, CH$_4$, and NH$_3$ abundances by factors of 1.5 to 3. With this criterion disabled, agreement between the two networks is improved, except for HCN and NH$_3$, where different reaction rates and included species results in lower abundances in the V19 network. While many rates differ between the networks, the lower quenched NH$_3$ abundances in the V19 simulations are, in particular, due to the choice of NH$_2$ + NH$_3$ $\rightarrow$ N$_2$H$_3$ + H$_2$ reaction rate, which is poorly constrained in the literature. This reaction also impacts the quenching of HCN, which is additionally affected by the lack of CH$_2$NH$_2$ in the V19 network. While there are reasons to favour the MiniCHEM HCN and NH$_3$ abundances, ultimately, improved experimental and theoretical determination of reaction rates are needed to address the uncertainties and better characterize the quenching behaviour.

We investigate rare special dileptonic decays of $ Λ_b$, $Σ_b$ and $Ξ_b $ baryons in the Standard Model and context of the general Two-Higgs-Doublet Model with Type III. Specifically, we consider the decays $ Λ_b \rightarrow Λ\ell^+ \ell^-$, $Σ_b \rightarrow Σ\ell^+ \ell^-$ and $Ξ_b \rightarrow Ξ\ell^+ \ell^-$, where $\ell$ represents $μ$ or $τ$ lepton. By studying these rare decays, we aim to assess the impact of the Two-Higgs-Doublet Model with Type III on various observables, such as the differential branching ratio, total branching ratio, and lepton forward-backward asymmetries using the decay amplitude and the transition matrix elements in terms of form factors calculated via light cone QCD in full theory. We compare our results to those of the Standard Model, as well as existing lattice QCD predictions and experimental data, to assess the agreement and viability of the Two-Higgs-Doublet Model with Type III. Furthermore, we highlight the potential for experimental investigations of these decay channels in the near future. The soon-to-be updated LHCb and/or Belle II detectors, renowned for their capabilities in studying rare decays, present excellent opportunities for probing the predicted branching ratios.

This paper introduces a safety-critical optimization-based control strategy that leverages control Lyapunov and control barrier functions to guide the spatial density of robotic swarms governed by the Fokker-Planck equation to a predefined target distribution. In contrast to traditional open-loop state-constrained optimal control strategies, the proposed approach operates in closed-loop, and a Voronoi-based variant further enables distributed deployments. Theoretical guarantees of safety are derived, and numerical simulations demonstrate the performance of the proposed controllers. Finally, a multi-robot experiment showcases the real-world applicability of the proposed controllers under localization and motion noises, illustrating how it is much easier for a sparse swarm to satisfy safety specifications than it is for a densely packed one.

Autonomous large language model (LLM) agents such as OpenClaw are pushing agentic commerce from human-supervised assistance toward machine actors that can negotiate, purchase services, manage digital assets, and execute transactions across on-chain and off-chain environments. Protocols such as the Trustless Agents standard (ERC-8004), Agent Payments Protocol (AP2), OKX Agent Payments Protocol (APP), the HTTP 402-based payment protocol (x402), Agent Commerce Protocol (ACP), the Agentic Commerce standard (ERC-8183), and Machine Payments Protocol (MPP) enable this transition, but they also create an attack surface that existing security frameworks do not capture well. This Systematization of Knowledge (SoK) develops a unified security framework for autonomous LLM agents in commerce and finance. We organize threats along five dimensions: agent integrity, transaction authorization, inter-agent trust, market manipulation, and regulatory compliance. From a systematically curated public corpus of academic papers, protocol documents, industry reports, and incident evidence, we derive 12 cross-layer attack vectors and show how failures propagate from reasoning and tooling layers into custody, settlement, market harm, and compliance exposure. We then propose a layered defense architecture addressing authorization gaps left by current agent-payment protocols. Overall, our analysis shows that securing agentic commerce is inherently a cross-layer problem that requires coordinated controls across LLM safety, protocol design, identity, market structure, and regulation. We conclude with a research roadmap and a benchmark agenda for secure autonomous commerce.

Variability in active galactic nuclei (AGN) probes the physics of accretion onto supermassive black holes. This variability is characterized using metrics derived from the flux distributions of temporally separated epochs. We studied the stability of two variability metrics, the Stetson index "J" and the smoothness "s", against baseline, cadence, and host galaxy contamination. We studied 23 nearby AGNs using Zwicky Transient Facility's Data Release 24. Both metrics are robust to baseline variations of $\sim 2$ years. However, s is sensitive to cadence, showing variations $\gtrsim 40\%$, while J shows minor variations $\lesssim10\%$. We studied the host galaxy impact using Mrk 493 as a representative case. We found that J remains unchanged after host subtraction, while s increases. We concluded that J is a robust tool for characterizing AGN variability, while s should be interpreted with caution.

In the effective field theory (EFT) description of binary inspirals, the radiated gravitational waveform receives universal corrections from the curved background, the so-called ``tail effects'', that resum into the so-called ``Sommerfeld factor''. We develop a systematic framework for computing this gravitational Sommerfeld factor for scalar perturbations with the presence of tidal effects on the system. Using the worldline EFT, we recast the diagrammatic resummation as a solution to the $d$-dimensional wave equation with a localized source, and derive a closed-form expression for the Sommerfeld factor in terms of the EFT connection matrix. We prove that the phase of the Sommerfeld factor is exactly the same as elastic Compton scattering phase shift when there is no tidal dissipation. By combining the renormalization techniques in EFT with the Mano--Suzuki--Takasugi method in black hole perturbation theory, we analytically solve the Sommerfeld factor for both the magnitude and phase to $O(G^{10})$ for the $\ell = 0, 1, 2$ partial waves. We further establish a new renormalization group equation for the radiative multipole moments, whose exact solution yields an improved resummation of the waveform beyond the universal tail logarithms. These high-precision data and exact relations pave the way for future waveform resummation.

Early observations from the James Webb Space Telescope (JWST) have revealed an overabundance of massive high-redshift galaxies, raising the question of whether this points to new physics beyond $Λ$CDM, or an enhanced formation efficiency of massive stars. We revisit this issue going beyond earlier analyses based on direct comparisons to theoretical bounds at a fixed cosmology, by performing a full Bayesian analysis of the most extreme galaxies in the CEERS imaging and FRESCO spectroscopic samples, jointly constraining cosmological parameters and the baryon-to-star conversion efficiency $ε$. We do so not only within the spatially flat $Λ$CDM model, but also in models where the dark energy equation of state $w$ and/or the spatial curvature parameter $Ω_K$ are allowed to vary, carefully discussing the impact of both $w$ and $Ω_K$ on the cumulative comoving stellar mass density. Within the flat $Λ$CDM model, once cosmological parameters are marginalized over, the CEERS sample provides a weak $2σ$ lower limit of $ε\gtrsim 0.07$, compatible with astrophysical expectations. In contrast, the FRESCO sample requires $ε\gtrsim 0.5$ at $2σ$, with values $ε\lesssim 0.2$ disfavored at $>5σ$. These results do not qualitatively change when we allow $w$ and/or $Ω_K$ to vary, with no evidence for deviations from $w=-1$ or $Ω_K=0$. Our results therefore suggest that the origin of the ``JWST tension'' is unlikely to be cosmological, but lies in the astrophysics of galaxy formation.

A fully fault-tolerant implementation of the quantum error-detecting Iceberg $[[2m, 2m-2, 2]]$ code applied to a Toffoli circuit achieved beyond-break-even error detection on a leading trapped-ion quantum computer, where the effect of encoding a circuit with a quantum error-detection code enables increased fidelity compared to an unencoded circuit. This code was also applied to Bell state preparation circuits, where a lean non-fault-tolerant implementation of the Iceberg code enables a fidelity gain as well. This highlights the important point that, at least for small-scale circuits with a substantial portion of error-free runs, it can be effective simply to use error detection to filter out the runs with errors. Furthermore, experiments performed in this work highlight the necessity for judicious compilation of circuits not only for a given hardware but also within a quantum error detection code.

This paper investigates the fundamental limits of integrated sensing and communication (ISAC) systems with 1-bit receiver quantization. We analyze a Gaussian fading ISAC channel with separate communication and monostatic sensing links, where both communication and sensing receivers are equipped with 1-bit quantizers. When the communication channel state information (CSI) is available at the receiver, we characterize the communication-sensing capacity region of 1-bit ISAC channel and show that no trade-off exists between communication and sensing performance. In particular, both communication and sensing capacities can be simultaneously achieved by a constant-amplitude input distribution with a specific rotational symmetry. For the scenario where communication CSI is also available at the transmitter, we formulate a weighted optimization problem that balances communication and sensing rates in 1-bit ISAC channel under an average power constraint and then derive the corresponding optimal power control policy. The results demonstrate how the optimal power control policy evolves with the weighting parameter, transitioning from a communication-centric, opportunistic transmission to a more uniform allocation as sensing becomes increasingly prioritized.

We study the simplicity of $C^{*}$-algebras built from group actions. For a faithful isometric action of a group $G$ on a countable metric space $X$, we use the associated action representation on $\ell^2(X)$ to define the action-based $C^{*}$-algebra $C^{*}_{X}G$. We define generalized versions of the properties $P_{\text{naive}}$ and $P_{\text{analytic}}$ relative to the action and show that the naive form implies the analytic form. We also prove that the properties $P_{\text{analytic}}$ associated with a continuous action ensure the simplicity of the action-based $C^*$-algebra. As an application, we deduce that big mapping class groups satisfy the property $P_{\text{naive}}^{\mathbb{X}}$ and the associated action-based $C^*$-algebra is simple.

We present a systematic analysis of scale-dependent properties of filamentary structures in seven nearby molecular clouds $-$ Taurus, Ophiuchus, Perseus, Orion A, California, IC 5146, Vela C $-$ using the multiscale extraction method $getsf$. Alongside the usual surface density profiles $Σ(r)$, we derive volume density profiles $ρ(r)$ for a large sample of filaments, providing new observational constraints on their three-dimensional structure. The half-maximum widths $H$ and $h$ of the surface and volume density profiles, respectively, increase systematically with spatial scale, following power laws $\tilde{H} \propto Y^{0.50}$ and $\tilde{h} \propto Y^{0.37}$, with distributions spanning $\sim 0.01 - 1 $ pc across all scales, challenging the notion of a universal filament width of $\sim 0.1$ pc. The median volume density slopes $\tildeβ \approx 2.1 - 2.4$ are systematically lower than the value $β= 4$ expected for an isothermal cylinder in hydrostatic equilibrium. For shallow profiles with $β\lesssim 1$, the volume density width $h$ falls below the surface density width $H$ by one to two orders of magnitude, demonstrating that surface density widths overestimate the true physical extent of filaments with shallow profiles. Volume density contrasts are substantially higher than surface density contrasts ($\tilde{C}_ρ \approx 17 - 52$ vs. $\tilde{C}_Σ \approx 1.1 - 2.7$), confirming that filaments are substantially more prominent in three dimensions than their projected appearance suggests. Measured filament widths and slopes depend systematically on angular resolution and distance, highlighting the importance of accounting for resolution bias in comparative filament studies.

We prove two results on the mixing times of Markov chains for two-spin systems. First, we show that the Glauber dynamics mixes in polynomial time for the Gibbs distributions of antiferromagnetic two-spin systems at the critical threshold of the uniqueness phase transition of the Gibbs measure on infinite regular trees. This completes the computational phase transition picture for antiferromagnetic two-spin systems, which includes near-linear-time optimal mixing in the uniqueness regime [Chen--Liu--Vigoda, STOC '21; Chen--Feng--Yin--Zhang, FOCS '22], NP-hardness of approximate sampling in the non-uniqueness regime [Sly--Sun, FOCS '12], and polynomial-time mixing at criticality (this work). Second, we prove an optimal $O(\log n)$ mixing time bound as well as an optimal $Ω(1)$ spectral gap for the Swendsen--Wang dynamics for the ferromagnetic Ising model with an external field on bounded-degree graphs. To the best of our knowledge, these are the first sharp bounds on the mixing rate of this classical global Markov chain beyond mean-field or strong spatial mixing (SSM) regimes, and resolve a conjecture of [Feng--Guo--Wang, IANDC '23]. A key ingredient in both proofs is a new family of localization schemes that extends the field dynamics of [Chen--Feng--Yin--Zhang, FOCS '21] by tilting general edge (or hyperedge) weights rather than vertex fields. This framework, which subsumes the classical Swendsen--Wang dynamics as a special case, extends the localization framework of [Chen--Eldan, FOCS '22] beyond stochastic and field localizations, and enables controlled tilting of interaction strengths while preserving external fields.

We present the numerical methods and GPU-accelerated implementation underlying a Total Lagrangian finite element framework for finite-deformation flexible multibody dynamics, introduced in the companion paper [1]. The framework supports 10-node quadratic tetrahedral (T10) elements and ANCF beam and shell elements, with quadrature-based hyperelastic response (St. Venant-Kirchhoff and Mooney-Rivlin) and an optional Kelvin-Voigt viscous stress contribution. Time stepping employs a velocity-based implicit backward-Euler scheme, yielding a nonlinear residual in velocity that couples inertia, internal and external forces, and bilateral constraints. Constraints are enforced via an augmented Lagrangian method (ALM), structured as an outer loop alternating an inner velocity solve with a dual-ascent multiplier update. We introduce a two-stage GPU parallelization strategy for internal force and tangent stiffness evaluation, and provide two inner solvers: a first-order AdamW optimizer and a second-order Newton solver that assembles and factorizes a sparse global Hessian on the GPU using cuDSS. A fixed-sparsity matrix strategy eliminates repeated symbolic analysis and enables efficient numerical refactorization across Newton iterations. For collision detection, we present a GPU-native two-thread asynchronous algorithm operating on triangle soups, avoiding bounding-volume hierarchies entirely. Systematic scaling benchmarks across all three supported element types and six mesh resolutions show that the Newton solver achieves approximately one order of magnitude reduction in real-time factor relative to CPU baselines at the largest resolutions tested. The frictional contact model is validated against closed-form rigid-body predictions through quasi-static and dynamic impact unit tests.

The use of free energy perturbation (FEP) methods to study protein-ligand complexes is one of the most important tools in structure-based drug design. Because FEP methods typically rely on force fields, they may suffer from force field parameter-related issues. Herein, we present a quantum mechanics/molecular mechanics (QM/MM) hybrid method to overcome deficiencies in force-field models by using QM bookending approaches on both classical and quantum hardware. In the MM part of this QM/MM FEP method, AMBER is used to simulate the protein receptor and the unperturbed moiety of the ligand, with the ff19SB and GAFF2 force fields. In the QM part, QUICK was used to conduct Hartree-Fock (HF) calculations, followed by heat-bath configuration interaction (HCI) as a benchmark on classical devices. To enable the HCI function in QUICK, we developed a Python-based interface to execute HCI from IBM's qiskit-addon-dice-solver. Moreover, the same interface also enabled this work to execute QM/MM FEP calculations on quantum hardware using the Local Unitary Cluster Jastrow (LUCJ) ansatz, followed by sample-based diagonalization (SQD) and extended-SQD (extSQD) post-processing. Using a series of thermolysis inhibitors as an example, we find reasonable agreement with experiment between the classical HCI method and the LUCJ-SQD/extSQD method, with the latter yielding a result closer to the experimental value. The execution time between the HCI-based FEP method and the LUCJ-SQD/extSQD-based FEP method is also comparable, indicating a high potential for utility in the noisy intermediate-scale quantum (NISQ) era.

We introduce an enriched notion of a coalgebra over an operad P in a symmetric monoidal V-category C. When C is semicartesian and P is unital, we construct a V-endofunctor on C associated to P and give conditions under which it is a V-comonad with co-Eilenberg-Moore V-category isomorphic to the V-category of P-coalgebras in C. In many cases, this permits computation of V-categories of coalgebras. The key example is the category of pointed topological spaces with wedge product, enriched over topological spaces with Cartesian product, where this construction recovers the comonadic description of C_n-coalgebras of Moreno-Fernández, Wierstra and the present author. We further recover one direction of Fox's theorem.

We study how Sachdev-Ye-Kitaev (SYK) interactions can arise from localized single-particle states on a system that is effectively one dimensional. If a local interaction is projected onto coarse localized orbitals, the resulting couplings do not immediately follow the standard SYK distribution. Instead, they have a finite probability of being exactly zero, a broad non-Gaussian distribution for the nonzero values, and strong correlations coming from the geometry of the localized states. We then show that this changes when each localization volume is resolved into $M>1$ smaller microscopic pieces with random phases. As $M$ increases, the distribution of the nonzero couplings moves toward the complex-Gaussian SYK form. At the same time, the large-$M$ limit is a sparse but asymptotically canonical SYK network: the nonzero couplings create SYK clusters, while the pattern of missing or very weak couplings is still determined by the real-space overlap of the localized orbitals. Finally, we map the interaction tensor to a graph in pair space. This makes it possible to follow the formation, merger, and growth of SYK clusters, which we characterize using connected components and clique/simplex counts. The result is a minimal real-space phenomenological theory of SYK-cluster formation, providing clear experimental criteria.

We present a constructive proof that a single C program, the \emph{Vulnerability Factory}, admits a countably infinite set of distinct, independently CVE-assignable software vulnerabilities. We formalise the argument using elementary set theory, verify it against MITRE's CVE Numbering Authority counting rules, sketch a model-checking analysis that corroborates unbounded vulnerability generation, and provide a Turing-machine characterisation that situates the result within classical computability theory. We then contextualise this result within the long-running debate on whether undiscovered vulnerabilities in software are \emph{dense} or \emph{sparse}, and introduce the concept of \emph{vulnerability abundance}: a quantitative analogy to chemical elemental abundance that describes the proportional distribution of vulnerability classes across the global software corpus. Because different programming languages render different vulnerability classes possible or impossible, and because language popularity shifts over time, vulnerability abundance is neither static nor uniform. Crucially, we distinguish between infinite \emph{vulnerabilities} and the far smaller set of \emph{exploits}: empirical evidence suggests that fewer than 6\% of published CVEs are ever exploited in the wild, and that exploitation frequency depends not only on vulnerability abundance but on the market share of the affected software. We argue that measuring vulnerability abundance, and its interaction with software deployment, has practical value for both vulnerability prevention and cyber-risk analysis. We conclude that if one programme can harbour infinitely many vulnerabilities, the set of all software vulnerabilities is necessarily infinite, and we suggest the Vulnerability Factory may serve as a reusable proof artifact, a foundational `test object',for future formal results in vulnerability theory.