Bi-incomplete Tambara functors are equivariant generalizations of commutative rings. The most common forms of bi-incomplete Tambara functors are coefficient systems of commutative rings, Green functors, and Tambara functors. In the 1980s, Lewis introduced prime ideals in Green functors, and in the 2010s, Nakaoka introduced prime ideals in Tambara functors. In this work, we define the spectrum of prime ideals for an arbitrary bi-incomplete Tambara functor, simultaneously generalizing Lewis and Nakaoka's notions. We then produce many computational tools which we apply to several examples of interest.

We present SpatialPrompt, an Extended Reality(XR) system that turns spatial sketches into executable constraints for controllable 3D generation. Users draw rough structures with a 3D pen and add voice prompts for semantic and stylistic intent. The system supports iterative refinement and synchronous co-creation in shared space with color-coded contributions. Implemented on Apple Vision Pro with Logitech Muse and Meshy, a heuristic evaluation suggests that the workflow is intuitive and supports shared understanding in collaborative creation, while revealing needs for faster generation and clearer feedback.

We construct an abstract elementary class $K_1$ of torsion-free abelian groups such that $K_1$ is not $(<\aleph_0)$-tame but is $\aleph_0$-tame. This answers a question of [BoVa17]. Furthermore, for every regular uncountable cardinal $μ$ less than the first measurable cardinal, we construct an abstract elementary class $K_2(2^μ)$ of torsion-free abelian groups such that $K_2(2^μ)$ is not $(<μ)$-tame. $K_1$ and $K_2(2^μ)$ are non-tame for algebraic reasons. Furthermore, they constitute the first examples of non-tame abstract elementary classes in a natural language.

The nitrogen-vacancy (NV) centre in diamond is a leading platform for room-temperature quantum sensing. Improvements in sensitivity require precise control of the NV charge state. Transitions from the neutral NV$^0$ charge state to the negative NV$^-$ charge state can occur during excitation with photon energies below the ZPL transition of NV$^0$. These sub-resonant charge transitions limit modern initialisation protocols and have not been studied in full detail. In this paper we show that sub-resonant charge cycling arises from phonon-assisted anti-Stokes excitation. We further uncover the phonon states which contribute most strongly to the anti-Stokes transition via the development of novel quantitative models. The models indicate that low energy acoustic phonons strongly contribute to the transition close to the ZPL. At longer wavelengths a 43\,meV mode additionally impacts the charge cycling dynamics.

Parafermions with non-Abelian statistics have been proposed as a promising platform for quantum computation, potentially enabling a broader set of topologically protected gates than Majorana fermions. The experimental and theoretical exploration of these exotic quasiparticles remains challenging, as their stability is linked to strong electron-electron interactions. A key step toward practical applications is the controlled shuttling of parafermionic modes, which is required for implementing geometric braiding operations. In the present work, we investigate the real-time dynamics of the elementary shuttling process by applying a combination of the density matrix renormalization group and the time-dependent variational principle approaches. We analyze the transport of $\mathbb{Z}_4$ parafermion edge states and assess the corresponding adiabatic speed limit under experimentally relevant conditions.

AI accelerator operators are compiled into multi-stage pipeline programs where DMA, vector, matrix, and scalar units execute concurrently on shared on-chip buffers. A missing or misplaced synchronization primitive introduces hardware-visible data races that escape both simulation and golden testing, because neither models the accelerator's cross-unit visibility semantics. We formalize accelerator pipeline programs as a restricted concurrent language, define a parameterized hardware event semantics with three ordering relations -- program order, synchronization order, and barrier order -- and reduce the correctness question to barrier sufficiency: whether every cross-unit write-read pair on the same buffer is ordered by happens-before. Here "barrier" denotes an abstract ordering primitive in the model, covering vendor pipe barriers, hard-event synchronization, and equivalent frontend-normalized synchronization points. We prove that barrier sufficiency is decidable in $O(|E|^2)$ time and that our checker is both sound and complete under the modeled semantics. We implement AccelSync, a static verification tool instantiated for Ascend 910B2 and Cambricon MLU370 by changing only the hardware model. On 6,292 production kernels from the CANN operator library, AccelSync identifies 3 previously unknown synchronization hazards -- one matching a hazard class for which we observed nondeterministic outputs on Ascend 910B2 under a specific toolkit/driver configuration (CANN 8.0.RC3), though this observation was not reproducible after a subsequent driver upgrade -- and on 120 LLM-generated kernels it flags a 19.2% defect rate (95% CI: [13.0%, 27.4%]). A mutation study on 688 non-equivalent mutants yields 100% detection, and a head-to-head comparison shows AccelSync detects hazards that Huawei's runtime sanitizer msSanitizer misses, at 400x lower cost per kernel.

Gravitational-wave memory is a low-frequency, non-oscillatory signal that provides a promising probe of strong-field gravity. We present the first computation of memory from full inspiral--merger--ringdown waveforms in a theory beyond GR, focusing on scalar Gauss--Bonnet gravity. We find percent-level deviations from GR, mainly driven by modified merger dynamics, while scalar-induced contributions to tensor memory are strongly suppressed. We found that including memory greatly enhances the mismatch between GR and beyond-GR waveforms, highlighting its potential as a complementary observable for tests of gravity with next-generation detectors.

Quantum compilers sit between an algorithm's theoretical promise and what executes on physical hardware. Existing benchmarks report aggregate post-transpilation metrics but cannot attribute where fidelity is lost within the compilation pipeline. We present HBR decomposition, a per-phase fidelity attribution model that quantifies relative fidelity loss across High-level structural decomposition (H), Basis translation (B), and Routing (R). We evaluate three production SDKs (Qiskit, PennyLane, TKET) across eight algorithms on two backend topologies: IBM Heron (heavy-hex) and IonQ Forte (all-to-all). The dominant compiler bottleneck is strongly circuit-class dependent: Routing accounts for up to 60% of relative fidelity loss in search-class circuits, while synthesis dominates Hamiltonian simulation workloads. Early synthesis choices amplify or compress downstream routing overhead depending on circuit connectivity. SDK rankings at diagnostic optimization level (opt=0) reverse at production levels (opt=2) for deep circuits, showing that stagewise diagnostics and production results answer different questions. HBR correctly predicts SDK rank ordering across noisy simulations (8 circuits x 3 SDKs x 2 tiers) and real IBM Fez hardware executions, revealing stage-specific bottlenecks that are not observable through aggregate compiler benchmarks.

Surface spin waves of the Damon-Eshbach type exhibit intrinsically nonreciprocal transport properties with a chiral dynamical field structure that localizes counterpropagating waves at opposite film surfaces. Such chirality has been predicted to suppress direct backscattering in thin films within frequency ranges free of bulk modes. However, how chirality influences reflection in thicker three-dimensional magnetic media, where a dense spectrum of bulk excitations overlaps with surface waves, remains unclear. Here we demonstrate that, in micrometer-thick yttrium iron garnet films, reflection of the chiral Damon-Eshbach wave from the boundary of the magnetic medium is accompanied by excitation of spatially localized thickness-quantized bulk modes, whereas reciprocal backward-volume waves reflect nearly elastically. Brillouin light scattering spectroscopy, infrared thermography, and micromagnetic simulations reveal standing bulk excitations at the reflecting boundary and quantify the associated magnon energy accumulation and dissipation. These results identify bulk-mode excitations as the physical pathway enabling reversal of chirally localized surface waves in thick films, thereby defining the limits of chirality-based backscattering immunity and providing a general framework for wave transport in nonreciprocal magnetic media.

Droplet impact on thin liquid films is commonly studied on quiescent surfaces, although practical systems often involve residual capillary waves generated by preceding droplets. This study examines how such traveling waves modify impact dynamics and mixing. Controlled surface disturbances were produced using an acoustic excitation system that replicated droplet-induced waves, and a two-color laser-induced fluorescence method was implemented to obtain simultaneous measurements of film thickness and dye concentration. Impacts on wavy films deviated markedly from quiescent conditions. Rim evolution, cavity collapse, and jet formation became asymmetric, governed by the phase of the wave relative to the impact. These behaviors were linked to local variations in film depth, which redirected cavity retraction and the associated mixing flow. Reconstructed concentration fields confirmed that droplet liquid is displaced according to these depth gradients, producing asymmetric mixing at moderate Weber numbers. A dimensionless asymmetry index quantified the dependence on wave amplitude, phase, and distance from the acoustic wave generator. At higher Weber numbers, inertial mixing attenuated these effects, and the dynamics approached those of static films.

Ultra-hot Jupiters (UHJs) are exceptional laboratories for studying planetary atmospheres under extreme irradiation conditions. With close-in tidally locked orbits, these planets can have daysides hot enough for metals to be significantly ionized while still maintaining nightsides cold enough for refractory species to potentially condense. We present an analysis of the ultra-hot Jupiter HAT-P-70b taken with the MAROON-X high-resolution spectrograph. Using cross-correlations, we detect 14 neutral and singly ionized species, including Fe I, Fe II, Ti I, Ca I, Ca II, Cr I, Na I, V I, Mn I, Ni I, Mg I, Ba II, O I, and Sr I, with tentative evidence for H I, Co I, and K I. The absorption signals exhibit blueshifts on the order of a few $\mathrm{km\,s^{-1}}$, consistent with day-to-night winds. We further constrain relative abundances with atmospheric retrievals and demonstrate that some inferred elemental abundance ratios depend strongly on modeling assumptions. In particular, we show that a well-mixed retrieval approach neglecting ionization can strongly bias highly ionizable elements such as Ca and Ti. Accounting for the effects of equilibrium chemistry and thermal ionization generally results in inferred elemental abundance ratios that are closer to expectations for a solar-like composition, although not in all cases. Interestingly, we find a distinct nickel enrichment on HAT-P-70b, adding to the growing number of UHJ studies where the Ni abundance is seemingly enhanced. Our results underline the importance of considering physical and chemical atmospheric processes such as ionization when interpreting high-resolution transmission spectra of UHJs.

We describe a scheme for generation of coherent $γ$-rays by backscattering intense visible laser light from a beam of partially stripped ions. The scheme is similar in principle to the proposed Gamma Factory at CERN, with the important difference that the scattering becomes coherent as a result of a collective instability which microbunches the ions. This instability is analogous to that which occurs in high-gain free electron lasers (FELs). The scheme potentially offers a route to a source of tuneable, coherent $γ$-rays, opening up a wide range of possible new applications and opportunities. We find that the parameter requirements for realization of coherent $γ$-ray generation regime are considerably more stringent than those proposed for the Gamma Factory, requiring significant increases in the pump laser intensity and possibly the ion beam current.

In a previous work with B. Garcia, the author considered the asymptotic for the second moment of Dirichlet $L$-functions along cosets, and exhibited a surprising secondary main term that is not predicted by the recipe of Conrey, Farmer, Keating, Rubinstein, and Snaith. In this paper, we re-examine this problem and propose a modified recipe that correctly predicts this secondary main term. The original recipe gives the incorrect answer for this family because the root number is not always independent of the Dirichlet series coefficients along certain cosets, and our proposed fix simply takes this feature into account. In addition, we consider a handful of other problems related to Dirichlet $L$-functions along cosets. One goal is to reformulate Heath-Brown's $q$-analog of van der Corput's shifting method in terms of cosets, which leads to an upper bound on a hybrid second moment. We also revisit the classical van der Corput bound and view it (in more modern terms) as an amplified second moment of a trigonometric polynomial.

Frequency crowding remains a major obstacle to scaling fixed-frequency transmon processors. Among the widely used all-microwave two-qubit gates, the cross-resonance (CR) gate is particularly sensitive to qubit-frequency spread because the conventional straddling regime condition constrains assignable qubit frequencies tightly and makes the system susceptible to frequency collisions. Here, we propose and analyze the CR gate outside the straddling regime, which we refer to as the far-detuned regime, and evaluate frequency collisions using a numerical method that remains accurate under high-intensity, smoothly ramped microwave drives. Based on this analysis, we perform systematic parameter sweeps and provide collision-free conditions that define designable frequency regions in which qubit frequencies can be assigned consistently with surrounding qubit frequencies. Furthermore, we formulate frequency allocation as a linear programming optimization on a unit-cell lattice with periodic boundary conditions to obtain an optimal allocation. We demonstrate that far-detuned designs significantly reduce collisions compared with designs in the straddling regime. Monte Carlo yield analysis indicates that 10% collision-free yield for a 1024-qubit square lattice at a 0.1% two-qubit-gate error threshold requires $σ_{\mathrm{f}}/2π\le 6.8~\mathrm{MHz}$. Our findings suggest that this is feasible with an approximately twofold reduction in the state-of-the-art qubit-frequency spread.

Cluster Monte Carlo algorithms are widely regarded as the most effective route to overcoming critical slowing down in lattice spin systems. Whether this acceleration persists in the presence of vacancies and multicritical fluctuations, however, remains unresolved. We address this question through a systematic dynamic-scaling study of hybrid cluster-local update schemes in the two-dimensional Blume-Capel model, which exhibits a line of continuous Ising-like transitions terminating at a tricritical point. Along the entire critical line, hybrid dynamics retain the near-optimal efficiency of pure cluster updates despite the presence of annealed vacancies. Strikingly, this acceleration collapses precisely at tricriticality, where the dynamic critical exponent reverts to the local-update value. We trace this breakdown to the correlated percolation of vacancies, whose emergent system-spanning geometry obstructs nonlocal relaxation in the spin sector. Our results identify a fundamental geometric limitation of cluster acceleration at tricriticality and establish vacancy percolation as the mechanism controlling dynamic universality in hybrid Monte Carlo dynamics.

Reliable pulsar candidate ranking requires probability estimates that are not only discriminative but also well calibrated. We evaluate hybrid quantum-calssical logistic regression on the imbalanced HTRU-2 dataset using three quantum feature encodings: angle encoding, amplitude encoding, and data re-uploading. The models are trained using analytic gradients and compared with classical baselines and a quantum support vector machine reference model under a paired-seed protocol. Evaluation combines rare-event discrimination, low-false-positive-rate recovery, probability calibration, and runtime analysis. Angle encoding gives the strongest performance among the quantum logistic regression variants. At shallow depth, the angle-encoded model remains close to the best classical baselines in discrimination and low-false-positive-rate recovery, while also giving the lowest calibration error at the benchmark configuration. Murphy decomposition shows that the angle-encoded model maintains low reliability error and high, stable resolution across circuit depths and training-set sizes. This means that its probability estimates preserve both calibration and meaningful separation between candidate groups. Data re-uploading is competitive at small depth but loses discrimination and resolution at larger depth in the present multi-qubit implementation, while amplitude encoding remains weaker across dataset sizes. Shallow angle-encoded quantum logistic regression therefore gives the best balance among the tested quantum logistic models, although simulation runtime remains a practical limitation.

In this article we use the sub$^n$-soft graviton theorems to construct the map $\Top$ from the spin-graded set of holomorphic functions on local celestial sphere patches to differential operators acting on the asymptotic data for massless particles at $\scrip$, in analogy with previous results in the literature for the sub$^n$-soft photon theorems. The result is an explicit closed-form formula. We show that the wedge subalgebras for both Yang-Mills and gravity are the natural domain on which $\Top$ becomes a representation.

SrCu2(BO3)2 (SCBO) is a paradigmatic realization of the Shastry-Sutherland model, hosting geometrically frustrated spin dimers and a variety of quantum magnetic phases and phenomena. Although its magnetic properties have been extensively studied, the high-energy electronic excitations that determine the crystal-field environment and Cu-O hybridization have remained largely unexplored. Here we combine Cu L3-edge resonant inelastic x-ray scattering (RIXS), broadband optical spectroscopy, and electronic-structure calculations to determine the relevant local and interband excitation energy scales in SCBO. RIXS resolves a well-defined manifold of localized Cu2+ d-d excitations between 1.8 and 2.4 eV, whose energies and polarization dependence are well reproduced by multireference quantum-chemistry calculations. In contrast, optical spectroscopy identifies charge-transfer excitations with an absorption onset near 1.2-1.6 eV and a broader higher-energy structure around 4.5 eV, which are qualitatively captured by DFT+U calculations. Taken together, these results define the characteristic energy scales of d-d and CT excitations, offering quantitative benchmarks for computational frameworks and providing essential input for refining superexchange-based magnetic models of this prototypical frustrated quantum antiferromagnet.

Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped with a tangent functor. To do so, we adapt methods from categorical semantics of type theory to linear-non-linear adjunctions. This is a first step towards unifying DILL and dependent types.

We investigate the photon-drag shift current in an isotropic single-valley two-dimensional massive chiral Dirac model with chirality index $J=1,2,3$ by directly evaluating the full finite-$q$ non-vertical response beyond the perturbative small-$q$ regime. Our central result is that chirality qualitatively reorganizes the sign topology of the finite-$q$ photocurrent $\mathbf{ j}(\mathbf{ q})$. For $J=1$, the photocurrent remains broadly positive, whereas higher-chirality sectors ($J \ge 2$) generically develop internal zero-current contours and sign reversals within the kinematically allowed region. We further show that the photocurrent is symmetry-constrained to be purely transverse, $\mathbf{j}(\mathbf{q}) \propto \hat{\mathbf{z}}\times\mathbf{q}$, and vanishes in the strictly vertical-transition limit $q=0$ in centrosymmetric systems. Pauli blocking further shapes the response by selecting the active portion of the resonance contour, while its extinction at large $Δ$ or $q$ follows from a simple kinematic cutoff. These results establish the isotropic massive chiral Dirac problem as a symmetry-controlled benchmark for chirality-dependent finite-$q$ shift currents.

Moving Target Defense (MTD) is commonly formulated as a repeated security game to mitigate persistent threats. Although the strong Stackelberg equilibrium (SSE) characterizes the defender's optimal strategy in the leader-follower framework, computing the SSE often incurs high computational complexity, which significantly limits its practical deployment in MTD problems with multiple targets. This paper proposes adopting a zero-determinant (ZD) strategy for constructing an MTD strategy that achieves both high defensive performance and substantially low computational complexity. We first derive a necessary and sufficient condition for the existence of ZD strategies and investigate the performance of ZD strategies, which shows their upper-bound performance matches that of the SSE strategy. We then formulate two programs to find the optimal ZD strategy parameters under different conditions. Moreover, we design an algorithm to compute the proposed ZD strategies, along with the computational complexity analysis in comparison with the traditional SSE computation. Finally, we conduct experiments on two practical applications to verify our results.

Let $G_Γ$ be a graph product over a finite simplicial graph $Γ$, and let $K_Γ$ denote the kernel of the canonical homomorphism from $G_Γ$ to the direct product of its vertex groups. It is known that, up to isomorphism, $K_Γ$ depends only on the underlying graph $Γ$ and the cardinalities of the vertex groups. In this paper we establish a functorial refinement of this fact. We show that any collection of set maps between the vertex groups naturally induces a homomorphism between the corresponding kernels, and that this construction is functorial. Several applications are discussed.

Changepoint detection identifies times when the generative process of a time series changes, with applications in healthcare, cybersecurity, and finance. In multivariate settings, changes in cross-variable and temporal dependence are particularly challenging to detect, as they are often less pronounced than shifts in marginal statistics such as the mean or variance. Existing methods detect changes using reconstruction error, which provides only an indirect measure of dynamical change, or rely on scalar functionals that may be too coarse to capture global structure. We introduce CHASM, an online nonparametric method that monitors the truncated eigenvalue sequence of the recursively estimated dynamic mode decomposition operator. Designing such an approach raises two challenges: the permutation invariance of eigendecompositions, resolved via optimal linear assignment, and the lack of online changepoint methods for multivariate complex-valued time series, addressed through a novel augmented monitoring scheme. We study the theoretical properties of the dynamics estimator under the canonical vector autoregressive model, which directly motivates our algorithmic design. The proposed method achieves competitive or superior performance to modern competitors across synthetic and real-world data sets, including challenging settings in video and text data. It is unsupervised, depends on a small number of interpretable parameters, and requires no distributional assumptions beyond finite moments, making it readily deployable across scientific domains.

Adults with ADHD may use a self-management technique known as Body Doubling, in which the participant employs the presence of one or more agents as a means of initiating and completing tasks. We developed a framework on body doubling with twelve dimensions to better understand the characteristics of body doubling and discover future research directions for developing and testing body doubling for adults with ADHD. Our framework accounts for individual motivation, agent-related dimensions, interaction related dimensions, contextual dimensions, and efficacy. These dimensions show existing research gaps such as limited mixed reality prototypes, possibilities for more interactive body doubles, and the need for empirical studies to further understand of body doubling and adults with ADHD.

Digital maps are used to communicate generalized spatial information and relationships, yet are commonly made "accessible" using tables that lack geographic information. This study examines whether these tables and interactive text maps (ITMs) may be comparable to visual maps. Twenty sighted and 20 blind and low-vision individuals (BLVIs) performed tasks designed to compare visual maps, ITMs, and tables. Participants answered numeric, geographic, and combined numeric geographic questions using each representation, and performance, preference, and NASA-TLX were measured. Across both participant groups, map representations (visual and ITMs) significantly outperformed tables on geographic-based questions, while performance differences were minimal for numeric questions. For sighted participants, performance on geographic questions did not significantly differ between visual maps and ITMs, indicating that a larger powered study may find an "equivalent purpose" across these two conditions. Participants preferred map-based representations over tables. Perceived workload was highest for the ITM, intermediate for the visual map, and lowest for the table. Consistent with the Map Equivalent Purpose Framework, these findings indicate that Web Content Accessibility Guidelines-compliant ITMs can provide access to spatial information, unlike tables. These findings challenge prevailing accessibility practice that recommends tables lacking geographic information as map alternatives, and motivate reconsideration of accessibility legislation exempting digital thematic maps.

Finite-temperature effects in magnetized electron plasmas create a new Weyl-point degeneracy between the warm Langmuir and right-circularly polarized waves. The associated topological charge at this warm Weyl point is found to be 1, which, by the index theorem, predicts a gap-traversing topological edge mode. Solving the full warm-fluid eigenmode problem In a 1D inhomogeneous equilibrium, we numerically identify this anticipated mode as the warm topological Langmuir-cyclotron wave, which is absent in the cold limit and occurs in a parameter regime relevant to the LArge Plasma Device (LAPD) at UCLA.

We give different perspectives on the notion of shape for condensed anima. We prove that it recovers more classical notions of shape for topological spaces in the cases of all paracompact compactly generated spaces and all locally contractible spaces. These recovering statements imply and extend comparison results on sheaf and condensed cohomology by Clausen-Scholze and Haine. Another homotopy-theoretical direction for condensed anima are their condensed homotopy groups. Connected to this, we give a description of the underlying topological group functor on condensed groups via quasi-topological groups.

Gabor phase retrieval for signals has attracted considerable attention in recent years. For the more general short-time linear canonical transform (STLCT), which arises naturally in optical systems and canonical time--frequency analysis, existing work has so far focused mainly on uniqueness and sampling conditions. Explicit reconstruction formulas, quantitative stability estimates, and robust reconstruction algorithms, however, are still missing. In this paper, we study uniqueness, stability, and robust reconstruction for phase retrieval from phaseless STLCT measurements in the complex Gaussian shift-invariant space $V_β^\infty(φ)$. We first prove that every signal in $V_β^\infty(φ)$ is uniquely determined, up to a global unimodular constant, by its phaseless STLCT measurements on the semi-discrete set $\fracβ{2}\mathbb Z\times\mathbb R$, and we derive an explicit reconstruction formula. We then establish stability on intervals under an anchor-point condition, showing that the stability constant is governed by the maximal spacing between adjacent anchor points rather than by the radius of the whole interval. This prevents exponential deterioration with respect to the interval size. Motivated by the practical setting in which only finitely many discrete noisy magnitude samples are available, we further develop an explicit reconstruction algorithm with quantitative robustness guarantees, where the reconstruction error is controlled by the discretization parameters, the noise level, and the conditioning induced by the anchor points. In the Fourier case, our results recover the corresponding Gabor phase retrieval results of Grohs and Liehr and provide improved stability constants.

Model Context Protocol (MCP) have quickly become the interface layer between LLM agents and external tools, yet they also introduce unsafe data flows that existing analyzers handle poorly. Vulnerabilities manifest in two directions: requester-controlled arguments may propagate to sensitive operations, while untrusted external or sensitive internal data may surface through MCP-visible outputs and subsequently influence host or model behavior. Accurate detection is complicated by the heterogeneous registration and dispatch patterns MCP servers employ, the need for MCP-specific taint semantics, and the fact that bugs often only materialize along complete tool-scoped execution paths. We present MCP-BiFlow, a bidirectional static analysis framework built around MCP-aware entrypoint recovery, protocol-specific taint modeling, and interprocedural propagation analysis. Against a benchmark of 32 confirmed MCP vulnerability cases, MCP-BiFlow identifies 30 (93.8% recall), substantially outperforming CodeQL, Semgrep, Snyk Code, and MCPScan. Across 15,452 real-world MCP server repositories, MCP-BiFlow surfaces 549 overlap-compressed candidate clusters; manual review confirms 118 vulnerability paths in 87 servers, establishing unsafe propagation as a recurring failure mode that resists detection without protocol-aware recovery of both request-side and return-side flows.

A growing number of scholars seek to estimate causal effects of unstructured data such as text, images, and video. However, existing methods typically treat each object as a single, static observation. We develop a statistical framework for dynamic causal inference with unstructured data by leveraging generative artificial intelligence (GenAI) models. Our approach enables researchers to estimate the causal effects of sequences of treatment features, including their positions within text and video. We first extract internal representations of unstructured objects from a GenAI model and then estimate a marginal structural model using a neural network architecture that jointly learns a deconfounder for each treatment feature in the sequence. Our semiparametric inference framework yields valid asymptotic confidence intervals. Simulation studies demonstrate that the proposed estimator recovers the target causal effects and that the confidence intervals achieve nominal coverage in finite samples. We further apply our method to a randomized experiment on the Hong Kong protests, showing that the effect of a treatment feature depends critically on its position within the text.