Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampires output. We describe ongoing efforts in reconstructing Vampire proofs as trusted proofs in Lean

The K130 Room Temperature Cyclotron (RTC) at the Variable Energy Cyclotron Centre (VECC), Kolkata has delivered a variety of ion beams for experimental programs with stable performance since the 1970s. The extracted beams are transported to experimental stations through four beamlines. In this work, a two-step semi-numerical optimization framework is presented to improve the transmission efficiency of these transport lines. At its core, the method relies on multiparticle simulations to account for beam losses and nonlinear effects, which render the problem analytically intractable. To address these complexities, a derivative-free global optimization framework is developed to systematically improve beam transmission in the cyclotron beamlines, and its effectiveness is demonstrated experimentally. In the first phase, the beam parameters at the beamline entrance are estimated using Bayesian optimization constrained by experimentally measured transmission ratios for selected optics configurations. In the second phase, the quadrupole gradients are optimized using the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to maximize beam transmission. Optimized settings computed using this simulation based semi numerical methodology were then experimentally validated, achieving beam transmissions exceeding 70%.

In this work, we want to show several properties of an unnodal, complex Coble surface $X$ with irreducible boundary curve $C \in |-2 K_X|$. Namely, we show that every isotropic sequence ${\cal E}_1, \ldots, {\cal E}_r$ with $r \le 8$ and ${\cal E}_i {\cal E}_j = 1 - δ_{i, j}$ can be extended to a sequence of length $10$. Moreover, such a surface admits a birational quintic model $\overline X \subset \mathbb{P}^3$, with equation $αX_0 X_1^2 X_2^2 + βX_0 X_1^2 X_3^2 + γX_0 X_2^2 X_3^2 + X_1 X_2 X_3 q = 0$, where $q$ is a quadric form. Finally, we use this birational model to show that every biregular involution $i : X \to X$ on such a Coble surface is the lift of a Bertini involution.

Repository-level code agents have shown strong promise in real-world feature addition tasks, making reliable evaluation of their capabilities increasingly important. However, existing benchmarks primarily evaluate these agents as black boxes based on final test correctness, providing limited insight into how they reason and where failures arise. To address this limitation, we introduce RACE-bench, a reasoning-augmented benchmark for evaluating code agents on repository-level feature addition tasks. RACE-bench contains 528 real-world feature addition instances from 12 open-source repositories. Each instance is paired with executable patch verification and structured intermediate reasoning ground truth covering issue understanding, file localization, implementation tasks, and step decomposition. Based on this design, we introduce a dual-track evaluation framework that jointly measures patch correctness and intermediate reasoning quality. We evaluate three representative repository-level code agents on RACE-bench. On the full benchmark, Resolved Rates range from 29% to 70% across different agents. Our reasoning-level analysis further shows that while current agents perform well at understanding high-level intent, their performance degrades substantially when translating intent into concrete implementation steps. We also find that apply-success but test-fail cases exhibit lower reasoning recall (35.7% decrease) and higher over-prediction (94.1% increase) compared to successful cases. These findings highlight the importance of evaluating repository-level code agents beyond final patch correctness by examining the quality of their reasoning processes.

We propose modeling absorption spectrum measurements as mixtures of Gaussian process experts. This enables us to construct a flexible statistical model for interpolating and extrapolating measurements, facilitating statistical integration of Kramers-Kronig relations to estimate the whole complex refractive index. Additionally, we statistically model the anchoring points used in subtractive Kramers-Kronig relations to account for possible measurement errors of the anchor point. In addition to flexible statistical modeling, the mixtures of Gaussian process formulation enables automatic selection of measurement points to use for extrapolation. We apply the method to experimental absorption spectrum measurements of gallium arsenide, potassium chloride, and transparent wood.

Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario where this may be realized by measurement of basic conjugate observables of a quantum system by the environment.

In this thesis, an approximation for the full (3+1)D dynamics of the Glasma is presented, which breaks boost-invariance on the level of the nuclear fields and leads to rapidity dependence in the final results. For this treatment, the Yang-Mills equations are linearized in covariant gauge, where lower-order, nonlinear contributions are neglected and the dynamics are captured by the (3+1)D dilute Glasma. The analytic solutions of the (3+1)D dilute Glasma are derived in both position and momentum space formulations, providing a comprehensive understanding of the involved (3+1)D dynamics. In position space, the field strength tensor results from the integration of free-streaming gluons that are produced in $2\rightarrow1$ scattering processes where the initial nuclear fields overlap. In momentum space, the event-averaged gluon number distribution for the (3+1)D dilute Glasma is derived in Coulomb gauge. A generalized, three-dimensional McLerran-Venugopalan nuclear model is developed for nuclei with realistic envelopes and intrinsic longitudinal correlations. Numerical results are presented for the rapidity structure of the energy-momentum tensor, the gluon number distribution, and the transverse energy of the (3+1)D dilute Glasma. In position space, the extended longitudinal collision geometry and finite longitudinal correlation length break boost-invariance. In momentum space, the results each follow universal parametrizations and are fixed by the values of two scaling parameters. Furthermore, the numerical results exhibit limiting fragmentation where the rapidity profiles approach a limiting distribution at large rapidities. This feature is also derived locally in position space for the analytic expressions of the field strength tensor and, in momentum space, for the transverse energy of the (3+1)D dilute Glasma.

The rapid integration of Large Language Models (LLMs) into software engineering practice is reshaping how software testing activities are performed. LLMs are increasingly used to support software testing. Consequently, software testing education must evolve to prepare students for this new paradigm. However, while students have already begun to use LLMs in an ad hoc manner for testing tasks, there is limited empirical understanding of how such usage influences their testing behaviors, judgment, and learning outcomes. It is necessary to conduct a systematic investigation into how students learn to evaluate, control, and refine LLM-assisted testing results. This paper presents a mixed-methods, two-phase exploratory study on human-LLM collaboration in software testing education. In Phase I, we analyze classroom learning artifacts and interaction records from 15 students, together with a large-scale survey conducted in a national software testing competition (337 valid responses), to identify recurring prompt-related difficulties across testing tasks. The results reveal systematic interaction breakdowns, including missing contextual information, insufficient constraints, rigid one-shot prompting, and limited strategy-driven iteration, with automated test script generation emerging as a particularly heterogeneous and effort-intensive interaction context. Building on these findings, Phase II conducts an illustrative classroom practice that operationalizes the observed breakdowns into a lightweight, stage-aware prompt scaffold for test script generation, guiding students to explicitly articulate execution-relevant information such as environmental assumptions, interaction grounding, synchronization, and validation intent, and reporting descriptive shifts in students' testing-related articulation when interacting with LLMs.

Recently, the GeV--sub-PeV spectrum of supernova remnant (SNR) Cassiopeia A (Cas A), one of the youngest and most well-studied SNRs in our Galaxy, has been updated by observations of Fermi-LAT and LHAASO. We revisit Cas A with our previous shell-plus-jet asymmetric model and investigate its particle acceleration ability. The broadband fitting results suggest that the double-peaked gamma-ray spectrum can be well attributed to proton-proton (PP) collisions and inverse Compton scattering within the SNR shell, while the synchrotron emission from a jet component with velocity of $\sim0.1c$ can account for the hard X-ray emission up to 220 keV. Furthermore, the PP collisions in the jet can produce a sub-PeV emission, but constrained by the LHAASO-KM2A limit to a flux below $\sim 1\times10^{-14}\rm erg/(cm^2s)$ at 100 TeV. The energy of accelerated protons in the jet of Cas A could be up to $5\times10^{47}$ erg, which, assuming that the PeV cosmic ray distribution is clumpy in the Galaxy with the clump size comparable to the thickness of the Galactic plane, derives a proton flux consistent with the observed one at 1 PeV, implying that the Cas A-like SNRs can still be PeVatrons in the Galaxy. It is encouraging for LHAASO and future telescopes to detect or constrain Cas A spectrum above 100-TeV more precisely.

Heteroepitaxy conventionally relies on rigid crystalline substrates, implicitly assuming that lattice and thermal mismatch must be accommodated within the epitaxial layer, leading to residual strain and defects that worsen with increasing substrate size. Here we demonstrate a substrate-mediated strain-partitioning regime in which lattice and thermal mismatch are preferentially partitioned into the substrate rather than stored in the epitaxial layer. We report the epitaxial growth of single-crystalline GaN on mechanically compliant yet crystallographically ordered single-crystalline copper foils. Atomic-resolution microscopy, geometric phase analysis and density functional theory reveal that mismatch-induced stress is primarily screened by elastic deformation of the Cu lattice, accompanied by localized interfacial slip confined to a few atomic layers, leaving the AlN and GaN epilayers nearly strain-free despite large nominal mismatch. Leveraging this strain-released epitaxial platform, we further demonstrate dense GaN micro-light-emitting diode arrays that benefit from efficient vertical electrical conduction and thermal dissipation enabled by the metallic substrate. By establishing compliant single-crystal metal foils as a new substrate class, this work identifies mechanical contrast as an underexplored governing parameter in heteroepitaxial design, with implications extending beyond GaN.

The isometric dilation of a pair of commuting contractions due to Andô is not minimal. We modify Andô's dilation and construct a minimal isometric dilation on $\mathcal H \oplus_2 \ell_2(\mathcal H \oplus_2 \mathcal H)$ for a commuting pair of strict contractions on a Hilbert space $\mathcal H$. In the same spirit, we construct under certain conditions a minimal Andô dilation for a commuting pair of strict Banach space contractions. Further, we show that an Andô dilation is possible even for a more general pair of commuting contractions $(T_1,T_2)$ on a normed space $\mathbb X$ provided that the function $A_{T_i}: \mathbb X \rightarrow \mathbb R$ given by $A_{T_i}(x)=(\|x\|^2-\|T_ix\|^2)^{\frac{1}{2}}$ defines a norm on $\mathbb X$ for $i=1,2$.

This article determines the structure of the group ring $\mathbb{Z}_nG$, where $G$ is a finite group and $\mathbb{Z}_n$ is the ring of integers modulo $n$, such that $n$ is relatively prime to the order of $G$. The decomposition of $\mathbb{Z}_nG$ is given as a direct sum of matrix rings over Galois rings, thereby extending the structural theory of group rings beyond the classical field setting. We also provide a method to compute a generating set of the unit group $\mathcal{U}(\mathbb{Z}_nG)$, in terms of elementary matrices, using Shoda pair theory. The results are illustrated with examples.

We prove that, up to subpolynomial or polylogarithmic factors, there is no tradeoff between preprocessing time, query time, and size of exact distance oracles for planar graphs. Namely, we show how given an $n$-vertex weighted directed planar graph $G$, one can compute in $n^{1+o(1)}$ time and space a representation of $G$ from which one can extract the exact distance between any two vertices of $G$ in $\log^{2+o(1)}(n)$ time. Previously, it was only known how to construct oracles with these space and query time in $n^{3/2+o(1)}$ time [STOC 2019, SODA 2021, JACM 2023]. We show how to construct these oracles in $n^{1+o(1)}$ time.

The structured singular value $μ_E$ for a linear subspace $E$ of $M_n(\mathbb C)$ is defined by \[ μ_E(A)=1 / \inf\{\|X\| \ : \ X \in E, \ \det(I_n-AX)=0 \} \quad (A \in M_n(\mathbb{C})), \] and $μ_E(A)=0$ if there is no $X \in E$ with $\det(I_n-AX)=0$. It is well-known that $μ_E(A)$ coincides with the spectral radius $r(A)$ when $E=\{cI_n: c \in \mathbb C \}$ and $μ_E(A)=\|A\|$ when $E=M_n(\mathbb C)$, for all $A\in M_n(\mathbb C)$. Also, for any linear subspace $E$ satisfying $\{cI_n: c \in \mathbb C \} \subseteq E \subseteq M_n(\mathbb C)$, we have $r(A)\leq μ_E(A) \leq \|A\|$. We prove that if $E=\{cI_n: c \in \mathbb C \}$ and $F$ is any linear subspace of $M_n(\mathbb C)$ containing $E$, then $μ_E=μ_F$ if and only if $E=F$. We prove the exact same rigidity theorem for the linear subspace consisting of the diagonal matrices of order $n$. On the contrary, when $E=M_n(\mathbb C)$, we show that there is a proper subspace $F$ of $M_n(\mathbb C)$, viz. the space of symmetric matrices such that $μ_E=μ_F=$ operator norm. Further, we characterize all linear subspaces $F\subseteq M_n(\mathbb C)$ such that $μ_F$ coincides with the operator norm. Next, we show that in general there is no subspace $E$ of $M_n(\mathbb C)$ such that $μ_E=$ the numerical radius, not even for $M_2(\mathbb C)$. We establish the rigidity of the structured singular value for each of the subspaces $E$ of $M_2(\mathbb C)$ such that the corresponding $μ_E$-unit ball induces the domains -- symmetrized bidisc, tetrablock, pentablock, hexablock.

We present a new type of a quantum error correction code, termed Majorana-XYZ code, where the logical quantum information scales macroscopically yet is protected by topologically non-trivial degrees of freedom. It is a $[n,k,g,d]$ subsystem code with $n=L^2$ physical qubits, $k= \lfloor L/2 \rfloor$ logical qubits, $g \sim L^2$ gauge qubits, and distance $d = L$. The physical check operations, i.e. the measurements needed to obtain the error syndrome, are $3$-local and nearest-neighbour. The code detects every 1- and 2-qubit error, and every error of weight 3 and higher (constrained by the distance) that is not a product of the 3-qubit check operations, however, these products act only on the gauge qubits leaving the code space invariant. The undetected weight-3 and higher operators are confined to the gauge group and do not affect logical information. While the code does not have local stabiliser generators, the logical qubits cannot be modified locally by an undetectable error, and in this sense the Majorana-XYZ code combines notions of both topological and local gauge codes while providing a macroscopic number of topological logical qubits. Taken as a non-gauge stabiliser code we can encode $k \sim L^2 - 3L$ logical qubits into $L^2$ physical qubits; however, the check operators then become weight $2L$. The code is derived from an experimentally promising system of Majorana fermions on the honeycomb lattice with only nearest-neighbour interactions.

Real-time control of tokamak plasmas encompasses sustaining a high-performance stationary state, avoiding disruptions, and managing ramp-up and ramp-down phases. Real-time estimation and control of electron density is fundamental for monitoring and controlling particle confinement, heating efficiency, exhaust conditions, impurity concentration, fusion power, and proximity to the density limit. Building on the integration of a multi-rate observer based on RAPDENS into the TCV control system, this study explores its application to density profile control for detachment studies, ECH, and NBH L-mode plasmas, and high-performance H-mode scenarios. TCV experiments demonstrate the observer's capability to support detachment studies in complex divertor geometries, controlling the line-averaged density within the last-closed flux surface while rejecting interferometer pick-up from Scrap-Off Layer density in the divertor. The estimated density profile enables local control of central density in ECH/NBH L-mode plasmas below cutoff conditions; heating-induced profile peaking modification is treated as a disturbance to the control task. Real-time estimation of time-varying transport coefficients, such as the pinch velocity-to-diffusivity ratio, improves model predictive capabilities, and the underlying turbulent transport is characterized via linear and non-linear gyrokinetic simulations with GENE. Simultaneous control of edge-normalized density and toroidal beta in H-mode plasmas is then demonstrated, yielding good confinement, scenario reproducibility, and a diagnostics-independent edge-density metric, while avoiding density limits and diagnostic faults propagation.

We establish a solution theory for the incompressible Navier--Stokes--Fourier system with thermal noise, posed on the three-dimensional torus. While in the incompressible deterministic setting the equation for the velocity can be solved independently of the temperature, the inclusion of the effects of thermal fluctuations by means of the GENERIC framework leads to a nonlinear gradient noise term, which couples the dynamics of both variables. Therefore, the analysis poses new challenges, which are absent in the deterministic incompressible Navier--Stokes--Fourier equations. In particular, the a priori estimates used in the deterministic setting are not readily generalizable, the noise introduces strongly nonlinear gradient terms and the total energy lacks convexity. These challenges are overcome in the present work by a novel variable transformation, and novel entropy dissipation estimates. Thereby, the existence of global-in-time weak solutions for $L_x^2$ initial data, the existence of local-in-time strong solutions for regular initial data, and weak-strong uniqueness are obtained.

Enterprise adoption of permissioned blockchains remains limited due to the complexity and cost of integrating legacy systems. We present a modular adapter architecture that bridges enterprise applications with blockchain networks, designed to support small and medium-sized enterprises with limited technical resources. The architecture provides five key modules: (1) configurable data extractors supporting diverse interfaces such as APIs and file uploads, (2) data transformers that can convert to standard formats, (3) messaging middleware to ensure operations can tolerate lack of connectivity and traffic spikes, (4) blockchain loader to commit transactions to the blockchain, and (5) status visibility to collect and expose runtime metrics that support operational transparency. We validated the adapters through a pilot deployment in a real-world fruit supply chain, involving three distinct enterprises. The pilot achieved blockchain integration with minimal workflow disruption, demonstrating the usefulness of these adapters for practical interoperability of existing systems with the blockchain.

The one-third monolayer Sn layer on Si(111) has long been considered a benchmark system for exploring two-dimensional Mott physics, owing to its narrow bandwidth and sizable on-site Coulomb repulsion. Previous experiments suggested the emergence of a low-temperature Mott insulating phase with an energy gap of only a few tens of meV, while theory predicted a possible antiferromagnetic ordering that remained experimentally elusive. Here, by combining low-temperature scanning tunneling microscopy/spectroscopy with first-principles calculations, we reveal that the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) surface undergoes a transition below 30K into a robust insulating state characterized by a remarkably large gap of about 440 $\pm$ 120 meV at 4K, five to ten times larger than previously reported. Quasiparticle interference imaging uncovers a well-defined $2\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) superstructure, providing direct evidence for a two-dimensional stripe-like antiferromagnetic order. Ab initio calculations reveal that the silicon substrate stabilizes this phase through strong nonlocal tin-tin interactions, highlighting the decisive role of substrate-driven correlations in the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) system.

For an N-extremal solution $μ$ to an indeterminate moment problem it is known by a theorem of M. Riesz that the measure $(1+x^2)^{-1}dμ(x)$ is determinate. For $0<α<1$ we show by contradiction that there exist indeterminate N-extremal solutions $μ$ such that $(1+x^2)^{-α}dμ(x)$ is determinate, and there exist also indeterminate N-extremal solutions $μ$ such that $(1+x^2)^{-α}dμ(x)$ is indeterminate. Explicit examples of such measures are so far only known when $α=1/2$. For indeterminate Stieltjes moment problems and for N-extremal solutions $μ$, we show that $(1+x^2)^{-1/2}dμ(x)$ is indeterminate except when $μ=μ_F$ is the Friedrichs solution in case of which $(1+x^2)^{-1/2}dμ_F(x)$ is determinate. We identify the Friedrichs and Krein solutions for some indeterminate Stieltjes moment problems.

Many causal discovery algorithms, including the celebrated FCI algorithm, output a Partial Ancestral Graph (PAG). PAGs serve as an abstract graphical representation of the underlying causal structure, modeled by directed acyclic graphs with latent and selection variables. This paper develops a characterization of the set of extended-type conditional independence relations that are invariant across all causal models represented by a PAG. This theory allows us to formulate a general measure-theoretic version of Pearl's causal calculus and a sound and complete identification algorithm for PAGs under selection bias. Our results also apply when PAGs are learned by certain algorithms that integrate observational data with experimental data and incorporate background knowledge.

Power iteration can improve the accuracy of randomized SVD, but requires multiple data passes, making it impractical in streaming or memory-constrained settings. We introduce a lightweight yet effective sketch-power iteration, allowing power-like iterations with only a single pass of the data, which can be incorporated into one-pass algorithms for low-rank approximation. As an example, we integrate the sketch-power iteration into a one-pass algorithm proposed by Tropp et al., and introduce strategies to reduce its storage cost. We establish meaningful error bounds: given a fixed storage budget, the sketch sizes derived from the bounds closely match the optimal ones observed in reality. This allows one to preselect reasonable parameters. Numerical experiments on both synthetic and real-world datasets indicate that, under the same storage constraints, applying one or two sketch-power iterations can substantially improve the approximation accuracy of the considered one-pass algorithms. In particular, experiments on real data with flat spectrum show that the method can approximate the dominant singular vectors well.

This article explores a general factor structure for high-dimensional nonstationary functional time series, encompassing a wide range of factor models studied in the existing literature. We investigate the asymptotic spectral behaviors of the sample covariance operator under this general data structure. A novel fundamental sufficient condition, formulated in terms of a newly introduced effective rank tailored to this setup, is established under which empirical eigen-analysis yields spurious results, rendering sample eigenvalues and eigenvectors unreliable for accurately recovering the underlying factor structure. This generalizes the results of Onatski and Wang [2021] from typical high-dimensional time series (HDTS) to the more intricate functional framework. The newly defined effective rank is rigorously analyzed through a decomposition of the effects attributable to functional factor loadings and functional factors. Contrary to the findings in the HDTS setting, empirical eigen-analysis of models with only a small number of strong non-stationary factors may still produce spurious limits in the functional framework. Therefore, additional caution is warranted when applying covariance-based statistical methods to potentially nonstationary functional data. Simulation studies are performed to determine conditions under which spurious limits occur. Real data analysis on age-specific mortality rate data from multiple locations is conducted for evidence of spurious factors induced by empirical eigen-analysis.

This study aimed to adapt the Dual-Dimensional Scale of Instrumental and Relational Dependencies on Large Language Models (LLM-D12) into Turkish and evaluate its psychometric properties among regular LLM users. A sample of 387 participants (68.5% female; mean age = 25.22 +/- 7.13) completed the translated scale, which underwent cultural-linguistic validation through forward-backward translation and expert review. Confirmatory factor analysis supported the original two-factor structure after removing one item, with strong model fit (CFI = 0.993, RMSEA = 0.073). Internal consistency was high across both subscales: Cronbach's alpha = 0.831 (instrumental), 0.876 (relational), and 0.868 (total); McDonald's omega = 0.834, 0.880, and 0.900, respectively. Test-retest reliability and item monotonicity were satisfactory. External validity was demonstrated via significant associations with ATAI, IA, and PTLLM scores. Interestingly, the lack of association with need for cognition (NFC) suggests that LLM dependency may reflect strategic cognitive offloading rather than cognitive avoidance. The Turkish version of the LLM-D12 is a valid and reliable 11-item tool for assessing both instrumental and relational dependencies on LLMs.

Van der Waals (vdW) layered materials with long-range magnetic order have the potential to enable novel optoelectronic and spintronic applications. Among these, CrSBr is an air-stable, direct band gap semiconductor that hosts interlayer antiferromagnetic order, a highly anisotropic electronic structure, and strongly bound excitons. In particular, excitons in CrSBr have been shown to inherit the quasi-one-dimensional nature of the material and also couple to the underlying spinorder. However, mechanisms of exciton formation, dissociation, and interaction with free carriers remain largely unexplored, despite being crucial for spintronic and optoelectronic applications. Here, we employ time- and angle-resolved photoemission spectroscopy to map the electronic structure and excited state dynamics in CrSBr. We directly resolve an exceptionally large exciton binding energy (~800 meV) and a highly anisotropic momentum space distribution of the exciton, revealing its quasi-1D real-space character. We observe an excitation-density-dependent interconversion between bound excitons and quasi-free carriers on sub- to few-picosecond timescales, indicating that many-body effects govern the excited-state dynamics and optical properties during the initial stages of relaxation. Our work highlights the strongly bound, anisotropic character of excitons in CrSBr, as well as the microscopic interactions steering relaxation pathways after photoexcitation in elevated density regimes relevant for future device applications.

Bitcoin's limited programmability and transaction throughput have historically prevented native Bitcoin from participating in decentralized finance (DeFi) applications. Existing solutions depend on honest-majority thresholds, or centralized custodial entities that introduce significant trust requirements. This paper introduces Bitcoin Smart Accounts (BSA), a novel protocol that enables native Bitcoin to access DeFi through trust-minimized infrastructure while maintaining self-custody of funds. BSA achieves this through a combination of emulated Bitcoin covenants using Partially Signed Bitcoin Transactions (PSBTs) and Taproot scripts, a Trusted Execution Environment (TEE)-based arbitration system, and destination chain smart contracts that enable DeFi platforms to accept self-custodial Bitcoin as collateral without necessitating protocol-level modifications. The setup leverages liquidity secured by the Lombard Security Consortium which provides a twofold advantage: for a DeFi protocol, liquidators rely on fungible assets with deep liquidity to quickly exit positions, while for a depositor, the general trust assumptions of honest majority (m-of-n) are reduced to existential honesty (1-of-k). We present the complete protocol design, including the Bitcoin architecture, the TEE-based arbitration mechanism, and the Smart Account Registry for protocol management. We provide a security analysis that demonstrates the correctness, safety, and availability properties under our trust model. Our design enables native Bitcoin to serve as collateral in lending markets and other DeFi protocols without requiring users to relinquish custody of funds.

We present a strictly monotone, provably convergent two-dimensional (2D) integration method for multi-period mean-conditional value-at-risk (mean-CVaR) reward-risk stochastic control in models whose one-step increment law is specified via a closed-form characteristic function (CF). When the transition density is unavailable in closed form, we learn a nonnegative, normalized 2D transition kernel in Fourier space using a simplex-constrained Gaussian-mixture parameterization, and discretize the resulting convolution integrals with composite quadrature rules with nonnegative weights to guarantee monotonicity. The scheme is implemented efficiently using 2D fast Fourier transforms. Under mild Fourier-tail decay assumptions on the CF, we derive Fourier-domain $L_2$ kernel-approximation and truncation error estimates and translate them into real-space bounds that are used to establish $\ell_\infty$-stability, consistency, and pointwise convergence as the discretization and kernel-approximation parameters vanish. Numerical experiments for a fully coupled 2D jump--diffusion model in a multi-period portfolio optimization setting illustrate robustness and accuracy.

Transfer-based anti-money laundering (AML) systems monitor token flows through transaction-graph abstractions, implicitly assuming that economically meaningful value migration is sufficiently encoded in transfer-layer connectivity. In this paper, we demonstrate that this assumption, the bedrock of current industrial forensics, fundamentally collapses in composable smart-contract ecosystems. We formalize two structural mechanisms that undermine the completeness of transfer-layer attribution. First, we introduce Principal-Execution-Beneficiary (PEB) separation, where intent originators, transaction executors (e.g., MEV searchers), and ultimate beneficiaries are functionally decoupled. Second, we formalize state-mediated value migration, where economic coupling is enforced through invariant-driven contract state transitions (e.g., AMM reserve rebalancing) rather than explicit transfer continuity. Through a real-world case study of role-separated limit order execution and a constructive cross-pool arbitrage model, we prove that these mechanisms render transfer-layer observation neither attribution-complete nor causally closed. We further argue that simply expanding transfer-layer tracing capabilities fails to resolve the underlying attribution ambiguity inherent in structurally decoupled execution. Under modular composition and open participation markets, these mechanisms are structurally generative, implying that heuristic-based flow tracing has reached a formal observational boundary. We advocate for a paradigm shift toward AML based on execution semantics, focusing on the restitution of economic causality from atomic execution logic and state invariants rather than static graph connectivity.

T. Kambayashi had shown that $\mathbb{A}^2$-forms over separable field extensions are necessarily polynomial rings. However, there exist inseparable $\mathbb{A}^2$-forms which are not necessarily polynomial rings. In this paper, we give a structure theorem for $\mathbb{A}^2$-forms over arbitrary field extensions admitting a nontrivial $\mathbb{G}_a$-action. From this structure theorem we derive some conditions under which an $\mathbb{A}^2$-form becomes trivial. In particular, we prove that over a field $k$, a factorial $\mathbb{A}^2$-form having a $k$-rational point and a non-trivial $\mathbb{G}_a$-action is trivial and we also give examples demonstrating that none of these hypotheses can be discarded. As a consequence of the structure theorem, we obtain a generalization of the Zariski Cancellation Theorem for the affine plane over an arbitrary field.

We study the next-to-leading order (NLO) virtual and thermal corrections to relativistic $2 \rightarrow 2$ scattering processes involving scalar particles in the early Universe thermal plasma. Taking the example of freeze-in production of scalar dark matter pairs through these scatterings, we evaluate the impact of the NLO corrections to the annihilation rate and the dark matter yield. We find that including only thermal mass corrections to a leading order interaction rate can overestimate the reduction in these rates, and the full NLO corrections can modify the DM abundance predictions by $\mathcal{O}(30\%)$. It is also observed that while the virtual NLO effects are larger, the finite temperature NLO corrections to the matrix elements in the relativistic regime can modify the DM abundance by $\mathcal{O}(10\%)$, in comparison to the virtual NLO corrections.