This paper studies alpha testing in a high-dimensional conditional time-varying factor model with temporally dependent observations. Both factor loadings and alpha processes are allowed to vary smoothly over time, and the cross-sectional dimension may be comparable to or larger than the sample size. Using a B-spline sieve method, we develop a sum-type test for dense alternatives, a max-type test for sparse alternatives, and a Cauchy combination test for adaptive inference. On the theoretical side, we derive explicit stochastic expansions for the estimated average alphas, establish asymptotic normality of the sum statistic, and develop the extreme-value limit theory for the max statistic by showing its Gumbel convergence under temporal dependence together with the validity of block-bootstrap calibration. We further prove asymptotic independence between the sum and max statistics and thereby justify the Cauchy combination test. Simulation results demonstrate that the proposed procedures achieve satisfactory size control and competitive power across a wide range of dense and sparse alternatives. An empirical application further illustrates the usefulness of the proposed methods in testing asset-pricing models with time-varying structure.

In \cite{HLZ2} and \cite{HHLZ}, using $E_8$ bundles, some modular forms over $SL(2,{\bf Z})$ were constructed on $12$-dimensional manifolds and the Witten-Freed-Hopkins anomaly cancellation formula was derived by these $SL(2,Z)$ modular forms. In this paper, we construct several similar $SL(2,Z)$ modular forms on any dimensional manifolds and some new anomaly cancellation formulas and applications are given.

We determine the explicit value of the optimal constant in the trace inequality for functions of bounded variations in the case the domain has a particular class of singularities.

We examine the leading-power fragmentation of fully heavy pentaquarks in high-energy hadronic collisions. To this end, we complete the release of the hadron-structure-oriented PQ5Q1.0 fragmentation functions, by discussing the $P_{5c}$ set and delivering the $P_{5b}$ one. These functions incorporate an improved computation of the initial-scale input for the constituent heavy-quark fragmentation channel, making them particularly suitable for describing both the direct formation of a compact multicharm state and the hadronization from a diquark-antiquark-diquark configuration. For phenomenological applications, we employ the data-validated (sym)JETHAD framework to compute and analyze NLL/NLO$^+$ semi-inclusive production rates of pentaquark-plus-jet systems at the upcoming HL-LHC and the future FCC. This study marks a further step toward connecting hadronic structure, precision QCD, and the emerging physics of exotic matter.

Chalcogenide perovskites have emerged as promising lead free materials for photovoltaic and thermoelectric applications. Among them, BaZrS3 has attracted particular attention due to its thermal and chemical stability, favorable optoelectronic properties, and low thermal conductivity. Here, we combine molecular dynamics and Monte Carlo simulations based on machine learned interatomic potentials with scanning transmission electron microscopy to investigate mixing thermodynamics and phase stability in the BaZr(S,Se)3 system. We identify an unusual ordered structure that persists at room temperature, most prominently at 33% S, where S and Se atoms form alternating layers within the crystal. Free energy calculations yield the temperature composition phase diagram, including a nonperovskite delta phase in the Se rich limit and a perovskite phase in the S rich limit, separated by a broad two phase region. Analysis of the dielectric function and the absorption coefficient demonstrates that composition, crystal structure, and anion ordering jointly control the optical band gap. Selenium alloying enables tuning between approximately 1.6 and 1.9eV, while anion ordering within a given composition reduces the gap by about 0.12eV. Lastly, variations between structural polymorphs give rise to band gap differences of up to 0.4eV.

AI Assurance -- producing the machine-readable evidence required to demonstrate compliance with AI governance frameworks -- has mature policy scaffolding but lacks the infrastructure to operationalize it. Organizations building high-risk AI systems under the EU AI Act face a gap: frameworks such as the EU AI Act, ISO/IEC 42001, and NIST AI RMF specify what to assure but provide no executable format for how. This paper proposes OSCAL -- the NIST standard adopted for FedRAMP cybersecurity compliance -- as a candidate interchange format for AI governance, complementing rather than replacing the emerging JTC21 standards stack. We define 16 property extensions covering lifecycle phases, enforcement semantics, risk traceability, and risk-acceptance justification, and present a three-layer Compliance-as-Code architecture (policy, evidence, enforcement) that generates assurance evidence as a byproduct of model training. The SDK produces native OSCAL Assessment Results validated against the NIST JSON schema. We test the approach on two Annex III high-risk systems: a credit scoring model and a medical imaging segmentation system. The architecture and reference implementation are open-source under Apache 2.0.

The rise of generative artificial intelligence (genAI) models poses new possibilities and risks for how the past is remembered by accelerating content production and altering the process of information discovery. The most critical risk is historical misrepresentation, which ranges from the distortion of facts and inaccurate depiction of specific groups to more subtle forms, such as the selective moralization of history. The dangers of misrepresentation of the past are particularly pronounced for high-risk memories, such as memories of past atrocities, which have a strong emotional load and are often instrumentalised by political actors. To understand how substantive this risk is, we empirically investigate how genAI applications deal with high-risk memories of the Second World War atrocities in Ukraine. This case is crucial due to the scope of the atrocities and the intense, often instrumentalised, contestation surrounding their memory. We audit the performance of three common genAI applications for different types of misrepresentation, including hallucinations and inconsistent moralization, and discuss the implications for future memory practices.

How do security scanners perform on real-world code? We present RealVuln, the first open-source benchmark comparing Rule-Based SAST, General-Purpose LLMs, and Security-Specialized scanners on 26 intentionally vulnerable Python repositories (educational and Capture-The-Flag applications) with 796 hand-labeled entries (676 vulnerabilities, 120 false-positive traps). We test 15 scanners (3 Rule-Based SAST, 10 General-Purpose LLM, 2 Security-Specialized) and rank them by F3 score (beta=3, weighting recall 9x over precision). A clear three-tier ranking emerges under all metrics. Under F3, the Security-Specialized scanner Kolega.Dev (73.0) leads, followed by the best General-Purpose LLM, Claude Sonnet 4.6 (51.7), which in turn scores nearly 3x higher than the best Rule-Based tool, Semgrep (17.7). Under F1, Sonnet 4.6 leads (60.9) with Kolega.Dev at 52.4. Rankings within tiers shift with beta, but the three-tier hierarchy holds across all weightings. All code, ground-truth data, scanner outputs, and scoring scripts are released under an open-source license. An interactive dashboard is at https://realvuln.kolega.dev/. RealVuln is a living benchmark: versioned, community-driven, with a roadmap toward multi-language coverage.

Spin shuttling has crystalized as a powerful and promising tool for establishing intermediate-range connectivity in semiconductor spin-qubit devices. Although experimental demonstrations have performed exceptionally well on different materials platforms, the question of how to handle areas of low valley splitting in silicon during shuttling remains unresolved. In this work, we explore the possibility of utilizing the valley degree of freedom, particularly in regions of low valley splitting, to allow mobile spin qubits to be shuttled through an occupied stationary quantum dot, thereby leapfrogging over the stationary electron. This not only grants a more enriched mobility for shuttled electrons, as it opens new possible routing paths, but also enables the implementation of an entangling SWAP$^γ$ two-qubit gate operation in the process. Simulating this process for different sets of parameters, we demonstrate the feasibility of such an operation and offer a unique use case for otherwise precarious regions of a quantum processor chip and propose a possible extension to the set of possible operations for silicon spin qubit devices.

We investigate both qualitative and quantitative issues related to the classification of non-negative energy solutions to the anisotropic critical $p$-Laplace equation in $\mathbb{R}^n$, for $1<p<n$. Specifically, we establish an anisotropic version of Struwe's decomposition, along with the interaction estimate for the family of bubbles in this decomposition. Moreover, we provide a short proof of the classification result as well as a quantitative stability result, proving that every energy solution to a perturbation of the anisotropic critical equation must be closed to a bubble, in the absence of bubbling.

The interaction of neutrons and nuclei at low energies may potentially lead to scattering lengths several orders of magnitude larger than the effective range of the interaction, well beyond the nuclear scale. If such cases existed, they could lead to the observation of the Efimov effect in nuclei, a remarkable universal phenomenon that has been observed only in atoms. The interaction parameters of neutrons scattering off unstable nuclei can be explored in neutron-nucleus systems created after the fast removal of a few nucleons from a slightly heavier beam. The case of the $^{17}$B-$n$ system is considered, and the implications of its potentially huge scattering length on the structure of $^{19}$B as a $^{17}$B-$n$-$n$ Efimov trimer are discussed.

The computation of excited states within the Complete Active Space Self-Consistent Field (CASSCF) framework remains a significant challenge in quantum chemistry, both theoretically and algorithmically. In this work, we extend the Kähler manifold formalism introduced in Part I of this series to the CASSCF theory, and draw a geometrical connection from the time-dependent CASSCF equations to state-specific and linear response methodologies for excited states. This is achieved by first investigating the underlying CASSCF manifold and identifying its Kähler structure, which is complicated by the nontrivial coupling of CI and orbital degrees of freedom. Building on these theoretical findings, we derive the CASSCF linear response equations in a straightforward manner, and develop a robust state-specific method that relies solely on first-order derivatives of the CASSCF energy functional. Numerical results on representative molecular systems-water, formaldehyde, and ethylene-demonstrate the effectiveness of the proposed state-specific method, while revealing the difficulty of reliable identification of excited states due to nonlinearity induced by the CASSCF theory.

The physical properties of matter are typically described by coefficient matrices governed by crystal symmetry. Applying spatial operations, such as rotation, inversion, and mirror, to these matrices provides an effective approach for investigating material properties. However, the diversity of coefficient matrix types complicates their transformation via simple matrix multiplication, and existing methods suffer from cumbersome notation, high computational cost, and lack of intuitive interpretation. Moreover, as coefficient matrices grow in size, conventional approaches become increasingly inadequate. We present a generalized ``input-coefficient-output (ICO)" approach for constructing spatial operation matrices applicable to coefficient matrices across diverse physical systems, including but not limited to high-order nonlinear optics, elastic mechanics, electricity and magnetism. Our approach offers a concise formalism that enables intuitive reasoning about spatial transformations while delegating intensive computations to computational tools, which is analogous to the role of Feynman diagrams in facilitating understanding in physics. This method also offers valuable insights for future theoretical and experimental research.

On the textbook example of an isolated antiferromagnetic Heisenberg dimer, we demonstrate that the magnetic form factor and the magnetic electron density distribution can be extracted from the momentum-dependence of the inelastic neutron scattering (INS) intensity of a magnetic excitation. We measure the three-dimensional (3D) magnetic structure factor of the singlet-to-triplet excitation in Cu(II) acetate monohydrate with INS. Using a minimal parametrization of the magnetic electron density, we deduce the real-space density of the spin-entangled electrons and the transfer of magnetic electron density between metal and ligand atoms from the experimental data. Density functional theory (DFT) calculations reproduce the measured structure factor quantitatively, providing a direct validation of DFT broken-symmetry spin densities against full 3D INS data. The quantitative agreement between experiment, parametrization, and theory establishes a robust framework for determining magnetic form factors and the magnetic electron density in a broad range of magnetic materials and demonstrates INS as a probe of the envelope of spatial electronic wavefunctions.

The purpose of this paper is to investigate the relationship between hairy graph complexes associated to cyclic operads and their counterparts for operads (and, more generally, dioperads). This is based on the author's interpretation of these as Koszul complexes for the associated modules over the respective appropriate twisted downward (walled) Brauer category. The general question of relating such Koszul complexes is addressed by analysing the relationships between the respective twisted Brauer-type categories, proceeding through a direct analysis. The passage from the walled to unwalled context involves functors induced by the disjoint union of finite sets. As an application, for the cyclic operad associated to an operad, this leads to an explicit relation between the respective (hairy) graph homologies.

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive specialization can induce negative transfer. We formulate adaptive pooling as a statistical decision problem and propose a validation-driven framework that determines when and how specialization should be applied. Rather than grouping series based on representation similarity, we define partitions through out-of-sample predictive performance, thereby aligning data organization with predictive risk, defined as expected out-of-sample loss and approximated via validation error. Cluster assignments are iteratively updated using validation losses for both point (Huber) and probabilistic (pinball) forecasting, improving robustness to heavy-tailed errors and local anomalies. To ensure reliability, we introduce a leakage-free fallback mechanism that reverts to a global model whenever specialization fails to improve validation performance, providing a safeguard against performance degradation under a strict training-validation-test protocol. Experiments on large-scale traffic datasets demonstrate consistent improvements over strong baselines while avoiding degradation when heterogeneity is weak. Overall, the proposed framework provides a principled and practically reliable approach to adaptive pooling in high-dimensional forecasting problems.

JUNO is designed to determine the neutrino mass ordering with an energy resolution of 3% at 1 MeV. In the real detector, however, deformations of the central stainless-steel structure during installation lead to deviations of the photomultiplier tube (PMT) positions from their design values. Based on the limited survey data of the PMTs and the stainless-steel truss, we perform a correlation analysis of the measured points and propose a method to predict the positions of all PMTs. Using the resulting realistic geometry, we demonstrate that the detector deformation has a negligible effect on the energy reconstruction. In contrast, inaccuracies in the assumed geometry can introduce vertex biases of up to 40 mm. Incorporating the realistic geometry into the calibration-based PMT response model removes this bias and preserves the stability of the reconstruction algorithms.

Network-controlled repeaters (NCRs) are a low-cost means to extend coverage and strengthen macro diversity in wireless networks. They operate in real time by amplifying and re-transmitting the incoming signal with only hardware-level delays, without requiring any channel state information (CSI) at the repeater itself. However, their power amplifiers (PAs) generate non-linear distortion that is jointly forwarded with the desired signal and can undermine multiuser performance unless the distortion statistics are exploited. This paper develops a distortion-aware (DA) uplink framework for repeater-assisted massive MIMO (RA-MIMO) under PA non-linearities. We adopt a memoryless third-order polynomial model for the repeater PA and characterize the achievable spectral efficiency (SE) using the Bussgang decomposition. Closed-form expressions are derived for the Bussgang gain matrix and the distortion covariance. We also design a DA combining vector that maximizes the effective signal-to-interference-plus-distortion ratio.

Multilayered thin-film structures are frequently encountered in industrial applications, where accurate thermal property characterization is essential for performance optimization. These films, typically ranging from nanometers to micrometers in thickness, often exhibit anisotropic thermal conductivity and non-bulk heat capacity, which are challenging to measure. In this study, we introduce a variable-spot-size and multi-frequency square-pulsed source (SPS) method for the simultaneous determination of anisotropic thermal conductivities, heat capacities, and interfacial thermal conductance in multilayered systems. By leveraging a broad modulation frequency range (1 Hz to 10 MHz) and tunable laser spot sizes, the SPS method enhances sensitivity to different thermal parameters across layers. We validate this approach on a silicon-on-insulator (SOI) sample comprising a 1.59 um Si layer, 1.03 um SiO2 layer, and a silicon substrate with a 122 nm aluminum (Al) transducer. The SPS method successfully extracts seven key thermal parameters, including the in-plane and cross-plane thermal conductivities and heat capacity of the Si film, the thermal conductivity and heat capacity of the SiO2 layer, the thermal conductivity of the substrate, and the interfacial thermal conductance between Al and Si. Temperature-dependent measurements from 80 to 500 K showed excellent agreement with literature values and first-principles predictions, confirming the method's accuracy and reliability. These results demonstrate the SPS method as a powerful tool for comprehensive thermal characterization of complex multilayered structures, with implications for both fundamental research and practical applications.

Disaggregated storage systems improve resource utilization and enable independent scaling of storage and compute resources by separating storage resources from computing resources in data centers. NVMe over fabrics (NVMeoF) is a key technology that underpins the functionality and benefits of disaggregated storage systems. While NVMeoF inherently possesses substantial computing and memory capacity, these resources are often underutilized for tasks beyond simple I/O delegation. This study proposes OffloadFS, a user-level file system that enables offloaded IO-intensive tasks primarily to a disaggregated storage node for near-data processing, with the option to offload to peer compute nodes as well, without the need for distributed lock management. OffloadFS optimizes cache management by reducing interference between threads performing distinct I/O operations. On top of OffloadFS, we develop OffloadDB, which enables RocksDB to offload MemTable flush and compaction operations, and OffloadPrep, which offloads image pre-processing tasks for machine learning to disaggregated storage nodes. Our evaluation shows that OffloadFS improves the performance of RocksDB and machine learning pre-processing tasks by up to 3.36x and 1.85x, respectively, compared to OCFS2.

Accurate characterization of heat transport across solid-liquid interfaces is essential for thermal management in micro and nanoscale systems. Yet existing techniques often require prior knowledge of liquid properties, which complicates the simultaneous resolution of interfacial and bulk behaviors, and lose sensitivity once interfacial conductance exceeds 100 MW m-2 K-1. Here we present a differential square pulsed source (DSPS) method that provides simultaneous, non-contact measurement of liquid thermal conductivity, volumetric heat capacity, and solid-liquid interfacial conductance without any predefined material parameters. Dual frequency excitation combined with in-situ substrate referencing enables property extraction from multilayer structures, and numerical simulations show a typical uncertainty of about 8 % in interfacial conductance, confirming robustness. The protocol is validated for a wide spectrum of liquids, including oils, lubricants, aqueous electrolytes, and pure water, with excellent agreement with literature values for bulk properties. Analysis of the data set clarifies how vibrational spectrum mismatch, ionic layering, and related interfacial phenomena govern heat transfer, and demonstrates that oleophilic hexadecyl silane modification of aluminum increases interfacial conductance by a factor of sixteen. The results reveal that conductance can be strongly tuned through surface wettability and chemical functionalization, offering direct guidelines for interface engineering. Because the approach is readily extendable to soft materials such as thermal interface gels, it promises broad applicability in emerging interface-dominated thermal technologies.

Solid-liquid interfacial thermal conductance (ITC) critically influences heat transport in microfluidic, electronic, and energy systems, yet most optical thermometry techniques are limited to specific metal-liquid interfaces. In this work, we introduce a universal broadband square-pulsed thermometry method that enables simultaneous quantification of ITC across a wide range of arbitrary solid-liquid interfaces, while also providing accurate measurements of nanoscale liquid-film thickness. To validate the method, we applied it to Al-water interfaces, yielding ITC values in the range of 50-55 MW m^(-2) K^(-1), consistent with prior studies. The technique also reveals markedly lower ITCs for glass-water (9.9 MW m^(-2) K^(-1)) and Si-water (5.7 MW m^(-2) K^(-1)), and further measurements on Al-silicone oil (~10 MW m^(-2) K^(-1)) and PMMA-silicone oil (~0.4 MW m^(-2) K^(-1)) extend the validation to highly viscous nonpolar liquids and polymer-liquid interfaces. These results highlight the capability of the method to capture thermal transport differences across diverse solid-liquid combinations. Further comparisons with acoustic/diffuse mismatch models and molecular dynamics simulations, together with theoretical analysis, highlight the influence of vibrational mismatch, wettability, and surface condition on interfacial thermal transport. This broadly applicable technique enables rapid, quantitative characterization of solid-liquid interfacial thermal transport, with broad implications for interfacial heat transfer science and technology.

In this paper we consider the volume-constrained minimization of a variant of the Ohta-Kawasaki functional with an anisotropic surface energy replacing the standard perimeter. Following and suitably adapting the second variation approach devised in arXiv:1211.0164, we prove local minimality results for the horizontal lamellar configuration, in analogy with the isotropic case, under the assumption that the anisotropy is uniformly elliptic. If instead the Wulff shape of the anisotropy has upper and lower horizontal facets, we prove that the lamella exhibits a rigid behavior and is an isolated local minimizer for all parameter values. We conclude by showing some global minimality results, mostly focusing on the planar case.

We study area- and length-preserving curvature flows for embedded closed curves on pinched Hadamard surfaces. In the variable-curvature setting, the evolution equations contain additional lower-order terms, so the PDE analysis requires refined comparison arguments and delicate curvature estimates. For smooth convex initial curves, we prove preservation and instantaneous strictness of convexity, long-time existence, and uniform bounds for the curvature and its higher derivatives. Under additional geometric assumptions, we obtain convergence of the curvature to a constant. In the rotationally symmetric case, the area-preserving flow exhibits a dichotomy: either the evolving curves converge exponentially to a geodesic circle, or they drift off to infinity and approach a constant-curvature limit curve. We also identify a geometric condition on the initial curve that prevents escape to infinity and guarantees convergence to a geodesic circle.

We study Poincare-Sobolev type inequalities for compactly supported smooth functions which are defined in the Euclidean $n$-space and whose absolute value of gradient are Choquet $δ/n$-integrable with respect to the $δ$-dimensional Hausdorff content, $n\geq 2$, $δ\in (0,n]$. In particular, our results imply a new Sobolev inequality for quasicontinuous functions defined in the Sobolev space $W^{1,1}_0(\mathbb{R}^n)$. As an application we extend a recently introduced superlevel Sobolev inequality into a context of the Hausdorff content.

Light-matter interactions are governed by conservation laws of energy and momentum. For harmonic generation in crystalline solids, energy conservation imposes that $m$ incoming photons with energy $\hbar ω_0$ are combined to form one photon at energy $m\hbar ω_0$. Linear momentum conservation governs phase matching, whereas angular momentum conservation connects the angular momentum carried by photons to the discrete rotational symmetry of the crystal lattice. As a consequence, circular harmonic generation exerts a torque on the lattice and, conversely, a macroscopic rotation of the crystal induces a nonlinear rotational Doppler shift. These cornerstone laws of nonlinear optics rely on macroscopic symmetry arguments, and therefore provide little insight into the microscopic origin of angular momentum transfer. Here we uncover a direct connection between angular momentum conservation in nonlinear optics and the electronic quantum geometry, by proving that the transferred angular momentum from light to the crystal is proportional to the local Berry curvature at one optical resonance. This relation is encoded in the nonlinear harmonic circular dichroism, which we measure experimentally in an atomically thin semiconductor. With this, we extend our understanding of nonlinear optics, and we establish a method for the all-optical control and read-out of the local Berry curvature.

In the context of spacecraft attitude control, parametrizations such as direction vectors or quaternions are often used to avoid singularities in the attitude representation. This, however, complicates the stability analysis of the system since, given the additional unit constraints, the resulting dynamics evolve on non-contractible manifolds. In this paper, we present a framework to verify almost global asymptotic stability of such systems using LaSalle's invariance principle and sum-of-squares programming, simplifying the search for Lyapunov functions. The framework is then applied to two examples: two-axis attitude acquisition utilizing aerodynamics in very low Earth orbits, and three-axis attitude acquisition for a satellite subject to gravity gradient torques in a circular orbit.

Let $γ$ be a constant such that $0 < γ< 1$, and let $n$ be a sufficiently large integer. Consider a $3$-uniform hypergraph $H$ on $n$ vertices. In 2013, Kühn, Osthus, and Treglown, along with Khan independently, proved that for large enough $n$ with $n\equiv 0\pmod{3}$, if $δ_1(H)\geq\binom{2n/3}{2}$, then $H$ admits a perfect matching. For any vertex $v\in V(H)$, we define $N_H(v)$ as the $2$-graph with vertex set $V(H)\setminus\{v\}$ and edge set $E(N_H(v)) = \{e\subseteq V(H)\setminus\{v\}: e\cup \{v\}\in E(H)\}$. In this paper, we show that if $ρ(N_H(v)) > (2/3+γ)n$ for all $v\in V(H)$, where $ρ(N_H(v))$ denotes the spectral radius of $N_H(v)$, then $H$ has a perfect matching. This bound is asymptotically tight. Furthermore, for integer $s$ satisfying $n\geq 3s+3$, we establish that if \[ ρ(N_H(v))>\frac{1}{2}(s-1+\sqrt{(s-1)^2+4s(n-s-1)})\] holds for every $v\in V(H),$ then $H$ admits a fractional matching of size $s+1$. Notably, this second spectral bound is tight.

Repository-level code intelligence tasks require large language models (LLMs) to process long, multi-file contexts. Such inputs introduce three challenges: crucial context can be obscured by noise, truncated due to limited windows, and increased inference latency. Context compression mitigates these risks by condensing inputs. While studied in NLP, its applicability to code tasks remains largely unexplored. We present the first systematic empirical study of context compression for repository-level code intelligence, organizing eight methods into three paradigms: discrete token sequences, continuous latent vectors, and visual tokens. We evaluate them on code completion and generation, measuring performance and efficiency. Results show context compression is effective: at 4x compression, continuous latent vector methods surpass full-context performance by up to 28.3% in BLEU score, indicating they filter noise rather than just truncating. On efficiency, all paradigms reduce inference cost. Both visual and text-based compression achieve up to 50% reduction in end-to-end latency at high ratios, approaching the cost of inference without repository context. These findings establish context compression as a viable approach and provide guidance for paradigm selection.

Vortex $γ$ photons in superposition states have important applications in photonuclear, high-energy, and strong-field physics. However, their controlled generation in the $γ$-ray regime remains a great challenge. Here, we put forward a novel method for the generation of vortex $γ$ photon in superposition states, with controllable orbital angular momentum (OAM) separation $Δ\ell^\prime$ and modal weights, via nonlinear Compton scattering driven by multifrequency circularly polarized laser fields. We develop a strong-field quantum electrodynamics (QED) framework to reveal the underlying mechanism and calculate the radiation probabilities. In our method, the superposition arises from interference between energy-degenerate multiphoton pathways carrying distinct OAM. For two-frequency fields, the OAM separation follows $Δ\ell'=ν\mp1$ (upper/lower sign for equal/opposite helicities), and modal weights are tunable by laser intensities, with $ν$ the frequency ratio. Vortex $γ$ photons in controllable superposition states from our method have significant applications in strong-field QED and nuclear photonics.