Cross-correlations between 21cm observations and galaxy surveys provide a powerful probe of reionization by providing robustness against foreground contamination while linking ionization morphology to galaxies. We quantified the constraining power of 21cm galaxy cross-power spectra for inferring the neutral hydrogen fraction, $x_\mathrm{HI}(z),$ and mean overdensity, $\langle 1+δ_\mathrm{HI} \rangle(z)$, exploring dependence on the field of view; redshift precision, $σ_z$; and minimum halo mass, $M_\mathrm{h,min}$. We employed our simulation-based inference framework EoRFlow for likelihood-free parameter estimation. Mock observations include thermal noise for 100h of SKA-Low with foreground avoidance and realistic galaxy-survey effects. For a fiducial survey ($\mathrm{FOV}=100\,\mathrm{deg}^2$, $σ_z=0.001$, $M_\mathrm{h,min}=10^{11}\mathrm{M}_\odot$), cross-power spectra yield unbiased constraints with posterior volumes (PVs) of $\sim$10% relative to priors. Cross-power measurements reduce the PV by 20-30% versus 21cm auto-power alone. With foreground avoidance, spectroscopic redshift precision is essential; photometric redshifts render cross-correlations uninformative. Notably, cross-power spectra constrain ionizing source properties, the escape fraction $f_\mathrm{esc,}$ and the star formation efficiency $f_*$, which remain degenerate in auto-power (PV >60%). Tight constraints require either deep surveys detecting faint galaxies ($M_\mathrm{h,min} \sim 10^{10}\mathrm{M}_\odot$) with moderate foregrounds (PV~11%) or conservative mass limits with optimistic foreground removal (PV~19%). 21cm galaxy cross-correlations enhance morphology constraints beyond auto-power while enabling previously inaccessible source property constraints. Realizing full potential requires precise redshifts and either faint galaxy detection limits or improved 21cm foreground cleaning.

Integrating contention-based random access procedures into low Earth orbit (LEO) satellite communication (SatCom) systems poses new challenges, including long propagation delays, large Doppler shifts, and a large number of simultaneous access attempts. These factors degrade the efficiency and responsiveness of conventional random access schemes, particularly in scenarios such as satellite-based internet of things and direct-to-device services. In this paper, we propose a deep learning-based random access framework designed for LEO SatCom systems. The framework incorporates an early preamble collision classifier that uses multi-antenna correlation features and a lightweight 1D convolutional neural network to estimate the number of collided users at the earliest stage. Based on this estimate, we introduce an opportunistic transmission scheme that balances access probability and resource efficiency to improve success rates and reduce delay. Simulation results under 3GPP-compliant LEO settings confirm that the proposed framework achieves higher access success probability, lower delay, better physical uplink shared channel utilization, and reduced computational complexity compared to existing schemes.

The variational quantum power method (VQPM), which adapts the classical power iteration algorithm for quantum settings, has shown promise for eigenvector estimation and optimization on quantum hardware. In this work, we provide a comprehensive theoretical and numerical analysis of VQPM by investigating its convergence, robustness, and qubit locking mechanisms. We present detailed strategies for applying VQPM to QUBO problems by leveraging these locking mechanisms, establishing systematic guidelines for their practical applications. Furthermore, we provide a comparative study against the Quantum Approximate Optimization Algorithm (QAOA). Our analysis evaluates classical optimization behaviors and evaluates performance using localized Hamming distance (bit difference of the combinatorial solution). Scaling simulations up to $n=18$ qubits demonstrate that the success probability in VQPM exhibits notable resilience. Finally, we evaluate VQPM under realistic quantum noise using the IBM Qiskit Aer framework. Our results indicate that VQPM serves as an effective quantum optimization algorithm for combinatorial problems, and this work can serve as an initial guideline for such applications.

We study the well-posedness of a non-linear heat equation with power nonlinearity with positive initial data on quantum Euclidean spaces. We prove a noncommutative analogue of the classical Fujita theorem by identifying the critical exponent separating finite-time blow-up from global existence for small initial data. Moreover, we establish a fundamental inequality in general semifinite von Neumann algebras that is of independent interest and plays a crucial role in the study of global existence and local well-posedness of solutions of nonlinear equations in noncommutative setting.

In piecewise omnigenous magnetic fields, charged particles remain perfectly confined in the abscence of collisions and turbulence. This concept extends the traditional notion of omnigenity, the theoretical principle upon which most of existing magnetic fusion reactor designs, including tokamaks, are based. While piecewise omnigenity broadens the range of potentially viable stellarator reactor candidates, it is achieved by relaxing the requirement of continuity in the magnetic field strength, which could appear to pose significant challenges for the design of magnetohydrodynamic equilibria. In this work, a stellarator magnetic configuration is presented that satisfies the ideal magnetohydrodynamic equilibrium equation and that achieves unprecedented levels of piecewise omnigenity. As a result, it exhibits favorable transport characteristics, including reduced bulk radial (neoclassical and turbulent transport), bootstrap current and fast ion losses. In addition, the configuration displays robust MHD stability across a range of \b{eta} values and possesses a rotational transform profile compatible with an island divertor. Collectively, these features satisfy the standard set of physics criteria required for a viable reactor candidate which, until now, were believed to be attainable only by certain types of omnigenous stellarators.

Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multi-stability, which arise from the geometry and configuration of the constituent building blocks. Lattice-based metamaterials, in particular, provide lightweight platforms where local instabilities can dictate the global response, with applications in energy routing and vibration isolation. In underdamped structures, perturbations have been found to propagate as nonlinear waves, e.g., transition waves or solitons. Here we investigate the opposite limit of overdamped, highly dissipative lattice metamaterials. Focusing on three-dimensional structures, we uncover how buckling instabilities, triggered by compression, propagate as fronts that shape the macroscopic behavior. We demonstrate in experiments on 3D-printed simple cubic lattices how global and local buckling modes can be controlled via the lattice geometry. By incorporating viscoelastic dissipation into a 3D-continuum model, we show that strain-driven buckling fronts obey coupled reaction-diffusion equations. The diffusion and reaction coefficients, determined by local geometry, material properties, and strain, select the propagation direction and enable steering of the fronts. This establishes a predictive and experimentally validated framework for the control of cascading mechanical instabilities in lattice-based metamaterials.

Originally, the Biswas--Chatterjee--Sen model was shown to exhibit an order/disorder phase transition for a sufficiently large number of negative interactions among actors. In this paper, the model is extended by the existence of anticonformists and inflexibles. Anticonformists are actors who define themselves in opposition to the group and may intentionally reject what most people accept, while inflexibles are those who do not change their opinions at all. Both discrete and continuous opinions are considered. With direct Monte Carlo simulations and mean-field calculations, we check the influence of fractions of anticonformists and inflexibles on the mean opinion in the system. With the mean-field calculations, we identify ranges of fractions of anticonformists where an ordered phase of the system is available. The results of the mean-field calculations perfectly match the results of the Monte Carlo simulations. We consider inflexibles adhered: (i) to extreme opinions; (ii) to specific opinions, and (iii) chosen independently of their initial opinion. For inflexibles adhered to specific and extreme opinions, they play a role of an effective bias suppressing the disordered phase in the system. The qualitative results of introducing anticonformists (inflexibles) in various ways (discrete/continuous opinions and annealed/quenched disorder) are roughly the same. However, for the model extended by inflexibles, we can observe a systematic shift of the mean order parameter to its higher values for quenched disorder compared with annealed disorder. On the other hand, for anticonformists modeled with a continuous space of opinions, we can observe a systematic shift of the mean order parameter to its higher values compared with the discrete space of opinions.

For a locally defined real analytic function $f$, we study the relation between the oscillation index of oscillatory integrals and the real log canonical threshold. The former is always negative, and its absolute value is greater than or equal to the latter. They coincide very often, but there are certain exceptional cases, and it is not very clear when the equality holds. In this note we give some sufficient conditions for the coincidence to hold or to fail. In the Newton-nondegenerate convenient homogeneous case, we show that the strict inequality holds if the number of variables $n$ is even and smaller than the degree $d$ of $f$ (or $f^{-1}(0)=\{0\}$), and the equality holds if $n$ is odd and $f^{-1}(0)=\{0\}$ (in particular, $d$ is even). The first assertion does not seem to be compatible with some standard formula in the literature, and there must be some error somewhere, although it does not seem easy to detect it inside this paper.

Incarceration-diversion treatment programs aim to improve societal reintegration and reduce recidivism, but limited capacity forces policymakers to make prioritization decisions that often rely on risk assessment tools. While predictive, these tools typically treat risk as a static, individual attribute, which overlooks how risk evolves over time and how treatment decisions shape outcomes through social interactions. In this paper, we develop a new framework that models reoffending risk as a human-system interaction, linking individual behavior with system-level dynamics and endogenous community feedback. Using an agent-based simulation calibrated to U.S. probation data, we evaluate treatment allocation policies under different capacity constraints and incarceration settings. Our results show that no single prioritization policy dominates. Instead, policy effectiveness depends on temporal windows and system parameters: prioritizing low-risk individuals performs better when long-term trajectories matter, while prioritizing high-risk individuals becomes more effective in the short term or when incarceration leads to shorter monitoring periods. These findings highlight the need to evaluate risk-based decision systems as sociotechnical systems with long-term accountability, rather than as isolated predictive tools.

Dark matter dominates the matter content of the Universe, and its properties can be constrained through large-scale structure probes such as the cross-correlation between the unresolved gamma-ray background (UGRB) and weak gravitational lensing. We analysed 15 years of Fermi-LAT data, constructing UGRB intensity maps in ten energy bins (0.5-1000 GeV), and cross-correlated them with KiDS-Legacy shear in six tomographic bins. The measurements were performed using angular power spectra estimated with the pseudo-$C_\ell$ method. No significant cross-correlation is found. Based on this non-detection, we present 95% upper bounds on the weakly interacting massive particle (WIMP) decay rate $Γ_{\rm dec}$ and velocity-averaged annihilation cross-section $\langleσ_{\rm ann} v\rangle$ as functions of mass. We compare our results with bounds from other cosmological tracers and from local probes, and found them to be complementary, particularly at low masses ($\rm GeV/TeV$). In addition, using a Euclid-like lensing survey cross-correlated with Fermi-LAT, we forecast $\sim$2 times tighter limits, highlighting the potential of forthcoming data to strengthen constraints on dark matter annihilation and decay.

Baryons can be described within several theoretical frameworks. Among them, the constituent approach is widely used. In this context, we aim to evaluate the accuracy of a particular model of baryons: the quark-diquark approximation. It consists in separating the three-body system into two subsequent two-body ones: a pair of two quarks, the diquark, and a second system consisting of the diquark and the third quark. This approximation is widely used, but its accuracy is rarely evaluated. The goal of this work is to perform this evaluation by comparing the quark-diquark model with a three-body model, both using the same semi-relativistic interaction. The baryon masses and some characteristic distances are computed and analysed within both approaches. Additionally, an original procedure to establish the quark-diquark potential will be presented with the aim to increase the precision of this approximation. It is shown that a diquark must not necessarily be compact to obtain good baryon masses.

To maximize performance, many modern blockchain systems rely on eventually-synchronous, Byzantine fault-tolerant (BFT) consensus protocols. Two protocol designs have emerged in this space: protocols that minimize latency using a leader that drives both data dissemination and consensus, and protocols that maximize throughput using a separate, asynchronous data dissemination layer. Recent protocols such as Partially-Synchronous Bullshark and Sailfish combine elements of both approaches by using a DAG to enable parallel data dissemination and a leader that paces DAG formation. This improves latency while achieving state-of-the-art throughput. Yet the latency of leader-based protocols is still better under moderate loads, which are common in practice. We present Angelfish, a hybrid protocol that adapts smoothly across this design space, from leader-based to Sailfish-like DAG-based consensus. Angelfish lets a dynamically adjusted subset of parties use best-effort broadcast to issue lightweight votes instead of reliably broadcasting costlier DAG vertices. This reduces communication, helps lagging nodes catch up, and lowers latency in practice compared to prior DAG-based protocols. Our empirical evaluation shows that Angelfish attains state-of-the-art peak throughput while significantly lowering latency under moderate throughput, delivering the best of both worlds.

Three-dimensional topological spin textures have attracted growing interest due to their rich geometry and potential for functional magnetic phenomena. In this work, we propose the concept of symmetry-transforming magnetic models as a novel route to generate and stabilize complex three-dimensional textures in an arbitrary magnetic background. Using this framework, we predict a screw chiral magnet model that stabilizes magnetic Hopfions and other three-dimensional magnetic textures within a ferromagnetic background. We show that the resulting solitons display distinctive physical properties, including unconventional Goldstone modes. Our results establish continuous symmetry transformations as a general strategy for uncovering new classes of magnetic solitons with unique dynamical signatures.

AI chatbots designed as emotional companions blur the boundaries between interpersonal intimacy and institutional software, creating a complex, multi-dimensional privacy environment. Drawing on Communication Privacy Management theory and Masur's horizontal (user-AI) and vertical (user-platform) privacy framework, we conducted in-depth interviews with fifteen users of companion AI platforms such as Replika and Character.AI. Our findings reveal that users blend interpersonal habits with institutional awareness: while the non-judgmental, always-available nature of chatbots fosters emotional safety and encourages self-disclosure, users remain mindful of institutional risks and actively manage privacy through layered strategies and selective sharing. Despite this, many feel uncertain or powerless regarding platform-level data control. Anthropomorphic design further blurs privacy boundaries, sometimes leading to unintentional oversharing and privacy turbulence. These results extend privacy theory by highlighting the unique interplay of emotional and institutional privacy management in human-AI companionship.

As quantum processors are deployed across different hardware platforms and remote cloud laboratories, a basic physical question is whether two black-box devices realize the same quantum process, without relying on a trusted classical description. We formulate the core primitive for this comparison task as \emph{distributed similarity estimation of quantum channels} (DSEC): given local access to two unknown channels, estimate the normalized inner product of their Choi states. We prove that the optimal query complexity of DSEC is $Θ(\max\{\sqrt{d}/\varepsilon,1/\varepsilon^2\})$, where $d$ is the channel dimension and $\varepsilon$ is the additive error. This matching query complexity is nontrivial: channel learning permits input choices and interleaving known operations, which makes channel learning strictly harder than state learning. We first prove an information-theoretic lower bound with this scaling, which holds even in the \emph{strongest setting}, allowing adaptive strategies, multiple rounds of classical communication, and coherent access with arbitrary ancillas. We then give a matching upper bound in the \emph{weakest setting}, namely non-adaptive and ancilla-free incoherent access, via a randomized measurement algorithm achieving this bound. Finally, we show that our algorithm achieves a quadratic improvement over classical shadow baselines. Our results provide theoretically optimal and practical algorithms for quantum device benchmarking and distributed quantum learning.

We propose to discuss the modular flavor model and the stabilization of single modulus field in the Jordan frame supergravity with non-minimal scalar-curvature coupling of the form $Φ(τ,\barτ)R$. Modular invariance, positivity of the scale factor and positive definiteness of the Kahler metric constrain stringently the form of the frame function, consequently the Kahler potential by the relation $Φ(τ,\barτ)=-3\exp[-K(τ,\barτ)/3]$. We discuss some general properties of scalar potentials after the scale transformation from the Jordan frame to the Einstein frame. We find that the shape of the resulting scalar potential in the Einstein frame is quite different from that of ordinary single modulus stabilization mechanism. The scalar potential could be stationary at the $i\infty$ fixed point, leading to a runaway type vacuum. Such a runaway-type vacuum can be properly stabilized at typical modulus VEV with large $\Imτ$. We also discuss numerically the modulus stabilization for some simplified scenarios.

We compute the full one-loop corrections to the primordial tensor power spectrum in an inflationary scenario with a {non-canonical spectator field}, using the in-in formalism. We derive semi-analytic results for the scalar-sourced one-loop tensor spectrum and the effective tensor-to-scalar ratio, $r_{\mathrm{eff}}$. We consider two representative coupling functions: a localized Gaussian dip (Model G), which leads to moderate loop corrections, and a rapidly oscillatory coupling (Model O), which can yield much larger loop contributions. For Model G, we find a $\mathcal{O}(1)$ correction to $r_{\mathrm{eff}}$ while Model O can significantly enhance $r_{\mathrm{eff}}$ by several orders of magnitude (relative to the tree-level value). We further calculate the energy density of primordial gravitational waves. Assuming that primordial black holes with mass $10^{-12}M_{\odot}$ generated in this scenario, constitute all of the dark matter, we find that the results are several orders of magnitude lower than the sensitivities of Taiji/TianQin/LISA.

In this paper, we consider an age-structured jump model that arises as a description of continuous time random walks with infinite mean waiting time between jumps. We prove that under a suitable rescaling, this equation converges in the long time large scale limit to a time fractional subdiffusion equation.

The usual definitions of algorithmic fairness focus on population-level statistics, such as demographic parity or equal opportunity. However, in many social or economic contexts, fairness is not perceived globally, but locally, through an individual's peer network and comparisons. We propose a theoretical model of perceived fairness networks, in which each individual's sense of discrimination depends on the local topology of interactions. We show that even if a decision rule satisfies standard criteria of fairness, perceived discrimination can persist or even increase in the presence of homophily or assortative mixing. We propose a formalism for the concept of fairness perception, linking network structure, local observation, and social perception. Analytical and simulation results highlight how network topology affects the divergence between objective fairness and perceived fairness, with implications for algorithmic governance and applications in finance and collaborative insurance.

Rotation is a natural tool in ultracold gases to break time-reversal symmetry, yet its impact on the collective excitations of supersolids remains largely unexplored. We show theoretically that tuning the rotation frequency, rather than the interparticle interactions, can trigger the superfluid-to-supersolid transition in Bose-Einstein condensates (dBECs). Computing excitation spectra in the presence of vortices and persistent currents, we uncover a vortex-driven de-softening mechanism whereby quantized vorticity elevates the gapless Goldstone mode to a finite-energy roton, restoring superfluidity. This effect results in re-entrant supersolid phases as a function of rotation frequency, revealing a fundamental coupling between topological defects and crystalline order.

We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit quantum electrodynamics (circuit-QED) platform. To this end, we develop a continuous family of deformed boson representations of the SU(2) algebra, which includes the Holstein-Primakoff and Dyson-Maleev transformations as special cases. For spin-1/2 systems, we introduce a procedure to circumvent the inherent non-Hermiticity of the representation, showing that this entire family yields the extended Bose-Hubbard (EBH) Hamiltonian. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.

We study the typical structure of games in terms of their connectivity properties. A game is `connected' if it has a pure Nash equilibrium and there is a best-response path from every action profile which is not a pure Nash equilibrium to every pure Nash equilibrium; a game is generic if it has no indifferences. In previous work we showed that, among all $n$-player $k$-action generic games that admit a pure Nash equilibrium, the fraction that are connected tends to $1$ as $n$ gets sufficiently large relative to $k$. Here, we consider the large-$k$ regime, which behaves differently: we show that the connected fraction tends to $1-ζ_n$ as $k$ gets large, where $ζ_n>0$ is an explicit constant. Thus, a constant fraction of many-action games are \emph{not} connected. However, for $n\geq3$, $ζ_n$ is small and tends to $0$ rapidly with $n$, so as $n$ increases all but a vanishingly small fraction of many-player-many-action games are connected. Since connectedness is conducive to equilibrium convergence, we find a simple adaptive dynamic that is guaranteed to converge to a pure Nash equilibrium in all but a vanishingly small fraction of generic games that have one. We rely on new probabilistic and combinatorial arguments to tackle the large-$k$ regime.

While in pristine bilayer graphene the Berry curvature dipole (BCD), a necessary ingredient for the nonlinear anomalous Hall effect, is zero, uniaxial strain can give rise to finite BCD. We investigate this by using a tight-binding (TB) approach build on the Slater-Koster parameterization to capture lattice deformation effects often missed by continuum models. We demonstrate that the BCD's evolution with strain and doping is highly sensitive to the choice in parameterization, particularly when including the longer range interlayer skew hoppings. Additionally, out-of-plane compression enhances the response by broadening the Dirac cones. These findings benchmark low-energy continuum models and highlight the necessity of realistic tight-binding models for accurately predicting strain-engineered Hall effects in bilayer graphene.

The aim of this work is to improve understanding of the resonant spectra of black holes under perturbations arising from e.g. compact objects or accretion disks in their vicinity. It is known that adding a weak perturbation to the radial potential can strongly disrupt the spectrum of quasinormal modes and Regge poles of a black hole spacetime. Here we examine the effect of (weak or strong) localised delta-function perturbations on the resonant spectra of spherically-symmetric systems, to address fundamental questions around linear and non-linear spectral stability. We examine two cases: the Nariai spacetime with a Poschl-Teller potential and the Schwarzschild spacetime. We show that, in either case, the spectrum deforms in a smooth and continuous manner as the position and strength of the perturbation is varied. As the strength of the perturbation is increased, resonances migrate along trajectories in the complex plane which ultimately tend towards attracting points determined by a hard-wall scenario. However, for weak perturbations the trajectory near the unperturbed resonance is typically strongly influenced by a set of repelling points which, for perturbations far from the system, lie very close to the unperturbed resonances; hence there arises a non-linear instability (i.e. the failure of a linearised approximation). Taking a dynamical systems perspective, the sets of attracting and repelling spectral points follow their own trajectories as the position of the perturbation is varied, and these are tracked and understood.

An example originally given by F.~Delon shows the existence of an algebraically maximal discretely valued field of characteristic $p>0$ which admits purely inseparable extensions of degree $p^2$ with defect $p$. These extensions are not generated by a single element. Using a trick introduced in an earlier paper of the author, we construct algebraically maximal valued fields, of characteristic $p$ as well as of characteristic $0$, which admit separable extensions of degree $p^2$ with defect $p$. They are of rank 2 and it is an open question whether such examples having rank 1 exist.

Quantum machine learning holds promise for advancing time series forecasting. The Quantum Recurrent Neural Network (QRNN), inspired by classical RNNs, encodes temporal data into quantum states that are periodically input into a quantum circuit. While prior QRNN work has predominantly used angle encoding, alternative encoding strategies like amplitude encoding remain underexplored due to their high computational complexity. In this paper, we evaluate and improve amplitude-based QRNNs using EnQode, a recently introduced method for approximate amplitude encoding. We propose a simple pre-processing technique that augments amplitude encoded inputs with their pre-normalized magnitudes, leading to improved generalization on two real world data sets. Additionally, we introduce a novel circuit architecture for the QRNN that is mathematically equivalent to the original model but achieves a substantial reduction in circuit depth. Together, these contributions demonstrate practical improvements to QRNN design in both model performance and quantum resource efficiency.

Alignment of artificial intelligence (AI) encompasses the normative problem of specifying how AI systems should act and the technical problem of ensuring AI systems comply with those specifications. To date, AI alignment has generally overlooked an important source of knowledge and practice for grappling with these problems: law. In this paper, we survey the emerging field of legal alignment that aims to fill this gap and systematize research that studies how legal rules, principles, and methods can be leveraged to address problems of alignment and inform the design of AI systems that operate safely and ethically. Our survey provides a taxonomy of the three core research pathways of legal alignment and explores how each can be operationalized in practice: (1) designing AI systems to comply with the content of legal rules developed through legitimate institutions and processes, (2) adapting methods from legal interpretation to guide how AI systems reason and make decisions, and (3) harnessing legal concepts as a structural blueprint for confronting challenges of reliability, trust, and cooperation in AI systems. These research pathways present new conceptual, empirical, and institutional questions, which include examining the specific set of laws that particular AI systems should follow, creating evaluations to assess their legal compliance in real-world settings, and developing governance frameworks to support the implementation of legal alignment in practice. Tackling these questions requires expertise across law, computer science, and other disciplines, offering these communities the opportunity to collaborate in designing AI for the better.

Sampling-based model predictive control (MPC) is effective for nonlinear systems but often produces non-smooth control inputs due to random sampling. To address this issue, we extend the model predictive path integral (MPPI) framework with deterministic sampling and improvements from cross-entropy method (CEM)--MPC, such as iterative optimization, proposing deterministic sampling MPPI (dsMPPI). This combination leverages the exponential weighting of MPPI alongside the efficiency of deterministic samples. Experiments demonstrate that dsMPPI achieves smoother trajectories compared to state-of-the-art methods.

We introduce a new two-parameter fractional time operator with Volterra structure, denoted by ${}^{W}D_{t}^{α,β}$, defined through the Laplace symbol \[ Φ_{α,β}(s) = \frac{s^α}{\bigl(1+(1-α)s^{α-1}\bigr)^β}, \qquad 0<α<1, \ β\ge0. \] The operator preserves the Caputo-type high-frequency behavior while allowing a controlled modification of the low-frequency regime via $β$. We develop an explicit symbolic/Volterra theory: Prabhakar-type kernels, a left-inverse Volterra integral, and a fractional fundamental theorem of calculus. A central contribution is a sharp clarification of the Bernstein structure of the symbol. We show that the natural factorization $Φ_{α,β}(s)=s^αh_α(s)^β$ does not fit the classical Bernstein product mechanism for any $β>0$. Nevertheless, by a direct complete-monotonicity argument on $Φ'_{α,β}$, we prove the exact Bernstein threshold \[ Φ_{α,β}\in\mathcal{BF} \quad\Longleftrightarrow\quad 0\leβ\le1. \] where $\mathcal{BF}$ denotes the class of Bernstein functions \noindent For $β>1$, the Bernstein property fails by a low-frequency asymptotic convexity obstruction. This shows that the Bernstein nature of the natural range $0\leβ\le1$ is genuine but is not produced by the standard product mechanism. We then establish well-posedness of abstract W-fractional Cauchy problems with sectorial generators by resolvent estimates and Laplace inversion, yielding a W-resolvent family with temporal regularity and smoothing properties. As an illustration, we apply the theory to a W-fractional diffusion model and discuss the effect of $β$ on the relaxation of spectral modes.

In strongly correlated electronic systems, Coulomb interactions frequently give rise to emergent electronic orders that spontaneously break rotational symmetry. Understanding how such symmetry breaking intertwines with other collective phenomena-such as unconventional superconductivity-and how it shapes experimental observables, particularly transport responses, remains a central challenge in modern condensed-matter physics. Here we report experimental signatures of charge stripe order, with a transport anisotropy rivaling that of quantum Hall stripe phases, coexisting with superconductivity and magnetism in rhombohedral hexalayer graphene. Strikingly, the low-temperature superconducting state not only inherits strong anisotropy but also exhibits a wide range of hysteretic transitions arising from the tunability of the underlying stripe order. Together, these findings reveal a previously unrecognized coexistence between superconductivity and charge stripe, shedding new light on the role of rotational symmetry breaking in shaping unconventional superconductivity in rhombohedral graphene.