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Automated Program Repair (APR) improves developer productivity by saving debugging and bug-fixing time. While APR has been extensively explored for C/C++ and Java programs, there is little research on bugs in PHP programs due to the lack of a benchmark PHP bug dataset. This is surprising given that PHP has been one of the most widely used server-side languages for over two decades, being used in a variety of contexts such as e-commerce, social networking, and content management. This paper presents a benchmark dataset of PHP bugs on real-world applications called BUGSPHP, which can enable research on analysis, testing, and repair for PHP programs. The dataset consists of training and test datasets, separately curated from GitHub and processed locally. The training dataset includes more than 600,000 bug-fixing commits. The test dataset contains 513 manually validated bug-fixing commits equipped with developer-provided test cases to assess patch correctness.

Based on a novel laboratory method, 14 mm-wave lines of the molecular ion H$_2$CCCH$^+$ have been measured in high resolution, and the spectroscopic constants of this asymmetric rotor determined with high accuracy. Using the Yebes 40 m and IRAM 30 m radio telescopes, we detect four lines of H$_2$CCCH$^+$ towards the cold dense core TMC-1. With a dipole moment of about 0.55 Debye obtained from high-level ab initio calculations, we derive a column density of 5.4$\pm$1$\times$10$^{11}$ cm$^{-2}$ and 1.6$\pm$0.5$\times$10$^{11}$ cm$^{-2}$ for the ortho and para species, respectively, and an abundance ratio N(H$_2$CCC)/N(H$_2$CCCH$^+$)= 2.8$\pm$0.7. The chemistry of H$_2$CCCH$^+$ is modelled using the most recent chemical network for the reactions involving the formation of H$_2$CCCH$^+$. We find a reasonable agreement between model predictions and observations, and new insights into the chemistry of C$_3$ bearing species in TMC-1 are obtained.

In a recent theoretical study, a new 2D carbon allotrope called pentagraphyne (PG-yne) was proposed. This allotrope is derived from pentagraphene by introducing acetylenic linkages between sp3 and sp2 hybridized carbon atoms. Due to its interesting electronic and structural properties, it is of interest to investigate the mechanical behavior of PG-yne in both monolayer and nanotube topologies. To achieve this, we performed fully atomistic reactive (ReaxFF) molecular dynamics simulations, and our results show that Young's modulus average of PG-yne monolayers is approximately 913 GPa, at room temperature. In comparison, it ranges from 497-789 GPa for the nanotubes studied. Furthermore, we observed that PG-yne monolayers exhibit a direct transition from elastic to complete fracture under critical strain without a plastic regime. In contrast, some PG-yne nanotubes exhibit an extended flat plastic regime before total fracture.

We propose that a multi-graphene of ABC-type stacking yields virtual bound states lying within the Coulomb insulating gap of an Anderson-like adatom. Wondrously, a virtual state constitutes the counterpart of the atomic collapse phenomenon proposed in relativistic atomic Physics, while the second emerges as its particle-hole symmetric, analogous to a positron state. Thus, we introduce the effect as the adatomic collapse, which occurs due to a flat band with a dispersionless state and a divergent density of states $\sim|\varepsilon-\varepsilon_{F}|^{2/J-1}$ near the Fermi energy $\varepsilon_{F}$ for $J\geq3,$ where $J\pi$ is the Berry phase. We conclude this scenario based on the Kramers-Kronig transformation of the quasiparticle broadening, from where we observe that the aforementioned van Hove singularity induces virtual bound states. Counterintuitively, near the singularity, we find these states above and below the Fermi energy correlated to the existence of the bottom and top edges of the Coulomb insulating region, respectively. As such a behavior rises without a twist, the system is known as Moir\'eless and the phenomenon emerges also assisted by the adatom Coulomb correlations. Similarly to Science 340, 734 (2013) we find the effective critical atomic number $\mathcal{Z}_{c}\sim0.96$ in contrast to an ultra-heavy nucleus. Thus, we point out that multi-graphene is a proper playground for testing a predicted phenomenon of the relativistic atomic Physics in the domain of the condensed matter Physics.

We theoretically analyze the Fano interference in a single impurity multi-Weyl semimetal hybrid system and show the emergence of the topological charge Fano effect in the bulk local density of states. In multi-Weyl semimetals, the number of Fermi arcs at the system boundaries is determined by the topological charge $J$, a direct consequence of the "bulk-boundary" correspondence principle. Analogously, we find that $J$ also modulates the bulk Fano profile of the system with an embedded quantum impurity. Thus, by increasing $J$, the Fano lineshape evolves from resonant, typical for $J=1$ (single Weyl), towards antiresonant, extrapolating to the so-called hyper Weyl semimetals with $J\gg1$. Specially for the maximum case protected by the rotational symmetry $C_{2J=6}$, namely the $J=3$ (triple Weyl), which acquires asymmetric Fano profile, the Fano parameter absolute value is predicted to be $\tan(C_{2J=6})$, where $C_{2J}\equiv(360^{\circ}/2J)$ defines the rotational angle. Hence, the Fano discretization in the $J$ term introduces the topological charge Fano effect in multi-Weyl semimetals. We also suggest a transport device where we expect that the proposed Fano effect could be detected.

The main goal of this paper is to size up the minimal graded free resolution of a homogeneous ideal in terms of its generating degrees. By and large, this is too ambitious an objective. As understood, sizing up means looking closely at the two available parameters: the shifts and the Betti numbers. Since, in general, bounds for the shifts can behave quite steeply, we filter the difficulty by the subadditivity of the syzygies. The method we applied is hopefully new and sheds additional light on the structure of the minimal free resolution. We use the Boij-S\"oderberg techniques for the Betti numbers to get polynomial upper bounds for them. It is expected that the landscape of hypersurface singularities already contains most of the difficult corners of the arbitrary case. In this regard, we treat some facets of this case, including an improvement of one of the basic results of a recent work by Bus\'e--Dimca--Schenck--Sticlaru., Comment: 30 pages

Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster mean-field approach, resulting in an effective single-cluster model. This effective model is treated within a one-step replica symmetry breaking (RSB) approach with exact evaluations for all intracluster interactions. Competing interactions are introduced by tuning the ratio $J_2/J_1$ (where $J_1$ and $J_2$ are first-neighbour and second-neighbor interactions, respectively), which can lead to a highly frustrated scenario when $J_2/J_1\rightarrow 1$, where a phase transition between AF orders takes place in the absence of disorder. In particular, the AF order appears at lower values of $J_2/J_1$, with the Neel temperature decreasing as the frustration increases. However, quenched disorder changes this description, introducing a RSB spin glass phase for strong enough disorder intensity $J$. In fact, for low levels of disorder, a RSB solution with staggered magnetization (mixed phase) emerges from the maximum frustration region. It suggests that, in the presence of weak quenched disorder, systems with competing interactions are prone to present a glassy behavior instead of conventional orders., Comment: 7 pages, 4 figures

We theoretically investigate atomic frustrated states in diatomic molecules hosted by the bilayer graphene setup twisted by the first magic angle and with broken inversion symmetry in the Dirac cones of the system mini Brillouin zones. Such states show local spectral features typically from uncoupled atoms, but counterintuitively, they also exhibit nonlocal molecular correlations, which turn them into atomically frustrated. By considering a particle-hole symmetric molecule in the Moir\'e superlattice length-scale, we reveal distinctly from the metallic Weyl counterparts, a molecular zero mode atomically frustrated at the spectral densities of the dimer's atoms. To this end, a strong metallic phase with a plateau in the density of states established by the broken inversion symmetry, together with pronounced blue and red shifts in the molecular levels, due to the magic angle condition, should occur synergistically with atomic Coulomb correlations. Consequently, an entire collapse of these molecular peaks into a single one atomically frustrated, taking place exactly at the Fermi energy, becomes feasible just by tuning properly opposite gate voltages attached to the graphene monolayers. Therefore, we propose that unusual molecular bindings can be engineered via the twistronics of the bilayer graphene system, in particular, if its metallic phase is fully established.

The intercalant alkaline metals, Ca, Sr, & Ba, are sources of a periodic perturbation on the bilayer graphene, which leads to the formation of an N-type semiconductors. The twist angle between graphene layers applies disorder to the intercalated bilayer graphene to tune the bandgap. The twisted bilayer graphene structures of C8MC8 (M: Ca, Sr, Ba) were studied for the Energy band diagrams, Density of States, transport properties of Seebeck coefficient, Hall coefficient, Thermal conductivity, and Electrical conductivity using Quantum-Espresso and BoltzTrap software. The bandgap enhances with respect to an increase in twist angle to values of technological requirements to implement in real applications. The peak of the Seebeck coefficient & Hall Effect increase, and Thermal Conductivity & Electrical Conductivity decrease for different twist angles. Therefore, C8MC8 has a significant impact of the twist angle, hence gives possible tailoring of material properties.

Graphene is a two-dimensional (2D) semimetal with high mobility in charge carriers due to the existence of Dirac points. Silicene is another promising material, with properties analog to graphene. Many silicon (Si) based electronic devices can be integrated via graphene-silicene (Gra/si) hybrid structures. These electronic applications are mostly based on the ability to tune the bandgap via electronic structure deformation that is expected to be achieved by multilayer stacking, applying a transverse external electric field (EF), and altering interfacial distance. In this work, we investigate the band structure, density of states (DOS) distribution, and the bandgap with respect to interfacial distance and transverse external EF for the unit cells of bilayer graphene, monolayer silicene, and hybrid Si2C6. First principle calculations were carried using Quantum espresso software based on the Density Functional Theory (DFT).

The use of Deep Learning in the medical field is hindered by the lack of interpretability. Case-based interpretability strategies can provide intuitive explanations for deep learning models' decisions, thus, enhancing trust. However, the resulting explanations threaten patient privacy, motivating the development of privacy-preserving methods compatible with the specifics of medical data. In this work, we analyze existing privacy-preserving methods and their respective capacity to anonymize medical data while preserving disease-related semantic features. We find that the PPRL-VGAN deep learning method was the best at preserving the disease-related semantic features while guaranteeing a high level of privacy among the compared state-of-the-art methods. Nevertheless, we emphasize the need to improve privacy-preserving methods for medical imaging, as we identified relevant drawbacks in all existing privacy-preserving approaches., Comment: 7 pages, 5 figures, accepted at Workshop on Interpretable ML in Healthcare at ICML2021

Many new strong gravitational lensing (SGL) systems have been discovered in the last two decades with the advent of powerful new space and ground-based telescopes. The effect of the lens mass model (usually the power-law mass model) on cosmological parameters constraints has been performed recently in literature. In this paper, by using SGL systems and Supernovae type Ia observations, we explore if the power-law mass density profile ($\rho \propto r^{-\gamma}$) is consistent with the cosmic distance duality relation (CDDR), $D_L(1+z)^{-2}/D_A=\eta(z)=1$, by considering different lens mass intervals. { It has been obtained that the verification of the CDDR validity is significantly dependent on lens mass interval considered: the sub-sample with $\sigma_{ap} \geq 300$ km/s (where $\sigma_{ap}$ is the lens apparent stellar velocity dispersion) is in full agreement with the CDDR validity, the sub-sample with intermediate $\sigma_{ap}$ values ($200 \leq \sigma_{ap} < 300)$ km/s is marginally consistent with $\eta=1$ and, finally, the sub-sample with low $\sigma_{ap}$ values ($\sigma_{ap} < 200$ km/s) ruled out the CDDR validity with high statistical confidence. Therefore, if one takes the CDDR as guarantee, our results suggest that using a single density profile is not suitable to describe lens with low $\sigma_{ap}$ values and it is only an approximate description to lenses with intermediate mass interval. }, Comment: 8 pages, 4 figures, I table, Accepted for publication in the JCAP

Single- and many-electron calculations and related dynamics are presented for a dimer and small Hubbard clusters. Floquet-Bloch picture for a periodic dimer is discussed with regard to the time dependence of the Peierls gap and the expectation of the current operator. In driven Fermi-Hubbard clusters, the time dependence of Charge Gaps and phase separation along with charge pairing at various cluster sizes indicate the presence and absence of paired electron states. We examine the effect of electromagnetic time dependent external perturbations on Hubbard many-electron systems in our search of for precursors to superconducting states and time crystals. Two principally different kinds of electromagnetic excitations are analyzed:(1) Recently demonstrated dynamic modulation of Hubbard parameters due to excitation of certain phonon modes within the far-infrared domain, and (2) Hubbard Hamiltonian, with fixed parameters in an electromagnetic field, resonant with transitions between the ground state and high-energy excited states as possible precursors to superconductivity, within visible-near-infrared domains., Comment: 7 pages, 9 figures

We compare the ground-state features of alternating ferrimagnetic chains $(1/2, S)$ with $S=1,3/2,2,5/2$ in a magnetic field and the corresponding Holstein-Primakoff bosonic models up to order $\sqrt{s/S}$, with $s=1/2$, considering the fully polarized magnetization as the boson vacuum. {The single-particle Hamiltonian is a Rice-Mele model with uniform hopping and modified boundaries, while the interactions have a correlated (density-dependent) hopping term and magnon-magnon repulsion.} The magnon-magnon repulsion increases the many-magnon energy and the density-dependent hopping decreases the kinetic energy. We use density matrix renormalization group calculations to investigate the effects of these two interaction terms in the bosonic model{, and display the quantitative agreement between the results from the spin model and the full bosonic approximation. In particular, we verify the good accordance in the behavior of the edge states, associated with the ferrimagnetic plateau, from the spin and from the bosonic models. Furthermore, we show that the boundary magnon density strongly depends on the interactions and particle statistics., Comment: 13 pages, 6 figures

We describe an analysis comparing the $p\bar{p}$ elastic cross section as measured by the D0 Collaboration at a center-of-mass energy of 1.96 TeV to that in $pp$ collisions as measured by the TOTEM Collaboration at 2.76, 7, 8, and 13 TeV using a model-independent approach. The TOTEM cross sections extrapolated to a center-of-mass energy of $\sqrt{s} =$ 1.96 TeV are compared with the D0 measurement in the region of the diffractive minimum and the second maximum of the $pp$ cross section. The two data sets disagree at the 3.4$\sigma$ level and thus provide evidence for the $t$-channel exchange of a colorless, $C$-odd gluonic compound, also known as the odderon. We combine these results with a TOTEM analysis of the same $C$-odd exchange based on the total cross section and the ratio of the real to imaginary parts of the forward elastic scattering amplitude in $pp$ scattering. The combined significance of these results is larger than 5$\sigma$ and is interpreted as the first observation of the exchange of a colorless, $C$-odd gluonic compound., Comment: D0 and TOTEM Collaborations

In this work, we study the extended viscous dark energy models in the context of matter perturbations. To do this, we assume an alternative interpretation of the flat Friedmann-Lema\^itre-Robertson-Walker Universe, through the nonadditive entropy and the viscous dark energy. We implement the relativistic equations to obtain the growth of matter fluctuations for a smooth version of dark energy. As result, we show that the matter density contrast evolves similarly to the $\Lambda$CDM model in high redshift; in late time, it is slightly different from the standard model. Using the latest geometrical and growth rate observational data, we carry out a Bayesian analysis to constrain parameters and compare models. We see that our viscous models are compatible with cosmological probes, and the $\Lambda$CDM recovered with a $1\sigma$ confidence level. The viscous dark energy models relieve the tension of $H_0$ in $2 \sim 3 \sigma$. Yet, by involving the $\sigma_8$ tension, some models can alleviate it. In the model selection framework, the data discards the extended viscous dark energy models., Comment: 19 pages, 8 figures, 8 tables. Updated to match the published version

We investigate the Tsallis holographic dark energy (THDE) models in the context of perturbations' growth. We assume the description of dark energy by considering the holographic principle and the nonadditive entropy to carry out this. We implement the perturbed relativistic equations to achieve the growth of matter fluctuations, being the growth rate of the cosmic structures is non-negligible at low redshifts. To constrain and compare the models, we carry out the Bayesian analysis using the recent geometrical and growth rate observational data. The main results are: (i) the models are compatible with cosmological observations, (ii) the cosmological constant recovered with a $1\sigma$ confidence level, furthermore (iii) they could cross the phantom barrier. Finally, the models can relieve $\approx 1\sigma$ the $\sigma_8$ tension in the non-clustered case and can alleviate in $\approx 2.8\sigma$ the $H_0$ tension. From the model selection viewpoint, the data discarded the THDE models., Comment: 13 pages, 5 figures, 4 tables. Updated to match the published version

In this paper, we present a unified scheme based on the fluid description of the dark sector of the universe. The scheme captures models with interaction between dark energy and dark matter, being the core of generalization the time-varying equation-of-state parameter $\omega(a)$ and the time-dependent interactions through the interaction function $\epsilon(a)$, where $a$ is the scale factor. Furthermore, we propose thermodynamics constraints on this generalized class of models using the laws of thermodynamics which are combined with observational data. In order to test the observational viability of the unified model, we perform a Bayesian analysis using cosmic chronometers, type Ia supernovae, cosmic microwave background, and angular baryon acoustic oscillation measurements., Comment: 9 pages, 4 figures, 2 tables. Version accepted for publication in EPJP

An important result from self-similar models that describe the process of galaxy cluster formation is the simple scaling relation $Y_{\rm SZE}D_{\rm A}^{2}/C_{\rm XSZE}Y_{\rm X}= C$. In this ratio, $Y_{\rm SZE}$ is the integrated Sunyaev-Zel'dovich effect flux of a cluster, its x-ray counterpart is $Y_{\rm X}$, $C_{\rm XSZE}$ and $C$ are constants and $D_{\rm A}$ is the angular diameter distance to the cluster. In this paper, we consider the cosmic distance duality relation validity jointly with type Ia supernovae observations plus $61$ $Y_{\rm SZE}D_{\rm A}^{2}/C_{\rm XSZE}Y_{\rm X}$ measurements as reported by the Planck Collaboration to explore if this relation is constant in the redshift range considered ($z<0.5$). No one specific cosmological model is used. As basic result, although the data sets are compatible with no redshift evolution within 2$\sigma$ c.l., a Bayesian analysis indicates that other $C(z)$ functions analyzed in this work cannot be discarded. It is worth to stress that the observational determination of an universal $C(z)$ function turns the $Y_{\rm SZE}D_{\rm A}^{2}/C_{\rm XSZE}Y_{\rm X}$ ratio in an useful cosmological tool to determine cosmological parameters., Comment: 6 pages, 1 figure, 2 tables, accepted by JCAP

The aim of this paper is to present a self-similar growth-fragmentation process linked to a Brownian excursion in the upper half-plane $\mathbb{H}$, obtained by cutting the excursion at horizontal levels. We prove that the associated growth-fragmentation is related to one of the growth-fragmentation processes introduced by Bertoin, Budd, Curien and Kortchemski., Comment: 33 pages, 7 figures

The cosmic distance duality relation (CDDR), $D_{\rm L}(1+z)^{-2}/D_{\rm A}=\eta=1$, with $D_{\rm L}$ and $D_{\rm A}$, being the luminosity and angular diameter distances, respectively, is a crucial premise in cosmological scenarios. Many investigations try to test CDDR through observational approaches, even some of these ones also consider a deformed CDDR, i.e., $\eta=\eta(z)$. In this paper, we use type Ia supernovae luminosity distances and galaxy cluster measurements (their angular diameter distances and gas mass fractions) in order to perform a Bayesian model comparison between $ \eta(z) $ functions. We show that the data here used are unable to pinpoint, with a high degree of Bayesian evidence, which $\eta(z)$ function best captures the evolution of CDDR., Comment: 10 pages, 3 figures, 3 tables. v3: matches version published in PRD

With the advent of the nanosat/cubesat revolution, new opportunities have appeared to develop and launch small ($\sim$\ts 1000 cm$^3$), low-cost ($\sim$\ts US\$ 1M) experiments in space in very short timeframes ($\sim$ 2\ts years). In the field of high-energy astrophysics, in particular, it is a considerable challenge to design instruments with compelling science and competitive capabilities that can fit in very small satellite buses such as a cubesat platform, and operate them with very limited resources. Here we describe a hard X-ray (30--200\ts keV) experiment, LECX ("Localizador de Explos\~oes C\'osmicas de Raios X" -- Locator of X-Ray Cosmic Explosions), that is capable of detecting and localizing within a few degrees events like Gamma-Ray Bursts and other explosive phenomena in a 2U-cubesat platform, at a rate of $\sim${\bf 5 events year$^{-1}$.} In the current gravitational wave era of astronomy, a constellation or swarm of small spacecraft carrying instruments such as LECX can be a very cost-effective way to search for electromagnetic counterparts of gravitational wave events produced by the coalescence of compact objects., Comment: submitted to MNRAS

Optical modes possessing orbital angular momentum constitute a very useful platform for experimental studies on the quantum limits of Thermodynamics. Here, we present experimental results for entangled photon pairs subjected to thin turbulence simulated with spatial light modulators and interpret them in the context of the generalized Jarzysnki's fluctuation relation. By holographic measurement of the orbital angular momentum, we obtain the work distribution produced by the turbulence for single and double-sided turbulence channels. The use of the Klyshko's advanced wave picture allows us to interpret the experimental scheme as two-way processes in a fully quantum picture., Comment: 10 pages, 11 figures, two new appendices

Non-relativistic quantum effects of the topology of the spacetime with the distortion of a vertical line into a vertical spiral on the harmonic oscillator are investigated. By searching for analytical solutions to the Schr\"odinger equation in this topological defect background, it is shown that the topology of the spacetime modifies the spectrum of energy of the harmonic oscillator. Besides, it is shown that there exists an Aharonov-Bohm-type effect for bound states., Comment: 5 pages

It is analysed Aharonov-Bohm-type effects when a spinless quantum particle is in an elastic medium with the distortion of a vertical line into a vertical spiral. By confining the spinless particle to a cylindrical box, the analogue of the Aharonov-Bohm effect for bound states is observed due to influence of the topological defect on the allowed energies of the system. It corresponds to the shift in the angular momentum quantum number yielded by the effects of the topology of the distortion of a vertical line into a vertical spiral. In addition, it is analysed the effects of rotation. It is shown that the Aharonov-Bohm effect for bound states exists. Besides, there is an analogue of the coupling between the angular momentum and angular velocity of the rotating frame., Comment: 13 pages, no figure

This paper introduces a new approach to measure the muon magnetic moment anomaly $a_{\mu} = (g-2)/2$, and the muon electric dipole moment (EDM) $d_{\mu}$ at the J-PARC muon facility. The goal of our experiment is to measure $a_{\mu}$ and $d_{\mu}$ using an independent method with a factor of 10 lower muon momentum, and a factor of 20 smaller diameter storage-ring solenoid compared with previous and ongoing muon $g-2$ experiments with unprecedented quality of the storage magnetic field. Additional significant differences from the present experimental method include a factor of 1,000 smaller transverse emittance of the muon beam (reaccelerated thermal muon beam), its efficient vertical injection into the solenoid, and tracking each decay positron from muon decay to obtain its momentum vector. The precision goal for $a_{\mu}$ is statistical uncertainty of 450 part per billion (ppb), similar to the present experimental uncertainty, and a systematic uncertainty less than 70 ppb. The goal for EDM is a sensitivity of $1.5\times 10^{-21}~e\cdot\mbox{cm}$., Comment: 24 pages, 14 figures

The Technical Design for the COMET Phase-I experiment is presented in this paper. COMET is an experiment at J-PARC, Japan, which will search for neutrinoless conversion of muons into electrons in the field of an aluminium nucleus ($\mu-e$ conversion, $\mu^- N \to e^- N$); a lepton flavor violating process. The experimental sensitivity goal for this process in the Phase-I experiment is $3.1\times10^{-15}$, or 90 % upper limit of branching ratio of $7\times 10^{-15}$, which is a factor of 100 improvement over the existing limit. The expected number of background events is 0.032. To achieve the target sensitivity and background level, the 3.2 kW 8 GeV proton beam from J-PARC will be used. Two types of detectors, CyDet and StrECAL, will be used for detecting the \mue conversion events, and for measuring the beam-related background events in view of the Phase-II experiment, respectively. Results from simulation on signal and background estimations are also described., Comment: A minor correction applied in Eq. 3

The search for charged lepton flavour violation (CLFV) has enormous discovery potential in probing new physics Beyond the Standard Model (BSM). Among the muonic CLFV processes, $\mu \to e$ conversion is one of the most important processes, having several advantages compared to other such processes. We describe the COMET experiment, which is searching for $\mu \to e$ conversion in a muonic atom at the J-PARC proton accelerator laboratory in Japan. The COMET experiment has taken a staged approach; the first stage, COMET Phase-I, is currently under construction at J-PARC, and is aiming at a factor 100 improvement over the current limit. The second stage, COMET Phase-II is seeking another 100 improvement (a total of 10,000), allowing a single event sensitivity (SES) of $2.6 \times 10^{-17}$ with $2\times 10^{7}$ seconds of data-taking. Further improvements by one order of magnitude, which arise from refinements to the experimental design and operation, are being considered whilst staying within the originally-assumed beam power and beam time. Such a sensitivity could be translated into probing many new physics constructions up to $\mathcal{O}(10^{4})$ TeV energy scales, which would go far beyond the level that can be reached directly by collider experiments. The search for CLFV $\mu \to e$ conversion is thus highly complementary to BSM searches at the LHC., Comment: 12 pages, 2 figures