arXiv subjects

Liang Gao

Publications and source records attributed to Liang Gao.

At least 37 records · Page 2Linked to original sources

arXiv2026

DSevolve: Enabling Real-Time Adaptive Scheduling on Dynamic Flexible Job Shop with LLM-Evolved Heuristic Portfolios

In dynamic flexible job shops, order arrivals, machine breakdowns, and processing-time deviations continually reshape the scheduling state and the priority trade-offs behind dispatching decisions. Dispatching rules are well suited to this setting because they are fast, interpretable, and easy to deploy, and recent LLM-assisted automatic heuristic design further expands their expressiveness by evolving composite priority functions. The key challenge is to make these evolved rule behaviors state-adaptive without losing the rapid response needed for online rescheduling. This paper proposes a dynamic self-evolutionary framework DSevolve, which separates offline rule-library construction from online state-conditioned rule selection. Offline, an LLM-guided quality-diversity search combines multi-persona seeding, a MAP-Elites behavioral archive, and behavior-guided variation to evolve a library of complementary rules rather than a single elite, and event-level simulation then trains a neural selector to rank the rules by state. Online, after each rescheduling event, a neural selector maps a 22-dimensional state fingerprint to rule scores and dispatches the top-ranked rule within about a second, meeting the response-time requirement after each disruption. Experiments on dynamic instances derived from standard flexible job shop benchmarks show that DSevolve achieves lower mean makespan than individual LLM-evolved rules, classical dispatching rules, and learning-based baselines under a one-active-rule deployment protocol. Trained only on small instances, the selector transfers zero-shot to substantially larger dynamic shops. These results show that state-conditioned selection preserves the speed and interpretability of dispatching rules while improving adaptability.

cs.AI↗

arXiv2026

An integrated super resolution THz 3D imaging system based on a linear nonlocal achromatic freeform Bessel beam lens and high power oscillator radiator array

High performance terahertz (THz) 3D imaging is critical for non-destructive evaluation. However, conventional architectures are fundamentally limited by severe chromatic aberrations, modest spatial resolution, restricted depths of focus (DOF), and the bulky nature of commercial transceivers. While metasurfaces offer a compact alternative, achieving broadband achromatic super-resolution with an extended DOF remains a formidable challenge. Here, we present a highly integrated 3D THz imaging platform that synergizes a 3D printed nonlocal freeform Bessel-beam lens with a high power, 65nm CMOS oscillator radiator array. Harnessing nonlocal interactions within the lens, we generate an achromatic super resolution Bessel beam (0.3 to 1 THz) with a subdiffraction full width at half maximum (FWHM) of 0.65λ and a robust 4.7-mm DOF. Crucially, the system overcomes conventional sidelobe limitations, enabling high-fidelity 2D imaging of intricate sub-millimeter targets (e.g., USAF 1951 charts and QR codes) alongside robust 3D volumetric imaging through highly scattering media, such as printed circuit boards. By converging standard CMOS technology with additive manufacturing, this work establishes a versatile, cost-effective paradigm for next-generation integrated THz photonics

physics.optics↗

arXiv2026

Hydrogen-induced lattice cohesion weakening favors atomic displacement

Atomic displacement -- the fundamental process underlying diverse deformation and damage phenomena in metals, from irradiation defect production to stress-driven dislocation motion -- is governed by interatomic cohesion strength. Here, lattice-dissolved hydrogen (LDH) occurring in metals under direct hydrogen exposure is identified to effectively weaken lattice cohesion, and thereby facilitating atomic displacement and dislocation movement upon plastic deformation in sub-threshold stress regime. This atomic-scale insight provides a physically transparent mechanism for hydrogen-enhanced localized plasticity implicated in hydrogen embrittlement. We quantitatively verify the hydrogen-induced lattice cohesion weakening effect on metal surfaces exposed to low-energy hydrogen plasma, where massive defects are generated despite the absence of sufficient ion momentum for direct displacement damage. By unprecedentedly quantifying the cohesion-weakening effect of LDH independently from defect-trapped H, we establish a new paradigm to understand hydrogen embrittlement.

cond-mat.mtrl-sci↗

arXiv2026

The dark matter halo mass function in the $Λ\mathrm{CDM}$ cosmology at all times and over all scales -- from planetary to galaxy cluster masses

The dark matter halo mass function is one of the most fundamental predictions of structure formation theory and cosmological simulations. We present the full halo mass function in the $Λ$ cold dark matter ($Λ\mathrm{CDM}$) model, ranging from a planetary mass ($10^{-6}\,\mathrm{M}_\odot$; the thermal cutoff in the initial power spectrum for a fiducial CDM particle mass of $100\,\mathrm{GeV}$) to the mass of a rich galaxy cluster ($10^{15.5}\,\mathrm{M}_\odot$), and from redshift, $z=30$ to the present. To span this very large dynamic range, we combine our earlier Voids-within-Voids-within-Voids (VVV) set of simulations (Wang et al) with large volume, lower resolution cosmological simulations. We develop a subsampling method to extract subvolumes from the original simulations, allowing us to reconstruct the global halo mass function from the biased underdense VVV regions. We show that the results agree reasonably well among the sets of simulations on different scales and environments. We provide a fitting formula for the dark matter halo mass function based on the work of Reed et al. calibrated with our simulations, such that it can be applied at all scales, all environments and all times, with deviations of $\sim2-3\%$ at $z < 2$ and $\sim 7\%$ at higher redshift $z \gtrsim 5$. This formula is also accurate at least for a restricted set of models we tested with modest deviations from $Λ\mathrm{CDM}$ in the values of some of the cosmological parameters. A python code is publicly available at https://github.com/haonan-zheng/hmfc.

astro-ph.CO↗

arXiv2026

Spherically Symmetric Fluid Simulations of Black Hole Accretion in Self-Interacting Dark Matter Halos

We investigate black hole accretion in self-interacting dark matter (SIDM) halos using a self-gravitating fluid model with thermal conduction. We develop a robust one-dimensional spherically symmetric hydrodynamic code based on an operator-splitting finite-volume method. Simulating both Singular Isothermal Sphere (SIS) and Navarro-Frenk-White (NFW) profiles, we find that black hole growth is regulated by the competition between gravity-driven inflow and SIDM heat transport. Our results demonstrate that an SIS-like environment facilitates rapid accretion, allowing a $100\,\mathrm{M_{\odot}}$ seed to grow to $10^4\,\mathrm{M_{\odot}}$ within $2\,\mathrm{Myr}$. Furthermore, we show that larger initial black hole masses, steeper density profiles, and higher scattering cross sections significantly enhance the accretion rate. This study provides a comprehensive fluid-dynamical picture of black hole growth in SIDM halos.

astro-ph.CO↗

arXiv2026

Stress-triggered atomic explosion of trapped hydrogen initiates crack nucleation

Hydrogen embrittlement (HE) has persisted for more than a century as one of the most intractable problems in materials science. The prevailing view1 that diffusive H governs embrittlement has fostered the widespread assumption that H trapping at crystal defects mitigates HE. Here we overturn this conventional paradigm. Using plasma/ion irradiation of tungsten, we decouple -- for the first time -- H-induced crack nucleation from subsequent cavity propagation, and reveal nucleation as a two-stage mechanochemical fracture instability enabled by trapped H in the absence of diffusive H. In the first stage, H accumulation to a critical occupancy at dislocation cores acts as a chemical fuse, collapsing the local cohesive strength to a threshold at which infinitesimal external loads can trigger atomic decohesion. This bond rupture instantaneously enables the second stage: confined recombination of atomic hydrogen into molecular form. The abrupt release of chemical energy within an atomically restricted volume generates a transient inflation pressure that drives a dynamic, brittle jump to an internal macroscopic cavity. By separating mechanical decohesion triggering from energetic crack driving, our results provide a deterministic framework for the onset of H-induced crack nucleation under low-stress conditions. Furthermore, we place experimentally the classical H-enhanced decohesion model on an atomistic foundation and elevate it from phenomenology to prediction. Finally, by shifting the focus from experimentally elusive diffusive H to directly measurable trapped H, this work reframes HE as a deterministic, quantifiable instability, establishing a new paradigm for understanding and mitigating H-induced failure in high-strength metals.

cond-mat.mtrl-sci↗

arXiv2026

Cosmological Simulation with Population III Stellar Feedback and Metal Enrichment I: Model Description And Convergence Test

We present SPARK (Simulation of Pop III in Arepo with Radiation and Kinetic feedback) framework, a new Pop III + Pop II subgrid framework implemented in the moving-mesh code {\sc arepo}, designed to study the impact of Pop III feedback on star formation in the early universe. The framework combines primordial non-equilibrium chemistry, metal-line cooling, IMF-sampled stellar evolution with SN feedback, and approximate Lyman-Werner (LW) and ionizing radiation transport. We run a suite of $1c{\rm Mpc}/h$ box simulations with different initial conditions and resolutions from $z=127$ to $z=10$. The highest gas mass and spatial resolution in the fiducial simulation reach $\sim10\,{\rm M_{\odot}}$ and $\sim4\,{\rm pc}$, respectively. The model successfully reproduces the Pop II star formation rate density (SFRD) consistent with previous theoretical works across all initial conditions, with minor variation mainly driven by local halo interactions and LW irradiation. We find that the volume filling factor of metal-enriched gas converges to $\sim0.5-2\%$ at $z=10$, with scatter driven by stochastic and mixing model variations. Convergence is achieved once subhalos with $M_{\rm subhalo}\gtrsim 10^{6.5}\,{\rm M_{\odot}}$ are resolved, and the total stellar mass at $z=10$ is largely insensitive to initial conditions or the resolution considered in this work. A fiducial simulation requires $\sim 10^4$ CPU hours, making the framework computationally tractable for larger box simulations and enabling future large parameter studies of stellar physics or environment effects such as Pop III IMF variations, X-ray radiation, or the streaming velocity at high redshift.

astro-ph.GA↗

arXiv2026

The FAST Hundred-Deg$^2$ HI Deep (HD$^2$) Survey: Early Results from the Pilot Survey

The Hundred-deg$^2$ HI Deep (HD$^2$) survey carried out with the Five-hundred-meter Aperture Spherical Telescope (FAST) is planned to map a contiguous region within the DESI DR1 footprint, achieving an effective integration time of 20 minutes for each pointing and a uniform detection sensitivity of 0.28 mJy beam$^{-1}$ at 4.8 km s$^{-1}$ resolution. We present early results from the pilot HD$^2$ survey: a 10 deg$^2$ field overlapping with HSC-SSP and the DESI EDR SV3, observed with an integration time of 7.3 minutes per beam and the rms of 0.45 mJy beam$^{-1}$ at 4.8 km s$^{-1}$ resolution. We identify 339 HI sources at $z<0.09$, corresponding to $\sim$34 detections per deg$^2$, nearly six times higher than the detection rate of the wide-field surveys. Optical counterparts are primarily identified using DESI redshifts, yielding a matching rate and correctness exceeding 90% for galaxies with $r<19.5$ mag, a substantial improvement over SDSS. Under the constraint of $r < 17.8$ mag and $0.01 < z < 0.05$, nearly 50% of galaxies in the DESI BGS samples have HI detections in this pilot survey. The optical properties of these HI-detected galaxies span nearly the entire parameter range of the DESI sample. The gas fraction scaling relations versus stellar mass, stellar mass surface density, NUV-r, and specific star formation rate are consistent with previous surveys, e.g., ALFALFA, DINGO, and xGASS. These results justify the feasibility of the full HD$^2$ survey, which will build a high-completeness HI census over a contiguous area to probe the cold gas scaling relations of galaxies over different scales.

astro-ph.GA↗

arXiv2026

APOSTLE vs. AURIGA Simulations: How Subgrid Models Shape Milky Way Analogs

Despite significant progress in cosmological simulations of galaxy formation, the role of subgrid physics in shaping the detailed properties of galaxies remains incompletely understood. In this work, we analyze two sets of zoom-in simulations that share identical initial conditions but adopt distinct implementations of baryonic physics, enabling a controlled comparison of their predictions. We examine the stellar properties, morphological structures, and satellite populations of the simulated galaxies at $z=0$. We find that AURIGA galaxies systematically exhibit higher stellar masses and surface densities than their APOSTLE counterparts. These differences are primarily driven by variations in the efficiency of gas cooling from the circumgalactic medium (CGM) into the star-forming gas. Both simulations form well-defined disk galaxies; however, AURIGA systems generally display higher disk-to-total mass ratios, earlier disk formation, and more prominent dynamical structures such as bars and spiral arms. Nevertheless, strongly disk-dominated systems are present in both simulations, although they do not arise in the same host haloes. The vertical disk structure in both simulations is well described by a sech density profile, with scale heights below ~ 1 kpc in the inner regions. The satellite populations also differ, with AURIGA producing systematically more massive satellites, including a ~ 0.3 dex increase in the most massive system, while the number of satellites above $10^6 M_{\odot}$ remains comparable in most halo pairs. Both simulations reproduce similar satellite stellar mass--metallicity relations, albeit ~ 0.25 dex higher than observation. This comparative study therefore provides useful benchmarks for future efforts to better constrain galaxy formation models.

astro-ph.GA↗

arXiv2026

Reproducing Abell 2744 with the HyperMillennium Simulation

We present the Hyper Millennium (HM) simulation, an extremely large cosmological simulation designed to support next-generation galaxy surveys. The simulation follows 4.2 trillion dark matter particles in a comoving box of $2.5\ h^{-1}{\rm Gpc}$, with a mass resolution of $3.2 \times 10^8\, {h^{-1}\rm M_{\odot}}$ and a force resolution of $3.0\ h^{-1}{\rm kpc}$. Its combination of scale and resolution is ideal for studying large-scale structures and rare cosmic objects. In this first paper of the HM project, we explore whether the massive galaxy cluster Abell~2744 (A2744) can be reproduced in detail in the simulation. Pixel-based statistics of galaxy number density $N_{\rm gal}$, luminosity density $L_{\rm gal}$, and projected mass density $κ$ show excellent agreement between A2744 and its analogues down to $\sim 50$ kpc, once field-selection biases toward high galaxy surface density are accounted for. This concordance, achieved in one of the most extreme known galaxy environments, is a validation of the underlying $Λ{\rm CDM}$ model in the extreme regime of A2744. It also showcases the robustness and accuracy of the HM simulation, which, when coupled with a sophisticated semi-analytic galaxy formation model, is capable of producing galaxy and mass catalogues of comparable quality out to high redshift across its full comoving volume of 50.4 ${\rm Gpc^3}$.

astro-ph.CO↗

arXiv2026

Halo abundance and clustering in cosmologies with massive and asymmetric neutrinos

Neutrinos are the most abundant fermions in the Universe and influence the formation of large-scale structure through both their non-zero masses and a possible chemical potential which can be described by a single asymmetry parameter. While most previous studies have focused on the impact of the neutrino mass, the role of neutrino asymmetry remains comparatively unexplored. In this work, we investigate how massive neutrinos ($M_ν=0-0.24\,\mathrm{eV}$) with a non-zero asymmetry parameter ($η^{2}=0-0.8$) modify the halo mass function (HMF) and halo bias using cosmological N-body simulations with cosmological parameters consistently refitted to CMB observations. We find that at all redshifts, neutrino mass suppresses the abundance of massive halos, whereas neutrino asymmetry enhances the HMF over a broad mass range. At z=0, the abundance of the most massive halos is reduced by up to ~30% in the largest-mass case ($M_ν=0.24\,\mathrm{eV}$), while neutrino asymmetry ($η^{2}=0.8$) produces a maximum ~5% enhancement. These effects become increasingly pronounced at higher redshifts: by z=4 and z=9, the enhancement induced by neutrino asymmetry reaches ~25% and ~75%, respectively, while the corresponding suppression due to neutrino mass deepens to below ~40% and ~70% of the massless case. For halo bias, we find that halos with masses above $10^{13.4}\,\mathrm{M_\odot}$ exhibit an enhanced large-scale bias due to neutrino mass, reaching up to ~5% at z=0, while neutrino asymmetry reduces the bias by a few percent on linear scales. These trends strengthen with redshift, with the enhancement and suppression growing to ~15% and ~10% at z=2, respectively. Linear bias models provide an adequate, though not exact, description of halo bias in massive-neutrino cosmologies. Our results demonstrate that halo abundance and clustering offer sensitive probes of both neutrino mass and asymmetry.

astro-ph.CO↗

arXiv2026

Modified-gradient methods for exact divergence-free in meshless magnetohydrodynamics

We present a novel gradient regularization to completely eliminate the magnetic divergence error in meshless magnetohydrodynamics (MHD), which offers a high spatial resolution and conservative advantage, due to its Lagrangian nature. Comparing with the counterpart of constrained-gradient (CG) technique, we reform $\nabla \cdot \mathbf{B}=0$ by an implicit projection method to modify the magnetic-field gradients. The accuracy of modified-gradient (MG) method is verified and it achieves exact divergence-free results with round-off precision, by using tests of shock tube, 2D and 3D vortex, magneto-rotational instability, and especially, advection experiment, compared with CG method and the GIZMO code. It leads to noticeable improvement in pattern, amplitude and numerical dissipation of divergence error of magnetic field.

astro-ph.IM↗

arXiv2026

Percolation-driven $β$ -relaxation enables resonant acceleration of crystallization in amorphous phase-change materials

Amorphous phase-change materials enable fast and reversible switching in optical and electronic devices, yet crystallization kinetics are still controlled primarily through empirical thermal protocols. Here we identify a microscopic picture governing crystallization in the prototypical phase-change material Ge2Sb2Te5, in which crystallization pathways are organized by the percolation of mobile atomic networks associated with $β$-relaxation. We show that this percolation transition distinguishes the dominance of diffusion-driven and diffusionless nucleation and growth during crystallization processes. We further demonstrate that frequency-selected ultrasonic excitation, applied in conjunction with heating, accelerates crystallization by enhancing percolation-mediated atomic dynamics. This acceleration is maximized near the $β$-relaxation frequency, consistent with resonant excitation of mobile atoms. Our results establish a direct link between glassy relaxation, atomic-scale percolation, and crystallization, and introduce a new route to modulating phase-change kinetics through targeted excitation of fundamental glassy dynamics.

cond-mat.mtrl-sci↗

arXiv2026

Probing Dark Matter Substructures with Free-Form Modelling: A Case Study of the `Jackpot' Strong Lens

Characterising the population and internal structure of sub-galactic halos is critical for constraining the nature of dark matter. These halos can be detected near galaxies that act as strong gravitational lenses with extended arcs, as they perturb the shapes of the arcs. However, this method is subject to false-positive detections and systematic uncertainties, particularly degeneracies between an individual halo and larger-scale asymmetries in the distribution of lens mass. We present a new free-form lens modelling code, developed within the framework of the open-source software \texttt{PyAutoLens}, to address these challenges. Our method models mass perturbations that cannot be captured by parametric models as pixelized potential corrections and suppresses unphysical solutions via a Matérn regularisation scheme that is inspired by Gaussian process regression. This approach enables the recovery of diverse mass perturbations, including subhalos, line-of-sight halos, external shear, and multipole components that represent the complex angular mass distribution of the lens galaxy, such as boxiness/diskiness. Additionally, our fully Bayesian framework objectively infers hyperparameters associated with the regularisation of pixelized sources and potential corrections, eliminating the need for manual fine-tuning. By applying our code to the well-known `Jackpot' lens system, SLACS0946+1006, we robustly detect a highly concentrated subhalo that challenges the standard cold dark matter model. This study represents the first attempt to independently reveal the mass distribution of a subhalo using a fully free-form approach.

astro-ph.CO↗

arXiv2026

The impact of cosmic filaments on the abundance of satellite galaxies

The impact of cosmic web environments on galaxy properties plays a critical role in understanding galaxy formation. Using the state-of-the-art cosmological simulation IllustrisTNG, we investigate how satellite galaxy abundance differs between filaments and the field, with filaments identified using the DisPerSE algorithm. When filaments are identified using galaxies as tracers, we find that, across all magnitude bins, central galaxies in filaments tend to host more satellite galaxies than their counterparts in the field, in qualitative agreement with observational results from the Sloan Digital Sky Survey. The average ratios between satellite luminosity functions in filaments and the field are $3.49$, $2.61$, and $1.90$ in the central galaxy $r$-band magnitude bins of $M_{r, {\rm cen}} \sim -22$, $-21$, and $-20$, respectively. We show that much of this excess can be attributed to the higher host halo masses of galaxies in filaments. After resampling central galaxies in both environments to match the halo mass distributions within each magnitude bin, the satellite abundance enhancement in filaments is reduced by up to $79 \%$. Additionally, the choice of tracers used to identify filaments introduces a significant bias: when filaments are identified using the dark matter density field, the environmental difference in satellite abundance is reduced by more than $70 \%$; after further resampling in both magnitude and halo mass, the difference is further suppressed by another $\sim 60$--$95 \%$. Our results highlight the importance of halo mass differences and tracer choice biases when interpreting and understanding the impact of environment on satellite galaxy properties.

astro-ph.GA↗

arXiv2025

Ultra-diffuse galaxies in the EAGLE simulation

We use the highest-resolution EAGLE simulation, Recal-L025N0752, to study the properties and formation of ultra-diffuse galaxies (UDGs). We identify 181 UDGs and find their properties closely match observations. The total masses of EAGLE UDGs range from ${\sim}5\times 10^{8}~M_{\odot}$ to ${\sim}2\times 10^{11}~M_{\odot}$, indicating that they are dwarf galaxies rather than failed $L_\star$ galaxies. EAGLE UDGs are not a distinct population, but rather a subset of dwarf galaxies, as their properties generally form a continuous distribution with those of normal dwarf galaxies. Unlike the situations in previous studies, the extended sizes of field UDGs in EAGLE are not driven by high halos spin or by supernova-induced stellar expansion, but instead largely arise from high spins in their star-forming gas and thus the newly formed stars at large radii. This might be attributed to galactic fountains, by which star-forming gas are launched to large halo-centric distances and acquire additional angular momentum through interactions with the circumgalactic medium. For satellite UDGs, ${\sim} 60 \%$ of them were already UDGs before falling into the host galaxy, while the remaining ${\sim} 40\%$ were normal galaxies prior to infall and subsequently transformed into UDGs due to tidal effects after infall.

astro-ph.GA↗

arXiv2025

Particle loads for cosmological simulations with equal-mass dark matter and baryonic particles

Traditional cosmological hydrodynamical simulations usually assume equal-numbered but unequal-mass dark matter and baryonic particles, which can lead to spurious collisional heating due to energy equipartition. To avoid such a numerical heating effect, a simulation setup with equal-mass dark matter and baryonic particles, which corresponds to a particle number ratio of $N_{\rm DM}:N_{\rm gas} = Ω_{\rm cdm} / Ω_{\rm b}$, is preferred. However, previous studies have typically used grid-based particle loads to prepare such initial conditions, which can only reach specific values for $N_{\rm DM}:N_{\rm gas}$ due to symmetry requirements. In this study, we propose a method based on the glass approach that can generate two-component particle loads with more general $N_{\rm DM}:N_{\rm gas}$ ratios. The method simultaneously relaxes two Poisson particle distributions by introducing an additional repulsive force between particles of the same component. We show that the final particle load closely follows the expected minimal power spectrum, $P(k) \propto k^{4}$, exhibits good homogeneity and isotropy properties, and remains sufficiently stable under gravitational interactions. Both the dark matter and gas components individually also exhibit uniform and isotropic distributions. We apply our method to two-component cosmological simulations and demonstrate that an equal-mass particle setup effectively mitigates the spurious collisional heating that arises in unequal-mass simulations. Our method can be extended to generate multi-component uniform and isotropic distributions. Our code based on Gadget-2 is available at https://github.com/liaoshong/gadget-2glass .

astro-ph.CO↗

arXiv2025

FLRW Kinematic-Induced Measurement of the Hubble Constant from Cosmic Chronometer and Redshift Drift Observations

We present a geometric embedding method that exploits the exact kinematic relation $\dot{z} = H_0(1 + z) - H(z)$ to transform redshift misalignment between Cosmic Chronometer (CC) and Sandage-Loeb (SL) datasets into fundamental constraints in observable space. The approach recognizes that $H_0$ encodes the orientation of the FLRW observational plane defined by $(z, H(z), \dot{z})$ coordinates, enabling direct algebraic determination without parametric assumptions or interpolation schemes. Validation using available CC measurements and forecasted redshift drift data from FAST, CHIME, SKA, and ELT demonstrates 1.9\% precision for optimal data combinations, yielding $H_0 = 66.26 \pm 1.26$ km s$^{-1}$ Mpc$^{-1}$ while maintaining complete cosmological model independence. While no actual SL measurements currently exist, requiring us to rely on simulations for validation, our geometric constraints show superior resilience against sparse redshift coverage compared to Gaussian Process (GP) methods, which exhibit systematic biases and large uncertainties when datasets lack substantial overlap. This kinematic framework establishes geometric embedding as a robust tool for precision cosmological measurements, offering a fundamentally different approach to $H_0$ determination through pure observational analysis based on FLRW kinematic principles. The full potential of this method awaits implementation with real SL measurements from next-generation facilities.

astro-ph.CO↗