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Tianqing Zhang

Publications and source records attributed to Tianqing Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Simulation Tests of PSF Modeling for Cosmic Shear with the Vera C. Rubin Observatory

Exceptional control of systematic effects is required in order to achieve unbiased cosmic shear two-point correlation function measurements with the next generation of galaxy imaging surveys, such as the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). One critical challenge is accurately modeling the point-spread function (PSF), as errors in PSF estimation can introduce spatially correlated biases in galaxy shape measurements. The LSST Science Pipelines, which will be used to process Rubin data, include an implementation of the PIFF (PSFs in the Full Field of View) package originally developed for, and demonstrated to perform well on, DES-Y3 and Y6 data. In this work we use semi-realistic image simulations, mimicking LSST observing conditions in $i$-band over 100 square degrees, to perform an end-to-end test of the Rubin PSF modeling pipeline. PSF model residuals are quantified using both second- and fourth-order moment parameters and performance is evaluated, for both LSST year 1 and year 10 depth, with a series of diagnostic tests. We find that the additive bias contribution from PSF modeling errors to the non-tomographic cosmic shear data vector is well below 30% of the cosmic shear uncertainty estimated from our analytic covariance matrix. Though our simulations exclude several known effects that may further challenge PSF modeling, these results demonstrate promising performance from PIFF on LSST-like data and provide an early benchmark for ongoing PSF validation efforts for LSST weak lensing analyses.

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arXiv2026

Modeling the impact of filter-substrate refraction in the Roman point spread function

For broadband imaging surveys, filter-substrate refraction causes light at different wavelengths to follow slightly different paths through the filter substrate before reaching the detector. This effect produces two chromatic perturbations to the point spread function (PSF): a shift in the effective focal position along the optical axis (longitudinal shift), which manifests as a defocus-like perturbation, and a wavelength-dependent displacement of the image position in the focal plane (lateral shift), which manifests as image decentering. Using image simulations, we provide the first study of these two effects independently across all eight Roman imaging bands and over the full focal plane. We compute the resulting PSF and photometric errors from images with and without the effect included, and compare the magnitude of the effect to the Roman science requirements. We find that the lateral shift is the dominant contribution, producing PSF size and ellipticity residuals in most bands of order ~0.3-0.4%. These exceed the Roman science requirements for weak lensing by roughly an order of magnitude. The effect is also strongly field dependent, increasing toward the edges of the focal plane. By contrast, flux residuals remain below one third of the 1% requirement for most bands, except in R062 and W146. We find the longitudinal shift to be subdominant and negligible in most bands, including the weak lensing bands. Finally, we implement the dominant lateral-shift effect in a framework suitable for large-scale image simulations and validate that the resulting PSF size and shape changes are accurately reproduced. Overall, we find that filter-substrate refraction is a relevant chromatic effect for Roman PSF modeling, and we provide tools to model and incorporate it in large-scale image simulations.

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arXiv2026

Constraining Extragalactic Proper Motion with Gaia Astrometry

The Solar System's secular motion with respect to the cosmic microwave background (CMB) rest frame is inferred from the CMB dipole and should induce a tiny, coherent apparent drift in the positions of nearby galaxies, referred to as the extragalactic proper motion. We test the feasibility of a purely geometric measurement of this effect by combining Gaia DR2 and DR3 astrometry with low-redshift spectroscopic galaxy catalogs to build a large, full-sky sample of $67,173$ galaxies. Although we do not obtain a statistically significant detection of the expected dipole signal, we place the tightest constraint to date on the extragalactic proper motion $\barπ$. Using galaxies with comoving distance $D>5 {\, \rm Mpc}$, we also place the tightest constraints on cosmic extragalactic proper motion $\barπ_{\rm cosmic}$, with uncertainty $\sim 10\times$ the measured CMB dipole value. Our $1σ$ uncertainty on the near field extragalactic proper motion $\barπ_{\rm nf}$ is approximately $\sim 1.3\times$ the expected CMB measurement, demonstrating that Gaia astrometry is approaching the sensitivity required for a direct detection of near field Hubble constant in future releases.

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arXiv2026

Hyrax: An Extensible Framework for Rapid ML Experimentation and Unsupervised Discovery in the Era of Rubin, Roman, and Euclid

The NSF-DOE Vera C. Rubin Observatory, Roman Space Telescope, Euclid, and other next-generation surveys will deliver imaging, spectroscopic, and time-domain data at scales that increasingly shift the bottleneck in astronomical machine learning (ML) projects from model design to infrastructure. We present Hyrax, an open-source, modular, GPU-enabled Python framework that supports the full ML lifecycle in astronomy: from data acquisition and training to inference and experiment comparison, with capabilities including multimodal dataset support, integrated vector databases for similarity search, and interactive two- and three-dimensional latent-space exploration for unsupervised discovery. We demonstrate Hyrax's versatility through five representative applications on real survey data: (i) unsupervised representation learning on $\sim 4\times10^5$ Rubin Legacy Survey of Space and Time (LSST) Data Preview 1 (DP1) galaxies, surfacing new merger and low-surface-brightness candidates missing from reference Euclid and Dark Energy Survey catalogs, while also isolating imaging artifacts -- all without labeled training data; (ii) hybrid density-based clustering for identifying cluster-scale gravitational lens candidates in DP1 data; (iii) multimodal early-time transient classification in the Zwicky Transient Facility leveraging light curves, spectra, images, and metadata; (iv) supervised false-positive filtering in shift-and-stack searches for distant solar system objects in the Dark Energy Camera Ecliptic Exploration Project survey; and (v) supervised detection of semi-resolved dwarf galaxies in Hyper Suprime-Cam and LSST-like imaging using synthetic source injection. Together, these results demonstrate that Hyrax provides astronomy-specific ML infrastructure that enables systematic discovery and rapid methodological iteration across next-generation astronomical surveys.

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arXiv2026

The Galaxy Luminosity Functions in ASTRID: Predictions for LSST

We present validated and forward-modelled galaxy luminosity functions and photometric predictions for the Vera C. Rubin Observatory Legacy Survey of Space and Time using the ASTRID cosmological hydrodynamical simulation. Galaxy magnitudes are computed by combining stellar population synthesis modeling with a physically motivated dust attenuation prescription in which the optical depth scales with metal surface density. The dust model is calibrated at z = 0 using SDSS luminosity functions and tested at intermediate redshifts (z = 0.5, 1.0, and 1.5) in rest-frame B, V , R, and I bands. We find that the attenuated luminosity functions reproduce observed galaxy statistics across multiple wavelengths and redshifts. Using this calibrated framework, we construct LSST-ready mock photometric catalogs over 0 <= z <= 2 in steps of Delta z = 0.1, containing ~378 million galaxies. We provide predicted apparent-magnitude luminosity functions in the LSST ugrizy bands, derive best-fit Schechter parameters as a compact analytic representation, and compute differential and cumulative galaxy number counts as a function of survey depth from Year 1 to Year 10.

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arXiv2026

Optimizing Deep Learning Photometric Redshifts for the Roman Space Telescope with HST/CANDELS

Photometric redshifts (photo-$z$'s) will be crucial for studies of galaxy evolution, large-scale structure, and transients with the Nancy Grace Roman Space Telescope. Deep learning methods leverage pixel-level information from ground-based images to achieve the best photo-$z$'s for low-redshift galaxies, but their efficacy at higher redshifts with deep, space-based imaging remains largely untested. We used Hubble Space Telescope CANDELS optical and near-infrared imaging to evaluate fully-supervised, self-supervised, and semi-supervised deep learning photo-$z$ algorithms out to $z\sim3$. Compared to template-based and classical machine learning photometry methods, the fully-supervised and semi-supervised models achieved better performance. Our new semi-supervised model, PITA (Photo-$z$ Inference with a Triple-task Algorithm), outperformed all others by learning from unlabeled and labeled data through a three-part loss function that incorporates images and colors for all objects as well as redshifts when available. PITA produces a latent space that varies smoothly in magnitude, color, and redshift, resulting in the best photo-$z$ performance even when the redshift training set was significantly reduced. In contrast, the self-supervised approach produced a latent space with significant color and redshift fluctuations that hindered photo-$z$ inference. Looking forward to Roman, we recommend using semi supervised deep learning to take full advantage of the information contained in the hundreds of millions of high-resolution images and color measurements, together with the limited redshift measurements available, to achieve the most accurate photo-$z$ estimates for both faint and bright sources.

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arXiv2026

Improved photometric redshift estimations through self-organising map-based data augmentation

We introduce a framework for the enhanced estimation of photometric redshifts using Self-Organising Maps (SOMs). Our method projects galaxy Spectral Energy Distributions (SEDs) onto a two-dimensional map, identifying regions that are sparsely sampled by existing spectroscopic observations. These under-sampled areas are then augmented with simulated galaxies, yielding a more representative spectroscopic training dataset. To assess the efficacy of this SOM-based data augmentation in the context of the forthcoming Legacy Survey of Space and Time (LSST), we employ mock galaxy catalogues from the OpenUniverse2024 project and generate synthetic datasets that mimic the expected photometric selections of LSST after one (Y1) and ten (Y10) years of observation. We construct 501 degraded realisations by sampling galaxy colours, magnitudes, redshifts and spectroscopic success rates, in order to emulate the compilation of a wide array of realistic spectroscopic surveys. Augmenting the degraded mock datasets with simulated galaxies from the independent CosmoDC2 catalogues has markedly improved the performance of our photometric redshift estimates compared to models lacking this augmentation, particularly for high-redshift galaxies ($z_\mathrm{true} \gtrsim 1.5$). This improvement is manifested in notably reduced systematic biases and a decrease in catastrophic failures by up to approximately a factor of 2, along with a reduction in information loss in the conditional density estimations. These results underscore the effectiveness of SOM-based augmentation in refining photometric redshift estimation, thereby enabling more robust analyses in cosmology and astrophysics for the NSF-DOE Vera C. Rubin Observatory.

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arXiv2026

Deep Spectroscopy with DESI for Photometric Redshift Training and Calibration

Deep spectroscopic samples can be used to improve photometric redshift (photo-$z$) estimates and reduce uncertainties on redshift distributions. Such improvements can increase the cosmological constraining power of large imaging-based experiments such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and mitigate what may be a limiting systematic effect. We present results from the ``DESI-Deep pilot'' program, which was designed to assess the capability of the Dark Energy Spectroscopic Instrument (DESI) on the 4m Mayall telescope to measure redshifts of galaxies as faint as expected lensing samples for early LSST data ($m_i \leq 24.5$). We find that DESI is remarkably efficient at this task, with redshift success rates comparable to the results of observations from 10m-class telescopes with only $\sim2\times$ longer integration time (rather than $\sim 8\times$ longer as would be expected from aperture-area scaling), while simultaneously achieving $\sim30$ times larger multiplexing. We also find that the signal-to-noise ratio of the spectra scales as expected for background-limited observations even for the longest exposure times ($\sim 7$ hours) and faintest targets in the program. These results demonstrate that DESI could provide the definitive redshift sample for the early years of LSST with a modest investment of observing time. Based upon the results of this program, we provide updated predictions for the time required to collect benchmark samples for photo-$z$ training and calibration using a variety of spectroscopic facilities. Finally, we describe a potential "DESI-Deep" survey designed to train and calibrate photo-$z$'s for imaging experiments, and provide forecasts of its impact on cosmological inference.

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arXiv2026

Hyper Suprime-Cam Y3 results: photo-$z$ bias calibration with lensing shear ratios and cosmological constraints from cosmic shear

We present an independent calibration of the photometric redshift (photo-$z$) distributions for source galaxies in the HSC-Y3 weak lensing survey using small-scale galaxy-galaxy lensing. By measuring the tangential shear around spectroscopic lens galaxies from GAMA, SDSS, and DESI, divided into fifteen narrow redshift bins, we compute shear ratios that are sensitive to the mean redshift of source galaxies. Using a blinded analysis, we derive constraints on the photo-$z$ bias parameters in source bins 2, 3 and 4, achieving signal-to-noise ratios of 59, 75, and 62, respectively. Our constraints for $Δz_2$, $Δz_3$ and $Δz_4$ are consistent with those from HSC-Y3 cosmic shear modeling. We observe a mild shift in the $Δz_3$--$Δz_4$ plane due to the heterogeneous depth of the lens sample, which disappears when using only DESI-DR1 lenses. Combining shear-ratio measurements with cosmic shear data, we obtain joint constraints on cosmological parameters: $Ω_{\rm m} = 0.304_{-0.029}^{+0.03}$ and $S_8 = 0.773_{-0.031}^{+0.031}$, consistent with cosmic shear-only results. This work demonstrates the utility of small-scale lensing as an independent probe for calibrating photometric redshift bias in weak lensing cosmology.

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arXiv2026

Optimizing the Roman Space Telescope High-Latitude Wide Area Survey for mitigating chromatic PSF effects on shear measurement

Chromatic point-spread-function (PSF) effects arise from differences between the spectral energy distributions (SEDs) of stars, used to model the PSF, and galaxies, used to measure shape distortions due to weak gravitational lensing, or shear. For the Roman Space Telescope, these effects can bias shear measurement and cosmological inference, making them an important systematic effect for shear calibration. These biases depend sensitively on survey design choices, particularly filter coverage and the availability of color information. In this work, we investigate how different Roman survey strategies affect the ability to mitigate chromatic PSF effects and whether residual biases in shear propagate into cosmological inference. Using realistic image simulations, we infer per-galaxy near-infrared SED slopes via radial basis function regression for four-, three-, two-, and single-band survey configurations. We quantify residual shear calibration biases under representative and non-representative training assumptions and propagate these biases into Markov Chain Monte Carlo analyses of cosmic shear and $3\times2$-point statistics. We find that three- and four-band strategies can reduce residual shear biases to $|m|\lesssim10^{-3}$, lowering the induced shifts in the lensing amplitude from $ΔS_8 \sim 0.6σ$ (cosmic shear) and $ΔS_8 \sim 0.7σ$ ($3\times2$-pt) in the uncorrected case to $ΔS_8 \lesssim 0.07σ$. Single-band surveys remain limited, with residual shear biases reaching or exceeding $|m|\sim 2\times 10^{-3}$ in some tomographic bins. Average, sample-wide corrections reduce but do not eliminate chromatic systematics, leaving residual biases of $ΔS_8 \sim 0.1σ$. Overall, our results demonstrate that we can robustly correct for these effects in the recommended three-band medium tier, but may encounter residual biases in a single-band wide tier.

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arXiv2026

Redshift Assessment Infrastructure Layers (RAIL): Rubin-era photometric redshift stress-testing and at-scale production

Virtually all extragalactic use cases of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) require the use of galaxy redshift information, yet the vast majority of its sample of tens of billions of galaxies will lack high-fidelity spectroscopic measurements thereof, instead relying on photometric redshifts (photo-$z$) subject to systematic imprecision and inaccuracy best encapsulated by photo-$z$ probability density functions (PDFs). We present the version 1 release of Redshift Assessment Infrastructure Layers (RAIL), an open source Python library for at-scale probabilistic photo-$z$ estimation, initiated by the LSST Dark Energy Science Collaboration (DESC) with contributions from the LSST Interdisciplinary Network for Collaboration and Computing (LINCC) Frameworks team. RAIL's three subpackages provide modular tools for end-to-end stress-testing, including a forward modeling suite to generate realistically complex photometry, a unified API for estimating per-galaxy and ensemble redshift PDFs by an extensible set of algorithms, and built-in metrics of both photo-$z$ PDFs and point estimates. RAIL serves as a flexible toolkit enabling the derivation and optimization of photo-$z$ data products at scale for a variety of science goals and is not specific to LSST data. We thus describe to the extragalactic science community, including and beyond Rubin the design and functionality of the RAIL software library so that any researcher may have access to its wide array of photo-$z$ characterization and assessment tools.

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arXiv2026

A Path to an All-Sky Survey with Roman

A deep, space-based, all-sky near-infrared survey carried out with the Nancy Grace Roman Space Telescope would constitute a foundational astronomical infrastructure for decades to come. In this white paper, we present a concrete and feasible path to imaging the entire sky at $\sim0.1''$ resolution, beginning with high-impact fields in Cycle 1 and scaling to ultra-wide coverage within the nominal mission. This first-epoch survey will reach $\mathrm{H}\sim25.5$ AB mag (5$σ$) and maximize synergies with contemporaneous observatories, while preserving substantial time for other ambitious Roman programs. We outline representative scheduling scenarios and an example Cycle 1 program that triples early Roman-LSST overlap and delivers high-value community data products such as LSST forced photometry, joint \textit{Gaia}-Roman astrometry, and catalogs of Galactic substructure, stong lenses, and other rare systems. The Cycle 1 program will lay the foundation for an eventual all-sky survey, while also delivering high-impact early science. We invite broad community participation in shaping and carrying out both the initial program and the long-term vision of an all-sky Roman survey.

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arXiv2026

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

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arXiv2026

Diagnosing the Effects of Spectroscopic Training Set Imperfection on Photometric Redshift Performance

Most LSST extragalactic science will rely on photometric redshifts (photo-$z$) to extract distance information for the galaxies. However, an incomplete or non-representative training set can introduce bias into photo-$z$ estimation. It is necessary to understand how various forms of training set imperfection, such as incompleteness and non-trivial spectroscopic target selection, affect photo-$z$ estimation algorithms, and to identify metrics best-suited to quantify the impact. This work aims to systematically study metrics for diagnosing how various photo-$z$ methods react to certain types of training set incompleteness and non-representativeness. We use methods available through the open-source Python library Redshift Assessment Infrastructure Layers (RAIL) to systematically test the algorithms CMNN, GPz, FlexZBoost, and PZFlow on mock training data degraded in accordance with several existing spectroscopic sky surveys, as well as under conditions of inverse redshift incompleteness, which approximately mimics observed patterns of incompleteness at high redshift. We employ the algorithm TrainZ as a control. Finally, we quantify photo-$z$ algorithm performance using a variety of statistical metrics implemented externally to RAIL. We determine that the Kullback-Liebler Divergence, Wasserstein Distance, and Probability Integral Transform are particularly informative metrics with which to assess the impact of training set imperfection on algorithmic performance. We also find that inverse redshift incompleteness effects alone lack the complexity to realistically represent anticipated training data.

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arXiv2025

Reanalysis of Stage-III cosmic shear surveys: A comprehensive study of shear diagnostic tests

In recent years, shear catalogs have been released by various Stage-III weak lensing surveys including the Kilo-Degree Survey, the Dark Energy Survey, and the Hyper Suprime-Cam Subaru Strategic Program. These shear catalogs have undergone rigorous validation tests to ensure that the residual shear systematic effects in the catalogs are subdominant relative to the statistical uncertainties, such that the resulting cosmological constraints are unbiased. While there exists a generic set of tests that are designed to probe certain systematic effects, the implementations differ slightly across the individual surveys, making it difficult to make direct comparisons. In this paper, we use the TXPipe package to conduct a series of predefined diagnostic tests across three public shear catalogs -- the 1,000 deg$^2$ KiDS-1000 shear catalog, the Year 3 DES-Y3 shear catalog, and the Year 3 HSC-Y3 shear catalog. We attempt to reproduce the published results when possible and perform key tests uniformly across the surveys. While all surveys pass most of the null tests in this study, we find two tests where some of the surveys fail. Namely, we find that when measuring the tangential ellipticity around bright and faint star samples, KiDS-1000 fails with a $χ^2$/dof of 121.1/16 and 257.7/16 for bins 4 and 5 for faint, weighted stars. We also find that DES-Y3 and HSC-Y3 fail the $B$-mode test when estimated with the Hybrid-$E$/$B$ method, with a $χ^2$/dof of 37.9/10 and 36.0/8 for the fourth and third autocorrelation bins. We assess the impacts on the $Ω_{\rm m}$ - S$_{8}$ parameter space by comparing the posteriors of a simulated data vector with and without PSF contamination -- we find negligible effects in all cases. Finally, we propose strategies for performing these tests on future surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time.

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arXiv2025

Neural Posterior Estimation for Cataloging Astronomical Images with Spatially Varying Backgrounds and Point Spread Functions

Neural posterior estimation (NPE), a type of amortized variational inference, is a computationally efficient means of constructing probabilistic catalogs of light sources from astronomical images. To date, NPE has not been used to perform inference in models with spatially varying covariates. However, ground-based astronomical images have spatially varying sky backgrounds and point spread functions (PSFs), and accounting for this variation is essential for constructing accurate catalogs of imaged light sources. In this work, we introduce a method of performing NPE with spatially varying backgrounds and PSFs. In this method, we generate synthetic catalogs and semi-synthetic images for these catalogs using randomly sampled PSF and background estimates from existing surveys. Using this data, we train a neural network, which takes an astronomical image and representations of its background and PSF as input, to output a probabilistic catalog. Our experiments with Sloan Digital Sky Survey data demonstrate the effectiveness of NPE in the presence of spatially varying backgrounds and PSFs for light source detection, star/galaxy separation, and flux measurement.

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arXiv2025

Variability-finding in Rubin Data Preview 1 with LSDB

The Vera C. Rubin Observatory recently released Data Preview 1 (DP1) in advance of the upcoming Legacy Survey of Space and Time (LSST), which will enable boundless discoveries in time-domain astronomy over the next ten years. DP1 provides an ideal sandbox for validating innovative data analysis approaches for the LSST mission, whose scale challenges established software infrastructure paradigms. This note presents a pair of such pipelines for variability-finding using powerful software infrastructure suited to LSST data, namely the HATS (Hierarchical Adaptive Tiling Scheme) format and the LSDB framework, developed by the LSST Interdisciplinary Network for Collaboration and Computing (LINCC) Frameworks team. This article presents a pair of variability-finding pipelines built on LSDB, the HATS catalog of DP1 data, and preliminary results of detected variable objects, two of which are novel discoveries.

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arXiv2025

Modelling Galaxy Clustering and Tomographic Galaxy-Galaxy Lensing with HSC Y3 and SDSS using the Point-Mass Correction Model and Redshift Self-Calibration

The combination of galaxy-galaxy weak lensing and galaxy clustering is a powerful probe of the cosmological model, and exploration of how to best model and extract this information from the signals is essential. We present the measurement of the galaxy-galaxy weak lensing signals using the SDSS DR11 spectroscopic galaxies as lens galaxies, and the HSC Y3 shear catalog as source galaxies, binned into four tomographic bins by their photometric redshift. The SDSS DR11 galaxies, with a redshift range $0.15<z<0.7$, are binned into three redshift bins, each as a probe for measuring the projected correlation function, $w_p(R_p)$. We measure the galaxy-galaxy lensing signal $ΔΣ(R_p)$ in 12 lens-source bin pairs and show that there is no evidence for significant systematic biases in the measurement with null testing. We combine our $w_p(R_p)$ and $ΔΣ(R_p)$ ($2\times2$pt) data vectors and perform likelihood inference with a flat $Λ$CDM model. For $ΔΣ(R_p)$, we extend the lower limit of the scale cut compared to previous HSC Y3 analyses to $2 h^{-1}$Mpc by including a point-mass correction term in addition to the minimal bias model. We present various tests to validate our model and provide extended consistency tests. In the $Λ$CDM context, our fiducial model yields $S_8 = 0.804^{+0.051}_{-0.051}$. The $2\times2$pt data vector provides redshift parameter constraints for the third and fourth redshift bins $Δz_3 = -0.079^{+0.074}_{-0.084}$, and $Δz_4 = -0.203^{+0.167}_{-0.206}$, which is consistent with results from the previous tomographic cosmic shear studies, and serves as the foundation for a future $3\times 2$pt analysis.

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