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Abstract The tip of the red giant branch (TRGB) is an apparent discontinuity of the luminosity function (LF) due to the end of the red giant evolutionary phase and is used to measure distances in the local universe. In practice, tip localization via edge detection response (EDR) relies on several methods applied on a case-by-case basis. It is hard to evaluate how individual choices affect a distance estimation using only a single host field while also avoiding confirmation bias. To devise a standardized approach, we compareunsupervised, algorithmic analyses of the TRGB inmultiplehalo fields per galaxy. We first optimize methods for the lowest field-to-field dispersion, including spatial filtering, smoothing, and weighting of LF, color band selection, and tip selection based on the number of likely RGB stars and the ratio of stars below versus above the tip (R). We findR, which we call the tipcontrast, to be themost importantindicator of the quality of EDR measurements; higherRselection can decrease field-to-field dispersion. Further, sinceRis found to correlate with the age or metallicity of the stellar population based on theoretical modeling, it might result in a displacement of the detected tip magnitude. We find atip-contrast relationwith a slope of −0.023 ± 0.0046 mag/ratio, an ∼5σresult that can be used to correct these variations in the detections. When using TRGB to establish a distance ladder, consistent TRGB standardization using tip-contrast relation across rungs is vital to make robust cosmological measurements. 

Abstract The tip of the red giant branch (TRGB) provides a luminous standard candle for constructing distance ladders to measure the Hubble constant. In practice, its measurements via edge-detection response (EDR) are complicated by the apparent fuzziness of the tip and the multipeak landscape of the EDR. Previously, we optimized an unsupervised algorithm, Comparative Analysis of TRGBs, to minimize the variance among multiple halo fields per host without relying on individualized choices, achieving state-of-the-art ∼<0.05 mag distance measures for optimal data. Here we apply this algorithm to an expanded sample of SN Ia hosts to standardize these to multiple fields in the geometric anchor, NGC 4258. In concert with the Pantheon+ SN Ia sample, this analysis produces a (baseline) result ofH₀= 73.22 ± 2.06 km s⁻¹Mpc⁻¹. The largest difference inH₀between this and similar studies employing the TRGB derives from corrections for SN survey differences and local flows used in the most recent SN Ia compilations that were absent in earlier studies. The SN-related differences total ∼2.0 km s⁻¹Mpc⁻¹. A smaller share, ∼1.4 km s⁻¹Mpc⁻¹, results from the inhomogeneity of the TRGB calibration across the distance ladder. We employ a grid of 108 variants around the optimal TRGB algorithm and find that the median of the variants is 72.94 ± 1.98 km s⁻¹Mpc⁻¹with an additional uncertainty due to algorithm choices of 0.83 km s⁻¹Mpc⁻¹. None of these TRGB variants result in anH₀of less than 71.6 km s⁻¹Mpc⁻¹.