The Tip of the Red Giant Branch provides a luminous standard candle for
calibrating distance ladders that reach Type Ia supernova (SN Ia) hosts.
However, recent work reveals that tip measurements vary at the ∼ 0.1 mag
level for different stellar populations and locations within a host, which may
lead to inconsistencies along the distance ladder. We pursue a calibration of
the tip using 11 Hubble Space Telescope fields around the maser host, NGC 4258,
that is consistent with SN Ia hosts by standardizing tip measurements via their
contrast ratios. We find F814W-band tips that exhibit a full 0.3 mag range
and 0.1 mag dispersion. We do not find any correlation between HI column
density and the apparent tip to 0.04 ± 0.03 mag/cm−2. We search for a
tip-contrast relation (TCR) and measure the TCR within the fields of NGC 4258
of −0.015±0.008 mag/R, where R is the contrast ratio. This value is
consistent with the TCR originally discovered in the GHOSTS sample (Wu et al.
2022) of −0.023±0.005 mag/R. Combining these measurements, we find a global
TCR of −0.021±0.004 mag/R and a calibration of MITRGB​=−4.025±0.035−(R−4)×0.021 mag. We also use stellar models to simulate single
age and metallicity stellar populations with [Fe/H] from −2.0 to −0.7 and
ages from 3 Gyr to 12 Gyr and reconstruct the global TCR found here to a factor
of ∼ 2. This work is combined in a companion analysis with tip
measurements of nearby SN Ia hosts to measure H0​.Comment: 20 pages, 12 figures, 3 tables. Submitted to Ap