= Solution
<annual stellar parallax> uses the known Earth-orbit baseline, with \b[$d(\mathrm{pc})=1/\varpi(\mathrm{arcsec})$]. Repeated positions separate parallax from <proper motion>; <calibration> offsets, binarity and noisy-parallax selection require checks. Nearby <stars> calibrate absolute <luminosities>. Extinction-corrected <distance modulus> then gives
$$
\boxed{m_\lambda-M_\lambda=5\log_{10}(d/10\,\mathrm{pc})+A_\lambda}.
$$
<main-sequence fitting> compares a cluster sequence with nearby calibrated <stars>; age, <metallicity>, reddening and unresolved binaries limit the match. <Cepheid variables> extend the range to nearby <galaxies>: measure periods and mean multiband magnitudes, calibrate the <Cepheid period-luminosity relation>, and correct for <extinction>, <metallicity>, crowding and pulsation mode. <RR Lyrae stars> and the <tip of the red giant branch> provide complementary population-II routes with their own composition and <calibration> dependence.
Some anchors bypass intermediate rungs. An <eclipsing-binary distance> starts from a double-lined <eclipsing binary>: velocities give $a\sin i$; eclipses give inclination $i$ and relative radii $R/a$, hence physical radii. An independently calibrated surface-brightness/colour relation gives angular radii and distance; alternatively corrected bolometric flux satisfies $F_{\rm bol}=\sigma T_{\rm eff}^4(R/d)^2$ for a component. <temperature>, <extinction>, third light and surface-brightness <calibration> remain systematic errors. Eight late-type binaries gave a 2.2%-accuracy <LMC> anchor in 2013.<An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent by G. Pietrzyński and others>[abstract, Nature 495, 76–79; photometric and orbital information]{ref}
A <maser-disk geometric distance> uses water <masers> orbiting in the nearly edge-on nuclear disk of <NGC 4258>. <very-long-baseline interferometry>, Doppler velocities, <proper motions> and accelerations constrain its orbit scale and distance. In an ideal circular, matched-radius example $R=v^2/a_{\rm orb}$ and $d=R/\theta$; real fits account for disk warp and different <maser> locations. This geometric method calibrated an extragalactic distance independently of stellar <luminosities>.<A 4% Geometric Distance to the Galaxy NGC4258 from Orbital Motions in a Nuclear Gas Disk by J. R. Herrnstein and others>[abstract; orbital proper motions and accelerations, 1999]{ref} These overlapping anchors cross-check the nearby-galaxy ladder; no Hubble-flow fit is needed here.
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