The Hubble-Lema\^{i}tre constant and sound horizon from low-redshift
  probes
  We revisit the claimed tension, or lack thereof, of measured values of the
Hubble-Lema\^{i}tre parameter $H_0$ from Cosmic Microwave Background (CMB) data
and low-redshift indicators. Baryon Acoustic Oscillations (BAO) rely on the
scale of the sound horizon at recombination $r_s$ to convert angular
measurements into angular-diameter distances, so fixing $r_s$ from CMB
measurements already constrains $H_0.$ If departures from concordance cosmology
are to be constrained, truly independent measurements of $H_0$ are needed. We
use the angular-diameter distances to three time-delay lenses from the H0LiCOW
collaboration to calibrate the distance ladder, combine them with relative
distances from Supernovae Ia and BAO, leaving $r_s$ completely free, and
provide the inferred coefficients ($q_{0},j_{0},s_{0}$) in the polynomial
expansion of H(z). We obtain $H_{0}r_{s}=(9895\pm161)$km/s and
$H_0=(72\pm7)$km/s/Mpc. Combined with $H_0$ from H0LiCOW, then
$r_s=(137\pm4.5)$Mpc is consistent with previous work and systematically lower
than the CMB-inferred value. Our results are independent of the adopted
cosmology, and removing Supernovae with z<0.1 has a negligible effect.
