Galaxy flows within 8,000 km/s from Numerical Action methods
  The trajectories since z=4 of systems of galaxies (`halos') with cz < 8,000
km/s are found through Numerical Action reconstructions. A set of 9,719 halos
from a 2MASS group catalog and Cosmicflows-3 catalogs are given attention.
Present distances are adjusted to minimize departures from observed redshifts.
For those with the most precisely determined distances, compromises are made
between distance and redshift agreement. $H_0$ is varied from 69 to 77 km
s$^{-1}$ Mpc$^{-1}$ with $\Omega_m$ set by the baryon acoustic oscillation
constraint from the Planck Satellite. A best fitting amplitude of the
mass-to-light relation is found. A uniform density associated with the
interhalo medium accounts for the matter not in halos. The solution paths
provide the histories of the formation of the nearby large structures and
depict how the voids emptied. Assuming no local over/underdensity, the best
model has $H_0=73$ km s$^{-1}$ Mpc$^{-1}$ with nearly the same density arising
from interhalo matter (IHM) as from halos. We examine local over/underdensities
by varying the IHM density and find a valley of best fit models along $H_0 =
73.0 (1 + 0.165\delta)$ km s$^{-1}$ Mpc$^{-1}$. Friedmann models with distinct
densities internal and external to the study region give a similar
relationship. The fraction of matter in the IHM seen in n-body simulations
roughly matches that in our $H_0=72$ scenario. Videos have been created to
visualize the complexities of formation of large-scale structures. Standard
n-body calculations starting from the first time-steps as tests of the NAM
solutions, and continue until cosmic scale factor $a=2$ provide glimpses into
the future.
