The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey:
  Cosmological Implications from two Decades of Spectroscopic Surveys at the
  Apache Point observatory
  We present the cosmological implications from final measurements of
clustering using galaxies, quasars, and Ly$\alpha$ forests from the completed
Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale
structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and
eBOSS, offer independent measurements of baryon acoustic oscillation (BAO)
measurements of angular-diameter distances and Hubble distances relative to the
sound horizon, $r_d$, from eight different samples and six measurements of the
growth rate parameter, $f\sigma_8$, from redshift-space distortions (RSD). This
composite sample is the most constraining of its kind and allows us to perform
a comprehensive assessment of the cosmological model after two decades of
dedicated spectroscopic observation. We show that the BAO data alone are able
to rule out dark-energy-free models at more than eight standard deviations in
an extension to the flat, $\Lambda$CDM model that allows for curvature. When
combined with Planck Cosmic Microwave Background (CMB) measurements of
temperature and polarization the BAO data provide nearly an order of magnitude
improvement on curvature constraints. The RSD measurements indicate a growth
rate that is consistent with predictions from Planck primary data and with
General Relativity. When combining the results of SDSS BAO and RSD with
external data, all multiple-parameter extensions remain consistent with a
$\Lambda$CDM model. Regardless of cosmological model, the precision on
$\Omega_\Lambda$, $H_0$, and $\sigma_8$, remains at roughly 1\%, showing
changes of less than 0.6\% in the central values between models. The inverse
distance ladder measurement under a o$w_0w_a$CDM yields $H_0= 68.20 \pm 0.81 \,
\rm km\, s^{-1} Mpc^{-1}$, remaining in tension with several direct
determination methods. (abridged)
