The SDSS-IV Mapping Nearby Galaxies at APO (MaNGA) program has been operating from 2014-2020, and has now observed a sample of 9,269 galaxies in the low redshift universe (z ~ 0.05) with integral-field spectroscopy. With rest-optical (lambdalambda 0.36 - 1.0 um) spectral resolution R ~ 2000 the instrumental spectral line-spread function (LSF) typically has 1sigma width of about 70 km/s, which poses a challenge for the study of the typically 20-30 km/s velocity dispersion of the ionized gas in present-day disk galaxies. In this contribution, we present a major revision of the MaNGA data pipeline architecture, focusing particularly on a variety of factors impacting the effective LSF (e.g., undersampling, spectral rectification, and data cube construction). Through comparison with external assessments of the MaNGA data provided by substantially higher-resolution R ~ 10,000 instruments we demonstrate that the revised MPL-10 pipeline measures the instrumental line spread function sufficiently accurately (<= 0.6% systematic, 2% random around the wavelength of Halpha) that it enables reliable measurements of astrophysical velocity dispersions sigma_Halpha ~ 20 km/s for spaxels with emission lines detected at SNR > 50. Velocity dispersions derived from [O II], Hbeta, [O III], [N II], and [S II] are consistent with those derived from Halpha to within about 2% at sigma_Halpha > 30 km/s. Although the impact of these changes to the estimated LSF will be minimal at velocity dispersions greater than about 100 km/s, scientific results from previous data releases that are based on dispersions far below the instrumental resolution should be reevaulated.
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