  In Sedgwick et al. (2019) we introduced and utilised a method to combat
surface brightness and mass biases in galaxy sample selection, using
core-collapse supernovae (CCSNe) as pointers towards their host galaxies, in
order to: (i) search for low-surface brightness galaxies (LSBGs); (ii) assess
the contributions of galaxies at a given mass to the star-formation-rate
density (SFRD); and (iii) infer from this, using estimates of specific
star-formation (SF) rate, the form of the SF-galaxy stellar mass function
(GSMF). A CCSN-selection of SF-galaxies allows a probe of the form of the SFRD
and GSMF deep into the dwarf galaxy mass regime. In the present work, we give
improved constraints on our estimates of the SFRD and star-forming GSMF, in
light of improved photometric redshift estimates required for estimates of
galaxy stellar mass. The results are consistent with a power-law increase to
SF-galaxy number density down to our low stellar mass limit of $\sim 10^{6.2}$
M$_{\odot}$. No deviation from the high-mass version of the surface brightness
- mass relation is found in the dwarf mass regime. These findings imply no
truncation to galaxy formation processes at least down to $\sim 10^{6.2}$
M$_{\odot}$.
