Goursat flags (or: 1-flags) became popular in the second half
of the 1990s. Moduli of their local classification were found towards
the end of 1997. (The first of them appears in length 8.) In 1999
Kumpera and Rubin had a 60+ pages long draft advertising [special]
MULTI-flags (published in a much shortened form only in 2002). The local
classification problem for such flags kept being one of the hottest. In
2010 a finite classification in length 4 and a modulus in length 7 were
produced. In 2020 the infinitesimal symmetries were (if only
recursively) described. Formally only for special 2-flags, but easily
generalizable to multi-. In the winter 2023/24 A. Weber implemented
those recurrencies in Mathematica, offering an explicit hold on the
infinitesimal symmetries of the special 2-flags. That greatly narrowed
the field of search for moduli in length 5 and 6. Eventually in July
2024 moduli were found in length 5, in three singularity classes out of
$41 = (1/2)(3^{5-1} + 1)$ existing in that length 5.