  In this paper we prove that there is a weakly universal weighted cellular
automaton in the heptagrid, the tessellation {7,3} of the hyperbolic plane,
with 6 states. The present paper improves the same result deposited on
arXiv:2301.10691v1 and also arXiv:2301.10691v2. In the deposited papers, the
result is proved with 7 states. In the present replacement the number of states
is reduced to 6. Such a reducing is not trivial and requires substantial
changes in the implementation. The maximal weight is now 34, a very strong
reduction with the best result with 7 states. Also, the table has 137 entries,
signifcantly less than the 160 entries of the paper with 7 states. The
reduction is obtained by a new implementation of the tracks which play a key
role as far as without tracks there is no computational universality result.
