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In this paper we prove that there is a weakly universal weighted cellularautomaton in the heptagrid, the tessellation {7,3} of the hyperbolic plane,with 6 states. The present paper improves the same result deposited onarXiv:2301.10691v1 and also arXiv:2301.10691v2. In the deposited papers, theresult is proved with 7 states. In the present replacement the number of statesis reduced to 6. Such a reducing is not trivial and requires substantialchanges in the implementation. The maximal weight is now 34, a very strongreduction 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. Thereduction is obtained by a new implementation of the tracks which play a keyrole as far as without tracks there is no computational universality result.

A weakly universal weighted cellular automaton in the heptagrid with 6 states