On a simple invariant of Turaev–Viro type

We define a 3-manifold invariant $t(M)=a+b\varepsilon$, where $a,b$ are integers and $\varepsilon=(1\pm\sqrt5)/2$. An advantage of the invariant is that it admits a very simple interpretation in terms of a fake surface and a simple geometric proof of the invariance. Actually, it coincides with the homologically trivial part of the Turaev–Viro invariant of degree $r=5$. Extensive tables for all closed irreducible orientable 3-manifolds of complexity less than or equal to six are explicitly presented. Similar tables for $r=3,4$ were composed by L. H. Kauffman and S. Lins. Bibl. 8 titles.