Classification of contraction algebras and pre-Lie algebras associated to braces and trusses

We develop tools for classification of contraction algebras and apply these to solve the problem on classification up to isomorphism of 8 and 9 dimensional algebras corresponding to 3-fold flops. We prove that there is only one up to isomorphism contraction algebra of dimension 8, and two algebras of dimension 9. The formulae for the dimension of algebra, depending on the type of the potential are obtained. In the second part of the paper we show that associated graded structure to brace and truss with appropriate descending ideal filtration is pre-Lie.