Primitivity Conjecture for homogeneous finite-dimensional permutation structures

A primitive homogeneous finite-dimensional permutation structure is a homogeneous finite-dimensional permutation structure with no nontrivial $\emptyset$-definable equivalence relation. A structure is fully generic when it is the Fraïssé limit of the resulting amalgamation class after passing to the indicated simpler language.

Primitivity Conjecture. Every primitive homogeneous finite-dimensional permutation structure can be constructed as follows: identify certain orders, up to reversal; then take the Fraïssé limit of the resulting amalgamation class, obtaining a fully generic structure, possibly in a simpler language.

Pierre Simon had confirmed a proof in personal communication before submission, although the thesis retained the conjecture for direct amalgamation arguments. Thus the claim is treated as solved.