Algebras of distributions of binary isolating formulas for almost $\omega$-categorical weakly $o$-minimal theories

We describe distribution algebras of binary isolating formulas over $1$-type for almost $\omega$-categorical weakly $o$-minimal theories. It is proved that an isomorphism of these algebras for two $1$-types is characterized by the coincidence of binary convexity ranks, as well as by the simultaneous fulfillment of isolation, quasirationality or irrationality of the two types. A criterion is established for an algebra of formulas over a pair of not weakly orthogonal $1$-types to be generalized commutative for almost $\omega$-categorical weakly $o$-minimal theories.