Translate path algebras of species to framed Mixed Tate Motives and motivic zeta elements

Ascertain the precise correspondence between the path algebra of the species used here to describe Mixed Tate Motives and the frameworks of Goncharov’s framed Mixed Tate Motives and Brown’s motivic zeta elements, by developing an explicit translation between these formalisms.

Background

In the Mixed Tate Motive setting, the authors obtain dimension bounds via path algebras of species and compare to earlier Tannakian approaches. They highlight related constructions by Goncharov (framed Mixed Tate Motives) and Brown (motivic zeta elements), which provide alternative motivic frameworks connected to multiple zeta values.

The paper does not provide a direct, explicit mapping between these approaches and the path algebra formalism, noting this as a gap to be addressed in future work.