Differential algebraicity of Hilbert series for finitely generated Koszul symmetric operads (Khoroshkin–Piontkovski Conjecture)

Establish that for every finitely generated Koszul symmetric operad P, the Hilbert series f_P(t) is differential algebraic over the polynomial ring Z[t].

Background

Building on the algebraic conjecture, Khoroshkin and Piontkovski proposed an operadic analogue asserting that Hilbert series of finitely generated Koszul symmetric operads satisfy a nontrivial differential algebraic equation with coefficients in Z[t]. The authors review this conjecture and verify it experimentally on many examples, using it as a broader backdrop for their classification and their own stronger conjecture in the single-binary-generator case.