PowerLogInv: A Third Independent Sheffer Operator Beyond EML and EDL

We introduce PowerLogInv (PLI), defined as pli(x,y) = ln(x)^(1/y), as a new binary Sheffer operator that, together with the constant 1, generates the standard scientific-calculator basis of elementary functions. Through systematic exhaustive search over 14,712 candidate binary operators, we identify exactly three non-equivalent Sheffer families: EML (Odrzywołek, 2026), EDL, and the present PLI. We prove the pairwise non-equivalence of these three operators by demonstrating that no finite composition rule maps one into another while preserving the calculator basis. This resolves an open question implicit in Odrzywołek's recent work and establishes that the binary Sheffer landscape is richer than previously known.