Finite–classical correspondence for Euler sums

Establish, for every weight \(w\), the conjectured isomorphism between the vector space generated by finite Euler sums of weight \(w\) and the quotient of the vector space generated by classical Euler sums of weight \(w\) by \(\zeta(2)ES_{w-2}\), with the map sending each finite Euler sum to its symmetric regularized classical counterpart modulo \(\zeta(2)\).

Background

The paper extends the Kaneko–Zagier philosophy from finite multiple zeta values to alternating multiple zeta values, also called Euler sums. For each weight, it defines a proposed map from finite Euler sums to classical Euler sums modulo $\zeta(2)$-products using symmetric stuffle-regularized values. The paper assumes that this map is well-defined throughout its constructions, so the asserted isomorphism remains a conjectural foundational problem rather than a theorem established in the paper.