Clarify the relation between Siegel-gauge level-truncation solutions and Schnabl’s analytic tachyon solution

Determine precisely how the Siegel-gauge level-truncation solutions describing tachyon condensation in open bosonic string field theory are related to Schnabl’s analytic solution in the KBC framework. In particular, identify the gauge transformation(s) and/or field redefinitions that connect the numerical Siegel-gauge solutions obtained via level truncation to the analytic tachyon vacuum solution, and characterize this relation at the level of observables (e.g., action, Ellwood invariants).

Background

Level truncation in Siegel gauge provides precise numerical evidence for tachyon condensation, matching the expected D-brane tension to high accuracy. Later, Schnabl constructed an explicit analytic solution using wedge states and the K,B,c algebra, establishing the tachyon vacuum in a different gauge.

Although both approaches describe the same physical endpoint, an explicit, complete mapping between the numerical Siegel-gauge solutions and the analytic solution has not been established. Understanding this relation would unify two cornerstone results in open string field theory and sharpen our control over gauge choices and solution spaces.