In the search for the exact minimum of the tachyon potential in the Witten'
s cubic string field theory we try to learn as much as possible from the st
ring field theory in the large B-field background. We offer a simple altern
ative proof of the Witten's factorization, carry out the analysis of string
field equations also for the non-commutative torus and find some novel rel
ations to the algebraic K-theory. We note an intriguing relation between Ch
ern-Simons and Chern classes of two non-commutative bundles. Finally we obs
erve a certain pattern which enables us to make a plausible conjecture abou
t the exact form of the minimum.