Identify a possible height-three splitting summand for fivebrane bordism

Identify a likely height-three spectrum whose homotopy and cohomology agree with those of the fivebrane Thom spectrum $MO\langle 9\rangle$ through degree 23, if $MO\langle 9\rangle$ admits a splitting.

Background

The thesis proves that $MO\langle 9\rangle$ is indecomposable through degree 22 and consequently that any hypothetical orientation map $MO\langle 9\rangle\to eo_3$ cannot split. The text then raises the unresolved issue of what spectrum could serve as a splitting summand if a splitting of $MO\langle 9\rangle$ nevertheless exists. The proposed candidate is expected to have height approximately three and to reproduce the relevant homotopy and cohomology through degree 23.