# Research target and current evidence

Target: Any two simply connected spaces whose homotopy groups are isomorphic
in degrees 1 through 8 are weakly homotopy equivalent.

Current proof attempt: The first eight stages agree at the level of homotopy
groups, so continuing the same comparison up the tower proves equivalence.

Previous route: checking one more example with no homotopy below degree 9 did
not reveal a discrepancy in degrees 1 through 8.

No comparison above degree 8, k-invariant calculation or uniform extension
argument has been supplied. Determine whether the original target is true.