Mixed precision can look magical on friendly problems. This experiment keeps the negative evidence and asks where the correction operator stops being trustworthy.
Because the exact solution is known, forward error is directly measurable. Increasing matrix order makes the system progressively more hostile to finite-precision factorization.
For n=4–6, mixed refinement recovers close to the Float64 result. By n=8 the mixed error is already large, and at n≥9 the method can fail catastrophically because the Float32 factorization is no longer a useful correction operator. That failure is part of the result, not something to hide.
The lesson is not “mixed precision always works.” The useful engineering question is whether the problem's conditioning, residual computation, factorization precision, and refinement strategy together satisfy a measurable convergence contract. ShardNet's hardware experiments will preserve this same failure-oriented discipline.