Arithmetic-aware transfer from a proxy

The supplied record provides no certified ${\alpha }_L$. A small isometry residual does not by itself bound the computed propagator's error relative to the exact propagator. Consequently, the manuscript does not turn the approximately $4.69\times 10^{-18}$ exact truncation allowance into an eighteen-decimal-place certification of the reported proxy values.

For a numerical continuum certificate, normalization error, eigendecomposition error, transcendental evaluation, and norm-evaluation error must be bounded at their actual interfaces. The tolerance $2\times 10^{-10}$ is not such an arithmetic certificate.