# Verification of the stated lower bound

The originating researcher accepted the complete scoped theorem after a
written audit of the coefficient-matrix equivalence, existence hypotheses,
boundary obstruction, Fourier phase, both endpoint prefactors and uniform
errors, and the double-limit argument producing the log-log term.

The source of mathematical proof is the manuscript and the retained
`reproducibility/proof.md`, not finite computation. In particular the two
endpoint errors are measured separately, so cancellation does not invalidate
the estimate. A nonnegative selected coefficient is only necessary, never
treated as sufficient for all coefficients to be nonnegative.

Two original checks are included. The exact integer checker proves the
reported finite minimum exponents by retaining a negative coefficient at
every earlier power and independently verifying every successful coefficient.
The second compares exact coefficient expressions with 70-digit numerical
quadrature in 27 cases. This is a diagnostic, not validated interval arithmetic.
Normal and optimized executions are compared as part of package construction.

The saved compiler result and visual-review receipt identify the inspected
source, PDF and page images. Mathematical acceptance, artifact readiness and
external publication remain separate. Neither a compiler pass nor a DOI is
independent mathematical review. The broad AIM source remains open here.