Audit 2: Gaussian estimates at the smallest edge scales

The external Gaussian argument uses scales with $k_p=n{p}^3$, capped resolvents, and a saddle equation. A representative variance assertion is

on stated disorder events and scale ranges OAI227Edge (prop:edge-estimates).

A complete verification would have to check:

1. the saddle's existence, uniqueness, and positive denominators;

2. uniformity over every admitted field, function, and scale;

3. how a threshold depending on a requested disorder confidence is chosen;

4. the integrability of accumulated relative errors across scales;

5. the transfer between spherical and cube quantities with their stated reference measures.

A threshold sent to infinity after a limsup in $n$ is not automatically a fixed-threshold probability tending to one. Nor is a static resolvent estimate a heat-bath mixing theorem. These Gaussian estimates are not reproved or assumed here.