# Validation reports

The `.json` files record rigorous bounds and the evaluated theorem conditions.
Each `.json.torus` sidecar specifies the exact Fourier-polynomial candidate in
hexadecimal dyadic coefficients. The action offset is the exact golden-ratio
frequency, as recorded in the JSON.

These files are generated by the commands documented in `../README.md`.
They can be rechecked with `--candidate`, without importing the CSV again or
repeating the optional numerical refinement.

The certificate is the result of this implementation of the stated estimates;
the JSON itself is not an independently verified formal proof object.