Golden Spectral Marker

Abstract

The reciprocal first golden exponent gives the explicit golden spectral marker.

Theorem 1.1 (The reciprocal first golden exponent is the spectral marker).

$$\frac{1}{beta(1)}=\frac{1}{ph{i}^2}.$$

Proof. Machine-checked in Lean as D5/S3/Midline/GoldenSpectralMarker.golden_spectral_marker (✓ std3). ∎

Source. Repository-derived.

Commentary.

The existing golden exponent power law proves beta(1) = phi^2. Taking reciprocals gives the displayed marker directly, so the Lean declaration is a thin wrapper around that repository theorem.

This is a partial closure of the source spectral chain. It does not identify beta(1) with the minimum positive model-set value, prove that its reciprocal is the Euler product’s absolute-convergence abscissa, or establish the concluding encoding-sensitivity and uniqueness claim. Those three subitems remain unresolved.

References

• Truth anchor: D5/S3/Midline/GoldenSpectralMarker.golden_spectral_marker