Golden Amplitude Enclosure

Abstract

The exact golden amplitude satisfies the source’s seven-digit enclosure.

Theorem 1.1 (The golden amplitude lies in its certified decimal interval).

$$\left|A_h-\frac{3408474}{10000000}\right|\le \frac{33}{100000000}$$

Proof. Machine-checked in Lean as D5/S3/Constants/Enclosures/GoldenAmplitudeEnclosure.ah_seven_digit_enclosure (✓ std3). ∎

Source. Repository-derived.

Commentary.

The amplitude A_h is the canonical exact value (5 sqrt(5) - 3) / 24. Exact rational square comparisons place sqrt(5) between 2.236065936 and 2.236069104; linear arithmetic then proves that A_h differs from 0.3408474 by at most 0.00000033. No floating-point premise is used.

References

• Truth anchor: D5/S3/Constants/Enclosures/GoldenAmplitudeEnclosure.ah_seven_digit_enclosure