Fibonacci Return Ratio

Abstract

Consecutive Fibonacci return scales converge to the golden ratio.

Theorem 1.1 (Fibonacci return ratio tends to the golden ratio).

$$\underset{n\to \infty }{\lim }\frac{F_{n+1}}{F_n}=\phi .$$

Proof. Machine-checked in Lean as D5/S3/ObserverMemory/RevivalSpectrum.fibonacci_return_ratio_tendsto (✓ std3). ∎

Source. Repository-derived.

Commentary.

The ratio of consecutive Fibonacci return scales converges to the golden ratio. This is the formalized return-spectrum clause; the remaining revival grading claims are outside this declaration.

References

• Truth anchor: D5/S3/ObserverMemory/RevivalSpectrum.fibonacci_return_ratio_tendsto