Exact Second-Order Transcription

Abstract

The exact T0 substitution yields the closed second-order golden-radical value.

Theorem 1.1 (The second-order transcription has an exact closed form).

$$(1-\sqrt{5})T_0+\frac{15\sqrt{5}-33}{8}=\frac{5\sqrt{5}-7}{24}.$$

Proof. Machine-checked in Lean as D5/S3/Constants/Transcription/PhiSecondTranscription.phi_second_transcription_exact (✓ std3). ∎

Source. Repository-derived.

Commentary.

Here T0 is the deposited exact Sturmian-Dirichlet value (27 - 13 sqrt(5)) / 24. Substitution reduces the statement to the standard identity sqrt(5)^2 = 5.

This theorem covers only the source’s exact second-order transcription clause; it makes no claim about the surrounding reconstruction program or numerical certificates.

References

• Truth anchor: D5/S3/Constants/Transcription/PhiSecondTranscription.phi_second_transcription_exact
• Dependency: D5/S3/Constants/SturmianDirichletValue