Low-Spectrum Leg Identity

Abstract

The recorded low-spectrum leg satisfies its exact integral quadratic-form identity.

Theorem 1.1 (The recorded leg satisfies the quadratic form).

$$4\cdot 4357=3\cdot 33^2+119^2$$

Proof. Machine-checked in Lean as D5/S3/PrimeForms/LowSpectrumLegIdentity.low_spectrum_leg_identity (✓ std3). ∎

Source. Repository-derived.

Commentary.

The concrete discriminant value 4357, denominator 33, and integral leg 119 obey 4 times 4357 equals 3 times 33 squared plus 119 squared. This is the exact natural-number check underlying the recorded low-spectrum value.

The statement records only this closed arithmetic identity. It makes no claim about the surrounding continued-fraction classification or spectral ordering.

References

• Truth anchor: D5/S3/PrimeForms/LowSpectrumLegIdentity.low_spectrum_leg_identity