Golden Prime Beat Second-Magnus Separation

Abstract

The golden long-short frequency gap is log p, so pi divided by log p maximizes the alternating two-slot Magnus kernel and twice that time restores resonance.

Theorem 1.1 (Half-beat separation and full-beat recurrence).

$$|\mathrm{secondMagnusSwapKernel}|=2,\mathrm{fullBeatKernel}=0.$$

Proof. Machine-checked in Lean as D5/S3/Observer/GoldenPrimeCircle/GoldenPrimeBeatSecondMagnus.prime_beat_separation_recurrence (✓ std3). ∎

Source. Repository-derived.

Commentary.

The deterministic alphabet frequencies phi log p and phi squared log p differ by exactly log p. At time pi divided by log p their relative phase is minus one, and the alternating kernel reaches its universal norm-two bound.

At twice that time the relative phase completes a full turn and the kernel vanishes. The calibration is prime dependent and does not provide one common window for an infinite prime family.

References

• Truth anchor: D5/S3/Observer/GoldenPrimeCircle/GoldenPrimeBeatSecondMagnus.prime_beat_separation_recurrence
• Dependency: D5/S3/Observer/AgencyHolonomy/SecondMagnusSwapCurvature
• Dependency: D5/S3/Observer/GoldenPrimeCircle/GoldenEulerStepPhaseLaw