Golden Euler Step Phase Law

Abstract

Deterministic Zeckendorf long-short steps become a two-letter Euler phase alphabet in each prime channel.

Theorem 1.1 (Each deterministic step obeys Euler’s formula).

$$\forall t:\mathbb{R},\forall p:Nat.Primes,\forall v:Nat,\mathrm{primeStepPhase}(t,p,v)=\cos (t\cdot \mathrm{primeStepFrequency}(p,v))+\sin (t\cdot \mathrm{primeStepFrequency}(p,v))\cdot i.$$

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

Source. Repository-derived.

Commentary.

Zeckendorf chooses the phi or phi-squared frequency increment before the phase is evaluated.

Scalar unit-circle multiplication forgets adjacent step order, exposing an endpoint chronology obstruction.

References

• Truth anchor: D5/S3/Observer/GoldenPrimeCircle/GoldenEulerStepPhaseLaw.prime_step_phase_euler
• Dependency: D5/S3/Analytic/PrimeZeckendorf/PrimeZeckendorfFrequencyBridge