Prime-Zeckendorf Temporalization

Abstract

Positive heat time preserves calibrated prime identity, while wrapped phase time has arbitrarily late finite-channel near-recurrence.

Theorem 1.1 (Positive heat time preserves prime identity).

$$\begin{gathered} \forall t:\mathbb{R},0<t\Rightarrow \\ \mathrm{Injective}(\mathrm{firstExcitedHeatMultiplier}(t)). \end{gathered}$$

Proof. Machine-checked in Lean as D5/S3/ObserverMemory/FourierFibers/PrimeZeckendorfTemporalization.first_excited_heat_multiplier_injective (✓ std3). ∎

Source. Repository-derived.

Commentary.

The real exponential is injective and positive time leaves a nonzero frequency scale. Equality of heat multipliers therefore reduces to equality of the calibrated first golden frequencies and then to equality of prime channels.

The same module transports the existing finite prime-phase recurrence through the phi-squared first-mode scaling. Thus the oscillatory phase observer can return arbitrarily close to coherence at late times even though the dissipative heat observer remains faithful.

References

• Truth anchor: D5/S3/ObserverMemory/FourierFibers/PrimeZeckendorfTemporalization.first_excited_heat_multiplier_injective
• Dependency: D5/S3/Analytic/PrimeZeckendorf/PrimeZeckendorfFrequencyRigidity
• Dependency: D5/S3/Weil/PrimeAddress/FinitePrimePhaseRecurrence