Cyclic Window Revival

Abstract

A full loop restores both generators of a finite cyclic observer window.

Theorem 1.1 (Cyclic window generators recur after one full loop).

$$S^M=1\wedge C^M=1.$$

Proof. Machine-checked in Lean as D5/S3/ObserverMemory/CyclicWindowRevival.cyclic_window_generators_recur (✓ std3). ∎

Source. Repository-derived.

Commentary.

For a finite observer window of size M, the address shift and phase clock each return to the identity after M updates. Together these recurrences certify perfect revival after a full cyclic loop. This statement is confined to the cyclic branch and does not claim a classification of revival scores in other branches.

References

• Truth anchor: D5/S3/ObserverMemory/CyclicWindowRevival.cyclic_window_generators_recur
• Dependency: D5/S3/Observer/WindowRegister