Coherent returns with persistent entry collision

Abstract

Coherent returns with persistent entry collision

Theorem 1.1 (Separation is not necessary for return coherence).

Lean statement: D5/S1/Digit/Infinite/SevenCycleCoherenceResult.result

Proof. Machine-checked in Lean as D5/S1/Digit/Infinite/SevenCycleCoherenceResult.result (✓ std3). ∎

Source. Repository-derived.

Commentary.

The same primitive seven-period rival has a cyclic component in the complete original product graph, reached immediately after a distinct-label edge. Both source projections and their ordered label pairs have synchronized returns throughout the whole component. Nevertheless the fixed entry tail survives every finite future horizon. A zero-label head feeds this component and cannot be reached from it. The conclusion concerns infinite actual sources and does not assert a failure of finite-source identification.

References

• Truth anchor: D5/S1/Digit/Infinite/SevenCycleCoherenceResult.result
• Dependency: D5/S1/Digit/Infinite/SevenCycleCoherenceRefutation
• Dependency: D5/S1/Digit/Infinite/SevenCycleCollisionResult