Temporal Reflection-Break Visibility

Abstract

A static scalar readout identifies reflected modal branches, while one nondegenerate time step separates them.

Theorem 1.1 (Time reveals a nondegenerate reflected split).

$$\forall z:\mathbb{C},z\ne z^{-1}\Rightarrow \mathrm{crystalTimeSample}(\mathrm{reflectedModes}(z),\mathrm{firstBranch}(),1)\ne \mathrm{crystalTimeSample}(\mathrm{reflectedModes}(z),\mathrm{secondBranch}(),1).$$

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

Source. Repository-derived.

Commentary.

The two reflected branch states collide at time zero. If their modal multipliers differ, the first time step produces different scalar readings.

The result formalizes temporal revelation of a pre-existing hidden distinction. It does not claim that the underlying difference is created by observation.

References

• Truth anchor: D5/S3/ObserverMemory/FourierFibers/TemporalReflectionBreakVisibility.reflected_branches_time_one_separation
• Dependency: D5/S3/ObserverMemory/FourierFibers/FiniteCrystalTimeFrequencyBridge