Degenerate-Mode Hidden Fiber

Abstract

Equal modal multipliers leave an antisymmetric amplitude invisible at every observation time.

Theorem 1.1 (Exact degeneracy defeats the full scalar time trace).

$$\forall z:\mathbb{C},\neg \mathrm{Injective}(a\mapsto \mathrm{crystalTimeSample}(\mathrm{degenerateModes}(z),a)).$$

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

Source. Repository-derived.

Commentary.

Two equal modal multipliers make the antisymmetric amplitude invisible for every natural observation time, so even the complete scalar time trace is noninjective.

This is a constructive hidden-fiber certificate. It isolates spectral degeneracy as an obstruction that time stacking alone cannot remove.

References

• Truth anchor: D5/S3/ObserverMemory/FourierFibers/DegenerateModeHiddenFiber.all_time_trace_not_injective
• Dependency: D5/S3/ObserverMemory/FourierFibers/FiniteCrystalTimeFrequencyBridge