Golden Scale Character Deck Blindness

Abstract

Integer golden Fourier characters are blind to one full scale deck step even though the golden helix level changes.

Theorem 1.1 (Quotient Fourier readout forgets the helix sheet).

$$\forall m:\mathbb{Z},\neg \mathrm{Injective}(\mathrm{goldenHelixFourierReadout}(m)).$$

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

Source. Repository-derived.

Commentary.

One full golden scale period leaves every integer Fourier character unchanged, although the universal-cover helix level increases.

The theorem reuses GoldenScaleHelix to separate quotient phase from completion-depth memory. Adding the level coordinate detects the deck step.

References

• Truth anchor: D5/S3/ObserverMemory/FourierFibers/GoldenScaleCharacterDeckBlindness.golden_helix_fourier_readout_not_injective
• Dependency: D5/S3/CompletionDynamics/GoldenMobius/GoldenScaleHelix