Golden Base-Four Digit Oracle

Abstract

Exact floor arithmetic supplies the base-four golden digit oracle and canonical power samples.

Theorem 1.1 (Canonical power samples decode exactly).

$$\mathrm{decode}(\mathrm{powerOccupiedIndices}(i))=\mathrm{pow}(4,i).$$

Proof. Machine-checked in Lean as D5/S1/Digit/GoldenBase4DigitOracle.decode_powerOccupiedIndices (✓ std3). ∎

Source. Repository-derived.

Commentary.

The input sample reuses the canonical Zeckendorf occupied-index representation already supplied by WDigits.

The output oracle is the final radix-four remainder of the exact natural floor of 4^(i+1) times the golden ratio.

Bit-stream serialization and the published Walnut input convention remain explicit later obligations.

References

• Truth anchor: D5/S1/Digit/GoldenBase4DigitOracle.decode_powerOccupiedIndices
• Dependency: D5/S0/Conventions/WDigits