Raw W-Digit Strings

Abstract

Raw W digits bridge finite multiplicities to mathlib Zeckendorf lists.

D5/S1/Digit/Raw represents raw W-digit strings as finitely supported maps from indices to natural coefficients, so a digit position may temporarily carry coefficients larger than one. Evaluation multiplies each coefficient by the W weight W_i = Fib (i + 2) and sums; evaluation is additive.

Canonical strings are the binary, nonadjacent ones. The file bridges canonical strings to the mathlib Zeckendorf representation in both directions, with the index offset W_i = Fib (i + 2) stated once at the bridge.

Example 1.1 (Illustrative Zeckendorf normalization).

$$Z\left(89\right)+Z\left(34\right)=Z\left(123\right)=1010000000_W$$

Source. Repository-derived.

Commentary.

This illustrative normalization is derived by the repository’s deterministic W-digit computation.

References

• Dependency: D5/S0/Conventions/WDigits