Computational analysis demonstrates optimal weight and smaller indices for Balanced Zeckendorf Decomposition across 275 hard cases, indicating more compact signed-digit representation.
Description: This archive contains the Python code and empirical data for the Balanced Zeckendorf Decomposition (BZD), a novel signed-digit Fibonacci representation. Unlike Alpert's (2009) method, which uses rigid gap rules that force index inflation, BZD uses a 3-tier optimization rule to minimize weight, maximum index, and cost. The upload includes scripts for the core BZD algorithm and a rigorous stress-test comparing BZD against Alpert's method on 275 hard cases. Results prove BZD matches Alpert's optimal weight 100% of the time while systematically choosing smaller, more compact indices, achieving an 18% average weight reduction over standard Zeckendorf.
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Gavin Roberts (2026) studied this question.
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