The Prime Alphabet: An Information-Theoretic Formalization of Local Prime Geometry in the Ulam Spiral

A 4-bit geometric encoding of prime neighborhoods in the Ulam spiral, with mutual information analysis, FDR-corrected connected component testing against three null models, scale invariance verification (N=256–1024), cross-channel independence analysis, and cross-implementation validation. Includes complete reproducible Python pipeline (13 scripts), data files, and the full paper (.docx). Adversarial review conducted independently by five AI systems (Claude, ChatGPT, Copilot, Grok, Gemini) with zero cross-access, all converging on identical structural conclusions. Structure attribution: ~95% modular geometry, ~5% polynomial trace residual.