The EOA Program, Part I: A Rank-Collapsed Deterministic Symbolic Representation From Convergent Recursive Sequences

Abstract

We introduce a deterministic operator called beta. It turns the spoken names of letters into number sequences. When we apply it to the 26 letters of the English alphabet, it produces an infinite sequence for each letter, and we release the first 43 terms. This first part of the program, EOA-43, is a deterministic symbolic representation built from this recursive process. After the first 38 terms, the ratio between one term and the next settles to a fixed number, λ. This ratio is the same for every letter, and it changes systematically if the phonetic encoding of the alphabet is changed. Because all 26 sequences share the same limiting ratio, they become nearly collinear beyond the 38th term. Any word vector built from them collapses to a low-dimensional subspace, effectively a single line. The 26 sequences group into 16 distinct sequence types and require 2.69 KB of storage. This small footprint follows from the representation's fixed low dimensionality. This paper is the first in the series. Here we report the sequences, the grouping structure, and the algebraic consequences of convergence. Later papers will study how the limiting ratio depends on the encoding (Part II), the structure of the early terms (Part III), and how this representation behaves on real tasks (Part IV).