Researcher Finds Degree-13 Recurrence in Letter-Sequence Operator, Limit Near π

A researcher developed a deterministic operator called EOA that converts spoken letter names into integer sequences using a fixed, rule-based process with no randomness or machine learning. Applying it under an encoding called English Modified #5 produced 20 distinct sequences, which split into two families sharing common algebraic properties. Over 600 terms of one sequence were generated, with the final term reaching 249 digits, and a Maple tool called gfun was used to identify a rational generating function of approximately degree 14. The sequence satisfies a degree-13 linear recurrence with constant coefficients, meaning it can be extended infinitely from its initial conditions. The limiting ratio of consecutive terms is algebraically close to π to five decimal places, but cannot equal π exactly since the limit is algebraic while π is transcendental — making the resemblance a numerical coincidence rather than a meaningful identity.