eoa-symbolic-sequences

EOA Symbolic Sequences

This repository contains a series of deterministic symbolic sequences generated from single English letter names using the EOA recursive operator under a particular limiting constant ratio (LCR). The sequences are not random; they are the output of a fixed deterministic process.

We begin with the letter ‘a’ at LCR ≈ 3.14.

Sequence 1: Letter ‘a’, LCR ≈ 3.14

Properties

• Letter: a
• LCR: ≈ 3.141593223578 (the limiting growth ratio matches π to six decimal places, 3.141593, without claiming exact equality)
• Alphabet: 16 distinct letters (permuted by a fixed 1–1 substitution for staged disclosure)
• Factor complexity: sublinear on the released initial segment; consistent with zero topological entropy
• Released initial segment: first 6,260 letters (cumulative through term 8)
• Full scale: the 25th term alone contains 1,777,496,641,819 Trillion letters

Files

• eoa_a_LCR3.14_symbolic_sequence_6260.txt — the 6,260-letter sequence as plain text.
• eoa_a_LCR3.14_symbolic_sequence_technical_note.pdf — 4-page technical note describing the observations and open questions.
• checksum.txt — SHA-256 checksum of eoa_a_LCR3.14_symbolic_sequence_6260.txt for verification.

Full Sequence (6260 letters)

The full sequence is provided in eoa_a_LCR3.14_symbolic_sequence_6260.txt. A short excerpt is shown below for reference:

gzhlvzggjzyihjgheqvzgzhlvzhlvbjzgyhzizygjzbjzhlvgjzehjdzzgheqvzgzhlvzggjzyihjgheqvzggjzyihjgheqvygpzajukbjzgzhlvyhzgjzzgizyzgyhzzhlvbjzgygpzajukbjzggjzyihjgheqvzhlvbjzgehjgjzbjzdzgzgzhlvgjzehjdzzgheqvzgzhlvzggjzyihjgheqvzgzhlvzhlvbjzgyhzizygjzbjzhlvgjzehjdzzgheqvzgzhlvzhlvbjzgyhzizygjzbjzhlvgjzehjdzzgheqvyhzzhlvpzzgzaabjuvzbygpzajukbjzgzhlvzggjzyihjgheqvyhzgjzzgzhlvbjzgzgzhlvizyzgyhzzgzhlvyhzgjzzgzggjzyihjgheqvygpzajukbjzgzhlvyhzzhlvpzzgzaabjuvzbygpzajukbjzgzhlvzhlvbjzgyhzizygjzbjzhlvgjzehjdzzgh

Observations

• Factor complexity on the released initial segment grows sublinearly up to k = 537. Beyond that point the counts plateau and then decrease, which is a finite-length artifact: in a word of length 6,260 every factor of length ≥ 700 is unique.
• The transition matrix is highly non-uniform. The most frequent letter pairs are e → a (365), y → e (286), e → i (207), i → g (207), and g → h (207). A small number of pairs dominate.
• The recurrent factor zgzhlv occurs 172 times. There are 30 distinct return words to zgzhlv and 41 distinct return words to the single letter z. The most frequent return words to z are g (267), hlv (113), ggj (92), and hlvbj (76).

Collaboration

The original mapping and the full operator are withheld under the EOA staged disclosure policy. They can be made available to qualified researchers under a signed collaboration agreement.

We welcome collaboration from symbolic dynamicists, combinatorists on words, and researchers in formal languages and automata theory.

Contact: Bahaa Budargham, bdarghamneurolabs@gmail.com

License

This dataset is released under the Creative Commons Attribution 4.0 International License (CC BY 4.0). See LICENSE for details.

DOI

https://doi.org/10.5281/zenodo.22882603