A deterministic, training-free word representation with a reproducible property: the ratio of consecutive terms in its sequence vectors stabilizes after the 43rd iteration. For the English modified #2 encoding used in this paper, the limiting constant ratio (LCR) is approximately 3.173. This ratio is constant across all 26 released sequences. The cross-encoding variation of the LCR is not part of this paper and will be treated in Part II.
The 16 distinct sequence vectors collapse to effective rank 1. PC1 captures more than 99 percent of the variance in the raw vectors, and more than 90 percent after standardization.---
Papers: EOA-43 (Part I) · EOA Program, Part 0 · EOA Program Main Page
Benchmark notebook: Colab
| File | Description |
|---|---|
eoa43-paper.pdf |
Full paper: EOA-43 from Convergent Recursive Sequences |
notebooks/allcolab.ipynb |
Main Colab notebook containing structural checks, PCA, rank diagnostics, and reproducibility |
notebooks/ocrs.ipynb |
Colab notebook for out-of-alphabet experiments, if applicable |
figures/ |
Figures from the paper |
data/ |
Pre-computed sequence vectors and related materials |
The internal deterministic operator that generates the sequence vectors is not in this repository. The generated outputs are available under the terms described in EOA-43, Section 2. See Disclosure status below.
The companion paper (EOA Program, Part II) formalizes open questions derived from the released sequences: stability within a fixed encoding, cross-encoding mapping, and inverse design. A bank of hypotheses H1 through H7 will be provided in the companion paper.
The 43-term sequence vectors are available to qualified researchers under the terms described in EOA-43, Section 2. They can be independently checked by researchers with access. The operator that generated them is the only gated piece. Submissions of theoretical explanations are tracked in LEADERBOARD.md.
EOA materials are released on a tiered basis. See the table below for what is open, restricted, or available by request.
| Tier | Access | Agreement | Materials | Purpose |
|---|---|---|---|---|
| 0 | Public | None | Published papers, sequence groupings, LCR values (3.306, 3.037, 3.173, 2.689), benchmark code, Colab notebooks | Priority and scientific disclosure; independently checkable empirical claims |
| 1 | Restricted | DUA (Data Use Agreement) | 43-term sequence vectors (english_alphabet_LCR3.173_v1.0.json) |
Independent verification of empirical claims; research use only, no redistribution, citation required |
| 2 | Restricted | ELA (Evaluation License Agreement) + click-through ToS | Interactive playground (eoa43-playground.html) |
Interactive testing; hosted, rate-limited, no scraping, no ML training on outputs |
| 3 | Restricted | Research API License | Batch API (text file to CSV of sequences) | Bulk evaluation; named-user, rate-limited, no data extraction |
| 4 | Restricted | MTA (Material Transfer Agreement) + Mutual NDA | Oracle binary (black-box callable) | Run on collaborator hardware; no source, no formula, anti-reverse-engineering clause, audit rights |
| 5 | Restricted | TLA (Technology License Agreement) + optional JDA | Full operator beta and closed-form formula | Commercial or funded collaboration; royalties, equity, or lump sum; co-inventorship on resulting patents |
| 6 | Future | TBD | Hypothesis bank H1-H7 | Will be released in a future paper or update |
- This graduated disclosure structure draws on practices from NIH (DUA), DeepMind AlphaFold (ELA/API), and pre-1997 RSA Laboratories (TLA).
- The operator is withheld under a staged disclosure policy while its theoretical scope is being mapped.
- Empirical claims, such as rank collapse, cross-encoding LCR variation, and memory footprint, can be checked at the output level using the released sequences and black-box oracle.
- A full specification will be released once the encoding-to-LCR mapping is theoretically characterized.
- For academic collaborators, access to Tiers 1 through 4 is available under standard academic agreements that permit research use and publication of derived results with appropriate citation.
- No agreement is required for Tier 0 materials.
For access to Tiers 1 through 5, contact: bdarghamneurolabs(at)gmail.com
If you use any materials from this repository in your research, please cite the relevant EOA paper.
EOA-43 (Part I): Budargham, B. (2026). EOA-43: A Rank-Collapsed Deterministic Word Representation from Convergent Recursive Sequences. GitHub. https://github.com/bahaa-budargham/eoa-part1-paper
EOA Program, Part 0: Budargham, B. (2026). The EOA Program, Part 0: The Engineering of Alphabets as an Open Frontier. GitHub. https://github.com/bahaa-budargham/eoa-part0-paper
BibTeX:
@article{Budargham2026EOA43,
author = {Bahaa Budargham},
title = {EOA-43: A Rank-Collapsed Deterministic Word Representation from Convergent Recursive Sequences},
year = {2026},
note = {GitHub: https://github.com/bahaa-budargham/eoa-part1-paper}
}