A beginning is worth one limit: robust unlearnable laws in noisy cellular automata
In plain wordsIn a noisy cellular automaton, a law read from a definite beginning can sit one level of uncomputability above any law its steady states agree on, and some rules reach that ceiling; started from random noise, they can take values no algorithm learns from finite histories.
The result
As the paper states it, in briefAt equal depth, a computable law of a cellular automaton that has a beginning reaches one arithmetical level above any law on which its stationary states agree; at depth one, a rule started from cloned uniform noise realizes every value in as a robust law.
Questionson the index
How this was checked
- Blind audits
- One blind audit with no critical findings
- Fix-checks
- A blind fix-check with no findings.
- Verification
- Two independent verifications
- Lean
- None.
- Peer review
- Not yet.
Every check here is internal. How we check results.
Label checked .
Novelty and credit
- Novelty
- Uses results of Hellouin de Menibus and Sablik, and of Miękisz and Taati, credited; the paper makes no exhaustive priority claim.
Versionsone, each with its own DOI
| Version | Date | DOI | Notes |
|---|---|---|---|
| 1.0.0 | 10.5281/zenodo.23782039 | PDF hosted here. |
Paper, code and links
papers/beginning-v1.0.0.pdf, version 1.0.0, 583,478 bytes, 19 pages.SHA-256 70e5b445e6a7448e313c15d4ed6daf27e1541316fd07cc3d2040bc94b0e31a42
Corrections
None so far.
All corrections, and what counts as one.
Cite
@misc{douglas2026beginning,
author = {Douglas, Seth and Mghirbi, Nidhal},
title = {A beginning is worth one limit: robust unlearnable laws in noisy cellular automata},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.23782039},
url = {https://doi.org/10.5281/zenodo.23782039}
}