Papers · Preprint
To XOR a Stone with Six Birds: Closure Diagnostics for Emergent Bits, Gates, and Booleanity
When does a system earn a logic?
In plain words
Boolean logic is usually the starting point. Here it has to be earned. A logic layer is an audited closure of packaged predicates under the system's own dynamics.
Bits are packaged classes. Gates are the updates induced on them. Diagnostics measure metastability, closure defect, gate error and lost input information.
Parity turns out to be an unusually robust bit. Erasing the output of a reversible XOR degrades closure sharply. A small unsupervised pipeline recovers a NOT gate straight from transition data.
What it shows
- A falsifiable criterion for having logic at a layer.
- Distinct closure regimes for NOT, AND and XOR under stress.
- Bit and gate discovery from dynamics.
What it does not claim
Logic is not treated as fundamental.
Cite
Tsiokos, I. (2026). To XOR a Stone with Six Birds: Closure Diagnostics for Emergent Bits, Gates, and Booleanity. Zenodo. https://doi.org/10.5281/zenodo.18919370