Papers · Preprint
To Cast a Stone with Six Birds: A Closure-Deficit Account of Randomness under Packaging and Budget
Randomness as the price of zooming out.
In plain words
Randomness is usually either in the world or in our ignorance. This paper gives a third account. Pick a way to package the micro state into a macro state. The closure deficit is the information about the next macro state that is still hidden inside the current micro state.
This gives an exact split of macro uncertainty into two parts: what the substrate itself does not know, and what packaging threw away.
The deficit vanishes on exactly lumpable partitions and rises with heterogeneity. Buying more memory buys back hidden distinctions. In toy hashing, one wayness and random lookingness turn out to be the same phenomenon.
What it shows
- An exact decomposition of macro entropy.
- Closure deficit tracked by route mismatch in benchmarks.
- Hash inversion scaling as a packaging and budget effect.
What it does not claim
Randomness is not treated as primitive, and no claim is made about quantum randomness.
Cite
Tsiokos, I. (2026). To Cast a Stone with Six Birds: A Closure-Deficit Account of Randomness under Packaging and Budget. Zenodo. https://doi.org/10.5281/zenodo.18926433