To Create a Stone with Six Birds: Emergent Geometric and Thermodynamic Regimes from a Minimal Stochastic Substrate

In plain words

Start with a finite state space and a random kernel. Add an algebra of six primitives whose interactions are set by a six by six enable matrix. That is PICA, the Primitive Interaction Closure Algebra.

For each timescale and lens, build the induced macro kernel and audit it along a resolution ladder.

Across 2,307 runs at four sizes, resolution dependent signatures appear that look like geometry and stochastic thermodynamics: least action dominance, diffusion consistent embeddings and time asymmetry.

What it shows

• A minimal substrate that grows geometric and thermodynamic regimes.
• An exhaustive ablation suite over the interaction algebra.
• PICA as a reusable object for other systems.

What it does not claim

Results are substrate specific; PICA is offered as a tool, not as a claim about nature.

Cite

Tsiokos, I. (2026). To Create a Stone with Six Birds: Emergent Geometric and Thermodynamic Regimes from a Minimal Stochastic Substrate. Zenodo. https://doi.org/10.5281/zenodo.18838994