Meta$^n$: Recursive Self-Improvement through Emergent Depth

Key points

It diagnosed existing self-improvement systems as unable to achieve a realized meta-depth beyond approximately 2 because their improvement mechanisms themselves remain fixed.
It recursively applies a fixed meta-operation to its own output and determines the depth itself until convergence, reaching 3–6 layers in practice.
Its decomposition of the gains attributes approximately 72% of the recursive benefit to context transfer between layers and approximately 15% to a callable code library.
On the ARC-AGI-2 holdout, the meta-stack was the only approach to rise above the floor, scoring 0.331, while Godel Agent and OpenEvolve scored 0.
Removing recursion reduced the CO-Bench validation score from 0.845 to 0.714, isolating recursion's own effect (+0.131).

External research summaries. These are not HDATF publications or measured product results.