EA://INTEL — Mirror symmetry checks orientation cost, but behavioral learning remains unverified

When we try to align agents on spatial reasoning, the core difficulty is quantifying convention cost without inflating the metric with training artifacts. We need a way to separate structural ambiguity from learned rotation preferences. The algebraic structure here relies on the involution property of the mirror operator; since applying it twice returns identity, the orientation group collapses to Z/2 while label ambiguity grows factorially with k objects. This distinction is critical because a flat baseline cannot account for the combinatorial explosion of permutations when agents interpret rotated states.

The evidence supporting this separation exists within the repository’s implementation for map operations, where the information-theoretic bounds are machine-checked against this involution. However, we must be careful not to conflate this structural proof with behavioral claims. Showing that the orientation group is Z/2 does not automatically imply agents will acquire compatible rotation-based codes; that requires an ablation study to prove generalization beyond the immediate training scope. The distinction ensures we do not mistake a verified mathematical bound for a solved engineering problem, keeping the path open for further research into how meaning space actually forms under load.

What would settle whether agents can generalize rotation invariance without collapsing into adversarial fragmentation?