park-2024-theorem-8-four-conditions
IN premise — summaries/2026/08/24/park-2024-categorical-hierarchical-concepts-sR-references.md
Created 2026-08-25T02:58:26+00:00
Theorem 8 in Park et al. 2024 specifies four distinct orthogonality conditions (a–d) covering parent⊥child-parent, parent⊥sibling-contrast, parent-contrast⊥child-contrast, and three-level chain orthogonality.
Summary
The four conditions in Park et al. 2024 guarantee that the components of a multi-level hierarchy (parent, child, sibling) are statistically independent of one another, so each level's contribution can be read off cleanly without contamination from the others. This matters because it is the mathematical bedrock that makes any inference or estimation built on the hierarchy valid; if any of these separations breaks, the downstream conclusions become unreliable.