Higher combinatorial principle behind self-replicating cube-like structures

Establish whether there exists a higher combinatorial principle that governs the self-replicating, Rubik's-cube-like transformation patterns observed in the factorization diagrams of split colax D-coalgebras arising in the comma 2-comonad on the 2-category of functors, colax squares, and their transformations.

Background

Within the paper, the author analyzes colax D-coalgebras for the comma 2-comonad generated by a strict 2-adjunction I ⊣ D on the 2-category whose objects are functors and 1-cells are colax squares. In the paper of split colax D-coalgebras, intricate diagrams exhibit a self-generating pattern that the author likens to Rubik's cubes, suggesting a structured, higher-order combinatorial behavior behind repeated factorization and transformation steps.

The author conjectures informally that a higher combinatorial principle may drive these transformations but notes that verifying this principle is not yet accomplished. The remark explicitly points to an unverified structural explanation for the replication phenomena, framing a concrete open question about the existence and characterization of such a principle.