4.14 Emergent closure of a Hyperfunction level

To distinguish the explicitly listed recursive coordinates from the properties generated by their interaction, define Core(H_n) as the typed recursive/primitive coordinates directly constituting H_n, and define Cl_Phi(H_n) as the property closure of that core under the canonical state-output/emergence rules.

Core(H_n) = explicit primitive + signed recursive coordinates

Expanded(H_n) = Cl_Phi(Core(H_n)) = Core(H_n) union Emergent(H_n)

The earlier DirectWidth(H_n)=2(n-1) formula therefore remains correct for the DIRECT recursive H/I coordinates. It must not be mistaken for the total number of emergent dimensions after closure. The expanded dimensionality can be much larger, and the exact count depends on the emergence mapping.

CoreWidth(H_n) = 2(n-1); ExpandedWidth(H_n) >= CoreWidth(H_n)