Density-Induced Dimensional Closure and a Non-Singular Black-Hole Core

We formulate a phenomenological scalar-tensor model in which ordinary space remains three
dimensional everywhere, D = 3, while the effective openness of the three spatial axes is described by 
a continuous field n(xµ) on the interval (0, 4). The interior integers n = 1, 2, 3 carry the dimensional 
content of the field — one, two, and three effectively open spatial axes — while the endpoints n = 0 
and n = 4 are boundaries of the field space rather than dimensions. The energy-organization law E(n) 
= xⁿ is retained as the primitive ΨD postulate. The field-space metric K(n) = 16/[n²(4−n)²] is induced 
by the map φ = ln[n/(4−n)], placing the boundaries n = 0 and n = 4 at infinite field-space distance. 
Matter is coupled through a conformal factor A(n), from which a density-dependent source for n 
follows as an effective low-energy limit. Gravitational field equations are obtained by varying a 
covariant action with respect to gµν and n. We state sufficient conditions for a finite-curvature core 
and make explicit that the static core sits at a strictly positive openness value n₀ > 0 — the limit n → 
0 is approached asymptotically in field-space distance, not attained at the centre. We list candidate 
observables, and we note a striking numerical coincidence — that x⁴ matches the Planck-volume 
count of the observable universe to within a percent — suggesting a physical interpretation of the 
otherwise primitive constant x. We keep the remaining open problems explicit: a first-principles 
origin of x, the microscopic form of the matter coupling A(n), explicit numerical solutions, particle 
content, and the size of the effective cosmological term.