BLACK HOLES A Consistent Effective Model Derived from Planckon-Based Cubic Structural Phase Theory and the ΨD Framework

This work presents a consistent, effective-theory-level interpretation of black holes within the framework of Dimensional Flow Cosmology (ΨD) and Planckon-based cubic structural phase theory. The central ontological premise is the following: matter — every structure, including subatomic particles — reduces to Planckons, the smallest, countable, pre-metric building blocks. A black hole is a local and extreme instance of the cosmic Big Crunch: matter in the d³ phase descends, passing through the d² and d¹ phases, to a finite d⁰ Planckon core. The algebraic core of the model is an energy–potential ledger that depends on the phase degree d: E (d) = N (d+1) εP, U (d) = N (3−d) εP, hence E (d) +U (d) = 4NεP = constant. d is continuous; its fractional part gives the conversion percentage within a phase transition. Under this conservation, collapse is not a loss of energy but a systematic reloading of active energy into closed potential; instead of a singularity, a finite core forms at the center. By equating the effective Planck density, the core radius r₁ = ℓP (3/4π) (M/mP) ^1/3 is derived. While the prefactor of the r₁/rₛ ratio is ≈ 0. 3102, the quantity μformal = √ (3/32π) ≈ 0. 1727 is the critical mass ratio (Mₜhreshold/mP) that satisfies the equality r₁ = rₛ — a dimensionless geometric threshold, not a mass. The fundamental counting quantity Nc ≈ M/mP is linear in mass; for this reason it cannot be directly equated with the area law (∝ M²) of Bekenstein–Hawking entropy. Nc is not an entropy but a linear matter count; the area law is attributed to the edge/surface degrees of the integer d³ phase. A rebound candidate simultaneously requires an energy condition (η·Ucore > Ebind) and a geometric condition (rᵣebound ≥ rₛ) ; the latter is satisfied only at Planck-scale masses (Mₜhreshold ≈ 3. 76 ng). From this a falsifiable prediction follows: since at astrophysical masses r₁/rₛ ~ 10⁻²⁶–10⁻³³, the model is indistinguishable from GR and black holes are stable Planckon-core remnants; rebound is expected only at primordial masses. The model retains the Schwarzschild exterior geometry as a boundary condition and is positioned comparatively against LQG/LQC, string theory, and Rovelli–Vidotto Planck stars.