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

This work presents a consistent effective-theory 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, extreme instance of the cosmic Big Crunch: matter in the d³ phase descends through the d² and d¹ phases into a finite d⁰ Planckon core. The algebraic core of the model is an energy–potential ledger depending on the phase degree d: E(d) = N(d+1)ε_P, U(d) = N(3−d)ε_P, hence E(d)+U(d) = 4Nε_P = constant. The variable d is continuous; its fractional part gives the percentage of conversion within a phase transition. Under this conservation law, collapse is not a loss of energy but a systematic re-loading of active energy into closed potential; instead of a singularity, a finite core forms at the center. Equating the mean density to the effective Planck density yields the core radius r₁ = ℓ_P [(3/4π)(M/m_P)]1/3. The prefactor of the ratio r₁/r_s is ≈ 0.3102, whereas the quantity μ_formal = √(3/32π) ≈ 0.1727 is the critical mass ratio (M_thresh/m_P) satisfying the equality r₁ = r_s — a dimensionless geometric threshold, not a mass. The fundamental counting quantity N_c ≈ M/m_P is linear in the mass; it therefore cannot be directly identified with the Bekenstein–Hawking entropy, which follows an area (∝ M²) law. N_c is not an entropy but a linear matter count; the area law is delegated to the edge/surface degrees of the integer d³ phase. A rebound candidate requires an energy condition (η·U_core > E_bind) and a geometric condition (r_rebound ≥ r_s) to hold simultaneously; the latter is satisfied only at Planck-scale masses (M_thresh ≈ 3.76 µg). A falsifiable prediction follows: at astrophysical masses r₁/r_s ~ 10⁻²⁶–10⁻³³, so the model is observationally indistinguishable from GR and black holes are stable Planckon-cored remnants; rebound is expected only at primordial masses. The model retains the exterior Schwarzschild geometry as a boundary condition and is positioned comparatively against LQG/LQC, string theory, and the Rovelli–Vidotto Planck stars.