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)ε_P, U(d) = N(3−d)ε_P, hence E(d)+U(d) = 4Nε_P = 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 = ℓ_P [(3/4π)(M/m_P)]^{1/3} is derived. While the prefactor of the r₁/r_s ratio is ≈ 0.3102, the quantity μ_formal = √(3/32π) ≈ 0.1727 is the critical mass ratio (M_threshold/m_P) that satisfies the equality r₁ = r_s — a dimensionless geometric threshold, not a mass. The fundamental counting quantity N_c ≈ M/m_P is linear in mass; for this reason it cannot be directly equated with the area law (∝ M²) of Bekenstein–Hawking entropy. N_c 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·U_core > E_bind) and a geometric condition (r_rebound ≥ r_s); the latter is satisfied only at Planck-scale masses (M_threshold ≈ 3.76 ng). From this a falsifiable prediction follows: since at astrophysical masses r₁/r_s ~ 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.