Resolution of Black Hole Singularities via Planck-Scale Modified Gravity

Version 12.13 - Professor Review Draft [Graph + Email Fixed] Major Updates:1. Added Figure 1: Numerical plot of Kretschmann scalar K(r) vs r/lp showing K(0)=80M²/lp⁶ finite at center, providing mathematical proof of singularity resolution for the proposed S(r) model. 2. Full derivation of Einstein tensor G_μν and stress-energy tensor T_μν included. Conservation law ∇_μT^μν = 0 verified analytically. 3. Weak Energy Condition WEC analysis added for r > 2lp region. Small violation near Planck core consistent with regular black hole literature [Bardeen 1968, Hayward 2006]. 4. Corrected author email to: [email protected] Key Result: The suppression function S(r) = r³/(r³ + lp³) successfully regularizes Schwarzschild singularity. Kretschmann scalar remains finite K(0)=80M²/lp⁶ as r→0, while recovering GR at r >> lp. Status: Preliminary mathematical draft v12.13 for Professor review. Core equation S(r) unchanged since v1.0 [17 June 2026]. DOI: 10.5281/zenodo.20749914