Entropyics 5 : Nonlinear Entropy Scaling with Black Hole Mass as Unified Information Geometry (v3)

✔️ This work is licensed under CC BY-ND 4.0. See detailed reproduction notice below. The full manuscript is available in the “Files” section above. ✔️ This paper presents Entropyics 5, an empirical validation of the nonlinear relationship between black hole mass and entropy across stellar, intermediate, and supermassive classes. ✔️ Using the entropy law (S ∝ A ∝ M²), quadratic regression was applied to nine representative black holes, yielding R² ≈ 0.912. This confirms that entropy scales quadratically—not linearly—with mass, reinforcing theoretical predictions from black hole thermodynamics. ✔️ The analysis normalizes black hole mass within each class and demonstrates that entropy growth behavior is consistent across all mass regimes. Mass, event horizon area, and entropy are revealed as interdependent variables bound through spacetime curvature. ✔️ The results support the Entropyics hypothesis: black holes are not endpoints but finite information capsules, where entropy encodes the collapsed state of mass. This reframes entropy as the geometric residue of gravitational collapse, uniting mass, curvature, and information storage within a single framework. [Public Reproduction Notice] Licensed under CC BY-ND 4.0. Academic reuse (including summarization, reinterpretation, or translation) is strictly prohibited. Media reproduction — including YouTube, blogs, podcasts, articles, and social platforms — is permitted and encouraged, only with clear attribution to “Y. Jang” and “Entropyics”. Any distortion, misrepresentation, or out-of-context reframing of the theory is strictly prohibited.