God Does Not Play Dice: Carbon Analysis through the Determinacy Equation – Part 2: Carbon

This paper reports the results of observing carbon allotropes by applying the Determinacy Equation. Carbon (Z = 6) forms diamond, graphite, graphene, fullerene, and nanotubes — materials with radically different physical properties — from the same atom. Through this application, we confirmed that the structural arrangement of carbon atoms, governed by the interplay between Pauli exclusion and electronegativity, solely determines the physical properties of each allotrope. The energy difference between diamond and graphite is a mere 0.02 eV per atom, yet their hardness differs by a factor of 10 and their thermal conductivity by a factor of 440. This paper demonstrates, with quantitative evidence, that energy cannot serve as the yardstick for explaining such disparities. Structure determines properties; energy is subordinate. This paper extends the framework established in Part 1 (Helium) from a three-body system to a many-body system, demonstrating that the principle — structure over energy — holds universally.