The proton is roughly 2000 times heavier than the electron. While the Stan- dard Model relies on this mass hierarchy (µ ≈1836.15) as an unexplained empir- ical parameter, we propose this ratio is a direct, derived consequence of a discrete Cuboctahedral Vacuum Geometry (K = 12). By analyzing the strict elastic limits of a single unit cell, we demonstrate that heavy hadronic masses cannot be local, microscopic defects. Modeling the electron as a localized surface defect and the proton as a macroscopic topological flux tube (a Trefoil knot, 31), we derive the proton’s mass from first principles: 1. Macroscopic Base Mass (1728): We establish the volumetric mass factor 123 = 1728 by presenting three distinct physical interpretations of the core topological lattice identity 3 i=1 K= K3 . 2. FCC Lattice Stick Number Conjecture (108): The 5.9% mass gap be- tween the 1728 bulk and the 1836 physical mass is resolved via topological surface tension. Using the geometric constraints of the Face-Centered Cubic (FCC) lattice, we utilize computational evidence to conjecture that the mini- mal stick number for a Trefoil knot is 9. This 9-segment dislocation boundary stresses its local K = 12 sheath, yielding exactly 108 nodes of surface tension. The sum yields an exact bare mass of µ = 1728 + 108 = 1836. Furthermore, the higher-order geometric limits accurately predict the Υ(4S) bottomonium meson (K4) and the Higgs Boson (K5), while the amphicheiral ground state of the 41 knot provides a mathematically rigorous, zero-cross-section candidate for Dark Matter at∼1.03 GeV.