The proton is 1836.15268 times heavier than the electron. This number is dimensionless and independent of any unit system — a pure number that nature has chosen. It determines the scale of atomic physics relative to nuclear physics. It has been measured to 11 decimal places. It has never been derived. Pentagon Physics derives it using the identity φ = 2cos(π/5), which connects the golden ratio to π through the geometry of the regular pentagon. Both φ and π trace back to the discriminant-5 axiom. The mass ratio follows from their relationship alone.