A Simple Formula for the Proton-Electron Mass Ratio: μ = 6⌊√5/α⌋

Abstract We report a simple formula derived from geometric considerations that predicts the proton-to-electron mass ratio with 0.008% precision: μp=6⌊5α⌋=1836\mu_p = 6\left\lfloor\frac{\sqrt{5}}{\alpha}\right\rfloor = 1836μp=6⌊α5⌋=1836 More remarkably, the same formula without the floor function automatically yields the neutron-to-electron mass ratio with 0.0006% precision: μn=65α=1838.42\mu_n = 6\frac{\sqrt{5}}{\alpha} = 1838.42μn=6α5=1838.42 Both predictions use only one known constant (the fine-structure constant α) with no adjustable parameters. We derive three independently testable predictions and explicitly identify the weak points in the theory. This work makes no assertions about physical mechanisms but honestly documents this finding and invites the community to explore its significance.