An Integer Proton Construction and a Numerical Coincidence with Neutron Beta Decay

Starting from a previously proposed mass–charge regularity for first-generation fermions , we construct an additive arithmetic model for the proton and the neutron based solely on mass and charge constraints. The proton solution naturally selects the integer pair (82, 161), while the neutron leads to non-integer effective multiplicities. The fractional component of the neutron solution generates a residual mass which is numerically close to the neutron beta decay energy Qβ . The purpose of this note is simply to document the internal arithmetic consistency of the construction and the resulting numerical coincidence.