The electron mass is the lightest of the three charged lepton masses. In the Koide framework, it is the hardest to derive precisely — the smallest eigenvalue of the circulant is most sensitive to the phase angle. This paper derives the electron mass via the chain: Rydberg constant → Bohr radius → electron mass, using the Pentagon Physics value of α and the Koide phase cos(δ) = −19/28. The agreement is 6.6% — the largest discrepancy in the programme, attributed to a structural correction mechanism not yet identified.