A numerical observation in Kocik's Descartes circle framework for the Koide lepton mass relation

Kocik (2012) showed that the Koide charged-lepton mass formula admits a geometric interpretation via the Descartes circle theorem, identifying curvatures with square roots of lepton masses. This note observes that the fourth Descartes circle in that framework yields a mass of 95.117 MeV, which agrees with the strange quark MSbar running mass evaluated at the scale equal to the sum of the three charged-lepton masses (1883 MeV) to within 0.002 MeV. Both the predicted mass and the evaluation scale emerge from the charged-lepton masses alone, with no free parameters. The agreement has improved monotonically across five FLAG lattice QCD reviews (2013–2024) as experimental precision has increased. This deposit timestamps the numerical coincidence and defines a falsifiable convergence test: the ratio of the QCD-evolved strange mass to the Descartes prediction should remain consistent with unity as future lattice determinations improve. No theoretical mechanism is proposed; the observation is presented as verifiable numerology. Full Python verification code using CRunDec 4-loop RG evolution is included.