The Charged-Lepton Koide Relation as a Unit-Dispersion Constraint

We record a scale-free reformulation of the charged-lepton Koide relation. Writing the square-root mass vector r_ = (√mₑ, √m_μ, √m_τ) with mean r and standard deviation σᵣ, the Koide quotient is exactly Q_ = (1 + CV(r_)²)/3 with CV(r_) = σᵣ/ r, so that Q_ = 2/3 CV(r_) = 1 σᵣ = r: the square-root masses have unit relative dispersion. This isolates the intrinsic shape content of Koide as a single dimensionless number and separates it cleanly from the mass hierarchy, which is fixed independently by the placement of one generation near a node of the square-root profile. We record two structural consequences for the Cosmochrony fermionic sub-programme. First, the specific cascade ladder (1, 12 + u, 12 - u) that carries the projected generation levels has a bounded dispersion, CV ≤ 1/√2 and Q ≤ 1/2, so it cannot by itself realise the Koide value. Second, CV(r_) = 1 is the coefficient of variation of the maximum-entropy positive variable at fixed mean; whether the projection entropy SΠ induces such a variational principle on the square-root mass observable is stated as a sharp, falsifiable open test. This note does not derive the masses: it fixes a target invariant for the fermionic-mass sector.