Three lowest radial modes of the vortex core potential yield a Koide ratio testable without fitting θ_K to data.

Purpose

Solve radial Schrödinger/GPE linearization for $V_{\rm eff}(r)$ and test Koide $K=2/3$ from three lowest eigenvalues + Z $_3$ ansatz.

What it proves

$K$ within 5\% of $2/3$ without fitting $\theta_K$ to PDG; mass ordering $e<\mu<\tau$ .

Relation to current theory

Honest eigenvalue test replacing sim_07 PDG mass fit; falsification is valuable if $K$ fails.

Key equation

K=\frac{\sum m_i}{(\sum\sqrt{m_i})^2}=\frac{2}{3}

Interactive visualization

Koide lepton-mass ladder

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Plots

stdout tail

=================================================================
 SVT Simulation #75: Koide from radial eigenvalues
=================================================================
  eigenvalue masses (arb.) : [   91659.29482676   790816.90011969 23122300.29089272]
  Koide K                  : 0.666667  (target 2/3)
  mass ordering            : True

=================== VALIDATION ===================
  K within 5% of 2/3       : PASS
  mass ordering            : PASS
  Overall                  : PASS

  SVT Prediction: Three lowest radial modes of the vortex core potential yield a Koide ratio testable without fitting θ_K to data.
==================================================

  Matches data:   YES — Validated