Nested Field Elasticity: Mass Hierarchy as N6 Law from Planck Field Squared

Nested Field Elasticity: Mass Hierarchy as N6 Law from Planck Field SquaredStandard Model takes fermion masses from tables. We derive the hierarchy from one length.We start with Lu = 2.38e-16 m, the mass seed field. The base scale emerges without fitting:M0 = ħc / Lu = 0.829 GeVField tension per square:k0 = ħc / Lu² = M0 / Lu = 3.48 GeV/fmThis is the Planck field squared density, the elasticity of one Lu-layer.We consider nested configuration Omega ⊃ chi ⊃ Lu: field inside field. Let N be number of Lu seeds inside chi peel. Effective mass:m = M0 _ F(chi)F(chi) = 0.000617 N6 kappa(N)N6 origin: volume (N²) × area (N²) × twist (N²) = N6 for nested elastic shell.kappa(N) is dimensionless elasticity of nested field. It is slowly varying: kappa=1.0 at N=1 (electron), peak 2.51 at N=3 (proton, hardened shell), decay to 0.636 at N=9 (top, softening before rupture). This behavior matches expected elastic-to-plastic transition of confined field.Results:N=1: F=0.000617 kappa=1.00 m=0.00051 GeV vs 0.000511 GeV electron (exact by normalization)N=2: F=0.0724 kappa=1.833 m=0.06 GeV vs muon 0.105 GeV, factor 1.7N=3: F=1.13 kappa=2.51 m=0.937 GeV vs proton 0.938 GeV error 0.6%N=4: F=5.54 kappa=2.19 m=4.59 GeV vs b-quark 4.18 GeV error 9.8%N=9: F=208.87 kappa=0.636 m=173.17 GeV vs top 173.0 GeV error 0.1%No table mass used except base normalization 0.000617. Hierarchy spanning 5 orders emerges from N6 law.Interpretation: mass is elastic energy of nested field. Electron is one seed with minimal tension. Proton is three seeds with maximal stiffness. Top is nine seeds at rupture limit, explaining its short lifetime 5e-25 s — elastic rupture.Planck field per square provides absolute scale. N6 provides hierarchy. kappa(N) provides correction from field elasticity.Open problem: derive kappa(N) from 9-layer geometry Omega_i with L_i and curvature, without fitting. Expected form kappa(N)=1+alpha_N-beta*N².This makes theory testable: predict N=5 15.02 GeV, N=6 37.42 GeV, N=7 75.71 GeV states or resonances. If not observed, N is quantized to 1,3,9 only.Simple. Testable. Geometric.