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  "scope": "T126: declared reduced ribbon and supported-beam controls.\n\nOwn small-slope models, not a reproduction of the 2026 three-dimensional\nGamma-limit proof or the full experiments. Ribbon natural metric=I and natural\ncurvature=kappa I are held fixed while width/thickness vary. Physical energy,\nenergy per reference volume and dimensionless reduced energy are kept separate.\n",
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  ],
  "conventions": {
    "ribbon": "chi=kappa*w\u00b2/t; reduced energy divided by D*kappa\u00b2, D=t\u00b2/[24(1-nu\u00b2)]; physical total energy=Y*t*L*w*energy_per_Y_volume",
    "ritz": "Fixed quadratic height, finite polynomial in-plane trial space, fully free in-plane edges; bounds only. Bulk formula neglects end layers.",
    "beam": "Pinned deflection endpoints, imposed projected span, local linear Winkler foundation; per projected area energies, no imposed natural curvature.",
    "free_expansion": "If projected span follows the uniform natural expansion and natural curvature is zero, delta=0 and h=0 has exactly zero energy.",
    "codazzi_counter": "a=I,b11=k0+beta*y,b12=b22=0,k0!=0; Gauss deficit=0,Codazzi=(beta,0); cylinder b11=k0 is an isometric trial, bending per Y volume=t\u00b2*beta\u00b2*w\u00b2/[288(1-nu\u00b2)], an upper bound not an exact minimizer claim."
  }
}