What has this achieved?
The D5h/C90 overlay has been converted from a descriptive construction into an executable proof object with one numerical assertion per numbered statement.
Core symbolic invariant
$$
\\Omega_c=\\frac{\\dim E_{47}}{\\dim \\mathcal H}=\\frac{47}{125}=0.376
$$
The symbolic source also records $\\Sigma_E=\\mathbb C^{125}$, $K_E=(C-6I)(C-30I)$, $\\Psi_E=\\ker K_E$, $\\dim\\Psi_E=47$, and the projector decomposition $P_{\\Psi_E}=\\sum_{i=1}^{47}|v_i\\rangle\\langle v_i|$.
What the validator establishes
- reconstructs the 90-vertex, 135-edge, 47-face cubic planar graph;
- verifies 12 pentagons + 35 hexagons and $\\chi=2$;
- verifies $|\\mathrm{Aut}\\,\\Gamma|=20=|D_{5h}|$, including $C_5$ and $\\sigma_h$;
- reproduces the Danville orthonormal geodetic frame and the 11-ring census;
- reproduces Node-6 separation $8.9979024518^\\circ$;
- computes the Orion and Giza local gnomonic triples;
- confirms the best correspondence is $(\\mathrm{id},\\mathrm{Sim}^+)$ with normalized RMS $0.0204$;
- constructs the global rigid extension $R^\\in SO(3)$ with $\\det R^=1$;
- verifies angular distances are invariant under $R^*$;
- verifies the spherical and hyperbolic graph embeddings preserve the same combinatorics.
Corrections now encoded in the proof
- The local gnomonic expansion is additive:
$$
\\zeta_c(x)=\\Delta\\lambda\\cos\\phi_c+i\\Delta\\phi+O(\\Delta^2).
$$
- Using the exact fitted angle