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E47-GR-QFT-INTERTWINER-20260911 · PASS
E0 exact symbolic structure + E1 deterministic NumPy/SymPy reconstruction. The new result closes the previously open typed covariant internal-fiber map. It does not relabel that map as spacetime emergence or full quantum gravity.
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$$ V_2^{\otimes3}\to C\to K=(C-6I)(C-30I)\to Q=K^2\to E_{47}=\ker Q\to P_{47} $$
$$ \operatorname{spec}(C)=\{0,2,6,12,20,30,42\},\qquad \dim E_{47}=47 $$
$$ \delta=11664,\qquad L=186624,\qquad \kappa_+=16, \qquad \varepsilon_=\frac1{99144},\qquad \rho_=\frac{15}{17} $$
$$ \mathcal L(x)=\frac12\|R(x)\|^2,\qquad R(x_)=0,\qquad J_=DR(x_*) $$
$$ \nabla\mathcal L(x_)=0,\qquad \nabla^2\mathcal L(x_)=J_^\dagger J_ $$
$$ J_^\dagger J_\succeq\sigma_^2I\Longrightarrow x_\text{ is a strict local minimizer} $$
$$ \langle\nabla\mathcal L(x)-\nabla\mathcal L(y),x-y\rangle\ge m\|x-y\|^2 \Longrightarrow \|x(t)-x_\|\le e^{-mt}\|x(0)-x_\| $$
For the exact E47 spectral generator,
$$ S_t=e^{-tQ}=P_{47}+e^{-tQ}(I-P_{47}),\qquad \|S_t-P_{47}\|_2=e^{-11664t}. $$
$$ \mathcal E=M\times\mathbb C^{125},\qquad \Pi=I\otimes P_{47} $$
$$ \mathfrak A_g=((\Box_g-m^2)\otimes I)-\kappa(I\otimes Q) $$
$$ [\mathfrak A_g,\Pi]=0,\qquad \mathfrak A_g\Pi=((\Box_g-m^2)\otimes P_{47}) $$
$$ v\in E_{47},\qquad \iota_v(\varphi)=\varphi\otimes v,\qquad \boxed{\mathfrak A_g\circ\iota_v=\iota_v\circ(\Box_g-m^2)} $$
Declare
$$ S[g,\Phi]=\int_M\sqrt{-g}\left[\frac{R-2\Lambda}{16\pi G}-\frac12\langle\nabla_\mu\Phi,\nabla^\mu\Phi\rangle-\frac{m^2}{2}\langle\Phi,\Phi\rangle-\frac\kappa2\langle\Phi,Q\Phi\rangle\right]d^4x. $$
Then