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MC-E47-INTRINSIC-SPACETIME-UNMARKED/1.0 · PASS 24/24
The two stronger Einstein obligations are closed for the full locked tensor-cube datum: intrinsic Lorentzian 3+1 construction and injectivity into a 47-real-dimensional image of the completely unmarked vacuum-Einstein quotient.
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The earlier geometry no-go remains true for the abstract rank-47 projector alone. The successor theorem uses the stronger canonical finite datum including the ordered tensor factors already present in the locked cube.
$$ \\mathfrak D_E=(V_2^{\\otimes3},\\langle\\cdot,\\cdot\\rangle,J_z^{(1)},J_z^{(2)},J_z^{(3)},C,K,P_{47}). $$
Define
$$ \\eta_E=2P_{47}-I. $$
It is a self-adjoint involution with inertia (47 positive, 78 negative).
For the normalized equal-amplitude cube state Ω, define
$$ r_0=K^2\\Omega,\\qquad r_i=P_{47}J_z^{(i)}\\Omega,\\quad i=1,2,3. $$
The machine certificate verifies that r0 is nonzero and lies in E47-perp, that the three spatial vectors are independent and lie in E47, and that their Gram matrix is positive definite. After canonical normalization and whitening,
$$ \\operatorname{Re}\\langle e_\\mu,\\eta_E e_\\nu\\rangle=\\operatorname{diag}(-1,1,1,1) $$
to operator-norm residual 1.3682514567976793×10^-14 with determinant -0.9999999999999856.
Hence the affine four-plane
$$ M_E=P_{47}\\Omega+\\operatorname{span}_{\\mathbb R}\\{e_0,e_1,e_2,e_3\\} $$
is an intrinsic Lorentzian four-manifold inside the finite carrier.
Choose the deterministic real orthonormal basis b0,…,b46 of E47 produced by pivot Gram-Schmidt in lexicographic cube order. For q with coefficients c_a(q), set
$$ F_q(u)=u^{78}+u^{47}+\\sum_{a=0}^{46}c_a(q)u^a $$
and