Universal coset field theory

We formulate a universal coset field theory, a four-dimensional Euclidean quantum field theory whose exceptional datum is the Albert algebra \(J\) and the associated compact Lie type \(E₆\). Its central result is that, under the two stated axioms, gravity is not a fundamental interaction: spacetime and the metric that propagates on it are emergent, induced structures rather than postulated inputs, and no fundamental graviton field ever appears. An \(E₆\)-invariant coercive potential has vacuum orbit Cartan's Hermitian symmetric space EIII,\[E₆/(Spin(10)× U(1)).\]Its \(32\) real tangent directions form the irreducible \(SO(10)× U(1)\) multiplet with complexification\[16₋₃⊕16̄₊₃\]and carry a unique positive invariant metric. For nondegenerate spacetime-filling maps into EIII, the pull-back of this metric gives a Riemannian first fundamental form, so the spacetime metric is derived from the coset field configuration rather than assumed a priori. Lorentzian physics is interpreted through Osterwalder--Schrader reconstruction, and one-loop matter determinants induce an Einstein--Hilbert term in the sense of Sakharov: gravity is thus a radiative effect of matter loops on the coset, not a fundamental field, at every stage of the construction. We compare this coset sector with the gauge-unfixed Higgs orbit of an \(E₈× E₈\) heterotic compactification with visible \(E₆\). At the level of the two-derivative bosonic action and the \((SO(10)× U(1))ψ\) current algebra, the visible sector matches; a \(Z₁₂\) asymmetric orbifold with three generations and an adjoint Higgs supplies the candidate realization. The resulting Albert--EIII criterion is relative: within the Albert-selected heterotic class, a theory can realize the correspondence only if its residual Higgs/moduli sector is the EIII coset with the stated tangent representation, metric, gauge data, anomaly and Green--Schwarz matching, and worldsheet consistency. In the stated truncation, the functional renormalization-group flow has a unique ultraviolet-attractive non-Gaussian fixed point and gives\[MGUT 2× 10¹⁶\,GeV.\]We also show that the Riemann hypothesis is equivalent to the absence of complex mass-squared modes, which is a spectral reformulation of the prime-orbit trace of the finite adelic zeta sector. We distinguish the representation-theoretic consequences from assumptions requiring further dynamical input.