Relational Four-State Microstructure and the Emergence of Massless Spin-2 Gravity

We present a deliberately minimal formulation of Homogeneous Compression Theory (HCT) as a relational pregeometric framework rather than as a claimed completed theory of quantum gravity. A binary cell with state label n = 2N_c - N_r, N_c,N_r in {0,1}, contains four states, three of which are active under the observable n. Equal pairwise relational weighting yields a singlet-plus-triplet decomposition, 4 = 1 + 3, and the triplet projection of the four states forms a regular tetrahedron. The corresponding active fraction is g = 3/4; with the HCT coherence convention chi = g/2 this gives chi_micro = 3/8 and, relative to the coherent fixed point chi_* = 1/2, epsilon = 1/8. An oriented antisymmetric relational sector admits normalized complex structures J satisfying J^2 = -I, providing a natural real representation of phase without claiming to derive quantum mechanics from combinatorics alone. We then formulate a minimal completion in which the fundamental state space is a tensor product of four-state quantum cells, dynamics is unitary and relational, and continuum geometry is emergent. Six independent tetrahedral edge deformations map naturally to a symmetric three-dimensional strain tensor. If its shear sector reaches a Lorentz-invariant massless fixed point and couples universally to the conserved stress tensor, the infrared gravitational sector has two transverse- traceless polarizations and admits the Einstein theory as its consistent nonlinear completion. We explicitly separate derived statements from completion postulates. In particular, HCT does not presently derive the dimensional value of Newton's constant G, and previously noted numerical relations involving 64 + 24 = 88 are not used as fundamental evidence. The framework is therefore a falsifiable candidate for relational emergent gravity, not a claim that quantum gravity has been solved.