The Other Half of Gravity: Torsion and the Two-Chamber Structure of the Tetrad Frame

The connection on the tetrad frame has K³ = 64 independent components. General relativity's zero-torsion condition removes 24 of them, the antisymmetric sector, retaining 40 Christoffel symbols determined by the metric. The companion letter proved that the tetrad equation produces two bounded tetrahedral regions related by spatial parity: TetA (the identity component) and TetB (the parity component). The present letter proves that a torsion-free connection cannot distinguish TetA from TetB (Lemma, Section 2): the torsion sector is the necessary carrier of the two-chamber distinction, and the zero-torsion condition collapses it. The exchange-symmetric partition derived in Supplementary Note 1 uniquely determines the TetB field fraction as 1/(x+1), where x = g/a₀ is the dimensionless acceleration. A coupling polynomial f(K,s) = 1 + sK + K² organises the full count structure and yields the torsion identity 24 = D × 2K exclusively at K = 4 (Section 5). The ratio of the removed to the retained field response is 1/x, which is algebraically identical to the dark-to-baryon mass ratio of the cold dark matter framework.