Proposition 2. 5 of the unified-description paper showed that, on a two-dimensional tangent space, the light cone determines the metric up to calibration (3 = 2 + 1). The state paper applied the same decomposition to the quantum state. This paper carries the decomposition through on the side of gravity: the metric is direction and calibration. A demarcation is placed first: the decomposition is kinematic — its object is the correspondence between the components of the metric and the operations of the triad (Δ, Λ, Ψ). The dynamics of gravity (the Einstein equations) is neither derived nor modified; of the dynamics, only the calibration side is constructed (by the calibration paper), and the directional side remains unconstructed. The content is in four stages. First, Proposition 2. 5 is re-derived mechanically: fixing the two null directions (the two poles, the domain of Ψ), two of the three components of a symmetric bilinear form vanish under the null conditions, and what remains is a single positive factor Ω (calibration, the domain of Λ) — 3 = 2 + 1; a metric with a fixed null pair automatically has Lorentzian signature. Second, in two dimensions the decomposition is complete: every two-dimensional Lorentzian metric is locally g = e^2θη, so the calibration field θ of the calibration paper acquires a geometric identity — the conformal factor of the two-dimensional metric. The properties of the conformal factor (boost-invariant scalar; transformation law θ′ = θ − ½ln (f′h′) ) are theorems; the identification of this conformal factor with the ratio field λ = exp (θ) of the calibration paper is an identification (agreement of transformation behavior is necessary, not sufficient). Furthermore, in two dimensions all curvature lives in the calibration: R = −2e^−2θ□_ηθ, computed directly from the Christoffel symbols — direction (the light cone) carries no curvature. Third, in four dimensions the pointwise decomposition is unique: θ = (1/8) ln (−det g) splits the metric into calibration (1 component) and direction (the conformal structure ĝ with det ĝ = −1, 9 components): 10 = 1 + 9. The Weyl tensor lives in ĝ; the dynamics of the directional side is demarcated as unconstructed — the next front. Fourth, the 2+2 decomposition is machine-verified on Kruskal spacetime: UV = (1 − r/2M) e^r/2M and F·dUdV = (1 − 2M/r) dudv, with e^2θ = F (r) = (32M³/r) e^−r/2M. The antipodal map JK of the non-orientable-spacetime paper acts on the null pair (U, V) as −id = Δ² = PT, and the pullback invariance JKᵀ gblock JK = gblock makes it a block isometry: the geometry of the antipodal quotient, the algebra of the unified-description paper, and the decomposition of this paper are sewn together at the single point of Kruskal. The T2 face is confirmed: the global rescaling g → k²g is a translation of the calibration θ → θ + ln k with the direction invariant — the value of the calibration belongs to the external scale (the root of row 29 of the consolidated demarcation), which this paper does not violate. All theorem-level claims are machine-verified by the accompanying script (verifygravitydirectioncalibration. py, 24 checks, all passing). The demarcation table (13 rows) states what is a theorem (the decomposition, the properties of the conformal factor, the whereabouts of curvature, the Kruskal identities, the junction JK = Δ², the externality of the value), what is a citation (2D conformal flatness; the whereabouts of Weyl), what is an identification (the conformal factor with the θ of the calibration paper), and what is unconstructed (the identification of the calibration potential with the gravitational action; the dynamics of direction — the Einstein equations in triadic form).
Makoto Saito (Thu,) studied this question.