Paper 9 of this series embedded the four-dimensional Riemannian scale-space framework in a five-dimensional Lorentzian parent theory and identified a factor-of-2 discrepancy in gravitational time dilation as an open problem: the block-diagonalmetric dΣ^2 =−c^2 dt^2 + e^(2s/L) dx^2 + α^2 ds^2 gives dτ/dt= sqrt[1−4GM/(Rc^2)] versus the Schwarzschild result sqrt[1−2GM/(Rc^2)] confirmed by GPS measurements. We resolve this discrepancy exactly. The correction requires a single modification: replacing the flat gtt =−c^2 with gtt =− (1 + 2/L)c^2, L= Rc^2/GM, yielding the corrected 5D metric dΣ^2corr = −(1 + 2/L)c^2 dt^2 + e^(2s/L) (dx^2 + dy^2 + dz^2 + α^2 ds^2). We prove four results by SymPy-verified computation. (1) All geodesics of Papers 1–8 are exactly preserved. Since gtt depends only on L (a body parameter), not on (x,y,z) or s, all Christoffel symbols with a t-index in the spatial sector vanish. The spatial and scale geodesic equations are algebraically identical to those of the block-diagonal metric. (2) The key algebraic identity. The resolution rests on the exact identity (1 + 2/L)−4/L= 1−2/L, where 4/L= α^2˙s^2/c^2 is the ˙s-contribution to the proper time formula. The +2/L correction to gtt precisely cancels the excess, yielding dτ/dt= 1−2/L= 1−2GM/(Rc^2) exactly — the Schwarzschild result, valid to all orders in GM/(Rc2), not merely to first order. (3) SR time dilation is exact. In the flat-space limit (L→∞), the correction 2/L→0 and ˙ s→0, recovering dτ/dt= sqrt[1−v^2/c^2] with universal c. (4) The L(s)-dependent case. When L is allowed to vary with s (the full dynamical theory), a new Christoffel symbol Γstt =−(c^2/L^3) dL/ds appears in the scale geodesic, sourcing a new s-force from the t-sector. For the current framework with L constant at a given scale position, this term vanishes and the scale geodesic is unchanged. The corrected metric is the unique minimal modification of the block-diagonal metric that satisfies the three constraints simultaneously within the current diagonal, spatially-uniform, constant-Lansatz: correct Newtonian force, exact SR time dilation, and correct gravitational time dilation. It is consistent with but not yet derived from the 5D field equations; the derivation from G^(5)MN + Λ5g^(5)MN = κ5T^(5) MN remains open.

The mathematical development in this paper was produced in dialogue with Claude.ai (Anthropic) in March 2026, directed by the author. Use of AI assistance is acknowledged in accordance with standard scholarly practice.