The invariant four-volume of an event's causal past is a well-defined geometric functional of a Friedmann-Lemaître-Robertson-Walker expansion history. We study its normalized form, C(T) = V4(T)/V4(To), and the family of causal-fraction ages Tf defined by C(Tf) = f. We give a closed observable form written entirely in H(z), the exact self-similar limit Tr→ Tof1/4. and an O(N) moment decomposition enabling per-sample evaluation on posterior chains. Two structural results follow. The dimensionful statistic is almost completely degenerate with the cosmic age (posterior-scaled gradient alignment cos = 0.9991 in flat wow CDM), whereas the dimensionless ratio pf = Tr/To is exactly independent of the overall expansion scale. Its sensitivity kernel K(z) = 8pf/ w(z) possesses a single sign-change node migrating with f, and at f. = 0.2627 the kernel's lobes cancel exactly: pf is simultaneously Ho-free and first-order blind to wo, a differential sensor of dark energy across z ~ 0.40 that within flat ACDM tracks the matter-dark-energy handover, 2A(z) = 0.46 ± 0.03. Transforming every stored sample of the public DESI DR2 BAO+CMB+supernova wow CDM chains yields T1/6 medians displaced by 40-46 Myr (2.5-2.9 posterior standard deviations) from the Planck ACDM value T1/6 = 8.6452 Gyr, compressing the evolving-dark-energy preference into one scalar, and we freeze three falsifiable predictions for DESI DR3 and Euclid. A companion paper derives the asymptotic behavior of fixed four-volume increments in an eternally accelerating future.