Projected Weyl stresses in a stabilised two-brane bulk: a finite-domain closure test

Brane field equations leave a projected bulk Weyl stress undetermined, making assumed relations among its components central to braneworld phenomenology. We quantify this deficit and test such relations against a solved bulk. For the linearised brane system, under stated operator assumptions, the static deficit is one function for a spherically symmetric source and three at each l ≥ 2; a time-dependent representation count gives five. A finite two-brane interval represents the missing data through discrete bulk mode coefficients. We solve a Goldberger–Wise-stabilised Randall–Sundrum interval by the Einstein–DeTurck method for a static spherical source on the positive-tension brane, validating the Weyl extraction against an analytic benchmark. At the reporting exterior radii, the dark anisotropic stress is nonzero and single-signed. The closures δP = 0 and P/U = −2 and a massive spin-2 template at the modulus mass fail pointwise. Independently, a wall-free infinite-radial-domain linear response violates all three relations at all 2001 sampled radii across the same window. Matched-spacing calculations on two radial domains, R = 28 and R = 50, agree in the anisotropic stress to 0.73%, and the finite-grid anisotropic stress agrees with the wall-free linear response to 3.07% at 505×241 and 1.16% at 505×401. Together these supply a bulk-derived test of the closure relations used in braneworld phenomenology.