How much of a gravitational shape can be recovered from a matrix describing its forces? A central configuration is an arrangement in which every body's gravitational acceleration points towards the centre of mass with the same proportionality factor. These special shapes organise important motions in the many-body problem. This paper studies a way to search for them through smaller spaces of possible shapes. Classical work by Yoccoz and Albouy provides the starting point: a strictly convex reconstruction problem has at most one answer on a fixed support. The present candidate does not claim that classical mechanism as a discovery. Its contribution is quantitative and computational. It gives explicit reconstruction bounds and exact certificates that can reject entire regions of possible force kernels. One distinction is especially important. A uniquely reconstructed metric need not describe a central configuration. In two seven-body parameter boxes, the certified optimum has rank one: all the bodies lie on a line. Yet its forces do not satisfy the central-configuration equations. A positive constrained-optimisation slack supplies an additional witness that the proposed complete kernel cannot be realised. These are whole-box results, not just checks at the middle of a box. The evidence package also contains fifty-four local reconstruction certificates and fifteen regions excluding configurations of higher dimension. A twelve-stage exact replay and a supplied, separately written checking implementation have been run. That is inspectable computational evidence, not authenticated independent reproduction or a formal proof-assistant result. The remaining limitation is substantial: the paper does not enumerate every planar eight-body or spatial seven-body configuration, and it establishes no solver speedup. This is Evidence Press, certified convex reconstruction for central configurations, released on the first of October twenty twenty-six. The paper, code and evidence are linked on this page. This synthetic AI voice is an explanation, not additional scientific evidence.