Symmetric configurations 24_5 whose point non-collinearity graph has two components

In a symmetric configuration 245 every point is non-collinear with exactly three others, so the non-collinearity graph A of the points and the analogous graph A′ of the lines are cubic. Suppose that A has exactly two connected components. We prove that then A′ also has exactly two connected components, with the same multiset of component sizes, and that this multiset is {6,18} or {12,12}; both occur. The result classifies the component-size multisets under the two-component hypothesis, not the configurations up to isomorphism. A quotient argument reduces the problem to four candidate multisets, and Boolean satisfiability (SAT) refutations with LRAT certificates, accepted by the checker lrat-check, exclude {4,20} and {8,16}. The {12,12} example is a classical cyclic configuration. This record contains the manuscript (PDF) and the supplementary archive: code, CNF formulas, LRAT proofs, cube lists, check scripts and outputs, and a SHA-256 manifest, with instructions for regenerating and checking every certificate.