Aazami, AB; Petters, AO, *A universal magnification theorem. III. Caustics beyond codimension 5*,
Journal of Mathematical Physics, vol. 51 no. 2
(2010),
pp. 023503 [repository], [doi] .
**Abstract:**

*In the final paper of this series, we extend our results on magnification invariants to the infinite family of A n(n≥2), D n(n≥4), E 6, E 7, E 8 caustic singularities. We prove that for families of general mappings between planes exhibiting any caustic singularity of the A n(n≥2), D n(n≥4), E 6, E 7, E 8 family, and for a point in the target space lying anywhere in the region giving rise to the maximum number of lensed images (real preimages), the total signed magnification of the lensed images will always sum to zero. The proof is algebraic in nature and relies on the Euler trace formula. © 2010 American Institute of Physics.*