Shape-Wilf equivalence through length eight

We determine the shape-Wilf-equivalence classes of single permutation patterns at lengths seven and eight. The known Backelin-West-Xin and Stankova-West equivalences, with right direct-sum extension, generate 4,862 and 39,326 components, respectively, and the retained separation certificates distinguish all of them. The paper proves a forest formula for the number of generated components, gives exact counting algorithms and fiber-cancellation arguments, and includes all final separation rows. Independent decisive recounts validate all 94 length-seven order-13 values and the required length-eight order-15 layers and finite cutoff premises. Full-root reconstructions retain the certified ordinary-Wilf atlas and independent earlier board arrays as explicit dependencies. The archive supplies sources, raw outputs, controls, acceptance reviews, and a portable retained-data verifier. The all-length classification question remains open.