This paper introduces the concept of Idempotent Materials, a new class of advanced materials where structural integrity is governed by the K=5 coherence layer of affine Hecke monoids. By utilizing the universal idempotence constraint (lambda squared + 3 lambda + 2 = 0) as a stability regulator, we propose a mechanism where physical damage (fractures, dislocations) is treated as algebraic perturbations. The system, anchored by the Golden Attractor (sqrt phi approximately 1.272), naturally forces the material to return to its minimal equilibrium state (x squared = x), enabling structural self-repair without external energy input or chemical agents.