Inverse Zero Operator (IZO) Idempotence

The Inverse Zero Operator (IZO) constitutes the idempotent core of recursive spacetime quantization. It serves as a spectral projector isolating stable solutions to the recursively-scaled Laplacian equation, and is defined via a complex contour integral. Simultaneously emerging as an idempotent monad on the category RecAdStrat of recursively stratified adelic spaces. Its monadic structure—comprising a functorial collapse mechanism, unit embedding, and identity multiplication—induces a reflective subcategory of actualized fixed points via the Eilenberg–Moore construction, while its Kleisli category encodes pre-collapse recursive dynamics.