SDRIS Algebra Foundation

This paper formalizes the axiomatic structure of the Static-Dynamic Recursive Information Space (SDRIS) within the framework of category theory. We define the ontological category $\mathcal{I}$ as a graded system of irreversible recursion operators. Based on this, we derive physical reality as a topological pushout (Ontogenesis) and measurable information as a pullback (Epistemology). Central to this theory is the non-commutative algebra of the Tilt Operator $J$, which generates the Lorentzian spacetime signature and enforces the dimensionality of the observable universe ($4D$) as a stability maximum of the recursive flow. Finally, we demonstrate that the saturation of the information space at $N=19$ necessitates a cyclic cosmology ("Big Bounce").