TAM Theory as an Extension over 𝔹-Formalism Systemic Topological-Affine-Modular Theory Built on the Foundation of △-Ontology

This work extends Topological-Affine-Modular theory (TAM) over 𝔹‑formalism — a strict axiomatics of discrete self‑similar space built from right isosceles triangles (RIT). Three functors are defined: topological Φ_τ, affine Φ_𝒜 and modular Φ_ℳ, acting from the category of limit relational complexes ℛ𝒞_∞ to the categories Top, Aff and Mod respectively. Explicit connection formulas and sketches of isomorphism proofs are established. Categorical genealogy is added — it is shown that Hilbert space H (ℑ) and Kähler manifold K (ℑ) are two branches growing from a single root ℑ through functors FH and FK. The metric problem in synthetic differential geometry (SDG) is solved via a unified definition of distance as the infimum of path lengths composed of legs (1) and hypotenuses (√2). A unified master diagram connecting all components is introduced, and the Theorem on the Unity of Mathematics in △-ontology is formulated.