Ramanujan Metatheory: Discrete State Spaces and Core Recursion

his paper proposes a testable metatheoretical hypothesis: Ramanujan’s extraordinary intuition was a direct perception of the topological structure of a discrete state space. We introduce two foundational tools—the Core Factor Formula N=2i3rR±1N=2 i 3 r R±1, which uniquely maps every integer to a three‑dimensional state vector and yields the core constraint r⋅p=0r⋅p=0, and the Core Recursion Formula (FCR) An=αn+βn(An+1+γn)t , which describes the evolution of states. Using these tools, we reinterpret Ramanujan’s partition congruences, the super‑convergent 1/π series, his continued fraction families, divergent series summation, and mock theta functions—all as manifestations of path interference, boundary residuals, and symmetry collapse within the same discrete space. We establish a three‑layer hierarchical architecture and three metatheoretical axioms, showing that Ramanujan was not guessing but systematically observing a complete discrete–continuous unified structure. Our work does not rewrite his formulae; it excavates the structural blueprint he left behind.