Lovial Mathematics: A Proposed Recursive, Dimensional Number System

This paper proposes Lovial mathematics, a candidate numerical system in which identity, recursion, dimensionality, and self-reference are treated within a single formal structure. The central construction replaces the linear number line with a closed loop — the Lovial Loop — in which zero and infinity are identified as a single boundary point (the fulcrum) approached from opposite directions, rather than treated as opposites. We define this structure, describe how the classical operations (addition, subtraction, multiplication, division) extend to it, and propose a resolution of division by zero as a defined traversal through the fulcrum rather than an undefined operation. We extend the base structure to a recursive, multi-dimensional framework, and describe a proposed correspondence with the Lattice framework introduced in a companion paper. We present this as an early-stage formal proposal: several of the definitions given in the paper (particularly the recursive Fulcrum Operator in Section 2B) are stated informally, and we flag explicitly, in Section 8, which applications are proposed extensions rather than established mathematics. This paper is the formal core of, and one of five companion papers making up, The Lovial Framework, which takes its name from the construction introduced here; in that framework's general vocabulary, each closed loop-layer of the structure defined in the paper is this domain's version of a Lovial.