Mathematics as Conservation of Existence A Formal Reconstruction from the Primitive Identity E = E + 0

This paper reconstructs the foundations of mathematics from a single irreducible fact: the conservation of existence.Instead of starting from sets, logic, or formal axiomatic systems, we take the statement E=E+0 as the minimal, pre-logical expression of existence itself.We show that numbers, arithmetic operations, and the scope of Gödel’s incompleteness theorem follow necessarily from this identity.In this framework, incompleteness is not a defect of formal systems but an unavoidable consequence of grounding mathematics in existence rather than in definitions.