Mathematics Branch

Prompt

Act as a world-class mathematician and theoretical synthesizer. Task: Invent a completely novel, rigorous, and logically consistent branch of mathematics that does not currently exist in academic literature. Determine your own methodology, internal logic, and generative process to construct this system. Your output must strictly contain the following deliverables: 1. Nomenclature & Scope: Name of the new branch and the novel abstract problem space it targets. 2. Axiomatic Foundation: A minimal set of foundational axioms and syntax/notation rules. 3. Core Definitions & Operators: Definitions of primary mathematical entities and unique operators within this framework. 4. Fundamental Theorems: At least two primary theorems derived directly from your axioms, complete with formal, step-by-step mathematical proofs. 5. Application Bridge: A demonstration of how this new branch resolves or reframes an existing unsolved problem in mathematics or theoretical physics.