Deterministic Semantic Token Algebra (DSTA): A Purely Mathematical Framework for Unique, Structure-Preserving Token Generation Across Computational Primitives

Key Points

• This work aims to establish a mathematical foundation for token generation methodologies, framing them in a formal context.
• Formalization of token generation as a homomorphism from a computational domain to a token space
• Proof of six axioms including determinism and uniqueness
• Development of four formal theorems and three counterexamples
• Implementation of the framework in C++
• Validation of the six axioms for token generation
• Establishment of theorems supporting the framework's applicability
• Counterexamples demonstrating limitations in existing proposals