Relational Foundations of Mathematics: Reformation of Peano Axioms and Symmetry Restoration

This work presents a foundational reformulation of mathematics based on relational, coherence-preserving axioms. By replacing singleton-based constructions with relational composites, the framework restores internal and external symmetry, aligns mathematical structures with physical and informational systems, and eliminates classical paradoxes such as Russell’s and self-referential statements. Derived arithmetic, logic, set theory, and higher mathematics are fully consistent within the relational coherence domain. The paper also reformulates and resolves the Millennium Prize Problems in this coherence-aligned framework, providing a unified paradigm connecting mathematics, computation, and physical reality.contact infinitykhushalic@gmail.com