Calculus Restructuring under PFUS Coupling Mechanism and Establishment of Integrated New Mathematical-Physical Cognitive System

Classical calculus contains the inherent logical paradox of infinitesimals, known as the ghost of vanished quantities, which has puzzled academic circles for centuries. Limit-based revisions only remedy superficial contradictions without resolving fundamental conflicts from the cosmic ontological perspective. Fully inheriting the zero-coupling interface axiom and the cosmic intrinsic rigid scale constant π₁ as dual foundations, this study completes comprehensive and essential restructuring of classical calculus under the Phase-Fusion Universal Structure (PFUS). The research systematically addresses the infinitesimal paradox, establishes an original operational symbol system, redefines differential and integral concepts from an ontological perspective, breaks the barrier between discrete and continuous operational systems, and constructs a logically self-consistent, ontology-oriented unified mathematical-physical cognitive system.