Version 3 Update: Axiomatic Consolidation and Theoretical Refinement This version maintains the original mathematical proof from Version 1 while providing the formal axiomatic foundation of the identity. The update establishes the functional necessity of the derivation, transitioning the exposition to a formal theoretical declaration. Theoretical Premise:The aggregate response is defined as a pointwise operator identity. By adhering to the principle of coordinate consistency (Axiom of Simultaneity), the derivation establishes that the summation of independent kernels is governed by functional superposition. This framework formalizes the distinction between combinatorial matching and pointwise addition. Key Revisions: Structural Refinement: Numerical validation tables have been removed. As the derivation establishes a deterministic identity within the functional space, the results are presented as mathematically self-consistent and independent of numerical confirmation. Axiomatic Foundation: Introduction of the Axiom of Simultaneity to formalize the requirement of coordinate unity. Terminological Alignment: Refinement of the Abstract, Discussion, and Conclusion to ensure absolute consistency with the operator-based nature of the identity.
Safak Ebesek (Sat,) studied this question.