Traditional mathematics is constrained by the linear superposition paradigm, making it difficult to precisely characterize the nonlinear synergistic mechanisms and holistic emergent properties of heterogeneous systems. Based on five-dimensional ontology, this paper constructs a new five-dimensional mathematical system, proves the five-dimensional minimal completeness theorem, and defines the synergy coefficient k through multiplicative coupling. The total intensity satisfies Ibase · (1+k), achieving the unification of physical conservation and systemic emergence. It is further demonstrated that traditional mathematics is a degenerate special case when k=0. Moreover, this paper reveals that the synergy coefficient exhibits reference-frame relativity—the same combination may present different k values under different functional intentions or observational scales. Based on differences in subjective initiative, systems are categorized into three types (none, weak, strong) with corresponding five-dimensional operation types, revealing the core reason why complex system problems such as entropy increase are difficult to resolve using traditional mathematics. This framework achieves a unified description of the full spectrum of systems and provides a new quantitative foundation for general system theory.
Guiru Zhao (Wed,) studied this question.
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