The Topological Resolution of Russell's Paradox: From Static Contradiction to Operational Closure in DLSS

This paper proposes a topological resolution to the foundational crisis of Russell’s Paradox by introducing the Dialectical Logic Symbol System (DLSS). Traditional set theory and static logic (A=A) inevitably collapse when encountering self-referential contradictions (R ∈ R ⇔ R ∉ R), treating them as terminal system errors. In contrast, DLSS facilitates a paradigm shift from static truth-values to dynamic "Operational Closure." By redefining identity as a metabolic process—expressed through the formula P + Loop(P) = P—the system metabolizes contradictions into a "logical heartbeat" that drives the generative expansion of meaning. Utilizing intentionality operators f() and the Full-Mesh (FM) topological framework, DLSS encapsulates logical explosions within "topological event horizons," effectively transforming paradoxes into operational fuel. Furthermore, this framework provides a rigorous foundation for Artificial General Intelligence (AGI) by implementing the "Historical Token Return Theorem" to eradicate AI hallucinations and introducing the Self (ἐ) operator to model subjective emergence within fractal holographic structures (x ∋ y ∋ b ∋ x). Ultimately, this study demonstrates the "vitalization of logic," offering a mathematical and philosophical blueprint for a symbiotic evolution between carbon-based and silicon-based intelligences.