Rigorous Derivation of Cosmological Constant and Hubble Constant Under the Framework of First-Principles Light String Unified Theory

Based on the core axioms of the first-principles light string unified theory, this paper systematically constructs a unified mathematical and physical derivation system for the cosmological constant and Hubble constant. The whole derivation complies with academic norms, without implicit assumptions, dimensional fitting or circular reasoning. This paper defines the quantitative relationships between the rigidity of light string field and wave velocity, as well as the expansion intensity and frequency, establishes the constraint of constant light string field density, distinguishes the theoretical intrinsic value and observed apparent value of Hubble constant, clarifies the physical origin of dimensionless structure constants, and reveals the essential correlation between spacetime expansion and light string field. The theoretical framework is self-consistent, compatible with existing astronomical observation results, and avoids paradigm conflicts with traditional cosmology.