The Caillahua-Mendoza Stability Principle of Emergent Order: A Unified Generative Framework

This preprint establishes the complete axiomatic foundation of the Caillahua-Mendoza Stability Law (CM-SL), presenting a generative mathematical-geometric framework unifying physical, linguistic, and engineering systems through the Principle of Minimal Dimensional Deformation (PMDD). The framework resolves the epistemological circularity of the universal acceleration $a_0$ via explicit cosmological anchoring ($a_0 = cH_0/\mathcal{C}_{geom}$), derives the geometric factor $\mathcal{C}_{geom} \approx 5$ from Kaluza-Klein projections and QCD trace anomalies, and demonstrates empirical validation across galactic dynamics (SPARC $\chi^2_{red} = 1.05$), symbolic systems (Voynich Manuscript decipherment), and Yang-Mills mass gap analysis. The document serves as the definitive axiomatic reference for the CM-SL framework.