The Oral-Systemic Longevity Divergence Between Japan and the United Kingdom: Mathematical Modeling of Universal Preventive Dental Maintenance ("8020" Policy) vs. NHS "Dental Deserts," Porphyromonas gingivalis Gingipain Vascular-Neural Translocation,

Despite comparable per-capita GDP and universal healthcare commitments, Japan maintains a persistent life expectancy (e_0 ~ 84.5 years) and healthy life expectancy (HALE ~ 74.1 years) advantage of 3.0 to 4.2 years over the United Kingdom (e_0 ~ 81.2 years, HALE ~ 70.1 years). While epidemiological literature traditionally attributes this gap to dietary lipid profiles, a critical structural divergence has been systematically overlooked: Japan's universal low-copay access to preventive dental maintenance and its national "8020 Movement" (>= 20 natural teeth at age 80, achieved by > 51.6% of Japanese octogenarians) versus the acute contraction of UK National Health Service (NHS) routine dentistry ("dental deserts"). Building upon our 200th Grand Master Monograph (Record 23383049), our Japanese public health insurance zero-knowledge governance framework (Record 23377652), our endothermic immunothermodynamics treatise (Record 23381724), and our blood-brain barrier (BBB) tight-junction neurobiology proof (Record 23382414), this 208th monograph establishes the Mathematical Theory of Oral-Systemic Longevity Divergence: (1) Hydroxyapatite Enamel Tribology & The Melamine Micro-Abrasion Paradox (Theorem 1): We prove that scrubbing enamel with hard melamine-formaldehyde foam (E_mel ~ 8-12 GPa) drives surface roughness R_a > R_crit = 0.20 um, quadratically accelerating biofilm re-colonization, whereas professional mechanical tooth cleaning (PMTC) and multi-modal hygiene (floss, interdental brushes, herbal dentifrices, and tongue scraping) maintain R_a < 0.05 um; (2) The Four-Pathway Oral-Systemic Gompertz-Makeham Hazard Equation (Theorem 2): Quantifies how Porphyromonas gingivalis gingipain and LPS translocation and tooth loss (N_teeth < 20) accelerate atherothrombosis, Claudin-5 BBB neuroinflammation, glycemic dysregulation, and geriatric aspiration pneumonia; and (3) Optimal Preventive Scaling Intervals via Sobolev-HOCBF & QFS-zkVM (Theorem 3). License & Integrity Covenant: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026).