Mathematical Derivation of the Human Lifespan Limit

Working paper (not peer-reviewed).This paper proposes a vitality-based framework for interpreting age-specific mortality as an expression of an internal degradation process. Using a gamma-mixture vitality model, it fits the age-specific mortality curves of Japanese males (1898–2020; complete life tables of the Ministry of Health, Labour and Welfare, Japan). It also introduces a reparameterization of the model (the MD transformation) and reports an empirical relationship between life expectancy at birth and the logarithm of cumulative vitality.Changes from the previous version (March 2026):Corrected the sign of the shift R in the MD-transformation formulas (Eqs. 13–16).Recomputed life expectancy at birth directly from the life-table death probabilities. This corrected the value for 1952 and updated the regression of e₀ on ln G_c (now e₀ ≈ 8.04 ln G_c − 17.44, R² = 0.995; previously R² = 0.988).Removed the numerical extrapolation of a theoretical lifespan limit (about 137.7 years) and the related discussion. Estimating the critical value of the cumulative vitality is now listed as future work. The abstract and discussion were toned down accordingly.Added sections on limitations and future work, in-text citations, and the data source.Changed the title to "Toward a Physical Interpretation of Age-Specific Mortality via a Vitality-Based Degradation Model".About the author's background. The author is not a demographer and has not surveyed the demographic literature beyond the references listed in the paper. Some of the results may therefore not be new, or may overlap with existing work that is not cited here. About possible errors. This is a working paper and may still contain errors. Please read it with this in mind.