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<th>Model Name</th>

<th>Formula (Simplified)</th>

<th>Description</th>

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<td><strong>Integrated Damage Model (proposed)</strong></td>

<td><code>ba(t) = P(t) · (1/N_r) · ∫[f_resp(u) / f(m,e)] du</code></td>

<td>Refines Escala’s theory by integrating respiration cycles over time, adjusted for species-specific maintenance (f) and life-phase acceleration (P). Can explain aging inflections and outliers like bats. Mechanistic and time-continuous.</td>

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<td><strong>Escala’s Respiration-Cycle Law</strong></td>

<td><code>t_life ≈ N_r / f_resp</code></td>

<td>Proposes organisms undergo a nearly fixed number (~10⁸) of respiration cycles per lifetime. Supported across ~300 species from microbes to mammals. Unifies metabolism and lifespan.</td>

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<td><strong>Entropy Generation Model (Silva & Annamalai)</strong></td>

<td><code>∫σ(t) dt ≈ constant</code></td>

<td>Connects aging to total entropy generated over lifetime. Predicts human lifespan from heat dissipation per kg. Conceptually links thermodynamics and aging.</td>

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<td><strong>Reliability Theory of Aging</strong></td>

<td><code>Vitality(t) = V₀ - k·t + noise</code></td>

<td>Models aging as loss of systemic redundancy. Predicts rising mortality even when components have fixed failure rates. Supports late-life mortality plateaus.</td>

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<td><strong>Kleiber’s Law</strong></td>

<td><code>B ∝ M^3/4</code></td>

<td>Basal metabolic rate scales as body mass to the 3/4 power. Foundational to metabolic and lifespan scaling laws across all taxa.</td>

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<td><strong>Lifespan–Mass Allometry</strong></td>

<td><code>t_life ∝ M^1/4</code></td>

<td>Empirical observation that lifespan increases with body mass. Follows from Kleiber’s law and constant energy-per-mass assumptions.</td>

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<td><strong>Rate-of-Living Hypothesis (Rubner)</strong></td>

<td><code>E_life/M ≈ constant</code></td>

<td>Suggests that organisms expend the same amount of energy per gram over a lifetime. Holds across mammals but breaks down across classes (e.g. birds).</td>

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<td><strong>Gompertz–Makeham Law</strong></td>

<td><code>μ(t) = α·e^β·t + λ</code></td>

<td>Classical model of mortality where death risk grows exponentially with age and includes a constant background risk. Very good empirical fit but not mechanistic.</td>

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<td><strong>Gompertz Law</strong></td>

<td><code>μ(t) = R₀·e^b·t</code></td>

<td>Simpler form of Gompertz–Makeham. Predicts exponential rise in mortality with age. Used widely in demography and aging studies.</td>

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<td><strong>Weibull Mortality Law</strong></td>

<td><code>μ(t) = k·λ·t^k-1</code></td>

<td>Predicts mortality using a power law. Used in reliability theory and some species. Less common for biological aging.</td>

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<td>DNA Methylation Clock (Horvath)</td>

<td><code>DNAmAge = β₀ + Σ(β_i·CpG_i)</code></td>

<td>Uses weighted DNA methylation levels at CpG sites to predict biological age. Highly accurate.</td>

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<td>Phenotypic Age (Levine)</td>

<td><code>PhenoAge = f(albumin, WBC, etc.)</code></td>

<td>Combines standard blood biomarkers to predict mortality risk and biological age.</td>

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