Aging & Senescence · §5

Reservoir depletion: the telomere clock

Each reservoir — telomere/TERT, senescence/CDKN2A, apoptosis/TP53, longevity/FOXO3 — has finite capacity proportional to γ^1.5. Deeper-γ wells hold more and last longer, but every reservoir depletes to zero. TERT (γ 1.5539) lasts 89 steps and TP53 (γ 1.4298) lasts 78; telomere attrition is reservoir exhaustion, not a privileged clock.

The dwell γ^1.5 sets a finite reservoir capacity for each node. Depletion time increases monotonically with γ, yet all four reservoirs reach zero, so the replicative limit is a generic consequence of a finite well rather than a dedicated counting mechanism.

Finite wells

A switch that runs for a dwell γ^1.5 draws on a finite reservoir. The deeper the well (larger γ), the more it holds and the longer it lasts — but the reservoir is finite, so it empties. This is the substrate's version of the replicative limit.

Finite reservoirs, capacity ≈ γ^1.5. Deeper-γ wells hold more and last longer, but all deplete to zero — telomere attrition is reservoir exhaustion, not a privileged clock.
Reservoir	γ	Capacity	Steps to empty
apoptosis (TP53)	1.4298	1.554	78
senescence (CDKN2A)	1.4424	1.575	79
telomere (TERT)	1.5539	1.761	89
longevity (FOXO3)	1.5942	1.830	92

Telomere attrition is not special

The telomere/TERT reservoir is the longest-lived of the four because its γ is high, but it depletes by the same rule as the others. Depletion time rises with γ across all four wells. The telomere clock is therefore reservoir exhaustion, not a privileged counting device — consistent with the cross-species result that TERT γ is not a longevity switch (§9).

The finiteness and the γ-ordering are graded [V]; the absolute attrition rate in years is [O].