mesopause_rung_upper
plain-language theorem explainer
The mesopause rung upper bound is fixed at the natural number 5 on the phi-ladder for atmospheric layer boundaries. Climate researchers assembling the Recognition Science layering certificate cite this assignment to place the mesopause between rungs 4 and 5. The definition is a direct numeric constant assignment.
Claim. The upper rung index for the mesopause layer boundary equals the natural number $5$.
background
The module treats Earth's atmospheric layers as boundaries on the phi-ladder, with altitude $z(k) = z_0 phi^k$ where $z_0 approx 7.5$ km is the recognition-base altitude set by J-cost minimum. Canonical rungs are assigned as tropopause at 0, stratopause at 3, mesopause in the interval from lower to upper bound, and thermosphere at 7. This supplies the concrete upper index 5 for the mesopause. Upstream rung definitions from mass and engineering modules establish the general pattern of assigning integer rungs to physical sectors.
proof idea
The declaration is a direct constant definition that assigns the value 5. No lemmas or tactics are invoked.
why it matters
This definition supplies the missing upper bound for the mesopause in the AtmosphericLayeringFromPhiLadderCert structure and the one-statement theorem that asserts the complete rung set together with strict ordering. It fills the Track P4 requirement by fixing the phi-ladder positions whose ratios reproduce observed altitude bands. The parent certificate uses the bound to guarantee tropopause < stratopause < mesopause < thermosphere.
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