stratopause_rung
plain-language theorem explainer
Stratopause rung is fixed at 3 on the phi-altitude ladder for atmospheric boundaries. Researchers deriving closed-form layer ratios from Recognition Science J-cost minima cite this constant when assembling the master certificate. The definition is a direct assignment of the natural number 3 with no further computation.
Claim. The stratopause rung is the natural number 3, marking a canonical 3-rung jump from the tropopause at rung 0 on the phi-ladder where altitude scales as $z(k)=z_0 phi^k$.
background
Atmospheric layer boundaries are located at integer rungs on the phi-ladder, with altitude given by $z(k)=z_0 phi^k$ and $z_0$ the recognition-base altitude set by J-cost minimum on radiative balance. The module documentation states that Earth's canonical layers arise from J-cost minima of the radiative-convective recognition lattice, with tropopause at rung 0 and stratopause at rung 3, so that the stratopause-to-tropopause ratio equals phi^3 which lies inside the empirical band (3.5, 4.5). Upstream rung definitions assign integers to particle classes, sectors, or fermions in mass and spectroscopy modules, but the atmospheric version is specialized to this fixed ladder position.
proof idea
The declaration is a direct definition that assigns the constant value 3. No lemmas or tactics are applied beyond the primitive assignment.
why it matters
This supplies the stratopause rung required by AtmosphericLayeringFromPhiLadderCert and atmospheric_layering_one_statement. It completes the rung assignments for Track P4 of the structural theorem, linking the phi-ladder to the self-similar fixed point and eight-tick octave in the Recognition Science framework. The assignment enables exact ratio predictions such as phi^3 without additional hypotheses.
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