atmosphericLayeringFromPhiLadderCert
plain-language theorem explainer
The declaration inhabits the master certificate structure for atmospheric layering on the phi-ladder. Climate modelers working within Recognition Science would cite it to certify the rung assignments for tropopause, stratopause, and thermosphere boundaries. The definition assembles the eight clauses by reflexivity on the rung equalities and direct reference to the pre-established ordering and ratio theorems.
Claim. The master certificate states that the tropopause rung equals 0, the stratopause rung equals 3, the thermosphere rung equals 7, the rungs satisfy strict ordering tropopause < stratopause < mesopause lower < thermosphere, altitudes scale geometrically as $z_{k+1} = z_k · ϕ$, the stratopause-to-tropopause ratio lies in the interval (4.22, 4.24), the thermosphere-to-tropopause ratio is positive, and the thermosphere lies above the stratopause.
background
In the Recognition Science framework, atmospheric layers arise from J-cost minima on the radiative-convective lattice, placing boundaries at integer rungs on the phi-ladder where altitude at rung k is z_0 times phi to the k. The module defines tropopause_rung as 0, stratopause_rung as 3, thermosphere_rung as 7, with mesopause between 4 and 5. Upstream, the altitude_geometric theorem establishes that adjacent rungs differ by exactly phi, while rung_strict_ordering proves the sequence tropopause < stratopause < mesopause < thermosphere. The stratopause_tropopause_ratio_band theorem confirms the ratio phi cubed falls inside the empirical band (3.5, 4.5).
proof idea
The definition constructs the certificate instance by assigning reflexivity to the rung equality fields and referencing the sibling theorems for the remaining clauses: rung_strict_ordering for the ordering, altitude_geometric for the scaling, stratopause_tropopause_ratio_band for the ratio band, and the two thermosphere ratio theorems for the positive and above-stratopause conditions.
why it matters
This definition closes the structural theorem for Track P4 by inhabiting the AtmosphericLayeringFromPhiLadderCert structure. It supplies the certified rung assignments that underpin the one-statement summary theorem in the module, linking the phi-ladder to observed atmospheric boundaries with ratios phi^3 and phi^7. The construction relies on the phi self-similarity from the forcing chain and confirms the layering without additional axioms.
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