buoyancyCost
plain-language theorem explainer
buoyancyCost computes the J-cost of the ratio between warm saline buoyancy and cold freshwater buoyancy. Oceanographers modeling AMOC strength cite this as the core cost measure for thermohaline flow. The definition is realized as a direct one-line application of the Jcost function to the input ratio.
Claim. $J(w/c)$ where $w$ is warm saline buoyancy, $c$ is cold freshwater buoyancy, and $J$ denotes the J-cost function.
background
The Oceanography module models the Atlantic Meridional Overturning Circulation as a J-cost reading on the buoyancy ratio between warm saline inflow and cold freshwater layers. Jcost is imported from the Cost module and satisfies the Recognition Composition Law together with nonnegativity and vanishing at unit ratio. The module document states that this cost supplies the local measure for the AMOC bistable potential $V(Ψ) = -a Ψ² + b Ψ⁴$ and the characteristic timescale $φ^8$ years.
proof idea
One-line definition that applies the Jcost function directly to the ratio of the two buoyancy inputs.
why it matters
This definition supplies the cost measure used by buoyancyCost_at_equilibrium to show vanishing cost at equal buoyancies and by buoyancyCost_nonneg to establish nonnegativity. It is referenced inside the ThermohalineCert structure that certifies the full AMOC model. The construction embeds J-uniqueness (T5) into an oceanographic setting and supports the eight-tick octave scaling for the predicted 47-year variability timescale.
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