amocTimescale_yr
plain-language theorem explainer
The definition assigns the characteristic AMOC timescale the value phi raised to the eighth power in years. Oceanographers comparing Recognition Science predictions to RAPID array records on multi-decadal variability would cite this value. The assignment is a direct power expression using the self-similar fixed point phi.
Claim. The characteristic timescale of the Atlantic Meridional Overturning Circulation is given by $phi^8$ years, where $phi$ is the golden ratio fixed point.
background
The module interprets thermohaline circulation through the J-cost function applied to buoyancy-force ratios between warm saline inflow and cold freshwater deepening. The Atlantic Meridional Overturning Circulation is treated as the thermohaline conveyor belt whose strength registers as a J-cost reading. The local setting states that the characteristic collapse timescale under freshwater forcing equals phi to the eighth power times a one-year baseline, yielding a multi-decadal interval consistent with RAPID array 2004-2023 observations.
proof idea
The declaration is a direct definition that sets the real number equal to phi raised to the natural number 8.
why it matters
This supplies the numerical timescale referenced by the positivity theorem amocTimescale_pos, the interval theorem amocTimescale_in_band, and the certification structure ThermohalineCert. It realizes the module prediction of an approximately 47-year AMOC variability scale and connects to the eight-tick octave period in the upstream forcing chain. The broader claim is falsified by any observed variability timescale lying outside the 20-to-100-year window.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.