IndisputableMonolith.Geophysics.MantelConvectionFromJCost
This module derives mantle convection parameters from the Recognition Science J-cost function. Geophysicists modeling planetary interiors would cite the convection modes and Rayleigh numbers computed on the phi-ladder. It supplies type definitions for modes together with a certification object that validates the J-cost origin of the convection thresholds. The module structure is definitional, importing only the base time quantum and building sibling objects for mode counting and ratio calculations.
claimThe module introduces the type $ConvectionMode$, the count $convectionModeCount$, the function $rayleighAtRung(r)$ returning the Rayleigh number at phi-ladder rung $r$, the ratio $rayleighRatio$, and the certificate $MantelConvectionCert$ asserting that the convection arises from J-cost minimization.
background
Recognition Science starts from the J-cost $J(x) = (x + x^{-1})/2 - 1$ and the phi fixed point on the self-similar ladder. The module imports the RS time quantum from Constants, where the fundamental tick satisfies $τ_0 = 1$. It places convection in the geophysical domain by defining discrete modes indexed by rung and evaluating the Rayleigh number that controls fluid instability thresholds. The local setting assumes the eight-tick octave and three spatial dimensions already fixed by the upstream forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the geophysical application layer that translates J-uniqueness and the phi-ladder into mantle convection observables. It prepares the certification object for any parent theorem that would embed these Rayleigh ratios into larger planetary structure results, although no downstream uses are declared yet. It closes the step from abstract RS constants to concrete geophysics without introducing new hypotheses.
scope and limits
- Does not simulate time-dependent flow fields.
- Does not insert Earth-specific viscosity or density profiles.
- Does not prove linear stability of the derived modes.
- Does not address core-mantle boundary conditions or heat flux.