IndisputableMonolith.Climate.AttractorStructure
The module supplies the core objects for embedding climate systems into Recognition Science, defining phase-space points as real vectors and their associated J-costs. Researchers modeling climate attractors or minima via the RS framework would reference it for the idealized setup. It is a definition module that establishes ClimatePhasePoint, climateJCost, non-negativity, and vacuum-minimum properties.
claimA climate phase point is an element of the real vector space $X = {x : x_i = x_i(x) , i=1..N}$ equipped with the J-cost $J(x)$ satisfying the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$. The vacuum state realizes the global minimum $J=0$.
background
The module imports the RS time quantum from Constants, where τ₀ = 1 tick, and the J-cost machinery from Cost. ClimatePhasePoint is introduced as an idealized real-valued state vector with N components in phase space. Sibling definitions include climateJCost (the cost functional on these points), climateJCost_nonneg (non-negativity), vacuum_climate_zero_cost (vacuum realizes J=0), and vacuum_is_global_minimum (vacuum is the global minimizer).
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
It supplies the phase-space and cost objects required for the AttractorStructureCert certificate that follows in the same module. The construction applies the J-cost and Recognition Composition Law to climate vectors, placing the climate attractor question inside the RS forcing chain (T5 J-uniqueness onward).
scope and limits
- Does not incorporate empirical climate time series or forcing data.
- Does not prove existence or stability of any specific attractor.
- Does not model explicit time evolution or differential equations.
- Does not address spatial discretization beyond the abstract N-vector.