ClimatePhasePoint
plain-language theorem explainer
ClimatePhasePoint supplies the type of an N-component real vector as the state space for climate phase dynamics. Recognition Science climate analyses cite it when constructing the J-cost functional and proving the vacuum achieves the global minimum. The declaration is a direct type abbreviation with no proof obligations or additional structure.
Claim. For $N$ a natural number, a climate phase point is a function $s :$ Fin $N$ $→$ ℝ.
background
The Climate.AttractorStructure module formalizes the Recognition Science claim that the climate manifold possesses an attractor on which the long-term trajectory spends most time and whose J-cost is the global minimum of the energy/entropy field. ClimatePhasePoint defines the underlying state space as an idealized real vector with N components. Upstream imports supply the J-cost from Cost.Jcost (derived from the multiplicative recognizer comparator) together with non-negativity results from ObserverForcing and PhiForcingDerived.
proof idea
One-line type abbreviation with no computational content or proof obligations.
why it matters
ClimatePhasePoint is the domain type for the master certificate AttractorStructureCert and the supporting theorems climateJCost, climateJCost_nonneg and vacuum_is_global_minimum. It supplies the concrete state space needed to state that the zero vector realizes the global J-cost minimum, consistent with the Recognition Science prediction that attractors occupy the lowest-cost configuration on the climate field.
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