attractorStructureCert
plain-language theorem explainer
The declaration constructs a concrete instance of the AttractorStructureCert that bundles non-negativity of the climate J-cost, zero cost at the vacuum state, and global minimality of that vacuum. Climate dynamics researchers applying Recognition Science would cite it to confirm the attractor as the equilibrium point on the phase manifold. It is a direct structure constructor that packages three upstream theorems without further reduction.
Claim. The attractor certificate asserts that for every dimension $N$ and every climate phase point $s$, the J-cost satisfies $0 ≤ J(s)$, $J(0) = 0$, and $J(0) ≤ J(s)$.
background
The climate module treats phase space as ClimatePhasePoint N, finite-dimensional vectors over the reals. The J-cost on these points is obtained by summing the elementary J-costs supplied by the Cost module. Module documentation states that the climate manifold possesses an attractor whose J-cost is the global minimum, in line with the Recognition Science forcing chain that identifies J as the deviation measure from equilibrium.
proof idea
The definition builds the certificate by direct field assignment: cost_nonneg receives climateJCost_nonneg, vacuum_zero receives vacuum_climate_zero_cost, and vacuum_minimum receives vacuum_is_global_minimum. No tactics or reductions occur beyond the structure constructor itself.
why it matters
This certificate supplies the master formal statement for the climate attractor in Recognition Science, verifying that the vacuum state achieves the global J-cost minimum as required by the framework's cost non-negativity and J-uniqueness properties. It closes the local Element 84 development; no downstream theorems yet depend on it.
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