Plain English (1): The declaration aggregate computes the weighted geometric mean of an n-component positive real vector x using weights α. Formally, it is the exponential of the dot product of α with the componentwise natural logarithm of x.
Role in Recognition Science (2): It lifts the scalar J-cost (reciprocal-symmetric cost function) to n dimensions by reducing a vector input to a single effective positive scalar that can be fed into Jcost. This supports multi-component recognition costs while preserving key properties such as positivity and reciprocity under inversion.
Reading the formal statement (3): noncomputable def aggregate {n : ℕ} (α x : Vec n) : ℝ := Real.exp (dot α (logVec x)). Here Vec n abbreviates Fin n → ℝ (n-tuples of reals), dot is the weighted sum ∑ α_i * t_i, and logVec applies Real.log to each component. The result is always a positive real.
Visible dependencies and certificates (4): Depends on the same-module definitions dot and logVec. Certificates include aggregate_pos (positivity) and JcostN_eq_Jcost_aggregate (direct use as input to scalar Jcost). Further supporting results in the module are JcostN_eq_cosh_logsum and JcostN_reciprocal.
What the declaration does not prove (5): It supplies only the definition and immediate algebraic consequences; it does not prove uniqueness of this aggregation operator, its derivation from a deeper functional equation, or any specific physical constants or forcing results.