The declaration aggregate_pos asserts that the n-dimensional aggregate is strictly positive.
(1) In plain English: for any dimension n and any real vectors α and x of length n, the value aggregate(α, x) = exp(∑ α_i · log(x_i)) is always greater than zero.
(2) In Recognition Science this matters because aggregate lifts the scalar J-cost kernel to vector inputs while preserving positivity; the surrounding module then uses this to define JcostN and prove JcostN_nonneg, ensuring the multi-component cost remains a valid non-negative ledger quantity.
(3) The formal statement theorem aggregate_pos {n : ℕ} (α x : Vec n) : 0 < aggregate α x is read as: “For every natural number n and every pair of functions α, x : Fin n → ℝ, the inequality 0 < aggregate α x holds.” The proof simply unfolds the definition of aggregate and invokes the library fact that the exponential is positive.
(4) Visible dependencies inside the supplied source are the definitions aggregate, dot, and logVec in the same module IndisputableMonolith.Cost.Ndim.Core; the proof relies only on Real.exp_pos and the local unfolding. No external axioms appear.
(5) The declaration does not prove reciprocity (JcostN_reciprocal), zero-cost characterization (JcostN_eq_zero_iff), or any link to physical constants or forcing-chain theorems; those appear in other modules or are left open.