Explanation of weightSum in IndisputableMonolith.Cost.Ndim.Calibration
(1) In plain English, the declaration defines a function that takes a vector α of n real numbers and returns the sum of its components. It is a simple aggregation operation over the vector entries.
(2) In Recognition Science this matters because the surrounding module develops calibration relations for uniform weights in N-dimensional settings. The sum appears in theorems that relate total weight to per-component values when weights are constant across dimensions, supporting structural claims about cost functions and recognition structures without introducing free parameters.
(3) The formal statement is read as follows: the definition is polymorphic in the natural number n, accepts an argument α of type Vec n (a vector indexed by Fin n), and computes the summation ∑ i : Fin n, α i using the scoped BigOperators notation. In standard mathematical notation this is simply the sum of the n entries of α.
(4) Visible dependencies and certificates in the supplied source include the import of IndisputableMonolith.Cost.Ndim.Core (supplying Vec and dot) and the theorems weightSum_uniform, sqNorm_uniform, uniform_weight_of_sum_one, and uniform_sqNorm_one. These theorems directly invoke weightSum to derive consequences for uniform vectors whose sum equals 1 or whose squared norm equals 1.
(5) This declaration does not prove any properties; it is a pure definition. All claims about uniform weights, normalization, or relations to squared norms are established in the separate theorems listed above. It also does not define Vec itself or supply any Recognition Science interpretation beyond the local calibration context.