Explanation of UniformWeights in IndisputableMonolith.Cost.Ndim.Calibration
(1) In plain English, the declaration defines a property of an n-dimensional vector α: it holds precisely when there exists a single real number a such that every component of α equals a. This means all entries are identical (uniform).
(2) In Recognition Science this property supports calibration relations for N-dimensional cost structures. The supplied module uses it to derive simplified formulas for vector sums and squared norms under the uniformity assumption, which streamlines analysis of weighted recognition costs in higher-dimensional settings.
(3) The formal statement is read as follows: UniformWeights is a predicate (Prop) taking a natural number n and a vector α of length n. It asserts the existence of a real a such that for every index i in the finite set of n indices, the i-th component of α equals a. In standard mathematical notation this is ∃ a ∈ ℝ. ∀ i ∈ {0,…,n−1}, α_i = a.
(4) Visible dependencies and certificates: the definition is stated directly after importing IndisputableMonolith.Cost.Ndim.Core (Vec type). The same module immediately supplies the theorems weightSum_uniform, sqNorm_uniform, uniform_weight_of_sum_one and uniform_sqNorm_one. No sorry, axiom or external certificates appear in the module.
(5) The declaration itself does not prove existence of uniform vectors, does not derive any RS constants or forcing theorems, and does not connect to modules outside this file (e.g., Foundation, Unification or RecognitionForcing).