Explanation of sqNorm in IndisputableMonolith.Cost.Ndim.Calibration

(1) In plain English, the declaration computes the squared Euclidean norm of an n-dimensional vector α by taking its dot product with itself. This yields the sum of the squares of the vector's components.

(2) In Recognition Science, sqNorm supports N-dimensional calibration of uniform weights in cost structures. It enables characterization of weight-vector magnitudes, which feeds into theorems relating uniformity, summation, and curvature constraints relevant to recognition-cost minimization.

(3) The formal statement reads:

def sqNorm {n : ℕ} (α : Vec n) : ℝ := dot α α

For any natural number n and vector α of type Vec n, sqNorm α is defined to be the result of the dot product operation applied to α and itself. Vec n denotes an n-component vector (typically a function from Fin n to ℝ), and dot is the imported dot-product primitive.

(4) Visible dependencies: the definition relies on dot from the Core module (imported at the top of the file). In the supplied source it appears in sqNorm_uniform and uniform_sqNorm_one, which derive explicit values under the UniformWeights predicate.

(5) The declaration itself proves nothing; it is a pure definition. All properties (e.g., the relation sqNorm α = n·a² for uniform α) are established only in the separate theorems listed above. It does not address physical constants, forcing chains, or Recognition Science interpretations beyond the local calibration context.