IndisputableMonolith.Cost.Ndim.Calibration
Calibration module supplies uniform weight definitions and normalization lemmas for N-dimensional reciprocal cost. It establishes that uniform weights summing to one equal 1/n each. Researchers extending Core aggregates to symmetric cases cite these results for normalization. The module structure consists of direct definitions plus algebraic verifications of sum and norm properties.
claimFor positive integer $n$, the uniform weight vector $w$ satisfies $w_i = 1/n$ for each $i$ whenever $w$ is uniform and $sum w_i = 1$.
background
The module sits inside the N-dimensional reciprocal cost construction, which lifts the scalar kernel through a weighted log aggregate as introduced in the Core module. It defines weightSum as the total mass of the weight vector, sqNorm as its squared Euclidean norm, and UniformWeights as the constant assignment across components. The supplied DOC_COMMENT records the central fact: if weights are uniform and sum to one, each weight is 1/n (for n > 0). Supporting lemmas such as weightSum_uniform and uniform_sqNorm_one verify these identities directly from the definitions.
proof idea
This is a definition module with supporting lemmas. UniformWeights is introduced as the constant 1/n vector. weightSum_uniform and sqNorm_uniform are one-line wrappers that substitute the constant value into the sum and norm expressions. The lemma uniform_weight_of_sum_one follows by solving the sum-equals-one equation under the uniformity assumption.
why it matters in Recognition Science
The module supplies the uniform-weight normalization required by the Symmetry module to establish permutation invariance of coefficient weights. It closes the calibration step that lets downstream arguments treat all components equivalently without extra hypotheses on the weight distribution.
scope and limits
- Does not derive the full N-dimensional reciprocal cost formula.
- Does not treat non-uniform weight vectors.
- Does not incorporate phi-ladder or Berry threshold relations.
- Does not provide numerical values for specific dimensions.