IndisputableMonolith.Cost.Ndim.Symmetry
The Cost.Ndim.Symmetry module asserts that coefficients in the N-dimensional cost model are unchanged under index permutations. Workers on uniform-weight calibration in the Recognition framework cite it to guarantee reordering consistency. The module delivers this via three sibling declarations that define the invariance property and prove its equivalence to uniformity.
claimFor coefficients $c_i$ in the N-dimensional cost, $c_{\sigma(i)}=c_i$ for every permutation $\sigma$ of the indices (equivalently, the coefficient vector is uniform).
background
The module sits inside the Cost domain and imports the Calibration module whose doc-comment states it supplies 'Calibration relations for uniform weights'. In Recognition Science the cost function on the phi-ladder uses a vector of coefficients whose values must be independent of index ordering once uniformity is imposed. The three sibling declarations introduce CoeffPermutationInvariant as the formal statement of this symmetry and the two implication theorems that relate it to the uniform case.
proof idea
This is a definition module, no proofs. It introduces the CoeffPermutationInvariant predicate and records the two one-line equivalences coeff_perm_invariant_of_uniform and uniform_of_coeff_perm_invariant.
why it matters in Recognition Science
The module supplies the symmetry step required by the uniform-weight calibration relations imported from Calibration. It therefore anchors the cost model before any downstream use in higher-dimensional forcing or mass-ladder constructions.
scope and limits
- Does not address non-uniform coefficient vectors.
- Does not derive the numerical values of the coefficients.
- Does not extend to non-permutation symmetries.
- Does not connect directly to the J-cost or defectDist functions.