IndisputableMonolith.Cost.Ndim.Symmetry
Module establishes that coefficients in the N-dimensional cost are invariant under index permutations. Researchers formalizing symmetric cost structures in Recognition Science would cite it. The argument applies uniform weight relations from the imported Calibration module to deduce the invariance.
claimCoefficients satisfy $c_i = c_{i'}$ for any reordering of indices, i.e., $c$ is fixed by every permutation of the index set.
background
The module resides in the Cost.Ndim namespace and imports the Calibration module, whose doc-comment describes calibration relations for uniform weights. It introduces the symmetry property that coefficients remain unchanged under index permutations, enforcing dimensional equivalence in the cost function. This builds directly on the uniform-weight setting to guarantee ordering independence.
proof idea
The module organizes its content around CoeffPermutationInvariant together with the supporting results coeff_perm_invariant_of_uniform and uniform_of_coeff_perm_invariant. It applies the calibration relations for uniform weights to show that any index permutation leaves the coefficients fixed.
why it matters in Recognition Science
The module supplies the symmetry requirement for N-dimensional cost constructions in the Recognition Science framework. It ensures index independence needed for consistent J-cost application across dimensions and closes a structural gap in the uniform calibration development, though no downstream uses appear in the current graph.
scope and limits
- Does not treat non-uniform weight assignments.
- Does not compute explicit coefficient values.
- Does not connect to the phi-ladder or physical constants.
- Does not extend the invariance claim beyond the N-dimensional case.