Matrix divisors, Christoffel transformations and symmetric $d$-connections

Source abstract

The Christoffel transformation $w(x)\mapsto x^2w(x)$ relates elementary bundle modifications to gap probability recurrences. The moment matrix determines normalization and the splitting type. We define the source and target moduli problems by their local data. The modifications identify common stable loci and conjugate their point-addition maps. For Pearson ratios $d(-z-1)/d(z)$ with $°d=1,2$, we construct rational spectral coordinates and compute the induced transformation. For positive even weights with finite moments, reweighting configurations yields the transformed gap probability recurrence. Its coefficient is a rational function of the transformed spectral coordinates. A local formula applies outside these charts under the stated hypotheses.