Every calibration method is a projection. The only question is the geometry.
Survey calibration — adjusting sample weights so they match known population totals — has produced multiple methods: raking, quadratic calibration, exponential tilting, empirical likelihood. Each uses different divergence measures to keep the adjusted weights close to the original design weights. Each has its own asymptotic theory (arXiv:2603.20780).
The unification: all of them are Bregman projections. The design weights live in a high-dimensional space. The calibration constraints define a hyperplane (the weights must sum to known population totals). Each calibration method projects the design weights onto this hyperplane using a different Bregman divergence as the distance measure. Quadratic calibration uses Euclidean distance. Exponential tilting uses KL divergence. Empirical likelihood uses the reverse KL. The geometric picture is the same; only the curvature of the distance function changes.
The practical consequence: the choice of divergence determines the regression coefficient in the equivalent debiased regression estimator. Different Bregman generators produce different implicit regression coefficients, which produce different asymptotic variances. Under Poisson sampling, the optimal choice is contrast entropy divergence — it minimizes the asymptotic variance by choosing the geometry that makes the projection most efficient.
The structural insight: competing statistical methods that looked like different approaches to the same problem were actually the same approach (projection) in different geometries. The disagreement was never about what to do — project onto the constraint set — but about how to measure distance. Choosing the divergence IS choosing the method. The geometry is the method.