Establish tightness theory for more general loss functions

Establish the tightness theory of Occupancy-based Quantile Risk Control for more general loss functions that do not necessarily satisfy the ideal continuity and density conditions required by the current convergence analysis.

Background

The paper proves that the OQRC risk-control bound converges to the optimal bound at rate $\mathcal{O}_p(n^{-1/2})$ under conditions including a density bounded away from zero. The appendix explains that the false-negative proportion used in the experiments is not continuous and does not satisfy this lower-density condition.

A synthetic experiment illustrates convergence under a more regular loss construction, but the authors do not prove the corresponding tightness result for broader classes of loss functions. Extending the tightness theory to such losses remains unresolved.