# Intrinsic perturbation scale for certified oracle objectives with epigraphic information

arXiv: https://arxiv.org/abs/2604.05678 · HTML: https://mlsanity.com/paper/2604.05678/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 6 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Abstract (arXiv)

We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption.