Sealed Audit Compression Progress Shown to Resist Goodhart's Law in AI Reward Design

A preprint posted to arXiv proposes and proves that a specific formulation of compression-progress reward, called 'signed compression progress on a sealed audit,' is resistant to Goodhart-style exploitation by AI agents. The core insight is that cumulative intrinsic reward telescopes exactly to the improvement in a fixed, sealed audit loss, meaning an agent cannot accumulate reward indefinitely while true performance stagnates. For finite audit panels, the guarantee holds with a quantified false-positive budget bounded by the uniform audit deviation of the model class, and crucially this bound is horizon-free. The authors identify precise failure modes — including clipped progress, self-scored streams, high-capacity models on reusable panels, and neural model classes with vacuous deviation bounds — that break the guarantee. The theoretical results are mechanized in Lean 4 using Mathlib, and experiments on ARC-TGI generators confirm that finite-audit deviation scales approximately as n^{-0.527} and that signed progress resists common reward-hacking strategies such as clip-farming and noisy-TV curiosity. The work positions signed compression progress as a principled, accountable signal for genuine learning rather than a gameable proxy.