Manuscript synopsis
A spurious counterexample induces opposite labels on the exact prefix and suffix witnesses at a selected cut. Refitting a label distribution in each observation cell gives Arimoto conditional Renyi entropy under exponential tilt of log loss. At unit temperature, an exact integer comparator ranks binary predicates by the sum of the geometric means of prefix and suffix mass in each child. A separating predicate extends to the least layered certificate at the cut, and refinement by its truth values excludes every descendant of the chosen path.
The nine-page, double-column PDF includes proofs of the risk identity, a weak-advantage contraction bound, a parity obstruction to strictly positive greedy gain, finite termination, and the higher-topos completion and blocking results. The companion includes a Lean 4 proof of integer score bounds, zero-score separation, and completion checking, plus a separate executable finite verifier and a deterministic comparison. The general entropy and higher-topos arguments appear as mathematical proofs in the manuscript. The work was developed with AI assistance.
Attachments
- entropy-guided-cegar.pdf
- entropy-cegar-reproducibility.zip