Layer-Edit Coverage Beyond Sampling: From Candidates to Selected Answers

Can layer-execution edits supply correct answers that ordinary sampling misses, and can a selector recover them? We study skipping, repetition, and substitutions that combine the two in frozen language models. Our grid contains approximately 14.2 million correctness evaluations over 1,261 paths, five mathematical difficulty strata, and four prompt conditions on Qwen2.5-3B-Instruct, with a Qwen3-4B comparison. Across three model–difficulty groups of 565 questions each, the exhaustive 1,260-edit pool covers 15–56 questions missed by all 57 unedited-model samples. Yet question-held-out path ranking and direct 57-path voting correctly answer only 0–3 of these additional questions and trail 57-sample self-consistency by 23–57 correct answers per group. Shortlists exclude many available answers, and voting rarely recovers those retained. The edit grid also has reproducible structure: average substitution performance tracks constituent effects, while 45–51% of discovered substitution events with failed constituents succeed again on the rewrite prompt. Tested pre-generation rankers show no improvement over a structural prior, despite informative post-generation correctness signals. These findings separate additional candidate coverage from the ability to select a correct answer. They use original-checker scores and previously inspected questions and outputs; unequal coverage pools and unmeasured end-to-end costs preclude an efficiency claim.