proof-readability

> **Author:** Moran Koren, Ben-Gurion University of the Negev (korenmor@bgu.ac.il). Part of the [Theorist Toolbox](https://github.com/morankor/theorist-toolbox). # Proof readability > **Relationship to `proofread`:** `proofread` is a *report-only*, whole-paper prose checker (11 categories, never edits source). `proof-readability` *edits in place*, is proof-specific, runs only after a correctness gate, and holds a content-preservation invariant `proofread` does not. Audit a whole paper's prose → `proofread`; edit the exposition of a verified proof → `proof-readability`. Edit verified proofs so a reader can follow them without reconstructing steps, chasing broken references, or decoding notation. This skill runs *after* a proof has been written (e.g., by `math-proof`) and *after* its correctness has been verified (by `domain-reviewer`, `lean-check`, or the user). It is an exposition pass, not a proving pass. ## Position in the pipeline ``` math-proof → verification (domain-reviewer / lean-check / user) → proof-readability (correctness) (acceptance) (exposition only) ``` **The prime invariant: never change the mathematics.** Every edit must be content-preserving — reorder, signpost, expand, annotate, rename consistently, fix references and typos. Do not strengthen, weaken, or "simplify" any claim; do not replace an argument with a different one; do not silently fill what you believe is a gap with new mathematics. **If you find an actua...