Claim Verification: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\) (where exp is the exponential function and ln is the principal branch of the natural logarithm). For every real \(x > 0\), the nested expression \(\text{eml}(1, \text{eml}(\text{eml}(1, x), 1))\) equals the natural logarithm \(\ln(x)\)." — Proved

Automated fact-verification of the claim: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\) (where exp is the exponential function and ln is the principal branch of the natural logarithm). For every real \(x > 0\), the nested expression \(\text{eml}(1, \text{eml}(\text{eml}(1, x), 1))\) equals the natural logarithm \(\ln(x)\)." Verdict: PROVED Files proof.py — Re-runnable Python verification script proof.md — Structured proof report proof_audit.md — Full verification audit trail proof_narrative.md — Plain-language summary proof.json — Machine-readable structured data provenance.json — W3C PROV-JSON provenance chain proof.ipynb — Jupyter Notebook (interactive re-verification) ro-crate-metadata.json — RO-Crate 1.1 research object manifest Generated by Proof Engine v1.18.0.