Claim Verification: "Every elementary function that appears on a standard scientific calculator — including \(+\), \(\times\), \(\div\), exponentiation \(x^y\), \(\sin\), \(\cos\), \(\tan\), \(\sqrt{x}\), \(\log_{10}\), \(\pi\), \(e\), \(i\), and their compositions and inverses — can be realised as a finite binary tree of the operator \(\mathrm{eml}(a, b) = e^{a} - \ln b\) whose leaves are the constant \(1\) and the input variables. Each construction is verified to machine precision at multiple test points on its natural domain." — Proved

Automated fact-verification of the claim: "Every elementary function that appears on a standard scientific calculator — including \(+\), \(\times\), \(\div\), exponentiation \(x^y\), \(\sin\), \(\cos\), \(\tan\), \(\sqrt{x}\), \(\log_{10}\), \(\pi\), \(e\), \(i\), and their compositions and inverses — can be realised as a finite binary tree of the operator \(\mathrm{eml}(a, b) = e^{a} - \ln b\) whose leaves are the constant \(1\) and the input variables. Each construction is verified to machine precision at multiple test points on its natural domain." 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.