Claim Verification: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\). There exists a finite binary tree consisting solely of eml operations, whose 9 leaves are drawn from \(\{1, x, y\}\), such that the tree evaluates exactly to \(x \times y\). The tree has K = 17 tokens (8 eml operations and 9 leaves), and the identity holds for all complex \(x\) and \(y\) (in the algebraic setting where \(\ln \circ \exp\) is the identity)." — Proved

Automated fact-verification of the claim: "The binary operator eml is defined by the expression \(\text{eml}(a, b) = \exp(a) - \ln(b)\). There exists a finite binary tree consisting solely of eml operations, whose 9 leaves are drawn from \(\{1, x, y\}\), such that the tree evaluates exactly to \(x \times y\). The tree has K = 17 tokens (8 eml operations and 9 leaves), and the identity holds for all complex \(x\) and \(y\) (in the algebraic setting where \(\ln \circ \exp\) is the identity)." 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.