lean_workbook_plus_31927

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Let $a=\frac{x}{y}, b=\frac{y}{z}, c=\frac{z}{x}$ , then clearing the denominator, we get \n\n $3\sum_{cyc}x^8z^4+6\sum_{cyc}x^6y^4z^2+6\sum_{cyc}x^5y^4z^3\geq 5\sum_{cyc}x^7y^2z^3+5\sum_{cyc}x^6yz^5+5\sum_{cyc}x^5y^3z^4$ \n

Why this node was retired

The posted statement is

theorem lean_workbook_plus_31927 : ∀ x y z : ℝ, (3 * (x^8 * z^4 + y^8 * x^4 + z^8 * y^4) + 6 * (x^6 * y^4 * z^2 + x^4 * y^6 * z^2 + x^2 * y^6 * z^4) + 6 * (x^5 * y^4 * z^3 + x^4 * y^5 * z^3 + x^3 * y^5 * z^4) ≥ 5 * (x^7 * y^2 * z^3 + x^6 * y * z^5 + x^5 * y^3 * z^4) + 5 * (x^6 * y^5 * z^2 + x^4 * y^6 * z^2 + x^2 * y^6 * z^4) + 5 * (x^5 * y^3 * z^4 + x^4 * y^5 * z^3 + x^3 * y^5 * z^4))   :=  by sorry

The cyclic sums were expanded incorrectly, including noncyclic terms and a monomial of the wrong total degree.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore each cyclic orbit from the source exponent triple, all of degree12, and recover positive nonzero x,y,z for the substitution; verify the resulting homogeneous inequality.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.