flt5_probe_norm_comp_v1

⚠️ 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.

Test norm computation for a+ζb

Why this node was retired

The posted statement is

theorem flt5_probe_norm_comp_v1 (a b : ℤ) (ζ : CyclotomicField 5 ℚ) (hζ : IsPrimitiveRoot ζ 5) : Algebra.norm ℤ (algebraMap ℤ (CyclotomicField 5 ℚ) a + ζ * algebraMap ℤ (CyclotomicField 5 ℚ) b) = a ^ 4 - a ^ 3 * b + a ^ 2 * b ^ 2 - a * b ^ 3 + b ^ 4 := by sorry

The norm is taken over ℤ on the entire cyclotomic field, which has no finite ℤ-module basis.

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

Proposed corrected statement

For ζ a primitive fifth root in K=ℚ(ζ₅), state Algebra.norm ℚ ((a:K)+ζ*(b:K))=(a⁴−a³b+a²b²−ab³+b⁴:ℚ). Alternatively take the norm over ℤ of the finite free ring of integers ℤ[ζ], not of the whole field.

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.