# Amphicheiral knot polynomials KT-1-H0-to-H5

## Setting

You are solving a mathematical proof problem. Establish the stated target result. Check the hypotheses, logical steps, and quantifiers in your argument as a careful referee would. End with a clear proof, or identify any gap you cannot close.

## Problem

Prove H5: Let \(K\subset S^3\) be an oriented knot admitting a finite-order orientation-reversing diffeomorphism of \(S^3\) that preserves the orientation of \(K\). Let \(\nabla_K(z)\in\mathbb Z[z]\) be its Conway polynomial, normalized by \(\nabla_{\rm unknot}=1\).
There exists \(f\in\mathbb Z[z]\) such that
\[
\nabla_K(z)\equiv f(z)f(-z)\pmod4,
\]
where the congruence is coefficientwise.

Write the full proof to answer.md in the workspace root. Write the statements and hypotheses of any external results you cite to cited_results.md; if none are used, write 'No external results cited.' Identify any gap you cannot close.