# Amphicheiral knot polynomials KT-1-H0-to-H6

## 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 H6: A knot \(K\subset S^3\) is called amphicheiral if an orientation-reversing homeomorphism of \(S^3\) maps \(K\) to itself; the homeomorphism may preserve or reverse the knot orientation.
For every amphicheiral knot \(K\), including the unknot, there exists \(f\in\mathbb Z[z]\) such that
\[
\nabla_K(z)\equiv f(z)f(-z)\pmod4.
\]
Here \(\nabla_K\) is the Conway polynomial normalized by \(\nabla_{\rm unknot}=1\), and 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.