{
  "statement": "Prove H2: Let \\(K\\subset S^3\\) be a smooth oriented knot admitting an orientation-reversing diffeomorphism \\(h:S^3\\to S^3\\) with \\(h^2=\\operatorname{id}\\), \\(h(K)=K\\), and \\(h|_K\\) preserving orientation.\nThere exists \\(\\varphi\\in\\mathbb Z[w]\\) such that\n\\[\n\\nabla_K(z)=\\varphi(z^2)^2.\n\\]\nHere \\(\\nabla_K\\) is the Conway polynomial normalized by \\(\\nabla_{\\rm unknot}=1\\).",
  "starting_statement": null,
  "target_statement": "Let \\(K\\subset S^3\\) be a smooth oriented knot admitting an orientation-reversing diffeomorphism \\(h:S^3\\to S^3\\) with \\(h^2=\\operatorname{id}\\), \\(h(K)=K\\), and \\(h|_K\\) preserving orientation.\nThere exists \\(\\varphi\\in\\mathbb Z[w]\\) such that\n\\[\n\\nabla_K(z)=\\varphi(z^2)^2.\n\\]\nHere \\(\\nabla_K\\) is the Conway polynomial normalized by \\(\\nabla_{\\rm unknot}=1\\).",
  "case_id": "KT-1-H0-to-H2",
  "given_context": {
    "premise": null
  },
  "protocol": "single"
}