{
  "abstract": "Lipshitz and Sarkar asked in an ICM 2018 question whether their homotopy-theoretic refinement of Khovanov homology can detect mirror reflection when ordinary integral Khovanov homology cannot. We give an affirmative answer by presenting a prime knot whose integral Khovanov homology agrees with that of its mirror in every bidegree, including torsion, and yet over $\\mathbb{F}_2$, the second Steenrod square has rank one for the knot and rank zero for its mirror in a specified bidegree. We also give a composite example. The construction, search and computations are done with the help of {\\it chat-GTP 5.6 sol Pro} combing over the {\\it Regina Census} of knots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00976",
  "author_total": 1,
  "authors": [
    {
      "name": "Yang-Hui He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwbmeh4ffwfha.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00976",
  "fulltext_url": null,
  "id": "fwbmeh4ffwfha",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00976",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7206186716",
  "pdf_url": "https://arxiv.org/pdf/2609.00976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fwbmeh4ffwfha.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:34Z",
      "native_id": "2609.00976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Lipshitz-Sarkar refines mirrors more than Khovanov",
  "title_text": "Lipshitz-Sarkar refines mirrors more than Khovanov",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/fwbmeh4ffwfha",
  "venue": "arXiv",
  "versions": []
}