{
  "abstract": "Jaramillo Puentes et al. define a Grothendieck--Witt-valued count by floor diagrams for rational curves in smooth toric del Pezzo surfaces with simple point conditions and quadratic double point conditions. We prove that, with the quadratic parameters kept in a fixed order, the count does not depend on which adjacent pairs form the double conditions. Given two merge configurations, we factor the difference between their floor counts as \\[ ΔN=C\\prod_{j=1}^s(\\ang{d_j}-\\ang{1}). \\] The coefficient~$C$ can be lifted to a free rank-three ring, independently of the field. Writing this lift as $n_1\\ang{1}+n_2\\ang{2}+μh$, invariance of the real broccoli count yields $n_2=-n_1$. The twin-tree parity condition enters through a residual calculation, which shows that $n_1$ is even. The relation $2(\\ang{1}-\\ang{2})=0$ now makes the wall-crossing vanish. The floor count is therefore independent of merge positions over each field to which the correspondence theorem applies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.09107",
  "author_total": 1,
  "authors": [
    {
      "name": "Yanis Hedjem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/62xgqe3tb50mz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.09107",
  "fulltext_url": null,
  "id": "62xgqe3tb50mz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.09107",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7160964387",
  "pdf_url": "https://arxiv.org/pdf/2605.09107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/62xgqe3tb50mz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2605.09107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.09107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Merge-position invariance in quadratically enriched tropical floor diagrams",
  "title_text": "Merge-position invariance in quadratically enriched tropical floor diagrams",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/62xgqe3tb50mz",
  "venue": "arXiv",
  "versions": []
}