{
  "abstract": "We show that a sequence of simplicial polytopes approximating a smooth convex body has primitive Betti numbers diverging from the upper bound given by the g-theorem. This complements a result of Adiprasito-Nevo-Samper, who proved the corresponding divergence from the lower bound. The proof uses a new lower bound for the size of the shadow of a set of monomials.",
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  "article_type": null,
  "arxiv": "2609.24790",
  "author_total": 1,
  "authors": [
    {
      "name": "Joel Hakavuori"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bt1wmkw570b7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24790",
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  "id": "bt1wmkw570b7y",
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  "landing_url": "https://hal.science/hal-05758926v1",
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  "pdf_url": "https://hal.science/hal-05758926/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bt1wmkw570b7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
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      "url": "https://arxiv.org/abs/2609.24790"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
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  "title": "The g-theorem in smooth approximation",
  "title_text": "The g-theorem in smooth approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/bt1wmkw570b7y",
  "venue": "HAL",
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