{
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  "problem_id": "vibemathed:virtual-surjection-conjecture",
  "title": "The Virtual Surjection Conjecture for Discrete Groups",
  "canonical_statement": "If a subgroup of a product of groups of type $F_k$ virtually surjects onto every $k$-tuple of factors, must it be of type $F_k$ itself? Yes, for discrete groups, and likewise for $FP_k$. The homological $n$-$(n+1)$-$(n+2)$ Conjecture follows for discrete groups when the common quotient is finitely presented, and that hypothesis cannot be dropped.",
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      "occurred_at": "2026-07-20T00:00:00.000Z",
      "title": "arXiv:2607.18079 - Virtual Surjection and the n-(n+1)-(n+2) Theorem for Discrete Groups",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "outcome": "The authors write that they developed the main arguments in the body of the paper in the course of interactions with GPT. The disclosure does not break the contribution down further.",
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          "label": "arXiv:2607.18079 - Virtual Surjection and the n-(n+1)-(n+2) Theorem for Discrete Groups",
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          "label": "arXiv:2607.18079 - Virtual Surjection and the n-(n+1)-(n+2) Theorem for Discrete Groups",
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      "kind": "primary-mathematical-source",
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    {
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    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
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  "generated_at": "2026-09-13T16:28:40.178Z"
}