{
  "date": "2026-10-20",
  "origin": "User-supplied external Web GPT Pro argument; model identity unverified",
  "source_edition": "25-page author-hosted manuscript, Lemma 3.6 pp.20-21",
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  "statement_status": "refuted in explicitly stated author-edition/literal-selection scope",
  "headline_status": "unresolved by this review",
  "repair_status": "not checked or completed",
  "paid_generation_calls": 0,
  "original_rejected_sol_status": "invalid_assessment; unchanged; not promoted to accepted review",
  "selection_caveat": "Family satisfies literal zero-offset short intervals, not necessarily every alternate pigeonhole-selected subinterval.",
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    "origin": "User-relayed Nikolay Bogachev Astra response; identity/history unverified",
    "adopted": "Valuation-layer exposition; finite-field versus lifting distinction; mixed-sign equivalence",
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