{
  "reviewed_on": "2026-10-01",
  "claim_searched": "For positive integer {1,K} Gasoline inputs, position-first exact-LP iterative rounding has IR <= initial LP + K - 2 and exact original-index worst-case ratio 2 - 2/K.",
  "conclusion": "No verified earlier resolution found in the searches performed. Priority is not established.",
  "sources": [
    {
      "url": "https://perso.limos.fr/~lulorieau/docs/thesis/Master_Thesis.pdf#page=27",
      "role": "Primary target",
      "finding": "Conjecture 3.1.1, printed page 21, concerns two-size iterative rounding. Proposition 3.1.4 concerns a different greedy algorithm."
    },
    {
      "url": "https://www.researchgate.net/publication/365161753_Approximation_Algorithms_for_the_Stock_Size_Problem_and_the_Gasoline_Problem",
      "role": "Original algorithm",
      "finding": "Rajkovic (2022), Algorithm 3.4.1, describes sequential LP look-ahead. Its broader 1D conjecture is not settled by this two-size result."
    },
    {
      "url": "https://arxiv.org/html/2601.16849",
      "role": "Recent primary paper",
      "finding": "Nikoleit et al. (2026), section 2.2.4, describes the unrestricted 1D guarantee as unknown. Its refutation concerns dimensions at least two."
    },
    {
      "url": "https://github.com/lumi-a/funsearch/tree/main/funsearch/gasoline",
      "role": "Research implementation",
      "finding": "The repository implements Gasoline iterative rounding using Gurobi. It does not supply a proof of the exact two-size claim in the inspected material."
    }
  ],
  "queries": [
    "\"gasoline\" \"iterative rounding\" \"K-2\"",
    "\"gasoline\" \"2-2/K\"",
    "site:github.com \"gasoline\" \"iterative rounding\" proof",
    "site:x.com \"gasoline\" \"iterative rounding\"",
    "\"Lorieau\" \"Conjecture 3.1.1\"",
    "\"gasoline problem\" \"two sizes\" \"rounding\"",
    "site:github.com \"gasoline\" \"SlotOrdered\"",
    "site:x.com \"gasoline problem\" approximation"
  ],
  "limitations": [
    "Several exact queries produced irrelevant or no useful matches; these are weak negative evidence.",
    "GitHub and X were queried through a public web index; this does not exhaust their content.",
    "A previous VibeMathed snapshot contained 755 entries and no matching terms; the snapshot is not a live exhaustive publication registry.",
    "AI-generated secondary summaries that misstate the 1D guarantee were excluded as evidence of a proof."
  ]
}