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  "summary": "The transition back to the Introduction's setup is supported by the supplied context. However, the announced Levelt theorem is not included, so its hypotheses, conclusion, and role as the starting point cannot be checked. This is a packet limitation, not an identified mathematical defect. The paragraph supports an organizational transition, not the headline classification or thinness claims.",
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    "If a substantive Beukers\u2013Heckman result is intended as a premise for this transition, its exact theorem or section and the relevant dated source version."
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    },
    {
      "kind": "unverified",
      "source_quote": "The starting point for studying $H(\\alpha,\\beta)$ is the following theorem of Levelt.",
      "explanation": "Neither the theorem statement nor its citation or proof is supplied. Consequently, this packet does not permit verification of the claimed starting point or any subsequent inference from it. No theorem-level defect follows from that omission."
    },
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      "source_quote": "We begin by reviewing \\cite{bh} which forms the basis of our analysis.",
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      "source_quote": "We begin by reviewing \\cite{bh} which forms the basis of our analysis.",
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      "label": "Levelt theorem announced immediately after the target",
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      "source_quote": "The starting point for studying $H(\\alpha,\\beta)$ is the following theorem of Levelt.",
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