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  "summary": "The target announces estimates at the scale of eq:cEN2bnd, but supplies neither those estimates nor their derivation. The surrounding section concerns only q<Q_0, so the packet does not establish the full mean-square error bound. This is a missing-context and mapping limitation, not an identified mathematical contradiction. No external theorem is imported; later knowledge potentially present in model weights is not used as evidence under the 2012-05-24 cutoff.",
  "used_dependencies": [
    "eq:cEN2bnd"
  ],
  "missing_context": [
    "Definitions and integration domains of eq:IQ0K0 and eq:IQ0, together with the estimates announced immediately after the target.",
    "The Fourier/arc decomposition relating those integrals to the contribution of q<Q_0 to the mean-square error.",
    "Definitions and permitted sizes of Q_0, K_0, U, X, T and N, including parameter inequalities that yield some eta>0 and the required uniformity of constants.",
    "For a claim of the full eq:cEN2bnd rather than only this section's contributions, estimates for the other arc regimes and the argument combining all contributions."
  ],
  "findings": [
    {
      "kind": "unverified",
      "source_quote": "Finally, we prove the desired estimates of the strength \\eqref{eq:cEN2bnd}.",
      "explanation": "This is an announcement rather than a demonstrated inference. To verify it, the actual estimates must exhibit a positive power saving sufficient for the benchmark sum_{n<N}|E_N^U(n)|^2 << N T^{2(delta-1)} N^{-eta}. No such estimates occur in the supplied target or section setup."
    },
    {
      "kind": "map_correction",
      "source_quote": "the desired estimates of the strength \\eqref{eq:cEN2bnd}",
      "explanation": "The reference to eq:cEN2bnd identifies the desired conclusion or comparison scale, not an established premise from which the target follows. The frozen source-reference edge should not be interpreted as proof dependence; using the bound itself to justify this announcement would be circular."
    },
    {
      "kind": "context",
      "source_quote": "\\section{Minor Arcs I: Case $q<Q_{0}$}\\label{sec:qQ0}",
      "explanation": "The supplied scope covers one minor-arc regime. Estimates proved here could support the full error bound only after identifying this regime's contribution and combining it with bounds for the remaining regimes. That assembly is not supplied."
    },
    {
      "kind": "context",
      "source_quote": "For $\\foh N<n<N$ and admissible, $n\\in\\sA$, we have",
      "explanation": "These restrictions qualify the major-term lower bound in the stated theorem. They do not qualify its separate displayed mean-square bound. Any eventual verification of the target must therefore control the stated error sum, not merely admissible integers satisfying the major-term estimate."
    }
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      "label": "eq:cEN2bnd",
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      "source_quote": "the desired estimates of the strength \\eqref{eq:cEN2bnd}",
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      "label": "eq:IQ0K0",
      "role": "conditional",
      "source_quote": "our goal in this section being to bound \\eqref{eq:IQ0K0} and \\eqref{eq:IQ0}.",
      "explanation": "The section identifies this integral as an intended object of estimation. Its definition and bound are needed before its contribution to the announced saving can be checked."
    },
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      "label": "eq:IQ0",
      "role": "conditional",
      "source_quote": "our goal in this section being to bound \\eqref{eq:IQ0K0} and \\eqref{eq:IQ0}.",
      "explanation": "This is the second intended integral contribution. Neither its definition nor a quantitative bound is supplied, so it remains a proposed input rather than an established dependency."
    }
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