{
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    "The statement immediately following the target, including all hypotheses and its label, if any.",
    "The proof associated with that statement and any preceding results it invokes. The supplied section setup ends at line 904, whereas the target begins at line 1106.",
    "If used in the missing statement or proof, the definitions of Cartan involutions and R_k(L), and the intervening distance-graph definitions and results."
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      "label": "Section setup: sufficient finite-image criterion",
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      "source_quote": "In this section we derive a sufficient condition for a subgroup $\\Delta$ of $\\textrm{O}(L)$ which is generated by Cartan involutions, to have finite image in $\\textrm{O}(L)/R_k(L)$ with $k=2$ or $4$.",
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