Working on generalizing v_t
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@ -65,7 +65,9 @@ Using the same argument as in $\gIJ$ yields
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\end{equation*}
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\end{equation*}
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Setting $T_3 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 0}\kMapParam{\wVec}$, $T_4 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 1}\kMapParam{\wVec}$ gives an exact calculation for each term given a fixed $\buck$:
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Setting $T_3 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 0}\kMapParam{\wVec}$, $T_4 = \sum\limits_{\wVec \in \pw \st \sketchPolarParam{\wVec} = 1}\kMapParam{\wVec}$ gives an exact calculation for each term given a fixed $\buck$:
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\begin{equation*}
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\begin{equation*}
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T_3 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(0)}, \kMapParam{\wVec} = \gVt{(k) }1\}\rightarrow T_3 \in [0, 2^{\numTup - rank(\matrixH')}]
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T_3 = \gVt{\sum_{\substack{k \in \{\wVec \st \\
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\matrixH \cdot \wVec = \buck^{(0)},\\
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\kMapParam{\wVec} = k\}}}k} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(0)}, \kMapParam{\wVec} = \gVt{(k) }1\}\rightarrow T_3 \in [0, 2^{\numTup - rank(\matrixH')}]
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\end{equation*}
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\end{equation*}
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\begin{equation*}
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\begin{equation*}
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T_4 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(1)}, \kMapParam{\wVec} = \gVt{(k) 1}\}\rightarrow T_4 \in [0, 2^{\numTup - rank(\matrixH')}]
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T_4 = \gVt{(k \cdot)} | \{\wVec \st \matrixH \cdot \wVec = \buck^{(1)}, \kMapParam{\wVec} = \gVt{(k) 1}\}\rightarrow T_4 \in [0, 2^{\numTup - rank(\matrixH')}]
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