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Manuscript IX-C-ST@1 · IX-C-ST.tex · section · 892f50c4

Both first stages and the placement ledger

Both first stages and the placement ledger · lines 1061–1085

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This retains IX-C's reverse normalization IXC ({:reverse}).

Define actual-functional subspaces

B = {B_{f} : f \in T}, W = {W_{g} : g \in T},

L_{4} = span {B_{f} W_{g}}, L_{2} = span {Q_{f, g}}, R_{4} = span {W_{g} B_{f^{'}}}, R_{2} = span {Q^{R}_{g, f^{'}}} .

Let

L = L_{4} \oplus L_{2}, R = R_{4} \oplus R_{2} .

The sums are direct by total field degree. The actual spaces $L_{4}, R_{4}$ coincide, but their ordered roles differ.

Displayed formulas in this passage

unlabeled · line 1067
$B = {B_{f} : f \in T}, W = {W_{g} : g \in T},$
unlabeled · line 1071
$L_{4} = span {B_{f} W_{g}}, L_{2} = span {Q_{f, g}}, R_{4} = span {W_{g} B_{f^{'}}}, R_{2} = span {Q^{R}_{g, f^{'}}} .$
unlabeled · line 1078
$L = L_{4} \oplus L_{2}, R = R_{4} \oplus R_{2} .$

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