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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 1166–1184

IX-C-ST@1#eq:twolab

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At this stage the desired two-edge placements are only labels:

G_{12, 23}^{lab} G_{12, 13}^{lab} G_{13, 23}^{lab} = 2 ⟨ V_{3} K (x, y) K (x^{'}, y), \partial_{t} ϕ (x) \partial_{t^{'}} ϕ (x^{'}) ⟩, = 2 ⟨ V_{3} K (x, y) S_{0 ν} (x, x^{'}), h_{00} (y) w^{ν} (x^{'}) ⟩, = 2 ⟨ V_{3} S_{μ 0} (x, x^{'}) K (x^{'}, y), w^{μ} (x) h_{00} (y) ⟩,

where $V_{3} = f \otimes g \otimes f^{'}$ .

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IX-C-ST@1#eq:twolab · line 1169
$G_{12, 23}^{lab} G_{12, 13}^{lab} G_{13, 23}^{lab} = 2 ⟨ V_{3} K (x, y) K (x^{'}, y), \partial_{t} ϕ (x) \partial_{t^{'}} ϕ (x^{'}) ⟩, = 2 ⟨ V_{3} K (x, y) S_{0 ν} (x, x^{'}), h_{00} (y) w^{ν} (x^{'}) ⟩, = 2 ⟨ V_{3} S_{μ 0} (x, x^{'}) K (x^{'}, y), w^{μ} (x) h_{00} (y) ⟩,$

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