Manuscript XV-B@2 · XV-B.tex · section · 4d3f12e8

Full branch content and the characteristic locus

The retained target and the available inherited formulas › Full branch content and the characteristic locus · lines 1686–1726

XV-B@2#eq:sum, XV-B@2#eq:supported, XV-B@2#eq:N

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The retained internal sum is

K_{ret} = K_{47} + K_{5} + K_{6} + K_{8} + K_{9}, K_{5} = K_{5}^{[a]} + K_{5}^{[z]} .

Here $K_{47}$ groups $B_{4} + B_{7}$ , while both placements of $K_{5}$ belong to $B_{5}$ . Thus five named summands represent the six original branches $B_{4}, \dots, B_{9}$ . The supported sector is only

K_{supp} = K_{6} + K_{8} + K_{9} .

It contains neither $K_{47}$ nor either $K_{5}$ placement CheungXIVI,CheungXVA,CheungXVE.

The supplied XIV-I record retains attachment variables

W = Ω_{A} \times Ω_{B} \times Ω_{Z} \times Ω_{Y}, w = (a, b, z, y),

on an open patch of $R^{16}$ , and identifies the characteristic stratum by

N = {a = z, y = a + α ℓ_{n}, b = a + β ℓ_{n}, 0 < α < β, ℓ_{n} = (1, n), n \in S^{2}} .

This is inherited geometric data CheungXIVI.

Displayed formulas in this passage

XV-B@2#eq:sum · line 1689
$K_{ret} = K_{47} + K_{5} + K_{6} + K_{8} + K_{9}, K_{5} = K_{5}^{[a]} + K_{5}^{[z]} .$
XV-B@2#eq:supported · line 1698
$K_{supp} = K_{6} + K_{8} + K_{9} .$
XV-B@2#eq:N · line 1712
$N = {a = z, y = a + α ℓ_{n}, b = a + β ℓ_{n}, 0 < α < β, ℓ_{n} = (1, n), n \in S^{2}} .$
unlabeled · line 1706
$W = Ω_{A} \times Ω_{B} \times Ω_{Z} \times Ω_{Y}, w = (a, b, z, y),$

Full branch content and the characteristic locus

Displayed formulas in this passage

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