Manuscript XV-C@1 · XV-C.tex · section · 5afd124d

The six original branches

Frozen branch and placement ledger › The six original branches · lines 245–311

XV-C@1#eq:retained

The retained kernel is

K_{ret} = K_{47} + K_{5} + K_{6} + K_{8} + K_{9}, K_{supp} = K_{6} + K_{8} + K_{9} .

The first sum contains six original branches $B_{4}, \dots, B_{9}$ : $K_{47}$ groups $B_{4} + B_{7}$ . The $K_{5}$ branch has two retained placements.

Write

K_{5} = K_{5}^{[a]} + K_{5}^{[z]} .

These superscripts label placements, not additional original branches.

Original branch content	Retained block	Placement record	Available information
$B_{4} + B_{7}$	$K_{47}$	One grouped block	Internal expression supplied; characteristic cross-line composition not supplied.
$B_{5}$	$K_{5}^{[a]} + K_{5}^{[z]}$	Both placements retained	Exact internal expressions supplied; neither full characteristic cross-line operation supplied.
$B_{6}$	$K_{6}$	One block	Internal expression supplied; included in the supported reference.
$B_{8}$	$K_{8}$	One block	Exact internal map reported; explicit map not reproduced in the supplied excerpts.
$B_{9}$	$K_{9}$	One block	Exact internal map reported; explicit map not reproduced in the supplied excerpts.

The operational list

K_{47}, K_{5}^{[a]}, K_{5}^{[z]}, K_{6}, K_{8}, K_{9}

has six entries, but it is not a list of six independently labelled original branches: the first entry groups two originals and the next two entries belong to the same original.

This ledger checks the supplied decomposition. It does not verify unsupplied tensor coefficients in a proposed joint operation.

Displayed formulas in this passage

XV-C@1#eq:retained · line 248
$K_{ret} = K_{47} + K_{5} + K_{6} + K_{8} + K_{9}, K_{supp} = K_{6} + K_{8} + K_{9} .$
unlabeled · line 259
$K_{5} = K_{5}^{[a]} + K_{5}^{[z]} .$
unlabeled · line 302
$K_{47}, K_{5}^{[a]}, K_{5}^{[z]}, K_{6}, K_{8}, K_{9}$