Manuscript XVI-L@1 · XVI-L.tex · section · 35081099

Kernel inventory

L.3 Products, power counting, and kernel inventory › Kernel inventory · lines 750–782

table (by sector and declared order). “Unord.” counts distinct unordered numerical labels ${a + p, b + q}$ contributed as placements by that sector's ordered budget (placement occurrence, not a claim that the assembled coefficient is nonzero). Sectors may overlap on some labels, but not on all: the order- $0$ label ${0, 0}$ ( $S^{2}$ ) arises in $C_{2}$ and does not arise in $M_{2}$ or $J_{3}$ . The graph uses a subfamily of the $255$ -label admissible inventory $Λ_{adm}$ ; cancellation-aware support $Λ_{graph}$ is recorded by two_edge_full.py.

Sector	$N$	Unord.	Homog.	$sd \leq$	Ordered $(a, b; p, q)$	Placement
$C_{2}$	$0$	$1$	$- 4$	$4$	$1 \times 1$	occurs
$C_{2}$	$1$	$4$	$- 5$	$5$		occurs
$C_{2}$	$2$	$20$	$- 6$	$6$	total ord.\ $45$	occurs
$C_{2}$	$\leq 2$	$25$		$6$	$=$ XVI-K $N$	$= V_{K}$
$M_{2}$	$1$	$4$	$- 5$	$5$		occurs
$M_{2}$	$2$	$20$	$- 6$	$6$		occurs
$M_{2}$	$3$	$60$	$- 7$	$7$	total ord.\ $360$	occurs
$M_{2}$	$\leq 3$	$84$		$7$	$8 \times 45$
$J_{3}$	$2$	$20$	$- 6$	$6$		occurs
$J_{3}$	$3$	$60$	$- 7$	$7$		occurs
$J_{3}$	$4$	$170$	$- 8$	$8$	total ord.\ $1620$	occurs
$J_{3}$	$\leq 4$	$250$		$8$	$36 \times 45$
$Λ_{adm}$	$\leq 4$	$255$		$8$	$2025$ ordered	admissible

The $C_{2}$ block is identical to XVI-K's inventory (types $S \cdot S$ , $S \cdot \partial S$ , $\partial S \cdot \partial S$ , $S \cdot \partial\partial S$ ; $1 + 4 + 10 + 10 = 25$ ). New admissible types include $S \cdot \partial^{3} S$ , $S \cdot \partial^{4} S$ , $\partial S \cdot \partial^{2} S$ , $\partial S \cdot \partial^{3} S$ , $\partial^{2} S \cdot \partial^{2} S$ .

Kernel inventory

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