Proposition: K 47 has no presentation space in the record

No direct sheet displays or names a presentation space, a reconstruction rule, or a coefficient class for $K_{47}$. XIV-I's module is constructed for the two $K_5$ placements II2; XIV-J's normal form is for $K_{\mathrm{supp}}$ Jreference; XIV-I's precomposition sum (eq:retained) writes $K_{47}$ directly with $L$ II2. On neither chart $w_{\pm }$ does $K_{47}$ have the form of the rule (P5), and it is not supported on $S_{\partial }$: it contains the product $R(d_{+})R(d_{+}+r_{+})$, carried by $\{b-a\in \partial J^{+}\}\cap \{b-z\in \partial J^{+}\}$, a set of codimension two not contained in $\{a=z\}$.

Proof. The first two sentences are the record. For the last: by (eq:L), $L^{\mu ,J}(b,z)$ contains $\partial R(b-z)$ and $L^{\nu ,I}(b,a)$ contains $\partial R(b-a)$, with $b-z=d_{+}+r_{+}$ in the chart $w_{+}$; the support of the pullback of $R\otimes R$ under $(a,b,z)\mapsto (b-z,b-a)$ is the stated set, which contains points with $a\ne z$ (e.g.\ $b=0$, $a$ and $z$ distinct points of the past cone); this is (P6).