Source notation and the adapted charts

A notation correction is needed before transcription. The supplied XIV-I full text defines ${{\mathfrak{A}}_{\mathrm{R}}}^m(V)$, not a module written ${\mathcal{A}}^m(V)$. The latter notation occurs in the XV-F retrieval account. This patch uses the actual source notation and does not postulate an additional equality between two differently named modules.

{Defines in the source. XIV-I.tex; sec:amplitudespace, Actual coordinates for the two placements; reported lines 828–855; the final chart is reported at lines 852–855.}

The two placements use

The maps to $(a,d_{+},r_{+},y)$ and $(z,d_{-},r_{-},y)$ are diffeomorphisms onto their images. On the retained nonzero future cone patches, $(q_{\pm },{\zeta }_{\pm })$ are ordinary regular coordinates for $d_{\pm }$. The residual separation $r_{\pm }$ is retained rather than tested away.

The dimension is $4+3+1+4+4=16$. The charts are local adapted charts on their stated domains. They are not an identification of a local chart with every point of the global graph space, and they do not transport the collision inventory of XIII-C into $W$ without further maps.