Adapted affine charts and framed peripheral holonomy

audit. For $\mathcal{A}=(L,a)$, the affine product convention is

Writing ${\mathcal{A}}_0=(L_0,a_0)$, the core word is

where $J$ in the expression for $K$ denotes its linear part. Full affine conjugation gives

No time translation is discarded.

Because $J^4=I$, a matrix product alone cannot distinguish a primitive meridian from a loop with winding $1+4m$, nor can it distinguish zero winding from winding four. The winding mark is indispensable.

The packet consists of a fixed geometric identifier, $\mu =\pi /2$, the worldsheet $\mathcal{W}$, reference rest vector $u_{\ast }=c^{-1}{\partial }_T$, particle-cell label $P$, and reference framing. It is constant. The incoming face normal has transverse components $(3,2,2)$; the outgoing ones have components $(5/4,3/4,0)$ or $(5/4,0,3/4)$, with axial component zero. Their rapidities relative to $u_{\ast }$ are respectively $\mathrm{arcosh}3$ and $\log 2$. Changing face-relative rapidity does not move the worldsheet.