Optional original-rod lapse attachment

This appendix gives a self-contained classical composition interface. It does not replace the conical metric by a polynomial lapse or claim to reproduce every native input of XX-A or Em02-E. Those manuscripts supply their own frozen background, clock, rods, and quantum admission contracts CheungXXA,CheungEm02E.

Throughout the appendix set $c=1$, and use $\epsilon$ for a perturbation parameter. It is neither a schedule tick nor a clock reading.