Conical product, signature, and rods

The completion adds the singular locus

It is a two-dimensional worldsheet. Fixing $z$ gives one worldline; the full defect is not a worldline. No smooth metric or ordinary pointwise Einstein tensor at the apex is used.

The geometry and its interpretation agree with the prescribed branch of I-B CheungIB. The conical and lapse comparisons in VIII-B and Em02-E remain separate source records CheungVIIIB,CheungEm02E.