Target and source discipline

The motivating target is Cheung's original-rod lapse in Em02-E CheungEm02E. The supplied record distinguishes:

It also distinguishes those rods from modified rods.

The available excerpts do not reproduce every native background constant, rod formula, domain, and normalization needed for a verbatim reconstruction of Em02-E. Consequently, this paper freezes an explicit original-rod variant in Sections sec:background–sec:lapse. Every equation used in its proofs is displayed here. An exact identification with Em02-E would require a separate comparison of all defining data; it is not asserted.

The variant retains the geometric original-rod rule: harmonic spatial coordinates on the actual matter-clock slices, with asymptotically fixed spatial labels. It does not insert a lapse weight into that rule.

The five quantum audit slots of XIX-D are used as a checklist XIXD. No unprinted predecessor proof, catalogue claim, reported artifact, or rebuild result is a theorem premise. Published mathematical frameworks are cited for context and for the precise analytic results identified where used.