### When a total preserves the full comparison

Combining several components into one total can hide exactly the information that distinguishes two chronological paths. There is a precise test for when this simplification is harmless. If every component in a combined block receives the same conversion factor, we may add first and convert afterward, or convert each component and then add. The two procedures agree for every possible set of component values.

If the factors differ inside a block, this universal agreement fails. A particular source total may still agree because its component weights make the differences cancel. That is a property of the supplied arrangement, not permission to forget its internal boundary.

The 483 carrier makes the distinction concrete. Keeping 402.5 fixed and expanding the final 80.5 by E gives 402.5|87.5. Applying P uniformly gives 408⅓|81⅔. Both total 490, but their two components differ by −35/6 and +35/6. The total erases a real internal displacement.

This is why a family comparison should retain intermediate boundaries as well as endpoints. An equal total answers a narrower question than an equal path. The same discipline helps relate regular, cumulative and Rounded objects: first specify the components and measurement, then state which internal distinctions the chosen total preserves and which it loses.

*Sources:* File63 Scale-Neutral 480/483/490 Carrier §1.3; c532_c631/journal.json C609: inherited internal-defect example; 490d_Unification_Research_Strategy_v0_2_20260906.md §§3.1–3.2; §5E.

*Research record:* C993, C994, C997, C1007.