C.29.1:10.2 - Why representative independence is constructive

When a summary merges cases, the key question is whether the desired answer is constant among those cases. This yields both a proof method and a method of discovery. Rewriting the query can construct its receiving form; a conflicting pair can identify the information the summary lacks.

An invertible coordinate change supports complete reconstruction of a source state within its domain. Many useful transfers need less. Requiring an inverse for available stock would defeat the purpose of the summary. Conversely, a map’s usefulness for one query does not establish that nothing has been lost. Query-specific preservation states the useful result without that stronger claim.

This also explains why changing the question can be a mathematical repair. The cost of a represented route may be undefined while the minimum over the represented routes is well-defined. That new minimum still needs its own composition and feasibility argument.