B.5.MPC:2 - Problem

Individually correct contributions can fail to support a joint result. A physical model may concern accumulated wheel rotation, a mathematical variable may represent orientation modulo one turn, and a program may accept an absolute target. Each account can be consistent while their composition loses the displacement that the user requested.

The same difficulty occurs without numerical approximation. A graph can correctly encode a chosen contact list, and a program can correctly colour that graph, while the contact list omits an actual mesh. A count invariant can be proved while the proposed admission procedure creates two independent stocks of cards. Improving the proof or the program leaves the missing physical correspondence untouched.

A simple division into “physics first, mathematics second, implementation last” also fails when a later contribution exposes an earlier omission. The interface may require initial state that the first model discarded. A measurement may distinguish fewer cases than the calculation assumes. A mathematical obstruction may make further computation unnecessary. The practitioner needs a way to construct the dependencies, use an available contribution at its point of need, and return a failure to the contribution that can change it.