B.5.MPC:4.6 - Keep joint requirements and alternative routes distinguishable

Recover dependencies by asking, for each needed result, “What results and conditions make this operation possible, and what other operation could supply the same receiving need?” Keep the answer with the actual derivation, diagram or working explanation. A short case may need only a sentence; a shared design may need an explicit dependency diagram.

An AND dependency means that contributions are needed together for the stated inference. The robot’s distance per motor increment uses the effective wheel radius, transmission ratio and increments per motor revolution together. Replacing any one can change the command.

An OR alternative is a different sufficient way to obtain the result needed by the receiving use. A proved upper bound and an exact computation can be alternatives for deciding whether a limit can be exceeded. Each route retains its own assumptions. Two different approximations do not become sufficient alternatives merely because both return a number.

For a conditional physical consequence, one useful small rendering is:

applicable physical account
AND mathematical interpretation
AND (sufficient direct consequence OR sufficient interpreted computation)
→ consequence for the physical question

The computational branch additionally depends on a procedure and an adequate realization for any claimed execution. A claim about observed physical behavior adds the observations and measurement relation it consumes. These are different claims and can end the work at different places.

Keep a shared premise attached to every contribution that consumes it. Both an analytical calculation and a numerical simulation can depend on the same no-slip assumption. Switching between them does not remove that dependency. Conversely, when an upper bound already answers the decision, the exact optimizer need not be obtained.

Enter a ready result at the place where it is used. Recover its inputs and conditions backward, then continue forward with its consequence. When a missing input blocks one route, compare another sufficient route using the available inputs. Do not combine an output from one route with the assumptions of another without establishing their compatibility.

A failed connection can send the inquiry back to its physical account, mathematical construction, notation, procedure, realization or question. Use B.5.MPC.R to locate the incompatibility, construct a sufficient repair and carry it through the affected contributions. If several causes remain compatible with the observations, obtain a discriminating contribution or use a sufficient conditional result. B.5.RA supplies argument recovery and B.5.RR supplies general reasoning revision; C.29.1, C.29.2 and C.29.3 supply the transfer, formulation and realization methods respectively. Retain unaffected contributions whose conditions and meanings still hold.