Worked connection for MMP-REPLACE-AND-COUPLE

Two components contribute distinct amounts u and v to a total, in the same units and over the same interval. MMP.18 establishes that the required combination is u+v and that neither contribution already contains the other. MMP.17 selects surrogates for these two amounts on the input region being used.

For the present input, suppose their estimates are 0.42 and 0.48, with supported absolute error bounds 0.03 and 0.04. The resulting total is in [0.83,0.97]. It is below a threshold of 1 throughout that interval. No independence assumption is needed for this worst-case sum bound. Errors measured only on a few training cases would not, by themselves, supply the stipulated bounds.

Now lower the threshold to 0.94. The interval no longer settles whether the total is below it. If obtaining the second component from its source model is worthwhile, and that calculation returns 0.46 with absolute error at most 0.001, retaining the first surrogate gives [0.849,0.911]. That narrower combination settles the new question without replacing both surrogates.

A different question can instead change what the interface must carry. A time of threshold crossing needs information about evolution within the interval; two final amounts do not supply it. MMP.18 then returns the missing temporal contribution, and MMP.17 changes the response that a replacement must preserve. More accurate final amounts alone would answer the wrong question.