MMP.14:5.3 - A failed numerical prediction need not require a new subject model

A normalized quantity is modeled by (u’(t)=-u(t)), (u(0)=1). A record at (t=1) is (0.370), with an established absolute recording error at most (0.005). A forward-Euler computation with step (h=1) predicts 0.

Before replacing the decay law, compare the numerical result with the model’s exact consequence (u(1)=e^{-1}\approx0.367879). Euler steps (h=1/2) and (h=1/4) give (0.25) and (0.316406); the sequence of approximations exposes a material computational error. The exact value lies in the observed admissible interval ([0.365,0.375]). Here the repair belongs to CMP.8, while this observation supplies no reason to change the decay relation.

That interval overlap establishes compatibility for this record under the error bound, not the correctness of the decay model at every time. If a relevant observation instead excludes the accurately computed consequence, the subject relation or observation account becomes live again. Numerically precise evaluation and adequate subject prediction remain separate achievements.