Divine v144 Source Corpus

9.7 Exact theorem for MRD >= 2

Divine v144 Corpus · Section 182 of 317

Assume x0=0 and the recursive equation x_k = r_k * product(1-x_j for j<k). If MRD=k>=2, then every earlier x_j is 0. Because the trigger product for each earlier anti-layer j was therefore 1, x_j=0 implies r_j=0. For the first active layer k, x_k=1 implies r_k=1.

MRD=k>=2 iff (under x0=0 and first-active semantics) r1=...=r_(k-1)=0 and r_k=1

This yields the decisive formal result: a repeatedly high MRD is repeated pressure on the Antilobe monitoring system itself. It is not, by itself, repeated evidence that the original function phi has a deeper positive mismatch than another task with MRD=1.

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