This paper studies the Discovery subsequence of Rowland's sequence and reports computational evidence for a new long-run law. The main result is that, after a short startup phase, each observed Discovery index is given exactly by the predictive constant of the immediately preceding non-trivial event. The paper builds on three earlier papers which introduced the predictive jump framework, described the Discovery and Consolidation cycle, and examined universality across perturbed prime starts. Using that framework, the present paper computes the first 2500 non-trivial events for the prime initial conditions 7, 11, 13, 17, 19, 23, 29 and 31. The same pattern appears in every tested case. The preceding predictive constant matches the new Discovery index exactly. Every observed Discovery index is congruent to 2 mod 3. The median normalised gap into Discovery is 1/2, and the median ratio of consecutive Discovery indices is 2 for every tested start. There are only four exceptions to the immediate reset law, and all of them occur at the initial Discovery step of certain non-canonical starts. After that, the same long-run structure takes over. The paper is computational in method and conjectural in outlook. Its aim is to record the law clearly, show that it persists across several prime initial conditions, and state the natural questions that now need proof. The main point is that the Discovery events do not seem to be scattered in an irregular way. They follow a much more rigid pattern than one might expect from the recurrence alone.