For an even integer E, Pmin(E) is defined as the smallest prime p for which E-p is also prime. This paper studies Pmin as the first Goldbach synchronization encountered from the small-prime boundary. A longitudinal BOUSSOLE series contains 100 studied scales of E = 10^N + 2 and reaches E = 10^4000 + 2. A separate frozenpredictive model was tested on 2000 new even integers E = 10^N + c, with N = 20,40,...,400 and c = 1002,1004,...,1200. The empirical scale D(E) = log(E) log log(E) was used with Q50 = 0.258D, Q90 = 0.790D and Q95 = 1.088D. Observedcoverage was 51.5%, 79.4% and 85.4%, respectively. The median Pmin/D was 0.24893, close to the frozen median coefficient, while the upper tail was much heavier than predicted. BOUSSOLE therefore uses prediction as a searchcompass, not as a stopping rule. Finally, Goldbach is reformulated as the finiteness of Pmin(E), and the future analytical target is uniform positivity of a boundary counting function R(E,H). The computational evidence is not presented as a proof of Goldbach's conjecture.