Tree seeds for every proper even cycle of length at least eight in rectangular grids

We construct a weakly C_L-saturated spanning tree in P_a □ P_b for all a,b ≥ 3 and even 8 ≤ L < ab. Consequently the weak saturation number is ab-1. The core reduction covers every nonsquare and leaves one critical target in each sufficiently large square. The remaining even-square construction keeps a remote bottom edge in every witness on six rows; a two-row graft transports that edge and raises the target by twice the width. An odd-height anchored construction covers the odd squares. The proof also uses deficit-band constructions and a direct protected-edge cycle construction. Expanded coordinate dependencies and exact small base certificates accompany this manuscript.