Testing the Dynamical Generation of Directional Balance and Residual Tensor Structure in Coupled Finite-Update Fields

This preprint tests whether coupled finite-update fields can dynamically develop directional tensor organization from statistically isotropic, band-limited initial conditions without a common externally imposed preferred axis, and whether the associated channel imbalance survives an independent-seed long-horizon test. The numerical analysis follows a prospectively locked sequence comprising baseline reproduction, fixed-point and linear-feasibility screening, solver and tensor-schema validation, positive-control recovery, short-horizon discovery, and extended-horizon survival testing. At N = 32 and T = 2, 128 trajectories covering 32 locked parameter points produced 30 eligible short-horizon candidates. Sixteen selected points were subsequently evolved to T = 8 using four independent expansion seeds each, yielding 64 extended trajectories. All extended trajectories completed without hard numerical failure, but none passed the locked finite-amplitude survival criterion. All 16 candidates fell below the minimum late-time imbalance-RMS threshold, and 12 also failed the cross-seed tensor-variability criterion. The results support robust short-horizon directional organization but do not support a persistent finite-amplitude directional-imbalance attractor in the tested basin. The work treats the trace-free tensor as a quadrupolar diagnostic and does not identify it with a physical spin-2 field, graviton, spacetime perturbation, or black-hole information-return mechanism.