Metastable Oscillons in k-Essence Scalar Fields: Phase Diagram, 3+1 Survival, and the D_K Identity Observable — First Evidence of Dynamic Proto-Entities in Coherential Field Theory

We study localized oscillating solutions (oscillons) in a scalar field theory with a double-well potential and k-essence kinetic corrections, motivated by the Radial Coherential Dynamics (RCD) 2.0 program. We first prove a formal static no-go result: the Derrick scaling argument shows that static localized solutions cannot exist within the perturbative domain of validity of K_eff(X). We then demonstrate numerically that dynamic solutions — metastable oscillons — evade this restriction and sustain long-lived plateaus of the configurational dissimilarity functional D_K in both 1+1 and 3+1 (spherically symmetric) dimensions. A systematic scan of 261 simulations in 1+1 yields a phase diagram with stability frontier A_max ≈ 0.27|β|^(−0.44), consistent with the perturbative validity boundary. Extended simulations (500 T_osc) reveal that D_K is a more robust configurational persistence marker than localized energy: the configurational signature persists long after the energy has radiated away. In 3+1 radial geometry, oscillons survive for ≥200 oscillation periods for |β| ≲ 0.05. We propose D_K as an operational observable for tracking configurational persistence and discuss implications for coherential individuation. Includes 16 figures documenting all simulation runs. Part of the Radial Coherential Dynamics (RCD) 2.0 program.