Three No-Go Results in One Note: Why the Coherential Field Cannot Self-Organize into Galaxies — and What Survives (RCD 2.0 Closure Note)

This note consolidates three closure results from the RCD 2.0 program. First, a reformulated P3 test with double-well potential V_B(C) = λ(C² − v²)² shows that no stable static spherical configuration of C exists in 3+1 dimensions: the radial friction term drives all regular solutions to C → 0 or to a uniform constant, producing no concentrated gradients and no useful galactic density profiles (KS-P3-2 reactivated). Second, the double-well mechanism does provide a viable binarization channel for O8: with v ≫ C_, the field concentrates near two well-separated values, giving δ = 2v/C_ ≫ 1 as required for the binary-Hamming regime of P1-bis (O8 partially closed). Third, with the tree-level coarse-graining no-go established in the P2-O3 investigation, no avenue achieves outcome (A) for the Baryonic Bridge: A(C) and D(X) are permanently declared level 3 in the current architecture. The self-structuring hypothesis — that C generates galactic structure without matter source — is closed by three converging results. The program's derivational frontier is now precisely delineated. Part of the Radial Coherential Dynamics (RCD) 2.0 program.