We demonstrate that structure emergence across physical, biological, and cognitive systems follows a unified mechanism: Coherence-Gated Formation (CGF). When local coherence rises sufficiently to narrow suppression barriers, regenerative forces can capture systems into stable states before noise destroys the aligned configuration. The threshold condition is: R_gen >= M_supp * rho_c + A * chi_tau where R_gen represents regenerative forces, M_supp * rho_c quantifies coherence-dependent suppression, and A * chi_tau captures constructive entropy recycling. This relationship emerges from the RMAxt gradient invariant framework and operates identically from nuclear fusion to ethical norm stabilization. Core results: - Three-stage dynamics identified: (1) Coherence Rise — local patterns align, creating pockets of reduced destructive interference; (2) Barrier Narrowing — coherence reduces effective barrier width, not height, enabling crossing through reduced path length; (3) Regenerative Capture — intrinsic restorative forces lock the system into a new configuration faster than noise can disrupt it. - Six diagnostic failure modes: C-rise failure (coherence cannot reach threshold), barrier narrowing failure (barrier geometry insensitive to available coherence), capture failure (regenerative forces insufficient), noise dominance (entropy recycling violated), well depth failure (shallow attractor, transient only), and oscillation breakdown (bounded dynamics exit persistence set). - CGF-CPC handoff: formation creates a coherence well; well depth determines the width of the Upsilon viability band for subsequent persistence. Deep wells tolerate perturbation; shallow wells do not. Formation without sufficient well depth is transient excitation, not structure emergence. - Oscillatory stabilization: persistent structures do not sit motionless — they oscillate within their coherence wells, maintaining correction capacity. Rigidity failure (zero oscillation) and dissolution failure (oscillation exceeds well boundary) bound the viable regime. - Five falsifiable predictions: coherence spikes precede formation events across domains, effective barrier width fluctuates with coherence amplitude, optimal noise bands exist for formation (non-monotonic response), entropy recycling is observable in forming systems, and deep coherence wells correlate with longevity. - Cross-domain validation: nuclear physics (isotope stability, fusion dynamics, magic numbers), stellar physics (ignition conditions, main sequence position, brown dwarf failure), chemistry (reaction dynamics, enzyme catalysis, oscillating reactions), biology (metabolic networks, glycolytic oscillations, cell cycle checkpoints), neuroscience (insight formation, gamma-band synchrony, memory consolidation), social systems (norm formation, institutional stability, reform success). CGF identifies the moment structure becomes possible (threshold crossing), the reason formation is nonlinear (barrier narrowing dynamics), the conditions for emergence (coherence + regeneration > suppression), and the boundary between stability and collapse. No new forces required — only recognition of how coherence reshapes probability landscapes. Part of the Coherence Institute publication sequence (paired with Coherence Propagation Constant). This paper governs formation; its companion governs persistence.