Unified Operator-Control and Field Framework (MAMBA PROTOCOL)

Title: Unified Operator-Control and Field Framework (MAMBA | PROTOCOL) Abstract: We formalize the capstone of the Omega-Sigma framework: a single, unified architecture in which physical admissibility is defined by an operator-valued coherence functional, controlled capture is realized by a dissipative inequality, and the resulting dynamics are expressed as a semilinear parabolic field equation. By fusing the MAMBA admissibility architecture with the Unified Ramanujan Field Equation, we prove that the admissible manifold is exponentially attractive under optimal steering. Quantum Intervention (Admissibility-Preserving Control): This manuscript introduces the Quantum Intervention Principle, formally collapsing the distinction between intrinsic physics and external control. Intervention is not an external input, but a structured, gradient-driven operator deformation constrained by admissibility. Under admissibility-preserving dynamics, there is no structural distinction between physics and control—both are trajectories strictly confined to the geometric kernel of the survival manifold. Field-Level Fast-Strong Capture: We prove that operator geometries can be actively driven into the zero-set of their regularized determinants. The dissipative capture inequality is constructively achievable via steepest descent in the Ramanujan potential, ensuring that the survival manifold is exponentially attractive and forward invariant. The Unified Classification & Instability Hierarchy: The absolute limits of physical realizability are bound not merely by raw energy, but by geometric constraint and structural control. The total state of realizability is classified as: Existence = Ellipticity Boundedness = Coercivity Pre-collapse = Non-normality Collapse = Singularity The Fundamental Law of Reality: Physical realizability, operator invertibility, and determinant coherence are strictly equivalent conditions. A system does not fail when energy grows—it fails when its governing operator loses the ability to remain invertible under its own dynamics.