Construct measured surgery topology for the extinction endgame

For every closed simply connected topological three-manifold $M$, construct an extracted surgery topology $E$ and one $W\ge0$ such that, for every $T>0$ with a nonempty final slice, measured surgery comparison data exist with initial-width bound $W$ and horizon $T$. The reference measure, uniform radial estimates, removed-volume budget and sweepout profiles must be supplied by the geometric construction. This Open statement refines the active width-controlled topology input; it does not claim a construction of a Ricci flow or a proof of finite extinction.