Model specification: Flag-controlled CNOT growth circuit

On a finite connected induced lattice graph $G=(V,E)$:

1. Place one payload qubit at each vertex. Attach an independent positive timer ${\tau }_e$ to each undirected edge.

2. Initialize classical flags $f_0=1$ and $f_x=0$ for $x\ne 0$. The flags are independent of every payload input.

3. When the first endpoint of an unarmed edge becomes flagged, start its one-shot timer.

4. If its timer expires while exactly one endpoint is flagged, apply a CNOT from that endpoint to the unflagged endpoint, then flag the latter. If both endpoints are already flagged, cancel the unused operation.

5. Keep all controller predecessors in the classical dependency description. No quantum-state-dependent flag update is permitted.

Timers and gates use an external calibrated time parameter. The ideal CNOT has zero duration in this timing contract. Finite-duration hardware is a separate approximation problem.