Internal Time as Local Memory: State–Phase Tradeoffs for Explicit Termination in Anonymous Dynamic Binary Consensus

We study deterministic binary consensus in anonymous synchronous 1-interval-connected dynamic networks under one-bit broadcast-counting communication, focusing on the persistent local state required for explicit termination when only partial timing information is supplied for free. Each round t exposes the common external phase φ_t = t mod P, while the full round number is unavailable. For known dynamic diameter D and unknown network size, the minimum number of persistent states S_D(D,P) satisfies max{3, ceil((ceil(D/2)+1)/P)}