Three figures and a formula.
Everything on this page is a simulation you can play with. It shows the mechanism, and doesn't say anything about real coins.
Figure 1. Every coin is a dot on a clock face. The needle's length is the sync figure r.
Figure 2. Each line is a coin, each tick a flash. Columns appear as the swarm agrees.
Figure 3. The same swarm, seen as a marsh. Set ε to zero and scatter it: it stays noise.
The clock
Each coin has a phase φ between 0 and 1. It advances alone, and buys above a floor push it forward, at most once per wallet per minute. Sells push it back. At 1 the coin flashes and restarts.
The flash
A flash moves the clocks of the neighbours. A push counts for more late in the cycle, because the clock is read through a concave curve. Without that curve, our tests on sparse networks never synchronised.
The limit
The theorem covers a network where everyone is linked to everyone. A real, sparse network of memecoins may never synchronise. This has not been measured on real coins yet.