AI can summarize a board meeting, but a family can still miss the same school email — one update arrives by email, another by chat, and the calendar never gets touched. Fire school updates into this little household and watch who misses what. Then switch on a shared hub and see the miss-rate collapse. Drag to orbit.
If an adult reliably checks k of the household's N channels, and a given update lands in one channel at random:
The whole family catches an update only when it lands in a channel everyone checks. With no shared channel, that probability is 0 / N = 0% — someone always misses. Over a school year of roughly 120 updates (estimate), fragmentation isn't an edge case; it's the default outcome.
A unified hub changes the structure, not the effort: every channel forwards into one place, so k/N becomes ≈ 1 for everyone (we model a 5% "saw it but forgot" residual — an estimate).