Dijkstra's algorithm floods outward from the beacon, always settling the nearest unsettled hex next. The instant a hex is settled, its distance is frozen — and it is provably the shortest, because every other route out is already longer.
That guarantee only holds for the current minimum on the rim. Any other shimmering hex may still be reached more cheaply — its tentative number is just the best route found so far.
Painting terrain changes the edge weights: marsh is costly to cross, road is nearly free, so the frontier bends around whatever you paint. A longer road can beat a short marsh.
Wager on a shimmering hex and you force it to settle early. If a cheaper path arrives later, you lose the bet — the reason greedy only ever trusts the minimum.
The survey flood seized mid-sweep. The lesson continues without it — everything you have already done is safe.