Multi-hop trade emerges from a Bellman reservation-value field

To make multi-hop spatial arbitrage EMERGENT (not a planner), give each agent a reservation-value field R(loc)=max(P_local, max_nbr[delta*R(nbr)-legcost]) solved by value iteration over its BELIEF graph. Key facts proven with an experiment harness: (1) the update operator is a delta-contraction in sup-norm, so an info-horizon cap H equals truncating value iteration at H steps (residual delta^H) — the info horizon and numerical horizon are the same object. (2) TWO knobs matter: belief-radius (SEE) and lookahead k (PLAN); a myope (k=0, values a hop at spot delta*P(nbr)-c) gains nothing from a data-grid, so info only pays when planning can use it. (3) At spatial equilibrium R==P, so foresight only buys convergence SPEED, decisive only under shocks (the telegraph effect). (4) On one path, no multi-hop is profitable if no single hop is (path cost=sum of hop costs). (5) Carry/storage cost is best grounded as the scarcity price of a location SPACE field priced by the same scarcity curve as goods, with the aggregate/LOD value summed over LEAF descendants only (unset leaf=abundant slack, unset container=0) so a prairie fades but a city-planet stays dear.