On ranked directed acyclic graphs coupled by vertex conflicts we study exact-arrival multi-agent path finding (departure and arrival pinned in place and time) posed as a distributed output task: every cell must emit its own bit of a valid joint path-support mask. The machines are cellular: one automaton per cell, state factored over cells, communication only along a fixed local fabric, synchronous rounds, a query-independent output round, no central decoder, and a per-topology transition code. "Necessary" here means: on an explicit hard topology, over all its feasible queries, no universally correct local-only architecture can renounce either temporal orientation; with global flags, impossibility becomes a bandwidth-round trade-off. The class is not vacuous: a flooding machine solves every instance in as many rounds as the diameter of the local fabric. The bound survives two concessions: we supply every agent's exact individual cavity, which alone solves the single-agent problem in zero rounds and makes the single-agent direction theorem vacuous; and we allow
k one-bit global aggregate flags. On a twelve-cell, two-agent, depth-three topology no forward-only machine with
k=0 is correct on two feasible queries, for any number of rounds; the time-reversed topology does the same to backward-only machines. Placing
p copies side by side gives, for forward-only machines,
JR+kR≥p at constant depth, where
JR measures how much of the query reaches the targets' cones and is
0 here. A backward-only machine solves that family in constant rounds and a flag-streaming one in
⌈p/k⌉+O(1), so the bound is tight in order; on the composite family neither orientation can be renounced. The finite lemmas of the gadget and the pair-invariance contradictions are checked in Lean 4; the semantic bridge, the cone lemma and the counting are paper proofs. We report no benchmarks.