1. Route Space Γ(s, t)
Plain English: Every legal road on the map from Point A to Point B.
In Markets: All valid trade paths (e.g., Call vs. Put, or EUR → JPY → USD).
2. Clue Operator C : w ↦ Cw
Plain English: A traffic report that updates travel times without building new roads.
In Markets: Put-Call Parity or 8-currency potential Φ_c revealing a cheaper route.
3. Redirection D(Cw) ≠ D(w)
Plain English: Your GPS switches you from the highway to the mountain pass!
In Markets: Abandoning a naive momentum chase for a locked-in option/FX surface gap.
4. Telescoping W_c(γ) = ΔΦ + L_c(γ)
Plain English: Walking in a closed circle back to your door means net altitude change ΔΦ = 0!
In Markets: Any nonzero gap around a closed option box or FX triangle is pure arbitrage.