Indistinguishability from Node-Swap Invariance

Two particles of the same type are two nodes at the same coupling position ρ on the C(r) lattice. The kernel sees only ρ — there is no internal label, no name tag, nothing that distinguishes node one from node two except where they sit. Swapping them leaves the lattice configuration unchanged. Indistinguishability is forced by the framework, not assumed.