Paper I introduced warp graphs (warps) as a well-founded "graphs all the way down" state object. This paper equips warp states with an operational semantics based on double-pushout rewriting with interfaces (DPOI) in an adhesive category of typed open graphs.The central result is a deterministic concurrent semantics at the level of a tick: for any scheduler-admissible batch of skeleton rewrites, the committed successor is independent (up to typed open graph isomorphism) of the internal serialisation order. States are packaged as two-plane objects U = (G; α, β), with a skeleton G ∈ OGraphT and recursively attached warps over each vertex and edge. We prove that attachment-plane rewrites commute with skeleton publication up to canonical transport along preserved structure, formalised via a projection functor π : WState → OGraphT equipped with a chosen reindexing (cleavage).To connect the mathematics to deterministic replay, we isolate the scheduler as a total policy σ : WState → Batch and define a tick receipt whose core is a "tick event poset" recording which candidate matches were accepted and which were rejected by deterministic conflict resolution. Under tick confluence, this poset quotients to the same committed state, providing a clean bridge to provenance traces (Paper III).