Yes—if “represented as a TSP” means represented within the same finite resource model, then you're very close to a precise theorem. But there's one important logical correction. Let \(C_{T,E}\) be the set of problems solvable by a particular computational system within time \(T\) and energy \(E\). Define \(R_{T,E}\) as the set of problems that can be encoded as TSP instances and decoded back to the desired answer within those same bounds. Then certainly \[ R_{T,E}\subseteq C_{T,E}. \] Your stronger claim is \[ \boxed{C_{T,E}=R_{T,E}} \] —that TSP is complete for the entire class of physically permissible computations. If that equality holds, then yes: \[ P\notin R_{T,E} \quad\Longrightarrow\quad P\notin C_{T,E}, \] so no AI operating under those constraints can solve \(P\). Where I would modify your statement It's not enough that a problem cannot be represented as a TSP in some particular encoding. There may simply be a better encoding. What you need is: There exists no resource-respecting reduction from the problem to TSP. That's a much stronger statement. And there's another subtlety: if your TSP solver is itself an AI, then saying “the AI can solve TSP” doesn't automatically mean it can solve every other problem. You need the TSP solver to be a sufficiently general oracle and the reduction to fit within the resource budget. Your idea can be stated very cleanly Let \[ \mathcal C_{T,E} \] be all computations realizable by the physical AI within \(T\) time and \(E\) energy. If you can prove \[ \forall P\in\mathcal C_{T,E},\quad P\leq_{\text{resource}} \mathrm{TSP}, \] then TSP is complete for physically realizable computation under those constraints. Consequently, \[ P\not\leq_{\text{resource}}\mathrm{TSP} \quad\Rightarrow\quad P\notin\mathcal C_{T,E}. \] That is a very interesting formulation because it shifts the question away from “Is TSP NP-complete?” and toward: Is TSP complete for bounded physical computation? That's not something standard NP-completeness by itself establishes. The difficult part would be proving the resource-preserving reduction, particularly when the TSP instance, its encoding, and the decoding of its answer all have to fit inside the same physical limits. And your stochastic-AI observation fits naturally into this framework: randomness can be treated as part of the finite computation tree, so it doesn't by itself enlarge the class of computations beyond what the bounded model permits.