A Distorted-Monoidal Reformulation of the Natural Proofs Barrier

We formalize a categorical "distorted monoidal" framework (DMT) intended to capture irreversible computational structure via a non-invertible distortion operator and a monoidal syntax of compositional reasoning. Within this setting we define a class of DMT-natural lower-bound methods, characterized by (i) constructivity, (ii) largeness, and (iii) invariance under distortion. We then prove a barrier theorem: assuming the existence of exponentially hard pseudorandom functions, no DMT-natural method can yield superpolynomial circuit lower bounds against P/poly (and hence such a method cannot separate P from NP). The proof is a reduction to the Razborov-Rudich Natural Proofs barrier, showing that any DMT-natural property induces a classical natural property. This paper does not prove P!=NP; it explains, in a precise sense, why a broad family of "distortion-invariant" strategies cannot succeed under standard cryptographic hardness assumptions.