Non–Evasiveness of the Generation Bottleneck and the Structural Boundary of P= NP

Recent work has shown that deterministic generation branching programs that output full witnesses are subject to exponential width lower bounds for explicit, satisfiable SAT instances. These bounds persist despite efficient verification and standard self–reductions, and they are invisible at the level of decision complexity. In this paper, we study the evasiveness of this generation bottleneck. Specifically, we ask whether the exponential lower bound can be avoided by modifying the computational model while remaining within the classical notion of deterministic polynomial–time computation. We introduce a minimal axiomatic framework for deterministic polynomial–time witness generation, formalizing determinism, uniformity, locality of transitions, and explicit output. We prove that any generation model satisfying these axioms collapses to a generation branching program with comparable dependency width. As a consequence, known exponential width lower bounds for generation branching programs are shown to be non–evasive under these axioms: they cannot be bypassed by any structure– preserving deterministic generation model. Therefore, any approach establishing P= NP via deterministic polynomial–time witness generation would necessarily require abandoning at least one of these foundational principles, such as locality, uniformity, or explicit constructive output. This work does not claim an unconditional separation of P and NP. Rather, it identifies a precise structural boundary: within the classical deterministic generation paradigm, the equality P= NP cannot be established without a substantive redefinition of what constitutes efficient deterministic computation.