On Identity, Solver Geometry, and the Structural Framing of the P vs NP Question

The P vs NP problem is commonly introduced through the slogan 'Is P equal to NP?'. While rhetorically effective, this formulation invites an identity-based reading that suppresses distinctions of type, role, and solver structure implicit in the formal theory. This paper argues that the difficulty of the P vs NP question is rooted in a structural framing issue rather than a literal equality. We introduce the notion of solver geometry to make explicit the dependence of solvability on representation, admissible operations, and cost structure. Within this framework, verification and decision emerge as geometrically distinct operations, and the classical P vs NP statement is recovered as a projection of a more general implication schema. No resolution of P vs NP is claimed.