Four Rivals, One Broken Recursion: Existentialism, the Will to Power, and the Holographic-Simulation Divide Measured Against the Trisductive Return

A verification architecture that shares ground with established frameworks is liable to be read as a notational variant of its nearest neighbor. Trisduction, a triaxial epistemic architecture that seals a claim only when three mutually independent lines of warrant converge, sits close to four such neighbors: existentialism and the will to power on one side, the holographic principle and the simulation hypothesis on the other. This paper argues that the resemblances are real but the identity fails, and that a single structural feature blocks every assimilation. Against the two philosophical schools the feature is an independent third axis, the registrational warrant, the recognition by which a verification closes and is read by a party distinct from the thing verified. The will to power folds that axis into the kinetic, existentialism folds it into the self, and because each spends its third warrant neither reaches the convergence the architecture calls the Return. Against the two cosmological frameworks the feature is the handling of the exterior: the simulation hypothesis requires an external host it cannot detect, while the holographic principle and the architecture both decline the exterior, the former by duality and the latter by a closed-world monism whose only opening is located and never crossed. The distinctions are typed. The dependency that no convergence-lock forms once a third axis collapses is theorem-grade; the assignments of each school to its fold are structural lenses anchored on the schools' own primary commitments; the architecture's own metaphysics is held throughout at premise grade. The irreducibility cuts both ways: the neighbors hold a first-person interior the architecture brackets out of band. The contribution is to show that proximity between frameworks is adjudicated structurally, by which terms each keeps free, rather than by doctrinal position on a shared field.