Retardation Without States: Structural Non-Uniqueness in Gravitational Reconstruction

Retarded reconstruction imposes a genuine causal constraint on the physical description of gravitational phenomena. It restricts admissible dependencies to the causal past and, together with the principal structure of the underlying hyperbolic operator, constrains the characteristic propagation of information. Yet these constraints do not by themselves determine a unique complete reconstruction. This work examines the second condition of physical fixation developed in the preceding analysis: non-eliminability under admissible reformulation (R2). The central question is whether differences between retarded reconstructions that share the same causal and principal characteristic structure can be dismissed as coordinate, gauge, or parametrization freedom, or whether differences may remain at the level of the complete mathematical operator. Using hyperbolic differential operators of the form \(P=\Box_g+V\), the analysis separates principal characteristic structure from lower-order dynamical structure. A minimal structural example demonstrates that operators with the same principal symbol can remain mathematically distinct and that their retarded Green operators need not coincide. Coordinate transformations, gauge identifications, and reparametrizations are then examined as possible mechanisms of elimination. The result is deliberately limited. Mathematical inequivalence does not by itself establish a physical distinction, and non-eliminability does not replace the independent operational condition of reconstructibility established in the preceding work. Physical fixation therefore requires both reconstructibility and non-eliminability. The analysis consequently identifies a structural boundary of retarded reconstruction: causal admissibility constrains physical access, but does not by itself fix the complete representational structure or establish the physical individuation of an instantaneous state. The implications of this boundary for cosmological state descriptions are left to the subsequent work.