RS-I.2 Mathematical core: Complex Projective Dynamics of Two Interacting Systems Observer Invariants, Nonlinear Projective Descent and Identifiability

We study the complex dynamics of two coupled scalar states and their projective representation. For the linear system we distinguish invariants under independent participant-preserving rescalings, common projective scaling, and arbitrary mixing of coordinates, and classify degenerate coordinate strata with vanishing entries.For nonlinear holomorphic systems we prove a necessary and sufficient criterion foran autonomous projective factor and establish a global representation through a rational map and a common nowhere-vanishing holomorphic multiplier. We addressidentifiability, the Schwarzian derivative, the continuous-time Riccati limit, counterexamples, corrected numerical examples, and reproducible tests. None of the resultinginvariants is claimed to measure consciousness, phenomenal experience, or the subjectivity of humans or artificial intelligence.