RS-I.2 Mathematical core: Complex Projective Dynamics of Two Interacting Systems Observer Invariants, Nonlinear Projective Descent and Identifiability
Year: 2026
Type: preprint
Abstract: 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.
Author: Malachevsky, A.A.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223661009