The Ouroboros Cycle: A Non-Unitary Evolution–Measurement Framewor

This preprint presents a closed, non-unitary evolution–measurement framework describing a cyclic process of distinction, probabilistic localization, reflexive stabilization, integration, and compression. Unlike standard quantum mechanics, where unitary Schrödinger evolution is taken as fundamental and measurement is treated as external, the present model treats measurement as an intrinsic structural step within the dynamics themselves. The framework introduces attention-modulated open-system evolution, explicit normalization-aware measurement probabilities, and a reflexive fixed-point construction for stabilized states. Physical observables arise through projection and partial tracing, yielding a reduced density matrix interpreted as physical reality. An internal, accumulated notion of time—distinct from the external evolution parameter—is also defined, allowing attention to modulate experienced temporal flow. The model is formulated at a formal and exploratory level, without assuming a specific physical Hamiltonian or experimental realization. It is intended as a conceptual and mathematical contribution to the foundations of quantum mechanics, particularly in relation to measurement theory, non-unitary dynamics, and information-theoretic structure. No claims of empirical validation are made.