Mathematical framework underlying Self-Encoding Geometry and attractor-stable systems
The self-encoding fixed point. Attractor-stable systems satisfy μ = e−μ, creating interpretable geometric structure.
Ω governs global integration structure. β controls balance between structure and dynamics.
Emerges from interaction of primitive and architectural constraints.
The framework is formalized as a spectral triple (A, H, D) in the sense of Connes' noncommutative geometry.
Systems capable of self-reference must cross six critical thresholds.
Emergence of distinct observables
Formation of coherent structures
Self-referential loops appear
Fixed points in dynamics
System observes its own state
Self-representation achieved