Awareness as an Involutive Invariant in Expanding Informational Geometry

This paper presents a geometric framework for understanding how conscious experience remains stable despite continual growth in informational degrees of freedom. Informational expansion is modeled as a scale-invariant process, while awareness is identified as an involutive operation that preserves a relational invariant under expansion. Within this framework, experienced time is defined by equal perceptual intervals along an involutive trajectory (the scalar clock), rather than by raw informational growth. Stable records emerge as configurations invariant under involutive transport, and apparent attraction between systems arises as a consequence of involutive alignment that reduces informational dissipation. A canonical spiral–involute construction unifies informational expansion, awareness, record formation, and interaction within a single geometric representation. The approach builds on and clarifies the scalar clock framework by providing an explicit geometric mechanism for invariant preservation in expanding informational systems.