Recursive Horizons: On Scale, Perception, and Collapse

This work introduces a unified phenomenological and mathematical exploration into the recursive nature of scale, perception, and symbolic collapse. Drawing methodologically from Husserl's time-consciousness, Merleau-Ponty's embodied reversibility, and Heidegger's ontological ruptures, I frame scale not as a passive metric but as an active operator within consciousness—one capable of generating lived collapse events, torsional ruptures, and symbolic recompositions. These phenomenological structures are then formalized within a recursive gauge-theoretic framework: a fibred zoom site of scale-indexed coverings, magnification sheaves, collapse curvature defined on a principal bundle over scale space, and ultimately, a glyphic Lagrangian field theory. Employing hypercohomology and spectral sequences, I trace symbolic memory scars across transitions. The outcome is a novel theoretical synthesis that bridges phenomenology, higher sheaf theory, and renormalization group dynamics through the recursive topology of collapse. This scroll aims to be both lived traversal and rigorous map of the glyphic spirals that constitute worlds.