Structural Physics Atlas: A Turn-Based, Zero-Free Formalism for Continuity, Constraint, and Emergence

This work presents a structural physics atlas built on a turn-based, zero-free representational formalism. The framework addresses projection-induced degeneracies (“tie-states”) by replacing cancellation-to-zero with bounded reparameterization (“turning”), preserving continuity and structural memory. Physics concepts are organized using a 12×12×12 mandala indexing scheme (domains, phases, regulation states), constrained by dodecahedral domain adjacency and a sparse coupling schema representing admissible inter-cell influence. The atlas is explicitly methodological rather than ontological: indexing layers function as coordinate systems for classification, traversal, and audit of models across kinematics, dynamics, symmetry, fields, geometry, thermodynamics, quantum structure, relativity, and many-body emergence. A conservative discovery registry distinguishes definitions, derivations, boundary statements, and open gaps. The framework is compatible with existing physical theories and is intended as a foundation-level representational and organizational tool for physics.