In this paper, we develop a connectivity-exact bond-resolved framework for quantifying structural accessibility and persistence in drug molecules. Representing a molecule as a heavy-atom graph Formula: see text each bond is classified uniquely as either a connectivity-critical Entry-point bond (Formula: see text) or a connectivity-preserving Fortress bond (Formula: see text) yielding the exact identity Formula: see text This exhaustive partition separates fragmentation capacity from invariant scaffold structure without adjustable parameters. To refine the invariance coordinate we introduce Total Structural Entrenchment (TSE) a persistence-weighted functional defined over cycle-supported bonds and modulated by local steric wall contributions Formula: see text. The resulting two-parameter embedding Formula: see text distinguishes superficial cyclic extent from deeply embedded structural reinforcement and resolves degeneracies inherent in raw bond counts. Metabolic progression is formalized as recursive bridge depletion generating a directed migration across the architectural plane toward a bridge-depleted refractory core. Within this framework scaffold persistence is interpreted as a connectivity-driven contraction governed strictly by graph topology. The resulting invariance-variation embedding establishes a mathematically controlled bond-level representation of structural accessibility and cyclic entrenchment.
Devi et al. (Wed,) studied this question.