Bond-resolved graph-theoretic modeling of structural invariance and metabolic accessibility in drug molecules

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.