Organic and Macromolecular Chemistry: The Flexible Assembly of Carbon-Based Topological Locks — Volume V of the Axiomatization of Chemistry in the Global-Realism Framework

This manuscript is Volume V of the program that seeks to axiomatize chemistry within the established global-realist framework. Its purpose is to derive the foundation of organic, stereochemical, polymer, and biomacromolecular chemistry from the previously admitted atomic, molecular, reaction-theoretic, and condensed-phase ontology, without introducing "functional group, " "aromaticity, " "chirality, " "polymer, " or "protein" as primitive empirical notions. Carbon's exceptional topological flexibility is derived from its simultaneously balanced four-channel valence sector, small atomic radius, intermediate electronegativity, and strong homonuclear -bond stabilization. Constitutional isomerism and stereochemical diversity are reconstructed from carbon-skeleton graph theory and the three-dimensional embedding sector. Functional groups are redefined not as lexical entities but as localized perturbation sectors on pre-existing carbon frameworks, whose reactivity descends from inherited local response, acid–base, donor–acceptor, and leaving-group indices. All principal organic elementary steps—substitution, addition, elimination, and rearrangement—are unified as competing minima of a single activation functional on local mechanism-coordinate surfaces. Stereochemistry is formulated as a dynamical theory of embedding-branch persistence, including enantiomerization kinetics, chiral amplification through autocatalytic networks, field-driven and photochemical handedness selection, and the retained bifurcation criterion for spontaneous symmetry breaking. Polymer physics is derived as the statistical mechanics of carbon-chain organizations, encompassing ideal and excluded-volume scaling, entanglement and reptation relaxation, Flory–Huggins demixing, and microphase selection in block copolymers. Biomacromolecules are treated as sequence-encoded folding architectures whose catalytic efficiency, template-directed copying fidelity, and informational homochirality arise as lawful branch-selection outcomes of one common free-energy functional. The retained error-threshold law is derived, establishing the maximal stably heritable sequence length as a joint function of monomer discrimination, proofreading amplification, and selective advantage. The volume closes by exporting a finite output layer and a lawful forward interface to the analytical chemistry volume. Throughout, no functional-group name, stereochemical label, polymer class, or biological-function term is admitted as a primitive causal principle; all are derived as compressed verdicts of previously defined physical and chemical ontology.