Solving the 160‑year‑old puzzle of the nature of the chemical bond via subject‑free mathematical‑physical equations —Chemical bonds originate from nature‑matter proportionality constraint rather than quantum‑mechanical orbital hybridization and resonance hypotheses

Traditional chemical‑bond theories are fragmented and rely on subjective empirical hypotheses. They cannot unify the essence of various bond types, intrinsically derive bond parameters, or resolve classic chemical puzzles such as carbon tetravalency and benzene aromaticity, lacking consistent underlying mathematical‑physical logic. Based on the nature‑matter proportionality constraint, this work constructs a set of global subject‑free mathematical‑physical equations. It establishes the core mechanism of chemical‑bond formation: a chemical bond is a dynamic process in which an atomic system spontaneously returns to a steady state after deviating from the benchmark proportional condition. This work shares the same underlying axiom system with the chirality theory and the periodic‑table theory, representing derived expressions at the particle, atomic and molecular scales. Energy acts as the fundamental driver for material‑system evolution; various proportional parameters serve as intermediate mathematical‑physical mechanisms through which energy drives structural rearrangement of matter. Equipped with derivable, quantitatively testable predictions, this framework unifies covalent bonds, ionic bonds, metallic bonds, and hydrogen bonds. Its deductions for bond energy, bond length and bond angle are compatible with standard experimental datasets. This study completely discards subjective hypotheses such as orbital hybridization and resonance, putting an end to theoretical fragmentation among bond categories. It builds a complete logical chain connecting atomic structure, chemical bonds and molecular structures, delivering a novel fundamental mathematical‑physical paradigm for the innovation and applied research of quantitative chemistry.