Wikipedia sayings about “electrons will not pair in a set of equal energy orbitals if an empty orbital is available” is a statement of

1.Glossary of engineering

mechanics, an atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This

https://en.wikipedia.org/wiki/Glossary of engineering

2.Schrödinger equation

states" or "energy eigenstates"; in chemistry they are called "atomic orbitals" or "molecular orbitals". Superpositions of energy eigenstates change their properties

https://en.wikipedia.org/wiki/Schrödinger equation