rareEarthFerromagnets
plain-language theorem explainer
Rare earth ferromagnets are enumerated as the atomic numbers 64, 65, and 66. Researchers classifying magnetic elements in the Recognition Science chemistry derivations cite this list when extending the ferromagnetic predicate beyond the transition metals. The implementation is a direct constant assignment of the three-element list.
Claim. The rare earth ferromagnets consist of the elements with atomic numbers $64$, $65$, and $66$.
background
The Ferromagnetism Derivation (CM-010) treats ferromagnetism as spontaneous alignment of atomic magnetic moments arising from exchange interactions that follow from the Pauli exclusion principle in the ledger's fermion statistics. Key RS mechanisms include 8-tick coherence in d-orbitals that enables Hund's rule coupling, the Stoner criterion requiring the product of exchange strength and density of states at the Fermi level to exceed unity, and Curie temperature scaling with exchange energy. The module explicitly predicts ferromagnetism for gadolinium (Z=64) and other rare earths in addition to iron, cobalt, and nickel.
proof idea
The definition is a direct constant assignment of the list [64, 65, 66] with no lemmas or tactics applied.
why it matters
This definition supplies the rare-earth component of the ferromagnetic classification and is referenced by the downstream isFerromagnetic predicate. It realizes the explicit prediction in the module documentation that gadolinium and rare earths are ferromagnetic, thereby connecting to the 8-tick coherence and Stoner criterion within the Recognition Science framework.
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