stonerCriterion
plain-language theorem explainer
The stonerCriterion definition encodes the ferromagnetism threshold as the inequality between exchange interaction strength and density of states at the Fermi level. Condensed-matter researchers using Recognition Science to classify transition-metal magnetism would cite it when testing alignment conditions for iron, cobalt, and nickel. The implementation is a direct Boolean predicate on the product of the two real parameters.
Claim. Ferromagnetism is present precisely when the product of exchange interaction strength $U$ and density of states at the Fermi level $D(E_F)$ exceeds unity.
background
The Chemistry.Ferromagnetism module derives permanent magnetism from spontaneous alignment of atomic moments. Exchange interaction originates in Pauli exclusion for d-electrons, while 8-tick coherence appears in the orbital degeneracy that favors maximum spin alignment per Hund's rule. The Stoner criterion supplies the explicit threshold condition, with the module noting its relation to phi-ladder scaling for Curie temperatures and domain energetics.
proof idea
This definition is a one-line wrapper that multiplies the two real inputs and compares the result against the constant 1, returning the Boolean outcome directly.
why it matters
The definition supplies the Stoner criterion step inside the CM-010 ferromagnetism derivation, supporting downstream element checks such as iron_ferromagnetic and curieTemperature. It links to the eight-tick octave through d-orbital degeneracy and to phi-ladder scaling for temperature thresholds. No open scaffolding questions are attached in the supplied results.
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