transitionMetalZ
plain-language theorem explainer
transitionMetalZ supplies the atomic numbers of d-block elements in periods 4-6 as an explicit list. Modelers of metallic bonding in Recognition Science cite this list to classify elements whose valence electrons delocalize into an electron sea minimizing J-cost. The definition is a direct concatenation of three hardcoded integer lists with no lemmas or external calls.
Claim. The list $T$ of atomic numbers for transition metals (d-block, rows 4-6) is $T = [21,22,23,24,25,26,27,28,29,30] ++ [39,40,41,42,43,44,45,46,47,48] ++ [57,72,73,74,75,76,77,78,79,80]$.
background
The MetallicBond module derives metallic bonding from delocalized valence electrons forming an electron sea that minimizes recognition cost (J-cost) rather than localizing on individual atoms. The RS mechanism highlights 8-tick coherence in the collective metallic state and φ-scaling of conductivity and cohesive properties. This definition supplies the concrete atomic numbers required to classify transition metals for downstream predicates such as isMetal and freeElectrons.
proof idea
The definition is a pure list expression formed by concatenating three explicit lists of natural numbers, one per period. No lemmas are invoked and depends_on_count is zero; the body is simply the concatenation operator applied to the three hardcoded segments.
why it matters
The list is referenced by isMetal, freeElectrons, cohesiveEnergyProxy, and the theorem transition_cohesive_gt_alkali that asserts higher cohesive energy for transition metals than alkali metals. It operationalizes the module's prediction of low ionization energy and high coordination numbers, connecting to the eight-tick octave and φ-related scaling in the Recognition Science framework.
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