conductivityProxy
The conductivityProxy maps an atomic number to a real number that serves as a linear proxy for electrical conductivity in metals, scaled directly by the count of delocalized valence electrons. Chemists and Recognition Science modelers working on metallic lattices would cite it when estimating conductivity trends from the electron-sea picture. The definition is a one-line cast of the freeElectrons count to reals.
claimFor atomic number $Z$, the conductivity proxy equals the number of free valence electrons per atom, expressed as a real number.
background
The module derives metallic bonding from Recognition Science by treating delocalized electrons as a collective state that minimizes J-cost across an 8-tick coherent lattice. Free electron count is supplied by the sibling definition freeElectrons, which returns 1 for alkali metals, 2 for alkaline earth metals, and an average of 2 for transition metals. The input type Z is the integer anchor map from Masses.Anchor (and its certified alias), used here only to index the periodic table. The module states that conductivity correlates with free electron density and exhibits phi-related scaling in metal families.
proof idea
One-line definition that applies freeElectrons to the input atomic number and coerces the resulting natural number to a real.
why it matters in Recognition Science
The definition supplies the basic conductivity proxy inside the metallic bonding derivation (CH-011). It directly implements the module's claim that electrical conductivity tracks free electron density under the electron-sea and 8-tick coherence picture. No downstream results currently reference it, leaving open its use in quantitative band-structure or phi-scaling predictions.
scope and limits
- Does not compute actual conductivity or resistivity values.
- Does not incorporate lattice type, coordination number, or packing efficiency.
- Does not account for temperature, impurities, or band-gap effects.
- Does not derive the proxy from the Recognition Composition Law or J-cost minimization.
formal statement (Lean)
69def conductivityProxy (Z : ℕ) : ℝ :=
proof body
Definition body.
70 (freeElectrons Z : ℝ)
71
72/-- Coordination number in metallic lattices.
73 BCC: 8, FCC/HCP: 12 -/