stabilityScore
plain-language theorem explainer
Stability score for a crystal structure is a weighted sum of its approximate packing efficiency and eight-tick coherence. Materials physicists modeling metal phase stability would cite this when comparing BCC versus FCC preferences under varying weight ratios. The definition is realized as a direct linear combination of the two component functions.
Claim. For crystal structure $s$ (BCC, FCC or HCP) and real weights $p$, $c$, the stability score equals $p · η(s) + c · κ(s)$, where $η$ denotes the approximate packing efficiency and $κ$ the eight-tick coherence.
background
The module classifies crystal structures inductively as BCC, FCC or HCP. Eight-tick coherence returns 1.0 for BCC to capture the direct ledger periodicity match and 2/3 for FCC and HCP. Packing efficiency approximation returns 0.68 for BCC and 0.74 for the close-packed cases.
proof idea
One-line definition that computes the linear combination packing_weight * packingEfficiencyApprox s + coherence_weight * eightTickCoherence s.
why it matters
This definition supplies the quantitative score evaluated inside the stability_tradeoff theorem, which shows BCC favored at high coherence weight and FCC at high packing weight (ratio >5.5). It encodes the module's RS mechanism of 8-tick coordination for BCC and close-packing for FCC/HCP, aligning with the eight-tick octave landmark. The HCP phi-stability ratio remains a separate factor.
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