The geometric thickness of K14 is 4

No straight-line drawing of K14 has its edges split into three crossing-free layers, so the geometric thickness of K14 is 4. Together with the upper bound of Dillencourt, Eppstein and Hirschberg this completes the values of the geometric thickness of Kn for n ≤ 16. The lower bound is a SAT computation over signotopes with a hull-size case split and an Euler-type edge bound; two independently written encoders give UNSAT, and every leaf LRAT proof was checked with cake_lpr. Code, case trees and a one-command checker: https://github.com/LeeMarshall1113/ai-math-results (results/thickness-k14).