A Half-Plane Derivation of the Symmetric 1 : λ : 1 Cevian-Web Hexagon Theorem, with Exact Positivity Certificates

This repository contains the complete symbolic verification scripts and draft manuscript studying the structural properties of cevian-web hexagons. We utilize exact half-plane clipping inside SymPy to derive area ratios and certify combinatorial stability over open intervals. Additionally, an interactive Matplotlib tool is included to visually simulate the structural crossing and divergence phenomena between outer and inner cevian families at the n=3 base case. A parametric family of cevian hexagons is developed that unifies the Marion and Abboud configurations. Explicit area-ratio formulas are derived and extended to arbitrary-dimensional simplices, yielding closed product formulas for associated polytope volumes together with geometric and probabilistic proofs.I think this wording highlights exactly what is novel: unification, closed formulas, and higher-dimensional extension, rather than just "another area of a hexagon" result.