Explicit real support fans for the handwritten geometric point set. The polynomial decompositions are proved by ring; their signs by positivity. Each cone carries one fixed triple on both endpoints. No Boolean checker is used.

noncomputable def ConwaySoifer.Simplified.acrossFourPoint (s : ℝ) : Fin 4 → Point

The four-point configuration used by the Across local obstruction.

Equations

• ConwaySoifer.Simplified.acrossFourPoint s = ![(-1 * s, 1), (0, 1), (1, 1 / 2), (1, 12 * s)]

theorem ConwaySoifer.Simplified.acrossFour_obstruction {Q : EquilateralTriangle} {s : ℝ} (hs0 : 0 < s) (hs : s ≤ 1 / 80) (hq : 0 < Q.side) (hpts : ∀ (i : Fin 4), acrossFourPoint s i ∈ Q.carrier) : 1 ≤ Q.side