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.adaptiveCoreLocalPoint (s : ℝ) : Fin 4 → Point

The four-point configuration used by the adaptive central-core obstruction.

Equations

• ConwaySoifer.Simplified.adaptiveCoreLocalPoint s = ![(1, 0), (1, -1 * s), (-1 / 3 * s ^ 2 + 1 / 3 * s, -1 / 3 * s ^ 2 + 1 / 3 * s), (1 + -1 * s, s)]

theorem ConwaySoifer.Simplified.adaptiveCoreLocal_obstruction {Q : EquilateralTriangle} {s : ℝ} (hs0 : 0 < s) (hs : s ≤ 1 / 2) (hq : 0 < Q.side) (hpts : ∀ (i : Fin 4), adaptiveCoreLocalPoint s i ∈ Q.carrier) : 1 ≤ Q.side