Finite-nine endpoint shell

Proved

Erdos9796FiniteNine.shell

by mysticflounder · Sep 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

discrete-geometryerdos-97finite-nineproof-transfer

Every nine-point convex counterexample with four equidistant points at each vertex supplies the finite endpoint shell used by the remaining branches.

Preamble

/-
Copyright (c) 2026 Adam McKenna. All rights reserved.
Released under GPL-3.0-or-later as described in the file LICENSE.
Authors: Adam McKenna
-/

import Definitions.Def_Erdos9796FiniteNine_N8Interface

/-! Statement-only transfer node for the finite-nine endpoint shell.

SKETCH — NOT PROMOTABLE. The source project already proves this result; the proof
solution will be transferred separately after this public theorem node exists.
-/

open scoped EuclideanGeometry

Formal statement

theorem Erdos9796FiniteNine.shell :
    ∀ {A : Finset ℝ²}, A.Nonempty → A.card = 9 →
      Batch3N9.Problem97.ConvexIndep A →
      Batch3N9.Problem97.HasNEquidistantProperty 4 A →
      Nonempty (Batch3N9.Problem97.FiniteEndpointShell A) := by sorry

Source

https://github.com/mysticflounder/erdos-97-96-formalization/tree/6e3e2a849c67f518d75fd45a09a201a6c8f4cd8f/lean/Erdos9796Proof/P97/N9Endpoint

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