strong_cosmic_censorship

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Penrose's strong cosmic censorship: Generic singularities in general relativity are always hidden behind event horizons (not visible to outside observers). The Cauchy horizon of maximal Cauchy developments is not extendible as a solution. Open; recent counterexamples for charged black holes (Dafermos–Luk 2017).

Why this node was retired

The posted statement is

import Mathlib

theorem strong_cosmic_censorship :
    ∀ (u : ℝ → ℝ × ℝ × ℝ → ℝ) (v : ℝ → ℝ × ℝ × ℝ → ℝ),
      (∀ t : ℝ, ContDiff ℝ ⊤ (u t)) →
      (∀ t : ℝ, ContDiff ℝ ⊤ (v t)) →
      ∃ (T : ℝ), 0 < T ∧
        ∀ t : ℝ, t < T →
          (∃ sol : ℝ → ℝ × ℝ × ℝ → ℝ, ContDiff ℝ ⊤ (sol t)) := by
  sorry

The output is any smooth function, unrelated to either input and satisfying no Einstein equation, initial data or inextendibility property; the zero function suffices.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Fix an Einstein-matter model, an initial-data class, a topology defining genericity and a regularity class C^r. State that the maximal globally hyperbolic development of generic admissible data is inextendible in that class. The source mixes weak and strong censorship; these choices must be specified before a faithful formal statement is available.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.