Prove2Me

For M > 0 the certified PG domain contains r = 2M with Ricci = 0 there

Proved
ExactVacuumAtlas.Schwarzschild.PG.horizon_point

by He Wang · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

exact-vacuum-atlasgeneral-relativitylean4mathlib

For all real M > 0 and ε with ε² = 1: there exists x ∈ domEF with x 1 = 2M such that Ric(gPG M ε, giPG M ε)_{bd}(x) = 0 for all b, d (witness: the equatorial point (0, 2M, π/2, 0)).

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_Core_Relation
import Definitions.Def_Atlas_Minkowski_Spherical
import Definitions.Def_Atlas_Schwarzschild_Defs
import Definitions.Def_Atlas_Schwarzschild_Domain
import Definitions.Def_Atlas_Schwarzschild_PGCertParts
import Definitions.Def_Atlas_Schwarzschild_PGDefs
import Definitions.Def_Atlas_Schwarzschild_PGRelation
open Real
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas
open ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas.Schwarzschild.PG
set_option maxHeartbeats 4000000
Formal statement
theorem ExactVacuumAtlas.Schwarzschild.PG.horizon_point (M ε : ℝ) (hM : 0 < M) (hε : ε ^ 2 = 1) :
    ∃ x ∈ domEF, x 1 = 2 * M ∧ ∀ b d, ricciOf (gPG M ε) (giPG M ε) b d x = 0 := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Schwarzschild/PGSpecial.lean#L59-L64; SHA-256 2eb0a573868512cad1044bf8af89a5f34de57d1da1c39075e5f4e87eecd7defa. Mathematical background: See mission/PHYSICS_BOUNDARY.md §A-F for registered definitions and literature references (Wald, Müller-Grave arXiv:0904.4184, Visser arXiv:0706.0622, Martel-Poisson gr-qc/0001069).
Human review

  • Endorsed by Shuze Chen · Oct 18, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 18, 2026

    Confirmed by the mission captain (proposal self-audit).

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