Prove2Me

Cartesian isotropic certificate on the slit domain

Proved
ExactVacuumAtlas.Schwarzschild.Iso.cert_cart_slit

by He Wang · Oct 15, 2026 · Mathlib 0df444a (Lean v4.33.1)

exact-vacuum-atlasgeneral-relativitylean4mathlib

For every real M ≥ 0: VacuumCertificate (gIsoCart M) (giIsoCart M) (domCartSlit M), domCartSlit M = {ρ > 0, ρ ≠ M/2, r_xy + x > 0} (the natural domain intersected with the slit condition; the radial exclusions are part of the slit domain).

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_Core_Relation
import Definitions.Def_Atlas_Isotropic_CartChart
import Definitions.Def_Atlas_Isotropic_CartMaps
import Definitions.Def_Atlas_Isotropic_Defs
import Definitions.Def_Atlas_Minkowski_Spherical
import Definitions.Def_Atlas_Schwarzschild_Defs
import Definitions.Def_Atlas_Schwarzschild_Domain
import Definitions.Def_Atlas_Transport_Connection
import Definitions.Def_Atlas_Transport_Curvature
import Definitions.Def_Atlas_Transport_MatrixCalc
open Real Matrix
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas
open ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas.Schwarzschild.Iso
set_option maxHeartbeats 4000000
variable {M : ℝ}
Formal statement
theorem ExactVacuumAtlas.Schwarzschild.Iso.cert_cart_slit (hM : 0 ≤ M) :
    VacuumCertificate (gIsoCart M) (giIsoCart M) (domCartSlit M) := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Isotropic/CartChart.lean#L273-L284; SHA-256 a978cca33484092eed822c5786ba958ae7ad983e09ca84ea1c69e67017f2162e. 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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