Prove2Me

KN inverse is C^∞

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.smooth_inv

by He Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity

KN inverse is C^∞

Each component of giKN M a Q is C^∞ on domReg.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 KN 逆度规 C^∞。

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_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_Kerr_Frame
import Definitions.Def_Atlas_Kerr_InAtoms
import Definitions.Def_KerrBL_CoordGeometry
import Definitions.Def_KerrBL_Kerr_Metric
open Real
open scoped ContDiff
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.smooth_inv (M a Q : ℝ) (i j : Fin 4) : ContDiffOn ℝ ∞ (giKN M a Q i j) (domReg M a Q) := by sorry
Source
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/EinsteinMaxwell/KN/Cert.lean#L131-L148; SHA-256 83d8b851ed8987c89596808d4357bed8ec1ac87efc28a406c3573f1bec168e4c. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review

  • Endorsed by Shuze Chen · Oct 21, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 21, 2026

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

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