Root 7 (own certificate)

Proved

ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.FiniteKS14.vii14_certificate

by He Wang · Nov 4, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-viiexact-vacuum-atlasfive-dimensional-gravitygeneral-relativitykerr-schild

Root 7 (own certificate). The candidate's own EMCertificateD (preconnected I, base point r₀) yields via Radial.vii03_certificate_radial_bvp one common actual Q = -q(r₀), J = -ℓ(r₀)/2 with the actual PaperBVP; q(r₀) ≠ 0, ℓ(r₀) ≠ 0 give Q ≠ 0, J ≠ 0, and the complete finite-KS outputs follow.

Scope. Supporting result in the formal proof chain of Atlas VII Unit A: the restricted geodesic Kerr–Schild obstruction on the actual asymptotic branch of the five-dimensional, $\Lambda = 0$ , source-free Einstein–Maxwell radial system with two equal-magnitude angular momenta. It asserts exactly the Lean statement of this node for the data stated there; it does not claim the existence of a solution, a horizon or a black hole.

Preamble

import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_D_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Cert
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Data
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Reduced
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Tables
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_ChargedTail
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_CompactifiedBridge
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_CompactifiedResiduals
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_CoordinateAcceleration
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_FiniteJetObstruction
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_FiniteTaylor6
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_FiniteTaylorJet
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_GeodesicCongruenceObstruction
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_JetRecursion
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_KSBackgroundEnergy
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_KSConnection
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_KSMetric
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_KSRicci
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_MaxwellFrame
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_NullRicciEnergy
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_OneSidedExtraction
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_PaperGauge
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_PolynomialJet
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_PrincipalGeodesic
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_RadialBVP
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_RadialBVPEquivalence
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_RicciNullDirections
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_ScalarCertificate
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_SmoothBranch
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_VII13FiniteBranchSpec
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_KerrSchild_VII14FiniteKSSpec
import Definitions.Def_Atlas_Transport_Connection
open scoped ContDiff Topology Matrix
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.ES5
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.Radial
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.Compact (FactorizedN)
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.NullDirections
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.NullEnergy
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.Geodesic
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.Geometry
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.BackgroundEnergy
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.VII13FiniteBranchSpec (FiniteBranch6)
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.VII14FiniteKSSpec
open ExactVacuumAtlas.EinsteinMaxwell.D (EMCertificateD)
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.ES5
open ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild
set_option autoImplicit false
variable {I : Set ℝ} {f m N w p a F b A : ℝ → ℝ} {s h ε Q J : ℝ}

Formal statement

theorem ExactVacuumAtlas.EinsteinMaxwell.ES5.KerrSchild.FiniteKS14.vii14_certificate (hP : PaperData I f m N w p a) (hI : IsPreconnected I) {r₀ : ℝ}
    (hr₀ : r₀ ∈ I)
    (hc : EMCertificateD (esMetric f (Dfun f m N) (Afun f m) (Hfun m N) w)
      (esInverse f (Dfun f m N) (Afun f m) (Hfun m N) w) (esFaraday p a) (esDomain I))
    (hN : FactorizedN I N s h) (hS : FiniteBranch6 I s ε f m a F b A)
    (hq0 : qFun f N w p a r₀ ≠ 0) (hl0 : ellFun f m N w p a r₀ ≠ 0) :
    OwnFiniteKSOutput I f m N w p a r₀ s ε := by sorry

Source

He Wang, Exact Spacetime Atlas VII, Unit A (restricted Kerr–Schild obstruction on the actual asymptotic branch, VII17). Local source, no public repository; commit f64ba9c823ec; Atlas/EinsteinMaxwell/ES5/KerrSchild/FiniteKSObstruction.lean#L238-L255; SHA-256 cf2b2fb71b3636279b11f01d7f25ef4f9bec6c681f19632424c6468f8c711741. Registered definitions: mission/PHYSICS_BOUNDARY.md (Atlas VII sections P–XVII). Physical Kerr–Schild obstruction: Fröb–Khavkine–Málek–Pravda, Eur. Phys. J. C 82 (2022) 215, arXiv:2112.13266 (Eqs. 23–25, 33, 59–60).

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