Prove2Me

Frame derivative of the KN connection component omL 0 3 1

Proved
ExactVacuumAtlas.EinsteinMaxwell.NP.fdir_omL_031

by He Wang · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-vexact-vacuum-atlasgeneral-relativitynewman-penrose

Frame derivative of the KN connection component omL 0 3 1

Closed form of a frame derivative of omL 0 3 1 on domReg (as printed).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 KN 联络分量的标架导数闭式。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
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_EinsteinMaxwell_NP_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_NP_CCalc
import Definitions.Def_Atlas_EinsteinMaxwell_NP_FrameConn
import Definitions.Def_Atlas_EinsteinMaxwell_NP_FrameNull
import Definitions.Def_Atlas_EinsteinMaxwell_NP_KNComm
import Definitions.Def_Atlas_EinsteinMaxwell_NP_KNFaraday
import Definitions.Def_Atlas_EinsteinMaxwell_NP_KNFrame
import Definitions.Def_Atlas_EinsteinMaxwell_NP_KNSpin
import Definitions.Def_Atlas_EinsteinMaxwell_NP_KNWeyl
import Definitions.Def_Atlas_EinsteinMaxwell_NP_NPScalars
import Definitions.Def_Atlas_EinsteinMaxwell_NP_Riemann
import Definitions.Def_Atlas_Kerr_InAtoms
import Definitions.Def_Atlas_Transport_Connection
import Definitions.Def_Atlas_Transport_MatrixCalc
open Real Complex
open scoped ComplexConjugate
open ExactVacuumAtlas.EinsteinMaxwell.KN (Sig Del gKN giKN faradayKN domReg)
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.NP
variable {M a Q : ℝ} {x : Pt 4}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.NP.fdir_omL_031 (hx : x ∈ domReg M a Q) :
    fdir (knE M a Q) 1 (omL (gKN M a Q) (giKN M a Q) (knE M a Q) (knTh M a Q) 0 3 1) x
      = ((-Del M a Q (x 1) / (2 * Sig a (x 1) (x 2)) : ℝ) : ℂ)
        * (-(I * ((a * Real.sin (x 2) : ℝ) : ℂ) * (((Real.sqrt 2 : ℝ) : ℂ) * (2 * qbarK a x)))
          / (((Real.sqrt 2 : ℝ) : ℂ) * qbarK a x ^ 2) ^ 2) := by sorry
Source
He Wang, Exact Spacetime Atlas V: From Linearized Einstein–Maxwell Equations to Kerr–Newman Radiation Systems. Local source, no public repository; commit b8cd107a558e153ed41fb4972ac5315499d14778; Atlas/EinsteinMaxwell/NP/KNWeyl.lean#L264-L279; SHA-256 13cac1a0822e84fed504493d4cce2dee2d08d9f7487c29671f1afdcefef95064. Registered definitions: mission/PHYSICS_BOUNDARY.md (§K–§M); literature: P. Hintz, arXiv:2609.33661 (v1); Mark–Yang–Zimmerman–Chen, arXiv:1409.5800 (v1).
Human review

  • Endorsed by Shuze Chen · Oct 24, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 24, 2026

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

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