Prove2Me

Commutator coefficients as contractions

Proved
ExactVacuumAtlas.EinsteinMaxwell.NP.NullFrameData.cL_eq_ccontr

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

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

Commutator coefficients as contractions

For a null frame: cL C A B = g(e_C, [e_A, e_B]) as a bilinear contraction.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 cL 为 g(e_C,[e_A,e_B])。

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_KNFrame
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 scoped ContDiff Matrix
open Complex
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.NP
open ExactVacuumAtlas.EinsteinMaxwell.NP.NullFrameData
variable {g gi : Metric 4} {E Θ : Fin 4 → Fin 4 → Pt 4 → ℂ} {U : Set (Pt 4)}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.NP.NullFrameData.cL_eq_ccontr (hN : NullFrameData g gi E Θ U) {x : Pt 4} (hx : x ∈ U) (C A B : Fin 4) :
    cL E Θ C A B x = ccontr g x (fvec E C x) (fun μ => brk E A B μ x) := 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/FrameNull.lean#L190-L198; SHA-256 89b93964d08a58f81f17ec29d939043c67b8a5c7a9a375bb5c15b99bf70dff0a. 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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