Prove2Me

Second Bianchi identity in a general frame

Proved
ExactVacuumAtlas.EinsteinMaxwell.NP.frame_bianchi

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

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

Second Bianchi identity in a general frame

Gauge form of the second Bianchi identity for the frame curvature, with the −c R term.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 一般标架下第二 Bianchi 恒等式。

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_Bianchi
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
variable {n : ℕ}
variable {g gi : Metric n} {E Θ : Fin n → Fin n → Pt n → ℂ} {U : Set (Pt n)}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.NP.frame_bianchi (hF : FrameData g gi E Θ U) {x : Pt n} (hx : x ∈ U) (C A B : Fin n) :
    bianchiX g gi E Θ C A B x + bianchiX g gi E Θ A B C x + bianchiX g gi E Θ B C A x = 0 := 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/Bianchi.lean#L154-L224; SHA-256 7a3a9c6ef7ae1ad57f306317ff9e948f3f7ad12cb60d92e1b8e75baaccf75870. 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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