Prove2Me

EF5 Einstein–Maxwell residual E_{13}

Proved
ExactVacuumAtlas.EinsteinMaxwell.EF5.einsteinMaxwellD_ef5_13

by He Wang · Oct 28, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity

EF5 Einstein–Maxwell residual E_{13}

For all real μ, β, Q and x ∈ domU5: einsteinMaxwellD (gEF5 μ β) (giEF5 μ β) (faraday5 Q) 1 3 x equals the closed form printed in the statement (a multiple of 3β − Q² or 0).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 EF5 Einstein–Maxwell 残差分量闭式。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_D_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_EinsteinMaxwellEF5
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_RicciOffDiag
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas.EinsteinMaxwell.EF5
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.EF5
set_option maxHeartbeats 400000000
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
variable (mu beta Q : ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.EF5.einsteinMaxwellD_ef5_13 {x : Pt 5} (hx : x ∈ domU5) :
    einsteinMaxwellD (gEF5 mu beta) (giEF5 mu beta) (faraday5 Q) 1 3 x =
      (3 * beta - Q ^ 2) * emFactorEF5 mu beta x 1 3 := by sorry
Source
He Wang, Exact Spacetime Atlas VI: Five-Dimensional Einstein–Maxwell Certificates and Equal-Spin Radial Reduction. Local source, no public repository; commit 4a4048a; Atlas/EinsteinMaxwell/EF5/EinsteinMaxwellEF5.lean#L455-L465; SHA-256 7d26c41e4b3fd19f383626d85f6a9ed218b2e2f2e7e727ac994cb3ce596b77ed. Registered definitions: mission/PHYSICS_BOUNDARY.md (§N–§O); literature: R. C. Myers, M. J. Perry, Ann. Phys. 172 (1986) 304; F. R. Tangherlini, Nuovo Cimento 27 (1963) 636.
Human review

  • Endorsed by Shuze Chen · Oct 29, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 29, 2026

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

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