Prove2Me

EF5 Ricci component R_{33}

Proved
ExactVacuumAtlas.EinsteinMaxwell.EF5.ricci_33

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

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

EF5 Ricci component R_{33}

For all real μ, β and x ∈ domU5: ricciOf (gEF5 μ β) (giEF5 μ β) 3 3 x equals the closed form printed in the statement.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 EF5 Ricci 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
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
variable (mu beta : ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.EF5.ricci_33 {x : Pt 5} (hx : x ∈ domU5) :
    ricciOf (gEF5 mu beta) (giEF5 mu beta) 3 3 x = 2 * beta * x 2 / x 1 ^ 4 := 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/Ricci.lean#L1960-L1998; SHA-256 f91de831e00ad5d30843158e5baae53dac8ca23c036652f5c758181c627b47f9. 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).

View graph