Prove2Me

MP02 (μ = 5, rotation constant −2/3): reduced equation number 4 vanishes

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.MP02.red_4

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

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

MP02 (μ = 5, rotation constant −2/3): reduced equation number 4 vanishes

For candidate MP02 (μ = 5, rotation constant −2/3): reduced equation 4 (0–4: redE_tt, redE_tσ, redE_rr, redE_uu, redE_σσ; 5–6: redJ_t, redJ_σ as printed) of the transcribed radial data vanishes for every r ∈ radR.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 候选的约化方程在 radR 上为零。

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_ES5_Cand_MP02_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Cand_MP02_Reduced
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Cert
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Data
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Reduced
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Tables
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas.EinsteinMaxwell.ES5
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.ES5
open ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand
open ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.MP02
set_option maxHeartbeats 8000000
set_option maxRecDepth 100000
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.MP02.red_4 (r : ℝ) (hr : r ∈ radR) : Generic.redE_σσ rB rD rA rH rW rPhi rPsi r = 0 := 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/ES5/Cand/MP02/Reduced.lean#L202-L206; SHA-256 ebf70422c698b70c0b292ddd5a2b49322f1372318f16fdce8cc573907eee782e. 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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