Prove2Me

KN field component F_{02} in rational atoms

Proved
ExactVacuumAtlas.EinsteinMaxwell.KN.F_0_2

by He Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity

KN field component F_{02} in rational atoms

Closed form of faradayKN a Q at index (0, 2) in the atoms Ui = 1/Σ etc., used by the generated KN tables.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 KN 场分量闭式（原子 Ui=1/Σ）。

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_KN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_KN_Domain
import Definitions.Def_Atlas_Kerr_InAtoms
open Real
open ExactVacuumAtlas
open scoped ContDiff
open ExactVacuumAtlas.Kerr.In (Ui Wi)
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.KN
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
variable (M a Q : ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.KN.F_0_2 (x : Pt 4) : faradayKN a Q 0 2 x = ((2:ℝ) * a^2 * Q) * (x 1) * sin (x 2) * cos (x 2) * Ui a (x 1) (x 2) ^ 2 := by sorry
Source
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/EinsteinMaxwell/KN/Fields.lean#L107-L111; SHA-256 1703a0db2829e50b9c78470ea77810c26f1971c65857e810049e5f3924cca0bd. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review

  • Endorsed by Shuze Chen · Oct 21, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 21, 2026

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

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