Prove2Me

RN b-family is FamilyData

Proved
ExactVacuumAtlas.Variation.RN.familyData_b

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

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

RN b-family is FamilyData

ε ↦ (gRN M (Q² + ε), giRN M (Q² + ε), faradayRN Q) satisfies FamilyData on domJ = ℝ × domRN.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 RN 的 b 族满足 FamilyData。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_RN_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_RN_Frame
import Definitions.Def_Atlas_EinsteinMaxwell_Variation_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_Variation_RN
import Definitions.Def_Atlas_Transport_MatrixCalc
open Real
open scoped ContDiff
open ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.RN
Formal statement
theorem ExactVacuumAtlas.Variation.RN.familyData_b (M Q : ℝ) :
    FamilyData (fun ε => gRN M (Q ^ 2 + ε)) (fun ε => giRN M (Q ^ 2 + ε)) (fun _ => faradayRN Q) domJ := 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/Variation/RN.lean#L68-L83; SHA-256 7513cd6c91a5e550bb62e1cac2f2c8a8c17fa469087ba3c27bf9c1eab933f66f. 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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