Prove2Me

On-shell corollary for LH

Proved
ExactVacuumAtlas.Variation.linFaraday_eq_zero_of_onShell

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

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

On-shell corollary for LH

For a FamilyData family whose H vanishes on all of W: LH(f) = 0 at every x with (0, x) ∈ W.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 解族的 LH = 0（推论，不是一般桥）。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_Variation_Defs
import Definitions.Def_Atlas_Transport_MatrixCalc
open Filter Topology
open scoped ContDiff
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas
open ExactVacuumAtlas.Variation
variable {n : ℕ}
Formal statement
theorem ExactVacuumAtlas.Variation.linFaraday_eq_zero_of_onShell {g ginv : ℝ → Metric n} {F : ℝ → TwoForm n} {W : Set (ℝ × Pt n)}
    {h : Metric n} {f : TwoForm n} (hfam : FamilyData g ginv F W) (ht : IsTangent g F W h f)
    (hH : ∀ p ∈ W, ∀ a b c, faradayCyclic (F p.1) a b c p.2 = 0)
    {x : Pt n} (hx : ((0 : ℝ), x) ∈ W) (a b c : Fin n) :
    linFaraday f a b c x = 0 := 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/Bridge.lean#L284-L291; SHA-256 c0401e780ed4e7fdf93b3fceb547d092276cb438ae1a341a5d661c712a8a09c4. 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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