Prove2Me

Composite standard → PG relation on domStd M

Proved
ExactVacuumAtlas.Schwarzschild.PG.relation_std_toPG

by He Wang · Oct 16, 2026 · Mathlib 0df444a (Lean v4.33.1)

exact-vacuum-atlasgeneral-relativitylean4mathlib

Exactly the statement of Release02.pg_std_restricted (composite relation on domStd M = {r > 0, r ≠ 2M, 0 < θ < π}, both sides), of which it is the source.

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_Core_Relation
import Definitions.Def_Atlas_Schwarzschild_Defs
import Definitions.Def_Atlas_Schwarzschild_Domain
import Definitions.Def_Atlas_Schwarzschild_EFRelation
import Definitions.Def_Atlas_Schwarzschild_PGDefs
import Definitions.Def_Atlas_Schwarzschild_PGRelation
open Real
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas
open ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas.Schwarzschild.PG
set_option maxHeartbeats 4000000
variable (M ε : ℝ)
Formal statement
theorem ExactVacuumAtlas.Schwarzschild.PG.relation_std_toPG (hM : 0 ≤ M) (hε : ε ^ 2 = 1) :
    CoordRelation (gStd M) (gPG M ε) (domStd M) (domStd M)
      (fun x => pgFromEF M ε (toEF M ε x)) (fun z => fromEF M ε (pgToEF M ε z))
      (fun x => jacInv M ε (toEF M ε x) * EFRelation.jac M ε x) := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Schwarzschild/PGStd.lean#L53-L59; SHA-256 088af667b69d8d88eec0c443d81d23005e87d943670ace1c3b33231a0350a279. Mathematical background: See mission/PHYSICS_BOUNDARY.md §A-F for registered definitions and literature references (Wald, Müller-Grave arXiv:0904.4184, Visser arXiv:0706.0622, Martel-Poisson gr-qc/0001069).
Human review

  • Endorsed by Shuze Chen · Oct 18, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 18, 2026

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

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