Prove2Me

ricci 0 2

Proved
ExactVacuumAtlas.Controls.Cylinder.ricci_0_2

by He Wang · Oct 15, 2026 · Mathlib 0df444a (Lean v4.33.1)

exact-vacuum-atlasgeneral-relativitylean4mathlib

Ricci component R_{02} of the cylinder control metric -dt^2 + dr^2 + dtheta^2 + sin^2theta dphi^2 (not vacuum; release-I source): for every real M (parameter unused) and (t,r,theta,phi) in domEF = {r > 0, 0 < theta < pi}, Ric(gCyl M, giCyl M){02} = 0. Used by Shear.ricci_transport as the reference cylinder Ricci values for the transformation law. Non-zero components: R{22} = 1, R_{33} = sin^2 theta.

Preamble
import Mathlib
import Definitions.Def_Atlas_Controls_CylinderTables
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_Schwarzschild_Defs
import Definitions.Def_Atlas_Schwarzschild_Domain
open Real
open ExactVacuumAtlas ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas
open ExactVacuumAtlas.Controls
open ExactVacuumAtlas.Controls.Cylinder
set_option maxHeartbeats 4000000
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
variable (M : ℝ)
Formal statement
theorem ExactVacuumAtlas.Controls.Cylinder.ricci_0_2 (x : Pt 4) (hx : x ∈ domEF)   :
    ricciOf (gCyl M) (giCyl M) 0 2 x = 0 := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Controls/CylinderTables.lean#L1498-L1503; SHA-256 6853c22124c397d8886c39820e0325b7348d66f0d0a916d41678b132205ebfee. 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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