Prove2Me

ricci 2 1

Proved
ExactVacuumAtlas.Controls.Shear.ricci_2_1

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

exact-vacuum-atlasgeneral-relativitylean4mathlib

Ricci component R_{21} of the sheared control metric gCtl lam: for every real lam and every (T,R,alpha,beta) in domEF = {R > 0, 0 < alpha < pi}, Ric(gCtl lam, giCtl lam){21} = 0. One of the 16 table entries assembled in Shear.ricci_direct (non-vacuum control route 1). Non-zero components: R{22} = 1 + lam^2 cos^2 alpha sin^2 alpha, R_{23} = R_{32} = lam cos alpha sin^2 alpha, R_{33} = sin^2 alpha.

Preamble
import Mathlib
import Definitions.Def_Atlas_Controls_ShearTables
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.Shear
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 (lam : ℝ)
Formal statement
theorem ExactVacuumAtlas.Controls.Shear.ricci_2_1 (x : Pt 4) (hx : x ∈ domEF)   :
    ricciOf (gCtl lam) (giCtl lam) 2 1 x = 0 := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Controls/ShearTables.lean#L1594-L1599; SHA-256 782cc8c1c151bbdb9e599ba53ea76ee6c2e4203bbca394d8de7a4b95ac66b98e. 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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