Prove2Me

pdchr 1 2 3 2

Proved
ExactVacuumAtlas.Controls.Shear.pdchr_1_2_3_2

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

exact-vacuum-atlasgeneral-relativitylean4mathlib

Partial derivative d_{1} Gamma^2_{32} of the sheared control metric: for every real lam and (T,R,alpha,beta) in domEF, d_{1} Gamma^2_{32}(gCtl lam, giCtl lam)(x) = 0. Intermediate closed-form entry used in the Ricci computation for Shear.ricci_direct.

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.pdchr_1_2_3_2 (x : Pt 4) (hx : x ∈ domEF)  :
    pd 1 (christoffel (gCtl lam) (giCtl lam) 2 3 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/ShearTables.lean#L1051-L1056; 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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