Prove2Me

chr 1 0 0

Proved
ExactVacuumAtlas.Schwarzschild.PG.chr_1_0_0

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

exact-vacuum-atlasgeneral-relativitylean4mathlib

Christoffel symbol Gamma^1_{00} of the PG metric: for every M >= 0, eps^2 = 1 and (T,r,theta,phi) with r > 0, r != 0, sin theta != 0, Gamma^1_{00}(gPG M eps, giPG M eps, x) = M / r² + -2 * M^2 / r³. Closed form in r, q = sqrt(2M/r), theta, eps; kernel-checked table entry used in PGCertParts.

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Lift
import Definitions.Def_Atlas_Schwarzschild_Defs
import Definitions.Def_Atlas_Schwarzschild_Domain
import Definitions.Def_Atlas_Schwarzschild_PGDefs
open Real
open ExactVacuumAtlas ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas
open ExactVacuumAtlas.Schwarzschild
open ExactVacuumAtlas.Schwarzschild.PG
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 ε : ℝ)
Formal statement
theorem ExactVacuumAtlas.Schwarzschild.PG.chr_1_0_0 (x : Pt 4) (hr : x 1 ≠ 0) (hs : sin (x 2) ≠ 0) (hrp : 0 < x 1) (hM : 0 ≤ M) (hε : ε ^ 2 = 1) :
    christoffel (gPG M ε) (giPG M ε) 1 0 0 x = M / (x 1)^2 + (-2*M^2) / (x 1)^3 := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Schwarzschild/PGTables.lean#L377-L385; SHA-256 dafc5aee5d354120cdf9c59509fdc80d2f2a8375b89a53da84edb04211eb1ae5. 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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