Prove2Me

Derivative of the PG velocity atom q = √(2M/r)

Proved
ExactVacuumAtlas.Schwarzschild.PG.hasDerivAt_qf

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

exact-vacuum-atlasgeneral-relativitylean4mathlib

For real M ≥ 0 and r > 0: u ↦ q(M, u) = √(2M/u) has derivative −q(M, r)/(2r) at r (HasDerivAt).

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 scoped ContDiff
Formal statement
theorem ExactVacuumAtlas.Schwarzschild.PG.hasDerivAt_qf {M r : ℝ} (hM : 0 ≤ M) (hr : 0 < r) :
    HasDerivAt (fun u => qf M u) (-(qf M r) / (2 * r)) r := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Schwarzschild/PGAtoms.lean#L32-L49; SHA-256 608cd138269990ef8e1653998f4250e275f3957f867d624dbee913f03ed06e21. 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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