Prove2Me

Four-dimensional certificate transport along a CoordRelation

Proved
ExactVacuumAtlas.VacuumCertificate.transport_of_relation

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

exact-vacuum-atlasgeneral-relativitylean4mathlib

Exactly the statement of Release02.certificate_transport (old certificate on V, CoordRelation g h U V Φ Ψ J, U open and nonempty, J K = I on U, ĝ g = I on U ⟹ certificate for (g, ĝ) on U), of which certificate_transport is the wrapper.

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_Core_Relation
import Definitions.Def_Atlas_Transport_Connection
import Definitions.Def_Atlas_Transport_Curvature
import Definitions.Def_Atlas_Transport_MatrixCalc
open scoped ContDiff
open Matrix
Formal statement
theorem ExactVacuumAtlas.VacuumCertificate.transport_of_relation {U V : Set (Pt 4)} {Φ Ψ : Pt 4 → Pt 4}
    {J K : Pt 4 → Matrix (Fin 4) (Fin 4) ℝ} {g gi h hi : Metric 4}
    (hcert : VacuumCertificate h hi V) (r : CoordRelation g h U V Φ Ψ J) (hU : IsOpen U)
    (hne : U.Nonempty) (hJK : ∀ y ∈ U, J y * K y = 1)
    (hgi : ∀ y ∈ U, metricMatrix gi y * metricMatrix g y = 1) :
    VacuumCertificate g gi U := by sorry
Source
He Wang, Exact Vacuum Atlas II, local source snapshot (public Git repository not yet available), commit 11fb317259353b71a41d6daed466c495cffd7db4; Atlas/Transport/Certificate.lean#L75-L103; SHA-256 ba79c925752e43cb527671a3db9842422fb083444c4304ff7763fdb1c1f68683. 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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