Prove2Me

ST03 (μ = 2, Q = 1, β = 1/3): Christoffel table entry Γ^{2}_{12}

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.ST03.chr_on_2_1_2

by He Wang · Oct 28, 2026 · Mathlib 0df444a (Lean v4.33.1)

einstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity

ST03 (μ = 2, Q = 1, β = 1/3): Christoffel table entry Γ^{2}_{12}

Generated table lemma for candidate ST03 (μ = 2, Q = 1, β = 1/3): christoffel gN giN 2 1 2 equals an explicit function of (r, u) (liftRU) on dom (Set.EqOn); gN, giN are the normalised closed forms bound to candG, candGi by bind_g/bind_gi.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 候选的 Christoffel 表项（dom 上 EqOn）。

Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Core_Certificate
import Definitions.Def_Atlas_EinsteinMaxwell_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_D_Basic
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Cand_ST03_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Defs
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas.EinsteinMaxwell.ES5
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.ES5
open ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand
open ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.ST03
set_option maxHeartbeats 8000000
set_option maxRecDepth 100000
set_option linter.unusedVariables false
set_option linter.unusedSimpArgs false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.ST03.chr_on_2_1_2 :
    Set.EqOn (christoffel gN giN 2 1 2) (liftRU (fun r u => ((1:ℝ)) / ((1:ℝ) * r) : ℝ → ℝ → ℝ)) dom := by sorry
Source
He Wang, Exact Spacetime Atlas VI: Five-Dimensional Einstein–Maxwell Certificates and Equal-Spin Radial Reduction. Local source, no public repository; commit 4a4048a; Atlas/EinsteinMaxwell/ES5/Cand/ST03/Chr.lean#L649-L654; SHA-256 8889db18705ed72c6ae6c0d74ac13a16045d5413d767d6b1650fd563c7ee8640. Registered definitions: mission/PHYSICS_BOUNDARY.md (§N–§O); literature: R. C. Myers, M. J. Perry, Ann. Phys. 172 (1986) 304; F. R. Tangherlini, Nuovo Cimento 27 (1963) 636.
Human review

  • Endorsed by Shuze Chen · Oct 29, 2026

    Confirmed by the moderator at approval.

  • Endorsed by He Wang · Oct 29, 2026

    Confirmed by the mission captain (proposal self-audit).

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