Prove2Me

Generic binding of g component (4, 2)

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Generic.bind_g_4_2

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

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

Generic binding of g component (4, 2)

Under ESData R B D A H W Φ Ψ: the component of esMetric / esInverse / esFaraday (according to g) at (4, 2) equals the normalised table gG / giG / FG on esDomain R (Set.EqOn).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 一般拟设：esMetric/esInverse/esFaraday 分量与规范化表在 esDomain R 上相等。

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_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Data
import Definitions.Def_Atlas_EinsteinMaxwell_ES5_Generic_Tables
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.Generic
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
variable {R : Set ℝ} {B D A H W Φ Ψ : ℝ → ℝ}
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.ES5.Generic.bind_g_4_2 (hE : ESData R B D A H W Φ Ψ) :
    Set.EqOn (esMetric B D A H W 4 2) (gG B D A H W 4 2) (esDomain R) := 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/Generic/Tables.lean#L196-L201; SHA-256 0b8e01dc10c5b67eb7077e8a1630f890465fbae34c4775d6930d2f09bf7ef196. 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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