Prove2Me

MP01 (μ = 3, a = 1/2): binding of g component (3, 3)

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.MP01.bind_g_3_3

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

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

MP01 (μ = 3, a = 1/2): binding of g component (3, 3)

For candidate MP01 (μ = 3, a = 1/2): the transcribed candidate component (candG / candGi / candF, according to g) (3, 3) equals the normalised closed form (gN / giN / FN) on dom (Set.EqOn).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 候选数据分量与规范化闭式在 dom 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_Cand_MP01_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.MP01
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.MP01.bind_g_3_3 : Set.EqOn (candG 3 3) (gN 3 3) 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/MP01/Defs.lean#L342-L347; SHA-256 5e312fea99565a4d89b7e21bb975047b15693166f96fa9be22c1fff2a8445421. 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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