Prove2Me

MP01 (μ = 3, a = 1/2): Ricci-flat VacuumCertificate

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.MP01.candidate_ricci_flat

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): Ricci-flat VacuumCertificate

VacuumCertificate candG candGi dom, where candG = esMetric rB rD rA rH rW and candGi = esInverse rB rD rA rH rW with A = r² + a², H = ((r²+a²)² + μa²)/(r²+a²), W = μa/((r²+a²)² + μa²), B = ((r²+a²)² − μr²)/((r²+a²)² + μa²), D = r²(r²+a²)/((r²+a²)² − μr²) at μ = 3, a = 1/2 (equal-spin Myers–Perry form, naming to be confirmed by the author), and dom = esDomain {r | 0 < r ∧ rX r ≠ 0}, rX r = (r² + (1/2)²)² − 3r². One fixed parameter instance; no horizon/axis regularity.

Scope. Fixed rational parameters transcribed from the candidate JSON; domain dom = esDomain radR with radR = {r | 0 < r ∧ rX r ≠ 0}; no horizon/axis regularity.

中文摘要 MP01（μ=3, a=1/2）的固定实例：在 esDomain{r>0, rX≠0} 上为 Ricci 平坦证书。仅此一组参数，不涉及视界/轴正则性。

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_Cand_MP01_EM
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.candidate_ricci_flat : VacuumCertificate candG candGi 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/Cert.lean#L38-L47; SHA-256 c0338b7c4b70d8f320a626f4069c15157b10273dd8b2ed022537df3ef75b90c4. 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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