Prove2Me

ST03 (μ = 2, Q = 1, β = 1/3): static charged Einstein–Maxwell certificate

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.ST03.candidate_certificate

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): static charged Einstein–Maxwell certificate

EMCertificateD candG candGi candF dom for B = (r⁴ − 2r² + 1/3)/r⁴ = 1 − 2/r² + (1/3)/r⁴, D = 1/B (as transcribed: r⁴/(r⁴ − 2r² + 1/3)), A = H = r², W = 0, Φ = −1/(2r²), Ψ = 0, candF = esFaraday rPhi rPsi = d(Φ dt), dom = esDomain {r | 0 < r ∧ rX r ≠ 0}, rX r = r⁴ − 2r² + 1/3. One fixed static charged instance (3β = Q² holds: 3·(1/3) = 1²).

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 ST03（μ=2, Q=1, β=1/3）静态带电固定实例的 Einstein–Maxwell 证书。

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_Cand_ST03_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.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.candidate_certificate : EMCertificateD candG candGi candF 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/Cert.lean#L36-L51; SHA-256 564f74cf05b6c7e73bbcbc3af7a380b2732bd50c7f512d2b726a794d3e2ce870. 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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