Prove2Me

EF5 counterexample: no certificate at (μ, β, Q) = (1, 1, 1)

Proved
ExactVacuumAtlas.EinsteinMaxwell.EF5.counterexample_no_cert

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

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

EF5 counterexample: no certificate at (μ, β, Q) = (1, 1, 1)

¬ EMCertificateD (gEF5 1 1) (giEF5 1 1) (faraday5 1) domU5. Proved through the explicit value E_22 = 1/8 at samplePtEF5 (r = 2, u = 1/2, other coordinates 0), consistent with 3β − Q² = 2 ≠ 0.

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 (μ, β, Q) = (1,1,1) 时没有证书：在 r=2、u=1/2 处 E_22 = 1/8。

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_EF5_CertificateEF5
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_EinsteinMaxwellEF5
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_Frame
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_RicciOffDiag
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas.EinsteinMaxwell.EF5
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.EF5
set_option maxHeartbeats 4000000
set_option linter.unusedVariables false
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.EF5.counterexample_no_cert :
    ¬ EMCertificateD (gEF5 1 1) (giEF5 1 1) (faraday5 1) domU5 := 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/EF5/CertificateEF5.lean#L113-L119; SHA-256 cfead95b85a714aef90d980c00d0cf62ef54959a25cf5716e7e611261a95d8d3. 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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