Prove2Me

NW01 (wrong rotation W): no Ricci-flat certificate

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.Cand.NW01.candidate_refuted

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

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

NW01 (wrong rotation W): no Ricci-flat certificate

¬ VacuumCertificate candG candGi dom for the MP01 data with the wrong W = μa/(r²+a²)² (μ = 3, a = 1/2; the term μa² is missing from the denominator), dom = esDomain {r | 0 < r ∧ rX r ≠ 0}, rX r = (r² + (1/2)²)² − 3r². Refutes the VACUUM certificate.

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 NW01（错误的 W）：不存在 Ricci 平坦证书（否定的是 VacuumCertificate）。

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_NW01_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.NW01
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.NW01.candidate_refuted : ¬ 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/NW01/Cert.lean#L18-L21; SHA-256 153facf7b53f94cdab80e60b994cc30b718f38d33d4f9285953032b39f749dec. 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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