Prove2Me

Equal-spin ansatz: Lorentz signature (−,+,+,+,+)

Proved
ExactVacuumAtlas.EinsteinMaxwell.ES5.esMetric_lorentz

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

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

Equal-spin ansatz: Lorentz signature (−,+,+,+,+)

If 0 < A(x 1), 0 < H(x 1), 0 < B(x 1)·D(x 1) and 0 < x 2 < 1, then IsLorentzian (metricMatrix (esMetric B D A H W) x). Both B, D > 0 and B, D < 0 are covered (the sign of B alone is not assumed).

Scope. Exactly the hypotheses printed in the formal statement.

中文摘要 A>0、H>0、BD>0 且 0<u<1 时 esMetric 为 Lorentz 号差；BD>0 同时覆盖 B,D>0 与 B,D<0 两种情形。

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_Defs
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas
open ExactVacuumAtlas.EinsteinMaxwell
open ExactVacuumAtlas.EinsteinMaxwell.ES5
set_option maxHeartbeats 8000000
variable (B D A H W : ℝ → ℝ)
Formal statement
theorem ExactVacuumAtlas.EinsteinMaxwell.ES5.esMetric_lorentz (x : Pt 5) (hA : 0 < A (x 1)) (hH : 0 < H (x 1))
    (hBD : 0 < B (x 1) * D (x 1)) (hu : 0 < x 2) (hv : x 2 < 1) :
    IsLorentzian (metricMatrix (esMetric B D A H W) x) := 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/Defs.lean#L152-L175; SHA-256 bb9c71fdcb4c409e9bfd1766a9ca9bb3118fe200aee50524ee3c961baaa00f90. 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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