VI-01 witness point
DefinitionAtlas_EinsteinMaxwell_EF5_CertificateEF5einstein-maxwellexact-spacetime-atlas-viexact-vacuum-atlasfive-dimensional-gravitygeneral-relativity
VI-01 witness point
samplePtEF5 = (0, 2, 1/2, 0, 0) (r = 2, u = 1/2).
中文摘要 VI-01 见证点。
Registry: PHYSICS_BOUNDARY §N (VI-01) N6.
Definition code
-- Generated by scripts/release06/gen_platform_tree.py (RELEASE06; copy of release05, header only) by skeleton subtraction from Atlas/EinsteinMaxwell/EF5/CertificateEF5.lean
-- definition bundle: kept ExactVacuumAtlas.EinsteinMaxwell.EF5.samplePtEF5
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_Defs
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_EinsteinMaxwellEF5
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_Frame
import Definitions.Def_Atlas_EinsteinMaxwell_EF5_RicciOffDiag
set_option maxHeartbeats 4000000
set_option linter.unusedVariables false
/-! # Einstein–Maxwell certificate for the 5D EF static family (ATLAS-VI-01)
Unconditional replacement of the CONDITIONAL statements in `Certificate.lean`: every field of
`EMCertificateD` is discharged from proved lemmas (`einsteinMaxwellD_eq_factor`,
`maxwellDiv_ef5`, `faradayCyclic_faraday5`, plus the structural lemmas of `Defs.lean` /
`Frame.lean`). Total dimension `5 = 4 + 1`, domain `domU5 = {0 < r, 0 < u < 1}`, all
`mu beta Q : ℝ` (no sign or horizon restriction).
* `cert_iff`: `EMCertificateD (gEF5 mu beta) (giEF5 mu beta) (faraday5 Q) domU5 ↔ 3β = Q²`.
* `vacuum_cert` (`β = 0`, `Q = 0`) and `vacuum_cert_iff` (`Q = 0`: certificate ↔ `β = 0`).
* `counterexample`: at `(μ, β, Q) = (1, 1, 1)`, `E_{22} = 1/8` at `r = 2`, `u = 1/2`,
so no certificate exists. -/
open scoped ContDiff
open ExactVacuumAtlas ExactVacuumAtlas.EinsteinMaxwell ExactVacuumAtlas.EinsteinMaxwell.D
open ExactVacuumAtlas.EinsteinMaxwell.EF5
namespace ExactVacuumAtlas.EinsteinMaxwell.EF5
/-- Witness point `r = 2`, `u = 1/2` (other coordinates `0`). -/
noncomputable def samplePtEF5 : Pt 5 :=
fun i => if i.val = 1 then (2 : ℝ) else if i.val = 2 then 1 / 2 else 0
/-! ## Pure vacuum: Ricci-flat certificate -/
end ExactVacuumAtlas.EinsteinMaxwell.EF5
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; 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
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.