`BookProof.VielbeinFock.vielbeinFock_stone_flow` (M alpha : ℝ) (d : ℕ) (om : Fin d → ℝ) : ∃ (T : UnboundedSelfAdjoint (vielbeinFock d)) (U : ℝ → (vielbeinFock d →L[ℂ] vielbeinFock

Proved

BookProof.VielbeinFock.vielbeinFock_stone_flow

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterVielbeinFiberFock.

BookProof.VielbeinFock.vielbeinFock_stone_flow (M alpha : ℝ) (d : ℕ) (om : Fin d → ℝ) : ∃ (T : UnboundedSelfAdjoint (vielbeinFock d)) (U : ℝ → (vielbeinFock d →L[ℂ] vielbeinFock d)), IsSelfAdjointExtension (vielbeinFockHamiltonian M alpha d om) T.op ∧ IsStoneFlow T U

Formalization note: Lean 4 identifier BookProof.VielbeinFock.vielbeinFock_stone_flow.

Preamble

-- Generated from ChapterVielbeinFiberFock.lean — theorem BookProof.VielbeinFock.vielbeinFock_stone_flow
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterScalaronCoreEsa
import Definitions.Def_ChapterScalaronFockEsa
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterVielbeinFiberFock
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterStoneResolvent
open BookProof.EsaClosure
open BookProof.StoneBridge
open BookProof.VielbeinFock


open Filter Topology MeasureTheory


open BookProof.Starobinsky BookProof.ScalaronEsa BookProof.ScalaronFock
open BookProof.DirectSumEsa BookProof.StoneBridge BookProof.EsaClosure
open BookProof.FarisLavine BookProof.ChapterStoneResolvent

noncomputable section

Formal statement

theorem BookProof.VielbeinFock.vielbeinFock_stone_flow (M alpha : ℝ) (d : ℕ) (om : Fin d → ℝ) :
    ∃ (T : UnboundedSelfAdjoint (vielbeinFock d))
      (U : ℝ → (vielbeinFock d →L[ℂ] vielbeinFock d)),
      IsSelfAdjointExtension (vielbeinFockHamiltonian M alpha d om) T.op ∧ IsStoneFlow T U := by sorry

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