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`BookProof.ScalaronFock.qgScalaronModeFock_stone_flow` : ∃ (T : UnboundedSelfAdjoint modeFock) (U : ℝ → (modeFock →L[ℂ] modeFock)), IsSelfAdjointExtension (qgScalaronModeFockHamilt

Proved
BookProof.ScalaronFock.qgScalaronModeFock_stone_flow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScalaronFockEsa.

BookProof.ScalaronFock.qgScalaronModeFock_stone_flow : ∃ (T : UnboundedSelfAdjoint modeFock) (U : ℝ → (modeFock →L[ℂ] modeFock)), IsSelfAdjointExtension (qgScalaronModeFockHamiltonian a b M alpha Rc phi) T.op ∧ IsStoneFlow T U

Formalization note: Lean 4 identifier BookProof.ScalaronFock.qgScalaronModeFock_stone_flow.

Preamble
-- Generated from ChapterScalaronFockEsa.lean — theorem BookProof.ScalaronFock.qgScalaronModeFock_stone_flow
import Definitions.Def_ChapterStarobinskyPotential
import Definitions.Def_ChapterScalaronCoreEsa
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterQuantumGravityDensitized
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterScalaronFockEsa
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterStoneResolvent
open BookProof.EsaClosure
open BookProof.FarisLavine
open BookProof.StoneBridge
open BookProof.ScalaronFock


open Filter Topology MeasureTheory SchwartzMap


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

noncomputable section

variable {E : ℕ → Type*} [∀ n, NormedAddCommGroup (E n)] [∀ n, InnerProductSpace ℝ (E n)]
  [∀ n, FiniteDimensional ℝ (E n)] [∀ n, MeasurableSpace (E n)] [∀ n, BorelSpace (E n)]
variable (a b : ℕ → ℕ → ℝ) (M alpha : ℝ) (Rc phi : ℕ → ℕ → ℝ)
Formal statement
theorem BookProof.ScalaronFock.qgScalaronModeFock_stone_flow :
    ∃ (T : UnboundedSelfAdjoint modeFock) (U : ℝ → (modeFock →L[ℂ] modeFock)),
      IsSelfAdjointExtension (qgScalaronModeFockHamiltonian a b M alpha Rc phi) T.op ∧
        IsStoneFlow T U := by sorry

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