(hκ : ∀ i, 0 ≤ κ i) (i₀ : Fin d) : commForm (ShiftData.shiftH (modeData hκ i₀)) (diagMax (fockSym κ)) (testState κ i₀) = 2 * (4 * κ i₀) * modeAmp κ i₀ 0

Proved

BookProof.NavierStokesFlow.FockManyMode.commForm_testState_self

by leonardopedro · Oct 2, 2026 · Mathlib 0df444a (Lean v4.33.1)

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.FockManyMode.commForm_testState_self (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble

-- Generated from ChapterNavierStokesFockManyMode.lean — theorem BookProof.NavierStokesFlow.FockManyMode.commForm_testState_self
import Mathlib
import Definitions.Def_ChapterNavierStokesFockManyMode
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesShiftHamiltonian
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow.HermiteFarisLavine
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.ShiftHamiltonian.ShiftData
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.FockManyMode

variable {d : ℕ} {κ : Fin d → ℝ}


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato ShiftHamiltonian

Formal statement

theorem BookProof.NavierStokesFlow.FockManyMode.commForm_testState_self (hκ : ∀ i, 0 ≤ κ i) (i₀ : Fin d) :
    commForm (ShiftData.shiftH (modeData hκ i₀)) (diagMax (fockSym κ)) (testState κ i₀)
      = 2 * (4 * κ i₀) * modeAmp κ i₀ 0 := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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