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The number operator is a projection: `N² = N`; its eigenvalues are `0` and `1`, the fermionic occupation numbers

Proved
BookProof.NavierStokes.ghostNumber_idem

by leonardopedro · Sep 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

ghostsnavier-stokestimepiece

The number operator is a projection: N² = N; its eigenvalues are 0 and 1, the fermionic occupation numbers.

Formalization Note. Lean 4 identifier: BookProof.NavierStokes.ghostNumber_idem (module BookProof.NavierStokes), line-linked source: ChapterNavierStokes.lean lines 121–126.

Preamble
-- Generated from ChapterNavierStokes.lean — theorem BookProof.NavierStokes.ghostNumber_idem
import Mathlib
import Definitions.Def_ChapterNavierStokes
open BookProof.NavierStokes












open Matrix
Formal statement
theorem BookProof.NavierStokes.ghostNumber_idem : ghostNumber * ghostNumber = ghostNumber := by sorry
Source
https://github.com/leonardopedro/timepiece/blob/61595bc/BookProof/ChapterNavierStokes.lean#L121-L126

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