pith. machine review for the scientific record. sign in
theorem proved term proof

Q3_vertices_eq

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

  31theorem Q3_vertices_eq : Q3_vertices = 2 ^ Q3_degree := by

proof body

Term-mode proof.

  32  unfold Q3_vertices Q3_degree; omega
  33
  34/-! ## Q₃ Laplacian Spectrum
  35
  36The graph Laplacian L = D − A of Q₃ has eigenvalues determined by the
  37Hamming weight of binary vectors in {0,1}³. For vertex v with Hamming
  38weight w(v), the eigenvalue is 2·w(v). The spectrum is:
  39- λ₀ = 0 (multiplicity 1, the all-ones eigenvector)
  40- λ₁ = 2 (multiplicity 3, the three coordinate functions)
  41- λ₂ = 4 (multiplicity 3, the three pairwise products)
  42- λ₃ = 6 (multiplicity 1, the parity function)
  43-/
  44

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (27)

Lean names referenced from this declaration's body.