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

spectralGapRatio

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)

  26theorem spectralGapRatio (k : ℕ) :
  27    spectralGap (k + 1) / spectralGap k = phi⁻¹ := by

proof body

Term-mode proof.

  28  unfold spectralGap
  29  have hk := (pow_pos phi_pos k).ne'
  30  rw [pow_succ, mul_inv]
  31  field_simp [hk, phi_ne_zero]
  32
  33/-- At k=2: spectral gap = 1/φ². -/

used by (1)

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

depends on (9)

Lean names referenced from this declaration's body.