pith. machine review for the scientific record. sign in
structure definition def or abbrev

EdgeLengthField

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)

  76structure EdgeLengthField (n : ℕ) where
  77  base_spacing : ℝ
  78  base_spacing_pos : 0 < base_spacing
  79  length : Fin n → Fin n → ℝ
  80  length_symm : ∀ i j, length i j = length j i
  81  length_pos : ∀ i j, 0 < length i j
  82
  83/-- The canonical conformal edge-length map:
  84    `L_{ij}(ε) = a · exp((ε_i + ε_j)/2)`.
  85
  86    In the flat vacuum `ε ≡ 0`, this reduces to `L_{ij} = a`. At leading
  87    order in small `ε`, `L_{ij}/a - 1 = (ε_i + ε_j)/2 + O(ε²)`. This is
  88    the standard conformal rescaling convention used when the recognition
  89    potential is identified with a scalar metric perturbation. -/

used by (18)

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.