diff --git a/src/basis/nedelec_reference.jl b/src/basis/nedelec_reference.jl
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+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Reference lowest-order **Whitney 1-forms** on the **linear reference tetrahedron**
+with vertices `(0,0,0)`, `(1,0,0)`, `(0,1,0)`, `(0,0,1)` ([`reference_coordinates(::Tet4)`](@ref)).
+
+Barycentric coordinates `λ₁ … λ₄` sum to `1`; gradients are constant.
+Each edge `local_edge ∈ 1:6` carries one Whitney basis
+
+``\\mathbf{N}_{ij} = \\lambda_i \\nabla\\lambda_j - \\lambda_j \\nabla\\lambda_i``,
+
+with `(i,j)` from [`edges(::Tet4)`](@ref).
+
+Push-forward to physical space uses [`piola_covariant`](@ref) with `J = ∂x/∂ξ`.
+
+[`nedelec_hierarchical_tet_edge_reference`](@ref) adds a second **edge-aligned**
+reference mode per local edge (product of barycentric factors on that edge with
+the Whitney form). This is a convenient hierarchical enrichment toward higher
+polynomial edge spaces; it is not a full enumerated `k = 2` Nédélec basis.
+
+This file intentionally stays reference-domain only — assembly kernels can call
+these helpers inside quadrature loops once `J` is available.
+"""
+
+using Tensors
+
+"""
+    nedelec_hierarchical_tet_edge_reference(local_edge::Int, slot::Int, ξ::Vec{3}) -> Vec{3}
+
+Two reference vector fields per `local_edge ∈ 1:6` on the reference `Tet4`:
+
+  - `slot == 1`: [`nedelec_whitney_tet_reference`](@ref) (lowest-order Whitney).
+  - `slot == 2`: ``λ_a λ_b \\, \\mathbf{N}^{\\mathrm{Whitney}}`` with `(a,b)` the
+    endpoints of that edge in [`edges(::Tet4)`](@ref) order.
+
+`slot` must be `1` or `2`.
+"""
+@inline function nedelec_hierarchical_tet_edge_reference(local_edge::Int, slot::Int, ξ::Vec{3})
+    w = nedelec_whitney_tet_reference(local_edge, ξ)
+    slot == 1 && return w
+    slot == 2 || throw(ArgumentError("slot must be 1 (Whitney) or 2 (λ_a λ_b enrichment), got $slot"))
+    ed = edges(Tet4())[local_edge]
+    va, vb = ed.vertices
+    ξ₁ = ξ[1]
+    ξ₂ = ξ[2]
+    ξ₃ = ξ[3]
+    λ1 = 1 - ξ₁ - ξ₂ - ξ₃
+    λ2 = ξ₁
+    λ3 = ξ₂
+    λ4 = ξ₃
+    λ = (λ1, λ2, λ3, λ4)
+    @inbounds bubble = λ[va] * λ[vb]
+    return bubble * w
+end
+
+"""
+    nedelec_whitney_tet_reference(local_edge::Int, ξ::Vec{3}) -> Vec{3}
+
+Whitney edge basis on the reference `Tet4`, `ξ` in Cartesian coordinates of the
+reference simplex (`ξ₁+ξ₂+ξ₃ ≤ 1`, `ξₖ ≥ 0`).
+"""
+@inline function nedelec_whitney_tet_reference(local_edge::Int, ξ::Vec{3})
+    ξ₁ = ξ[1]
+    ξ₂ = ξ[2]
+    ξ₃ = ξ[3]
+    λ1 = 1 - ξ₁ - ξ₂ - ξ₃
+    λ2 = ξ₁
+    λ3 = ξ₂
+    λ4 = ξ₃
+    ∇λ1 = Vec((-1.0, -1.0, -1.0))
+    ∇λ2 = Vec((1.0, 0.0, 0.0))
+    ∇λ3 = Vec((0.0, 1.0, 0.0))
+    ∇λ4 = Vec((0.0, 0.0, 1.0))
+    λ = (λ1, λ2, λ3, λ4)
+    ∇λ = (∇λ1, ∇λ2, ∇λ3, ∇λ4)
+    ed = edges(Tet4())[local_edge]
+    va, vb = ed.vertices
+    @inbounds return λ[va] * ∇λ[vb] - λ[vb] * ∇λ[va]
+end