diff --git a/AGENTS.md b/AGENTS.md
index 5655079..1fbd825 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -1,4 +1,4 @@
-# DiffusionGeometryJ
+# DiffusionGeometryJL
 
 Julia port of the Python `DiffusionGeometry` package — data-driven calculus,
 geometry, and topology on point clouds via heat diffusion and the carré du champ
diff --git a/Project.toml b/Project.toml
index 8a53c3a..eefdae2 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,4 +1,4 @@
-name = "DiffusionGeometryJ"
+name = "DiffusionGeometryJL"
 uuid = "f8140dce-05b1-4e22-80fe-cf341a3061cb"
 version = "0.1.0"
 authors = ["Iolo Jones", "David Lanners"]
@@ -19,7 +19,7 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
 
 [extensions]
-DiffusionGeometryJMakieExt = "Makie"
+DiffusionGeometryJLMakieExt = "Makie"
 
 [compat]
 Convex = "0.16.6"
diff --git a/README.md b/README.md
index 3e78193..9d5f93a 100644
--- a/README.md
+++ b/README.md
@@ -1,4 +1,4 @@
-# DiffusionGeometryJ
+# DiffusionGeometryJL
 
 Data-driven calculus, geometry, and topology on point clouds — via heat
 diffusion and the carré du champ operator.
@@ -20,7 +20,7 @@ cite the original authors when using this software:
 
 ## What it does
 
-Given nothing but a point cloud, `DiffusionGeometryJ` builds a discrete
+Given nothing but a point cloud, `DiffusionGeometryJL` builds a discrete
 approximation of the manifold the points are sampled from and lets you do
 differential geometry on it: take gradients and Hessians, build the exact and
 Hodge Laplacians on differential forms, measure lengths and angles with the
@@ -32,7 +32,7 @@ the heat diffusion of the data — no mesh, no charts, no prescribed metric.
 
 ```julia
 using Pkg
-Pkg.add(url="https://github.com/wardjm/DiffusionGeometryJ")
+Pkg.add(url="https://github.com/wardjm/DiffusionGeometryJL")
 ```
 
 Plotting is provided through a package extension that loads only when a
@@ -45,7 +45,7 @@ Pkg.add("GLMakie")   # or CairoMakie
 ## Quick start
 
 ```julia
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 
 # a point cloud: n points in d ambient dimensions (n × d)
 data = randn(200, 3)
diff --git a/bench/bench.jl b/bench/bench.jl
index 185d002..aa8e540 100644
--- a/bench/bench.jl
+++ b/bench/bench.jl
@@ -1,6 +1,6 @@
 #!/usr/bin/env julia
-# Timing benchmark for the Julia DiffusionGeometryJ tracer-bullet pipeline.
-using DiffusionGeometryJ
+# Timing benchmark for the Julia DiffusionGeometryJL tracer-bullet pipeline.
+using DiffusionGeometryJL
 using Random, Statistics, Printf
 
 const SIZES = [200, 500, 1000, 2000, 3000, 5000]
diff --git a/bench/bench_ops.jl b/bench/bench_ops.jl
index 5ea259c..9d53bbc 100644
--- a/bench/bench_ops.jl
+++ b/bench/bench_ops.jl
@@ -1,6 +1,6 @@
 #!/usr/bin/env julia
 # Timing benchmark for the Julia operator-build path (weak-matrix contractions).
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 using Random, Statistics, Printf
 
 const SIZES = [500, 1000, 2000, 3000, 5000]
diff --git a/bench/betti_vs_ripserer.jl b/bench/betti_vs_ripserer.jl
index 6840b5f..1038ef5 100644
--- a/bench/betti_vs_ripserer.jl
+++ b/bench/betti_vs_ripserer.jl
@@ -1,4 +1,4 @@
-# Compare DiffusionGeometryJ's `betti_numbers` against persistent homology
+# Compare DiffusionGeometryJL's `betti_numbers` against persistent homology
 # (Ripserer) on a few point clouds with known topology.
 #
 # Ripserer is NOT a dependency of this package. Run this in a scratch env:
@@ -17,7 +17,7 @@
 # NOTE: `betti_numbers` needs the FULL coefficient basis
 # (n_coefficients == n_function_basis) or the harmonic forms are truncated away.
 
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 using Ripserer
 using Random
 
diff --git a/docs/Project.toml b/docs/Project.toml
index 5ec6819..363fcc4 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,5 +1,5 @@
 [deps]
-DiffusionGeometryJ = "f8140dce-05b1-4e22-80fe-cf341a3061cb"
+DiffusionGeometryJL = "f8140dce-05b1-4e22-80fe-cf341a3061cb"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 
 [compat]
diff --git a/docs/doctest_setup.jl b/docs/doctest_setup.jl
index ae4a53b..90914c8 100644
--- a/docs/doctest_setup.jl
+++ b/docs/doctest_setup.jl
@@ -7,12 +7,12 @@
 # hard to read. It is documented for the reader in `docs/src/index.md`.
 
 const DOCTEST_SETUP = quote
-    using DiffusionGeometryJ
+    using DiffusionGeometryJL
     using LinearAlgebra
 
     # Nothing unexported is imported here on purpose. The internal helpers documented on
     # the "Utilities" page (`np_reshape`, the batch helpers, `_from_pointwise_basis`) are
-    # *not* exported, so their examples spell them `DiffusionGeometryJ.np_reshape(...)` —
+    # *not* exported, so their examples spell them `DiffusionGeometryJL.np_reshape(...)` —
     # as a reader would have to.
 
     # 60 points on the unit circle in ℝ² — the running example. Its intrinsic
diff --git a/docs/make.jl b/docs/make.jl
index 1c0a361..cf5a284 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,19 +1,19 @@
 using Documenter
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 
 include(joinpath(@__DIR__, "doctest_setup.jl"))
-DocMeta.setdocmeta!(DiffusionGeometryJ, :DocTestSetup, DOCTEST_SETUP; recursive=true)
+DocMeta.setdocmeta!(DiffusionGeometryJL, :DocTestSetup, DOCTEST_SETUP; recursive=true)
 
 makedocs(;
-    sitename="DiffusionGeometryJ",
+    sitename="DiffusionGeometryJL",
     authors="Jeffrey Ward",
-    modules=[DiffusionGeometryJ],
+    modules=[DiffusionGeometryJL],
     doctest=true,
     checkdocs=:exports,          # every exported name must appear in an @docs block
     # No `warnonly`: an undocumented export, a broken doctest or a dead cross-reference
     # must fail the build, not warn.
     format=Documenter.HTML(;
-        canonical="https://wardjm.github.io/DiffusionGeometryJ",
+        canonical="https://wardjm.github.io/DiffusionGeometryJL",
         prettyurls=get(ENV, "CI", "false") == "true",
     ),
     pages=[
@@ -32,4 +32,4 @@ makedocs(;
     ],
 )
 
-deploydocs(; repo="github.com/wardjm/DiffusionGeometryJ", devbranch="main")
+deploydocs(; repo="github.com/wardjm/DiffusionGeometryJL", devbranch="main")
diff --git a/docs/src/api/diffusion.md b/docs/src/api/diffusion.md
index af09161..4cfa372 100644
--- a/docs/src/api/diffusion.md
+++ b/docs/src/api/diffusion.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 ```
 
 # Diffusion core
diff --git a/docs/src/api/geometry.md b/docs/src/api/geometry.md
index 43401d4..9b5a688 100644
--- a/docs/src/api/geometry.md
+++ b/docs/src/api/geometry.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 DocTestSetup = Main.DOCTEST_SETUP
 ```
 
diff --git a/docs/src/api/methods.md b/docs/src/api/methods.md
index 11873ed..813b3fa 100644
--- a/docs/src/api/methods.md
+++ b/docs/src/api/methods.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 ```
 
 # Numerical methods
diff --git a/docs/src/api/operators.md b/docs/src/api/operators.md
index 1aa7870..6848aee 100644
--- a/docs/src/api/operators.md
+++ b/docs/src/api/operators.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 DocTestSetup = Main.DOCTEST_SETUP
 ```
 
diff --git a/docs/src/api/tensors.md b/docs/src/api/tensors.md
index 6a6a531..a508b12 100644
--- a/docs/src/api/tensors.md
+++ b/docs/src/api/tensors.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 ```
 
 # Tensor fields
diff --git a/docs/src/api/utils.md b/docs/src/api/utils.md
index 9e2629e..7e8d3c7 100644
--- a/docs/src/api/utils.md
+++ b/docs/src/api/utils.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 ```
 
 # Utilities
diff --git a/docs/src/conventions.md b/docs/src/conventions.md
index 15119e8..1ddb652 100644
--- a/docs/src/conventions.md
+++ b/docs/src/conventions.md
@@ -1,5 +1,5 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 DocTestSetup = Main.DOCTEST_SETUP
 ```
 
@@ -41,7 +41,7 @@ carries its own [`broadcast_batch_shape`](@ref).
 julia> batch_shape(dg_function(dg, ones(3, 60)))     # three functions in one tensor
 (3,)
 
-julia> DiffusionGeometryJ.broadcast_batch_shape((3, 4), (4,))           # right-aligned
+julia> DiffusionGeometryJL.broadcast_batch_shape((3, 4), (4,))           # right-aligned
 (3, 4)
 ```
 
diff --git a/docs/src/index.md b/docs/src/index.md
index 7c28df2..9db32e4 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,9 +1,9 @@
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 DocTestSetup = Main.DOCTEST_SETUP
 ```
 
-# DiffusionGeometryJ
+# DiffusionGeometryJL
 
 Data-driven calculus, geometry, and topology on point clouds — via heat diffusion
 and the carré du champ operator.
@@ -25,7 +25,7 @@ No mesh, no charts, no prescribed metric.
 
 ```julia
 using Pkg
-Pkg.add(url="https://github.com/wardjm/DiffusionGeometryJ")
+Pkg.add(url="https://github.com/wardjm/DiffusionGeometryJL")
 ```
 
 Plotting comes from a package extension that loads when a
diff --git a/docs/src/plotting.md b/docs/src/plotting.md
index 85b5876..1fdbdc1 100644
--- a/docs/src/plotting.md
+++ b/docs/src/plotting.md
@@ -7,7 +7,7 @@ functions exist but have no methods, and calling one prints a hint telling you t
 load a backend.
 
 ```julia
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 using GLMakie          # interactive; or CairoMakie for vector (PDF/SVG/PNG) output
 
 dg = from_point_cloud(points)
@@ -111,7 +111,7 @@ deliberately absent:
 ## API
 
 ```@meta
-CurrentModule = DiffusionGeometryJ
+CurrentModule = DiffusionGeometryJL
 ```
 
 The plot functions have no methods until a Makie backend is loaded, so their examples
diff --git a/ext/DiffusionGeometryJMakieExt.jl b/ext/DiffusionGeometryJLMakieExt.jl
similarity index 92%
rename from ext/DiffusionGeometryJMakieExt.jl
rename to ext/DiffusionGeometryJLMakieExt.jl
index 7788384..370f33b 100644
--- a/ext/DiffusionGeometryJMakieExt.jl
+++ b/ext/DiffusionGeometryJLMakieExt.jl
@@ -1,4 +1,4 @@
-# Makie plotting for DiffusionGeometryJ.
+# Makie plotting for DiffusionGeometryJL.
 #
 # Loaded automatically once the user loads Makie (via GLMakie, CairoMakie, …).
 # Replaces the Python `diffusion_geometry/visualisation.py` and
@@ -7,7 +7,7 @@
 # The plotting functions themselves are declared in `src/visualisation/api.jl`; the
 # `@recipe` calls below add methods to *those* functions (the macro escapes the
 # function name, so it extends the imported binding rather than shadowing it), which
-# is what lets `DiffusionGeometryJ` export names an extension implements.
+# is what lets `DiffusionGeometryJL` export names an extension implements.
 #
 # Three pieces of `visualisation.py` are deliberately not ported:
 #
@@ -23,7 +23,7 @@
 # and locks the aspect ratio of the axis it creates. `LScene` draws a 3D axis by default,
 # so this is not something Makie gives for free.
 
-module DiffusionGeometryJMakieExt
+module DiffusionGeometryJLMakieExt
 
 using Makie
 using Makie: Point, Point2f, Point3f, Vec, Vec3f, lift, to_value
@@ -33,13 +33,13 @@ using Statistics: median, mean
 
 const GeometryBasics = Makie.GeometryBasics
 
-using DiffusionGeometryJ:
+using DiffusionGeometryJL:
     AbstractTensor, ScalarFunction, VectorField, Form, Tensor02, Tensor02Sym,
     DIVERGING_COLORMAP, CYCLIC_COLORMAP,
     ambient_dim, batch_shape, degree, full_tensor, geometry, hodge_star_2_form,
     immersion_coords, to_ambient, to_pointwise_basis
 
-import DiffusionGeometryJ:
+import DiffusionGeometryJL:
     dgplot, dgplot!, dgscatter, dgscatter!, dgquiver, dgquiver!,
     dg2form, dg2form!, dg3form, dg3form!, dgellipsoids, dgellipsoids!,
     dgeiglines, dgeiglines!, dgtangentplanes, dgtangentplanes!, dganimate
diff --git a/src/DiffusionGeometryJ.jl b/src/DiffusionGeometryJL.jl
similarity index 99%
rename from src/DiffusionGeometryJ.jl
rename to src/DiffusionGeometryJL.jl
index 6c6f251..88c48a8 100644
--- a/src/DiffusionGeometryJ.jl
+++ b/src/DiffusionGeometryJL.jl
@@ -1,4 +1,4 @@
-module DiffusionGeometryJ
+module DiffusionGeometryJL
 
 # ── Phase 1: combinatorics + utils ────────────────────────────────────────────
 include("utils/basis_utils.jl")
diff --git a/src/tensors/base_tensor/base_tensor_space.jl b/src/tensors/base_tensor/base_tensor_space.jl
index e13a753..b3e0ce3 100644
--- a/src/tensors/base_tensor/base_tensor_space.jl
+++ b/src/tensors/base_tensor/base_tensor_space.jl
@@ -123,10 +123,10 @@ gram(space::AbstractTensorSpace) = gram(_u_coeffs(space.dg), cdc_components(spac
 
 # Examples
 ```jldoctest
-julia> DiffusionGeometryJ._is_orthonormal(function_space(dg))
+julia> DiffusionGeometryJL._is_orthonormal(function_space(dg))
 true
 
-julia> DiffusionGeometryJ._is_orthonormal(vector_field_space(dg))
+julia> DiffusionGeometryJL._is_orthonormal(vector_field_space(dg))
 false
 ```
 """
@@ -149,7 +149,7 @@ but the weakest are two orders of magnitude down on the rest. Those are the ambi
 directions *normal* to the circle, which the metric barely sees:
 
 ```jldoctest
-julia> vals, vecs = DiffusionGeometryJ._gram_spectrum(vector_field_space(dg));
+julia> vals, vecs = DiffusionGeometryJL._gram_spectrum(vector_field_space(dg));
 
 julia> length(vals)
 16
diff --git a/src/utils/basis_conversions.jl b/src/utils/basis_conversions.jl
index 5119dd0..5a1db1e 100644
--- a/src/utils/basis_conversions.jl
+++ b/src/utils/basis_conversions.jl
@@ -26,7 +26,7 @@ coefficients 2 and 3 are non-zero — and by Parseval they carry all of its L²
 `∫cos²θ = 1/2`:
 
 ```jldoctest
-julia> c = DiffusionGeometryJ._from_pointwise_basis(reshape(cos.(θ), 60, 1), function_space(dg));
+julia> c = DiffusionGeometryJL._from_pointwise_basis(reshape(cos.(θ), 60, 1), function_space(dg));
 
 julia> findall(>(1e-3), abs.(c))          # supported on the λ = 1 eigenspace alone
 2-element Vector{Int64}:
@@ -75,7 +75,7 @@ Evaluating the coefficients of `f` back at the 60 sample points recovers `cos θ
 to the error of the 8-function truncation:
 
 ```jldoctest
-julia> values = DiffusionGeometryJ._to_pointwise_basis(f.coeffs, function_space(dg); basis_count=8);
+julia> values = DiffusionGeometryJL._to_pointwise_basis(f.coeffs, function_space(dg); basis_count=8);
 
 julia> size(values)
 (60,)
diff --git a/src/utils/batch_utils.jl b/src/utils/batch_utils.jl
index 8104248..3846f1c 100644
--- a/src/utils/batch_utils.jl
+++ b/src/utils/batch_utils.jl
@@ -16,16 +16,16 @@ function rather than a delegation. Throws `DimensionMismatch` if the shapes conf
 
 # Examples
 ```jldoctest
-julia> DiffusionGeometryJ.broadcast_batch_shape((3, 4), (4,))       # right-aligned: (4,) fills the last axis
+julia> DiffusionGeometryJL.broadcast_batch_shape((3, 4), (4,))       # right-aligned: (4,) fills the last axis
 (3, 4)
 
-julia> DiffusionGeometryJ.broadcast_batch_shape((3, 1), (1, 4))     # length-1 axes stretch
+julia> DiffusionGeometryJL.broadcast_batch_shape((3, 1), (1, 4))     # length-1 axes stretch
 (3, 4)
 
-julia> DiffusionGeometryJ.broadcast_batch_shape((), (5,))           # an unbatched tensor joins any batch
+julia> DiffusionGeometryJL.broadcast_batch_shape((), (5,))           # an unbatched tensor joins any batch
 (5,)
 
-julia> DiffusionGeometryJ.broadcast_batch_shape((3,), (4,))
+julia> DiffusionGeometryJL.broadcast_batch_shape((3,), (4,))
 ERROR: DimensionMismatch: Incompatible batch shapes: ((3,), (4,))
 ```
 """
@@ -83,10 +83,10 @@ axes it already has. Julia's own broadcasting then reproduces numpy's semantics:
 
 # Examples
 ```jldoctest
-julia> size(DiffusionGeometryJ.pad_batch_dims(zeros(4, 6), 2))         # batch (4,), coeff axis 6
+julia> size(DiffusionGeometryJL.pad_batch_dims(zeros(4, 6), 2))         # batch (4,), coeff axis 6
 (1, 4, 6)
 
-julia> size(DiffusionGeometryJ.pad_batch_dims(zeros(4, 6), 1))         # already rank 1: untouched
+julia> size(DiffusionGeometryJL.pad_batch_dims(zeros(4, 6), 1))         # already rank 1: untouched
 (4, 6)
 ```
 """
@@ -106,7 +106,7 @@ rule. Both arrays keep their `ntail` trailing (non-batch) axes.
 
 # Examples
 ```jldoctest
-julia> a, b = DiffusionGeometryJ.align_batch_pair(zeros(3, 4, 6), zeros(4, 6));
+julia> a, b = DiffusionGeometryJL.align_batch_pair(zeros(3, 4, 6), zeros(4, 6));
 
 julia> size(a), size(b)                # b gained a leading singleton axis
 ((3, 4, 6), (1, 4, 6))
@@ -129,12 +129,12 @@ einsum; prefer [`pad_batch_dims`](@ref) when plain broadcasting will do.
 
 # Examples
 ```jldoctest
-julia> size(DiffusionGeometryJ.broadcast_batch_to(ones(4, 6), (3, 4)))     # copied along the new axis
+julia> size(DiffusionGeometryJL.broadcast_batch_to(ones(4, 6), (3, 4)))     # copied along the new axis
 (3, 4, 6)
 
 julia> A = ones(4, 6);
 
-julia> DiffusionGeometryJ.broadcast_batch_to(A, (4,)) === A                # already the target: no copy
+julia> DiffusionGeometryJL.broadcast_batch_to(A, (4,)) === A                # already the target: no copy
 true
 ```
 """
@@ -155,7 +155,7 @@ axis, giving `(prod(target), tail...)` — the layout the einsum kernels want.
 
 # Examples
 ```jldoctest
-julia> size(DiffusionGeometryJ.broadcast_flatten_batch(ones(4, 6), (3, 4)))    # batch (3, 4) → 12 rows
+julia> size(DiffusionGeometryJL.broadcast_flatten_batch(ones(4, 6), (3, 4)))    # batch (3, 4) → 12 rows
 (12, 6)
 ```
 """
@@ -174,12 +174,12 @@ return the array together with its leading batch shape. This is the check every
 
 # Examples
 ```jldoctest
-julia> _, batch = DiffusionGeometryJ.infer_batch_shape(zeros(3, 5, 16), (16,));
+julia> _, batch = DiffusionGeometryJL.infer_batch_shape(zeros(3, 5, 16), (16,));
 
 julia> batch
 (3, 5)
 
-julia> DiffusionGeometryJ.infer_batch_shape(zeros(3, 15), (16,); name="VectorField")
+julia> DiffusionGeometryJL.infer_batch_shape(zeros(3, 15), (16,); name="VectorField")
 ERROR: AssertionError: VectorField coefficients must have trailing shape (16,), got (3, 15)
 ```
 """
@@ -201,12 +201,12 @@ Undone by [`restore_batch_dims`](@ref).
 
 # Examples
 ```jldoctest
-julia> flat, batch = DiffusionGeometryJ.flatten_batch_dims(zeros(2, 3, 16));
+julia> flat, batch = DiffusionGeometryJL.flatten_batch_dims(zeros(2, 3, 16));
 
 julia> size(flat), batch
 ((6, 16), (2, 3))
 
-julia> flat, batch = DiffusionGeometryJ.flatten_batch_dims(zeros(16));    # unbatched: one row, empty batch
+julia> flat, batch = DiffusionGeometryJL.flatten_batch_dims(zeros(16));    # unbatched: one row, empty batch
 
 julia> size(flat), batch
 ((1, 16), ())
@@ -230,12 +230,12 @@ Inverse of [`flatten_batch_dims`](@ref): reshape a `(prod(batch), L)` matrix bac
 ```jldoctest
 julia> A = reshape(1.0:96.0, 2, 3, 16);
 
-julia> flat, batch = DiffusionGeometryJ.flatten_batch_dims(A);
+julia> flat, batch = DiffusionGeometryJL.flatten_batch_dims(A);
 
-julia> DiffusionGeometryJ.restore_batch_dims(flat, batch) == A            # a round trip
+julia> DiffusionGeometryJL.restore_batch_dims(flat, batch) == A            # a round trip
 true
 
-julia> size(DiffusionGeometryJ.restore_batch_dims(zeros(1, 16), ()))      # empty batch → a plain vector
+julia> size(DiffusionGeometryJL.restore_batch_dims(zeros(1, 16), ()))      # empty batch → a plain vector
 (16,)
 ```
 """
diff --git a/src/utils/reshape_utils.jl b/src/utils/reshape_utils.jl
index bd0a3d5..a433a74 100644
--- a/src/utils/reshape_utils.jl
+++ b/src/utils/reshape_utils.jl
@@ -18,7 +18,7 @@ every coefficient vector in the package (`(i, a) ↦ i·C + a`, basis index slow
 Reading order is by rows, not columns — this is what `Base.reshape` would *not* do:
 
 ```jldoctest
-julia> DiffusionGeometryJ.np_reshape([1 2 3; 4 5 6], 3, 2)
+julia> DiffusionGeometryJL.np_reshape([1 2 3; 4 5 6], 3, 2)
 3×2 Matrix{Int64}:
  1  2
  3  4
@@ -36,7 +36,7 @@ It round-trips, so a flattened coefficient vector can always be unpacked again:
 ```jldoctest
 julia> A = reshape(1:12, 2, 2, 3);
 
-julia> DiffusionGeometryJ.np_reshape(DiffusionGeometryJ.np_reshape(A, 2, 6), 2, 2, 3) == A
+julia> DiffusionGeometryJL.np_reshape(DiffusionGeometryJL.np_reshape(A, 2, 6), 2, 2, 3) == A
 true
 ```
 """
diff --git a/src/visualisation/api.jl b/src/visualisation/api.jl
index 0a049c4..13c080a 100644
--- a/src/visualisation/api.jl
+++ b/src/visualisation/api.jl
@@ -1,6 +1,6 @@
 # Public plotting API.
 #
-# The implementations live in `ext/DiffusionGeometryJMakieExt.jl`, a package
+# The implementations live in `ext/DiffusionGeometryJLMakieExt.jl`, a package
 # extension that loads only once the user has loaded Makie (via a backend such as
 # GLMakie or CairoMakie). The names are declared here so they are exported and
 # documented from the package proper, and so `@recipe` in the extension adds
@@ -47,7 +47,7 @@ are forwarded to the underlying recipe — see [`dgscatter`](@ref), [`dgquiver`]
 
 # Examples
 ```julia
-using GLMakie, DiffusionGeometryJ
+using GLMakie, DiffusionGeometryJL
 
 θ = range(0, 2π; length=61)[1:60]
 dg = from_point_cloud([cos.(θ) sin.(θ)]; knn_kernel=16, n_function_basis=8)
@@ -177,7 +177,7 @@ being renormalised each frame. Replaces the Python `methods/pde.py::gif_from_fun
 
 # Examples
 ```julia
-using GLMakie, DiffusionGeometryJ
+using GLMakie, DiffusionGeometryJL
 
 u = solve_differential_operator(-laplacian(dg, 0), f, range(0, 2; length=60))
 dganimate(u, "heat.mp4"; framerate=30)
diff --git a/test/doctests.jl b/test/doctests.jl
index 26e89e7..4d01b2a 100644
--- a/test/doctests.jl
+++ b/test/doctests.jl
@@ -10,11 +10,11 @@
 using Documenter
 
 include(joinpath(@__DIR__, "..", "docs", "doctest_setup.jl"))
-DocMeta.setdocmeta!(DiffusionGeometryJ, :DocTestSetup, DOCTEST_SETUP; recursive=true)
+DocMeta.setdocmeta!(DiffusionGeometryJL, :DocTestSetup, DOCTEST_SETUP; recursive=true)
 
 @testset "doctests" begin
     # `manual=true` also runs the `jldoctest` blocks in the manual pages under
     # `docs/src`, so the examples in the guide are held to the suite too, not just
     # the ones in docstrings.
-    doctest(DiffusionGeometryJ; manual=true)
+    doctest(DiffusionGeometryJL; manual=true)
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 16fa3c8..fe74cf2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,11 +1,11 @@
 using Test
 using LinearAlgebra
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 
 include("parity.jl")
 include("pysuite.jl")
 
-@testset "DiffusionGeometryJ" begin
+@testset "DiffusionGeometryJL" begin
     include("test_basis_utils.jl")
     include("test_regularise.jl")
     include("test_diffusion_core.jl")
diff --git a/test/test_makie_ext.jl b/test/test_makie_ext.jl
index 907d7f2..c1f7076 100644
--- a/test/test_makie_ext.jl
+++ b/test/test_makie_ext.jl
@@ -6,13 +6,13 @@
 
 using CairoMakie
 using CairoMakie: Makie
-using DiffusionGeometryJ: batch_shape, full_tensor
+using DiffusionGeometryJL: batch_shape, full_tensor
 using LinearAlgebra: norm, eigen, Symmetric
 using Random: MersenneTwister
 
 # Loading CairoMakie triggers the package extension; reach into it for the recipe
 # plot types and internal helpers the structural tests assert against.
-const Ext = Base.get_extension(DiffusionGeometryJ, :DiffusionGeometryJMakieExt)
+const Ext = Base.get_extension(DiffusionGeometryJL, :DiffusionGeometryJLMakieExt)
 @assert Ext !== nothing "Makie extension failed to load"
 
 # ── Fixtures: a 2D disc and a 3D torus, each with a diffusion geometry ─────────
diff --git a/test/test_notebooks.jl b/test/test_notebooks.jl
index 3c97570..64e460c 100644
--- a/test/test_notebooks.jl
+++ b/test/test_notebooks.jl
@@ -18,7 +18,7 @@ using Statistics: mean, median, cor
     aeq(a, b; rtol=1e-8, atol=1e-10) = isapprox(a, b; rtol=rtol, atol=atol)
 
     "Pointwise data of an unbatched tensor as an `(n, C)` matrix (C-order, as Python)."
-    pointwise(t, n, c) = DiffusionGeometryJ.np_reshape(vec(to_pointwise_basis(t)), n, c)
+    pointwise(t, n, c) = DiffusionGeometryJL.np_reshape(vec(to_pointwise_basis(t)), n, c)
 
     @testset "manifold_diffusion_geometry_intro: torus scalar curvature" begin
         fx = load_fixture("notebook_curvature")
diff --git a/test/test_pyclasses.jl b/test/test_pyclasses.jl
index b3bdbc3..68b78c3 100644
--- a/test/test_pyclasses.jl
+++ b/test/test_pyclasses.jl
@@ -12,7 +12,7 @@
 using Combinatorics: combinations
 using OMEinsum: @ein_str
 # Internal accessors the tests need: none of these are exported.
-using DiffusionGeometryJ: coeffs, space, geometry, batch_shape, np_reshape,
+using DiffusionGeometryJL: coeffs, space, geometry, batch_shape, np_reshape,
                           _spectral_decomposition, regularise_fn
 using SparseArrays: sparse, findnz
 
diff --git a/test/test_pysrc.jl b/test/test_pysrc.jl
index 01cc3ca..ffd2133 100644
--- a/test/test_pysrc.jl
+++ b/test/test_pysrc.jl
@@ -16,7 +16,7 @@
 using Combinatorics: combinations
 # `coeffs` and `np_reshape` are internal; the tests need them to poke at the
 # coefficient layout, which flattens C-order like numpy.
-using DiffusionGeometryJ: coeffs, np_reshape
+using DiffusionGeometryJL: coeffs, np_reshape
 
 # ── test_cache_properties.py ──────────────────────────────────────────────────
 @testset "cache_properties" begin
diff --git a/test/test_topology.jl b/test/test_topology.jl
index ec282da..fe0871b 100644
--- a/test/test_topology.jl
+++ b/test/test_topology.jl
@@ -5,7 +5,7 @@
 # contract. Higher Betti numbers are a spectral-gap heuristic (see the caveats in
 # src/methods/topology.jl) and are not asserted for their topological value here.
 
-using DiffusionGeometryJ
+using DiffusionGeometryJL
 using Random: MersenneTwister
 
 # Build a geometry with the FULL coefficient basis — betti detection needs it.