From f4c3a2098b3638b15374451e56404f8975ba81bd Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 10:23:19 +0100
Subject: [PATCH 01/23] remove TK from project.toml

---
 Project.toml | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Project.toml b/Project.toml
index 65904cb..1d8b729 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "MultiTensorKit"
 uuid = "f0555a46-f681-4ef1-bed5-d64870568636"
-authors = ["Boris De Vos, Laurens Lootens and Lukas Devos"]
 version = "0.1.0"
+authors = ["Boris De Vos, Laurens Lootens and Lukas Devos"]
 
 [deps]
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
@@ -15,7 +15,6 @@ LinearAlgebra = "1"
 Pkg = "1"
 Random = "1"
 SafeTestsets = "0.1"
-TensorKit = "0.16, 0.17"
 TensorKitSectors = "0.3.7"
 TensorOperations = "5"
 Test = "1.10"
@@ -27,10 +26,9 @@ Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
-TensorKit = "07d1fe3e-3e46-537d-9eac-e9e13d0d4cec"
 TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TestExtras = "5ed8adda-3752-4e41-b88a-e8b09835ee3a"
 
 [targets]
-test = ["Aqua", "LinearAlgebra", "Random", "SafeTestsets", "TensorKit", "TensorOperations", "Test", "TestExtras"]
\ No newline at end of file
+test = ["Aqua", "LinearAlgebra", "Random", "SafeTestsets", "TensorOperations", "Test", "TestExtras"]

From 89a72868ec0d04f2fe5a84ff46ab0999653981a3 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 10:46:09 +0100
Subject: [PATCH 02/23] add TK as weakdep

---
 Project.toml | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/Project.toml b/Project.toml
index 1d8b729..beb6f30 100644
--- a/Project.toml
+++ b/Project.toml
@@ -8,6 +8,9 @@ DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 TensorKitSectors = "13a9c161-d5da-41f0-bcbd-e1a08ae0647f"
 
+[weakdeps]
+TensorKit = "07d1fe3e-3e46-537d-9eac-e9e13d0d4cec"
+
 [compat]
 Aqua = "0.8.9"
 DelimitedFiles = "1.9"
@@ -15,6 +18,7 @@ LinearAlgebra = "1"
 Pkg = "1"
 Random = "1"
 SafeTestsets = "0.1"
+TensorKit = "0.17.2"
 TensorKitSectors = "0.3.7"
 TensorOperations = "5"
 Test = "1.10"

From 817fac38496ab33d30f36c5734f110cc8a162443 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 10:47:05 +0100
Subject: [PATCH 03/23] fix bounds in constructor

---
 src/bimodulesector.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 4ea5896..a02a80a 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -7,9 +7,9 @@ struct BimoduleSector{Name} <: Sector
     function BimoduleSector{Name}(i::Int, j::Int, label::Int) where {Name}
         Name ∈ ImplementedBimoduleSectors ||
             throw(ArgumentError("BimoduleSector $Name not implemented"))
-        i <= size(BimoduleSector{Name}) && j <= size(BimoduleSector{Name}) ||
+        1 <= i <= size(BimoduleSector{Name}) && 1 <= j <= size(BimoduleSector{Name}) ||
             throw(DomainError("object outside the matrix $Name"))
-        return label <= _numlabels(BimoduleSector{Name}, i, j) ? new{Name}(i, j, label) :
+        return 1 <= label <= _numlabels(BimoduleSector{Name}, i, j) ? new{Name}(i, j, label) :
             throw(DomainError("label outside category $Name($i, $j)"))
     end
 end

From b00fcfacd80ea317f97eca6bc0bededfd6d10673 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 12:18:46 +0100
Subject: [PATCH 04/23] clearer domain errors

---
 src/bimodulesector.jl | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index a02a80a..ae348e9 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -7,10 +7,11 @@ struct BimoduleSector{Name} <: Sector
     function BimoduleSector{Name}(i::Int, j::Int, label::Int) where {Name}
         Name ∈ ImplementedBimoduleSectors ||
             throw(ArgumentError("BimoduleSector $Name not implemented"))
-        1 <= i <= size(BimoduleSector{Name}) && 1 <= j <= size(BimoduleSector{Name}) ||
-            throw(DomainError("object outside the matrix $Name"))
+        r = size(BimoduleSector{Name})
+        (1 <= i <= r && 1 <= j <= r) ||
+            throw(DomainError((i, j), "subcategory outside the $r×$r matrix $Name"))
         return 1 <= label <= _numlabels(BimoduleSector{Name}, i, j) ? new{Name}(i, j, label) :
-            throw(DomainError("label outside category $Name($i, $j)"))
+            throw(DomainError(label, "label outside category $Name($i, $j)"))
     end
 end
 

From d9c2354f79f30686f7016b7b3f614ad3c86da742 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 12:22:51 +0100
Subject: [PATCH 05/23] iterate over sector values row-major to match isless

---
 src/bimodulesector.jl | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index ae348e9..7c6cbf2 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -44,16 +44,16 @@ Base.size(::Type{A4Object}) = 7
 
 Base.IteratorSize(::Type{<:SectorValues{<:BimoduleSector}}) = Base.SizeUnknown()
 
-function Base.iterate(iter::SectorValues{<:BimoduleSector}, (I, label) = (1, 1))
+function Base.iterate(iter::SectorValues{<:BimoduleSector}, (n, label) = (1, 1))
     A = eltype(iter)
     s = size(A)
-    I > s * s && return nothing
-    i, j = CartesianIndices((s, s))[I].I
+    n > s * s && return nothing
+    i, j = fldmod1(n, s)
     maxlabel = _numlabels(A, i, j)
     return if label > maxlabel
-        iterate(iter, (I + 1, 1))
+        iterate(iter, (n + 1, 1))
     else
-        A(i, j, label), (I, label + 1)
+        A(i, j, label), (n, label + 1)
     end
 end
 

From 3fcb4ac185bdc5d4a11397616ffa1368405b270a Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 12:46:29 +0100
Subject: [PATCH 06/23] proper Nsymbol column check

---
 src/bimodulesector.jl | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 7c6cbf2..5ce3c2b 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -93,10 +93,12 @@ function extract_Nsymbol(::Type{I}) where {I <: BimoduleSector}
     filename = joinpath(artifact_path, name, "Nsymbol.txt")
     isfile(filename) || throw(LoadError(filename, 0, "Nsymbol file not found for $name"))
     Narray = readdlm(filename) # matrix with 7 columns
+    size(Narray, 2) == 7 ||
+        throw(ArgumentError("Nsymbol file for $name has wrong number of columns: $(size(Narray, 2)) != 7"))
 
     data_dict = Dict{NTuple{3, Int}, Dict{NTuple{3, Int}, Int}}()
     for row in eachrow(Narray)
-        i, j, k, a, b, c, N = Int.(@view(row[1:size(I)]))
+        i, j, k, a, b, c, N = Int.(@view(row[1:7]))
         colordict = get!(data_dict, (i, j, k), Dict{NTuple{3, Int}, Int}())
         push!(colordict, (a, b, c) => N)
     end

From 36e378670dbc44d33e1413fb3c069a82d10c2d6a Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 12:56:07 +0100
Subject: [PATCH 07/23] correctly search for units, allow to error on time

---
 src/bimodulesector.jl | 31 +++++++++++--------------------
 1 file changed, 11 insertions(+), 20 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 5ce3c2b..35ed552 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -135,37 +135,28 @@ end
 function extract_dual(::Type{I}) where {I <: BimoduleSector}
     N = _get_Ncache(I)
     ncats = size(I)
-    Is = zeros(Int, ncats)
+    nobj = [maximum(first, keys(N[i, j, j])) for i in 1:ncats, j in 1:ncats]
 
-    map(1:ncats) do i
+    Is = map(1:ncats) do i
         Niii = N[i, i, i]
-        nobji = maximum(first, keys(N[i, i, i]))
         # want to return a leftunit and rightunit for each entry in multifusion cat
         # leftunit/rightunit needs to at least be the unit object within a fusion cat
-        Is[i] = findfirst(1:nobji) do a
+        u = findfirst(1:nobj[i, i]) do a
             get(Niii, (a, a, a), 0) == 1 || return false # I x I -> I
-            for othera in 1:nobji
-                get(Niii, (othera, a, othera), 0) == 1 || return false # a x I -> a
-                get(Niii, (a, othera, othera), 0) == 1 || return false # I x a -> a
-            end
 
-            # check leftunit
-            map(1:ncats) do j
-                nobjj = maximum(first, keys(N[j, j, j]))
-                for b in 1:nobjj
-                    get(N[i, j, j], (a, b, b), 0) == 1 || return false # I = leftunit(b)
-                end
+            # I = leftunit(b) for every b in C_ij, I x b -> b in C_ii x C_ij -> C_ij
+            for j in 1:ncats, b in 1:nobj[i, j]
+                get(N[i, i, j], (a, b, b), 0) == 1 || return false
             end
 
-            # check rightunit
-            map(1:ncats) do k
-                nobjk = maximum(first, keys(N[k, k, k]))
-                for c in 1:nobjk
-                    get(N[k, i, k], (c, a, c), 0) == 1 || return false # I = rightunit(c)
-                end
+            # I = rightunit(c) for every c in C_ki, c x I -> c in C_ki x C_ii -> C_ki
+            for k in 1:ncats, c in 1:nobj[k, i]
+                get(N[k, i, i], (c, a, c), 0) == 1 || return false
             end
             return true
         end
+        isnothing(u) && throw(ArgumentError("no unit object found in subcategory ($i, $i) of $I"))
+        return u
     end
 
     allduals = Matrix{Vector{Int}}(undef, ncats, ncats) # ncats square matrix of vectors

From b57c798f94be7c37eb53c8889f684a344447b4ae Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 13:53:49 +0100
Subject: [PATCH 08/23] fix ranges of dual calculations

---
 src/bimodulesector.jl | 22 +++++++++-------------
 1 file changed, 9 insertions(+), 13 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 35ed552..86cc7e0 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -160,20 +160,16 @@ function extract_dual(::Type{I}) where {I <: BimoduleSector}
     end
 
     allduals = Matrix{Vector{Int}}(undef, ncats, ncats) # ncats square matrix of vectors
-    for i in 1:ncats
-        nobji = maximum(first, keys(N[i, i, i]))
-        for j in 1:ncats
-            allduals[i, j] = Int[]
-
-            nobjj = maximum(first, keys(N[j, j, j]))
-            # the nested vectors contain the duals of the objects in 𝒞_ij, which are in C_ji
-            Niji = N[i, j, i] # 𝒞_ij x 𝒞_ji -> C_ii
-            Njij = N[j, i, j] # 𝒞_ji x 𝒞_ij -> C_jj
-            for i_ob in 1:nobji, j_ob in 1:nobjj
-                get(Niji, (i_ob, j_ob, Is[i]), 0) == 1 || continue # leftunit(c_ij) ∈ c_ij x c_ji
-                get(Njij, (j_ob, i_ob, Is[j]), 0) == 1 || continue # rightunit(c_ij) ∈ c_ji x c_ij
-                push!(allduals[i, j], j_ob)
+    for i in 1:ncats, j in 1:ncats
+        Niji = N[i, j, i] # 𝒞_ij x 𝒞_ji -> 𝒞_ii
+        Njij = N[j, i, j] # 𝒞_ji x 𝒞_ij -> 𝒞_jj
+        allduals[i, j] = map(1:nobj[i, j]) do m
+            mbar = findfirst(1:nobj[j, i]) do n
+                get(Niji, (m, n, Is[i]), 0) == 1 && # leftunit(m) in m x mbar
+                    get(Njij, (n, m, Is[j]), 0) == 1 # rightunit(m) in mbar x m
             end
+            isnothing(mbar) && error("no dual found for $I($i, $j, $m)")
+            return mbar
         end
     end
     return Is, allduals

From 10fbfed05987baabcafcfd88b9b5bdb5cb16e8ba Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 14:01:04 +0100
Subject: [PATCH 09/23] add unitstyle, make allunits allocate less and have
 isunit not build allunits in the fallback

---
 src/bimodulesector.jl | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 86cc7e0..e836af9 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -180,9 +180,15 @@ function TensorKitSectors.unit(a::BimoduleSector)
     return typeof(a)(a.i, a.i, _get_dual_cache(typeof(a))[1][a.i])
 end
 
+TensorKitSectors.UnitStyle(::Type{<:BimoduleSector}) = GenericUnit()
+
 function TensorKitSectors.allunits(::Type{I}) where {I <: BimoduleSector}
-    s = size(I)
-    return I[I(i, i, _get_dual_cache(I)[1][i]) for i in 1:s]
+    Is = _get_dual_cache(I)[1]
+    return ntuple(i -> I(i, i, Is[i]), Val(size(I)))
+end
+
+function TensorKitSectors.isunit(a::BimoduleSector)
+    return a.i == a.j && a.label == _get_dual_cache(typeof(a))[1][a.i]
 end
 
 function TensorKitSectors.unit(::Type{<:BimoduleSector})

From d7a6c6991fb8247dd1ec2944acc2a9c34d6c95e2 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 14:16:58 +0100
Subject: [PATCH 10/23] return number of objects matrix in dual cache, allowing
 easier counting and not hard-coding size

---
 src/bimodulesector.jl | 16 ++++++++--------
 1 file changed, 8 insertions(+), 8 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index e836af9..bd03fbe 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -40,7 +40,7 @@ function Base.convert(::Type{BimoduleSector{Name}}, d::NTuple{3, Int}) where {Na
     return BimoduleSector{Name}(d...)
 end
 
-Base.size(::Type{A4Object}) = 7
+Base.size(I::Type{<:BimoduleSector}) = size(_get_dual_cache(I)[3], 1)
 
 Base.IteratorSize(::Type{<:SectorValues{<:BimoduleSector}}) = Base.SizeUnknown()
 
@@ -57,10 +57,7 @@ function Base.iterate(iter::SectorValues{<:BimoduleSector}, (n, label) = (1, 1))
     end
 end
 
-function Base.length(::SectorValues{I}) where {I <: BimoduleSector}
-    s = size(I)
-    return sum(_numlabels(I, i, j) for i in 1:s, j in 1:s)
-end
+Base.length(::SectorValues{I}) where {I <: BimoduleSector} = sum(_get_dual_cache(I)[3])
 
 TensorKitSectors.FusionStyle(::Type{A4Object}) = GenericFusion()
 TensorKitSectors.BraidingStyle(::Type{<:BimoduleSector}) = NoBraiding()
@@ -77,7 +74,7 @@ function TensorKitSectors.:⊗(a::I, b::I) where {I <: BimoduleSector}
 end
 
 function _numlabels(::Type{T}, i, j) where {T <: BimoduleSector}
-    return length(_get_dual_cache(T)[2][i, j])
+    return _get_dual_cache(T)[3][i, j]
 end
 
 # User-friendly functions
@@ -103,6 +100,9 @@ function extract_Nsymbol(::Type{I}) where {I <: BimoduleSector}
         push!(colordict, (a, b, c) => N)
     end
 
+    ncats = maximum(maximum, keys(data_dict))
+    ncats == size(I) ||
+        throw(ArgumentError("Nsymbol data for $name has $ncats subcategories, but size($I) = $(size(I))"))
     return data_dict
 end
 
@@ -123,7 +123,7 @@ function TensorKitSectors.Nsymbol(a::I, b::I, c::I) where {I <: BimoduleSector}
     return get(_get_Ncache(I)[i, j, k], (a.label, b.label, c.label), 0)
 end
 
-const Dualcache = IdDict{Type{<:BimoduleSector}, Tuple{Vector{Int64}, Matrix{Vector{Int64}}}}()
+const Dualcache = IdDict{Type{<:BimoduleSector}, Tuple{Vector{Int64}, Matrix{Vector{Int64}}, Matrix{Int64}}}()
 
 function _get_dual_cache(::Type{T}) where {T <: BimoduleSector}
     global Dualcache
@@ -172,7 +172,7 @@ function extract_dual(::Type{I}) where {I <: BimoduleSector}
             return mbar
         end
     end
-    return Is, allduals
+    return Is, allduals, nobj
 end
 
 function TensorKitSectors.unit(a::BimoduleSector)

From b348ba18c06ab10feff19327192a9c47e4dc3630 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 14:18:37 +0100
Subject: [PATCH 11/23] remove duplicate convert

---
 src/bimodulesector.jl | 2 --
 1 file changed, 2 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index bd03fbe..8ac42da 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -19,8 +19,6 @@ BimoduleSector{Name}(data::NTuple{3, Int}) where {Name} = BimoduleSector{Name}(d
 BimoduleSectorName(::Type{BimoduleSector{Name}}) where {Name} = Name
 const A4Object = BimoduleSector{:A4}
 
-Base.convert(::Type{<:BimoduleSector{Name}}, labels::NTuple{3, Int}) where {Name} = BimoduleSector{Name}(labels...)
-
 function Base.show(io::IO, a::BimoduleSector{Name}) where {Name}
     if get(io, :typeinfo, nothing) === typeof(a)
         print(io, (a.i, a.j, a.label))

From 8743fe5fdcc925f6d08f950c557a321bf8243d21 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:23:04 +0100
Subject: [PATCH 12/23] fix not knowing size at compile time

---
 src/bimodulesector.jl | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 8ac42da..7c764ae 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -1,4 +1,4 @@
-const ImplementedBimoduleSectors = [:A4]
+const ImplementedBimoduleSectors = (:A4,)
 
 struct BimoduleSector{Name} <: Sector
     i::Int
@@ -98,9 +98,6 @@ function extract_Nsymbol(::Type{I}) where {I <: BimoduleSector}
         push!(colordict, (a, b, c) => N)
     end
 
-    ncats = maximum(maximum, keys(data_dict))
-    ncats == size(I) ||
-        throw(ArgumentError("Nsymbol data for $name has $ncats subcategories, but size($I) = $(size(I))"))
     return data_dict
 end
 
@@ -132,7 +129,7 @@ end
 
 function extract_dual(::Type{I}) where {I <: BimoduleSector}
     N = _get_Ncache(I)
-    ncats = size(I)
+    ncats = maximum(maximum, keys(N))
     nobj = [maximum(first, keys(N[i, j, j])) for i in 1:ncats, j in 1:ncats]
 
     Is = map(1:ncats) do i
@@ -181,8 +178,7 @@ end
 TensorKitSectors.UnitStyle(::Type{<:BimoduleSector}) = GenericUnit()
 
 function TensorKitSectors.allunits(::Type{I}) where {I <: BimoduleSector}
-    Is = _get_dual_cache(I)[1]
-    return ntuple(i -> I(i, i, Is[i]), Val(size(I)))
+    return I[I(i, i, u) for (i, u) in enumerate(_get_dual_cache(I)[1])]
 end
 
 function TensorKitSectors.isunit(a::BimoduleSector)

From d09aaa2bc8340e2be3e8c5be86dcbcef2832ab41 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:25:30 +0100
Subject: [PATCH 13/23] fix seed for test reproducibility, add constructor test

---
 test/test_A4.jl | 17 ++++++++++++++---
 1 file changed, 14 insertions(+), 3 deletions(-)

diff --git a/test/test_A4.jl b/test/test_A4.jl
index 59fa329..95f61bf 100644
--- a/test/test_A4.jl
+++ b/test/test_A4.jl
@@ -9,6 +9,9 @@ using .SectorTestSuite
 
 using MultiTensorKit
 using Test, TestExtras
+using Random
+
+Random.seed!(1234)
 
 const MTK = MultiTensorKit
 
@@ -23,6 +26,17 @@ println("----------------------")
     @time SectorTestSuite.test_sector(I)
 end
 
+@testset "$Istr construction and ordering" begin
+    @test_throws DomainError I(1, 1, 0)
+    @test_throws DomainError I(1, 1, -1)
+    @test_throws DomainError I(0, 1, 1)
+    @test_throws DomainError I(r + 1, 1, 1)
+    @test_throws DomainError I(1, 1, MTK._numlabels(I, 1, 1) + 1)
+    vals = collect(values(I))
+    @test issorted(vals)
+    @test length(vals) == length(values(I))
+end
+
 @testset "$Istr ($i, $j) basic properties" for i in 1:r, j in 1:r
     Cii_obs = I.(i, i, MTK._get_dual_cache(I)[2][i, i])
     Cij_obs = I.(i, j, MTK._get_dual_cache(I)[2][i, j])
@@ -36,7 +50,6 @@ end
             u = I.(i, i, MTK._get_dual_cache(I)[1][i])
             @test u == @testinferred(leftunit(u)) == @testinferred(rightunit(u)) ==
                 @testinferred(unit(u))
-            @test isunit(@testinferred(unit(c)))
             @test dual(c) == I.(i, i, MTK._get_dual_cache(I)[2][i, i][c.label])
         end
     else
@@ -159,5 +172,3 @@ end
         end
     end
 end
-
-# include("TK_compat.jl")
\ No newline at end of file

From b44ea5dc80d767989730b76454b3632ec09dd4ec Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:26:22 +0100
Subject: [PATCH 14/23] be exhaustive with unitarity checks

---
 test/test_A4.jl | 60 ++++++-------------------------------------------
 1 file changed, 7 insertions(+), 53 deletions(-)

diff --git a/test/test_A4.jl b/test/test_A4.jl
index 95f61bf..10ae5c2 100644
--- a/test/test_A4.jl
+++ b/test/test_A4.jl
@@ -92,59 +92,13 @@ println("-----------------------------")
 
 # explicitly test everything related to F-symbols
 # other option is to edit smallset to sample more
-for i in 1:r, j in 1:r
-    @testset "Unitarity of $Istr F-move ($i, $j)" begin
-        if i == j
-            @testset "Unitarity of fusion F-move ($i, $j)" begin
-                fusion_objects = I.(i, i, MTK._get_dual_cache(I)[2][i, i])
-                for a in fusion_objects, b in fusion_objects, c in fusion_objects
-                    @test SectorTestSuite.F_unitarity_test(a, b, c)
-                end
-            end
-        end
-
-        i != j || continue # do this part only when off-diagonal
-        mod_objects = I.(i, j, MTK._get_dual_cache(I)[2][i, j])
-        left_fusion_objects = I.(i, i, MTK._get_dual_cache(I)[2][i, i])
-        right_fusion_objects = I.(j, j, MTK._get_dual_cache(I)[2][j, j])
-
-        # C x C x M -> M or D x D x Mop -> Mop
-        @testset "Unitarity of left module F-move ($i, $j)" begin
-            for a in left_fusion_objects, b in left_fusion_objects, A in mod_objects
-                @test SectorTestSuite.F_unitarity_test(a, b, A)
-            end
-        end
-
-        # M x D x D -> M or Mop x C x C -> Mop
-        @testset "Unitarity of right module F-move ($i, $j)" begin
-            for A in mod_objects, b in right_fusion_objects, c in right_fusion_objects
-                @test SectorTestSuite.F_unitarity_test(A, b, c)
-            end
-        end
-
-        # C x M x D -> M or D x Mop x C -> Mop
-        @testset "Unitarity of bimodule F-move ($i, $j)" begin
-            for a in left_fusion_objects, A in mod_objects, α in right_fusion_objects
-                @test SectorTestSuite.F_unitarity_test(a, A, α)
-            end
-        end
-
-        @testset "Unitarity of mixed module F-move ($i, $j) and opposite ($j, $i)" begin
-            modop_objects = I.(j, i, MTK._get_dual_cache(I)[2][j, i])
-
-            # C x M x Mop -> C or D x Mop x M -> D
-            # M x Mop x C -> C or Mop x M x D -> D
-            # Mop x C x M -> D or M x D x Mop -> C
-            for a in left_fusion_objects, A in mod_objects, Aop in modop_objects
-                @test SectorTestSuite.F_unitarity_test(a, A, Aop)
-                @test SectorTestSuite.F_unitarity_test(A, Aop, a)
-                @test SectorTestSuite.F_unitarity_test(Aop, a, A)
-            end
-
-            # M x Mop x M -> M or Mop x M x Mop -> Mop
-            for A in mod_objects, Aop in modop_objects
-                @test SectorTestSuite.F_unitarity_test(A, Aop, A)
-            end
+@testset "Unitarity of $Istr F-move" begin
+    objs = collect(values(I))
+    for a in objs, b in objs
+        a.j == b.i || continue
+        for c in objs
+            b.j == c.i || continue
+            @test SectorTestSuite.F_unitarity_test(a, b, c; atol = 1.0e-12, rtol = 1.0e-12)
         end
     end
 end

From 52ada8af256fa42d45c4513a1f6be44fbe24f405 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:32:37 +0100
Subject: [PATCH 15/23] test duals more rigorously

---
 test/test_A4.jl | 11 +++++++++--
 1 file changed, 9 insertions(+), 2 deletions(-)

diff --git a/test/test_A4.jl b/test/test_A4.jl
index 10ae5c2..61a8f65 100644
--- a/test/test_A4.jl
+++ b/test/test_A4.jl
@@ -50,7 +50,6 @@ end
             u = I.(i, i, MTK._get_dual_cache(I)[1][i])
             @test u == @testinferred(leftunit(u)) == @testinferred(rightunit(u)) ==
                 @testinferred(unit(u))
-            @test dual(c) == I.(i, i, MTK._get_dual_cache(I)[2][i, i][c.label])
         end
     else
         @testset "Basic module properties" begin
@@ -61,7 +60,6 @@ end
             @test unit(d) == rightunit(m) == leftunit(mop)
             @test_throws DomainError unit(m)
             @test_throws DomainError unit(mop)
-            @test dual(m) == I.(j, i, MTK._get_dual_cache(I)[2][i, j][m.label])
         end
 
         @testset "$Istr Fusion rules" begin
@@ -86,6 +84,15 @@ end
     end
 end
 
+@testset "$Istr units and duals of all objects" begin
+    for a in values(I)
+        ā = dual(a)
+        @test dual(ā) == a
+        @test Nsymbol(a, ā, leftunit(a)) == 1
+        @test Nsymbol(ā, a, rightunit(a)) == 1
+    end
+end
+
 println("-----------------------------")
 println("|    F-symbol data tests    |")
 println("-----------------------------")

From 4b7b94e6179c812347e0ccf56e75e08ef4ea0067 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:43:09 +0100
Subject: [PATCH 16/23] clean up readme where possible

---
 README.md | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/README.md b/README.md
index 91ca994..2a8f3a5 100644
--- a/README.md
+++ b/README.md
@@ -1,15 +1,15 @@
 # MultiTensorKit.jl
 
-[TensorKit.jl](https://github.com/jutho/TensorKit.jl) extension for multi-fusion categories.
+[TensorKit.jl](https://github.com/QuantumKitHub/TensorKit.jl) extension for multi-fusion categories.
 
 
 | **Documentation** | **Digital Object Identifier** |
 |:-----------------:|:-----------------------------:|
 | [![][docs-stable-img]][docs-stable-url] [![][docs-dev-img]][docs-dev-url] | [![DOI][doi-img]][doi-url] |
 
-| **Build Status** | **PkgEval** | **Coverage** |
-|:----------------:|:------------:|:------------:|
-| [![CI][ci-img]][ci-url] | [![PkgEval][pkgeval-img]][pkgeval-url] | [![Codecov][codecov-img]][codecov-url] |
+| **Build Status** | **PkgEval** | **Coverage** | **Quality assurance** |
+|:----------------:|:------------:|:------------:|:---------------------:|
+| [![CI][ci-img]][ci-url] | [![PkgEval][pkgeval-img]][pkgeval-url] | [![Codecov][codecov-img]][codecov-url] | [![Aqua QA][aqua-img]][aqua-url] |
 
 [docs-stable-img]: https://img.shields.io/badge/docs-stable-blue.svg
 [docs-stable-url]: https://QuantumKitHub.github.io/MultiTensorKit.jl/stable
@@ -29,3 +29,5 @@
 [pkgeval-img]: https://JuliaCI.github.io/NanosoldierReports/pkgeval_badges/T/MPSKit.svg
 [pkgeval-url]: https://JuliaCI.github.io/NanosoldierReports/pkgeval_badges/T/MPSKit.html
 
+[aqua-img]: https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg
+[aqua-url]: https://github.com/JuliaTesting/Aqua.jl
\ No newline at end of file

From 2fa08af8cb6112cbad689a194b76329d84b349ab Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:47:12 +0100
Subject: [PATCH 17/23] remove allocations in Fsymbol call

---
 src/bimodulesector.jl | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 7c764ae..a578b10 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -262,11 +262,14 @@ function TensorKitSectors.Fsymbol(a::I, b::I, c::I, d::I, e::I, f::I) where {I <
     Nbcf = Nsymbol(b, c, f)
     Nafd = Nsymbol(a, f, d)
 
-    zero_array = zeros(sectorscalartype(I), Nabe, Necd, Nbcf, Nafd)
+    T = sectorscalartype(I)
     Nabe > 0 && Necd > 0 && Nbcf > 0 && Nafd > 0 ||
-        return zero_array
+        return zeros(sectorscalartype(I), Nabe, Necd, Nbcf, Nafd)
 
     i, j, k, l = a.i, a.j, b.j, c.j
     colordict = _get_Fcache(I)[i, j, k, l]
-    return get!(colordict, (a.label, b.label, c.label, d.label, e.label, f.label), zero_array)
+    return get!(
+        () -> zeros(sectorscalartype(I), Nabe, Necd, Nbcf, Nafd),
+        colordict, (a.label, b.label, c.label, d.label, e.label, f.label)
+    )
 end

From 939ac59a2d752c782896a5ac2e4b0e348550ccfa Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 15:48:20 +0100
Subject: [PATCH 18/23] final test cleanup

---
 test/test_A4.jl | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/test/test_A4.jl b/test/test_A4.jl
index 61a8f65..cc22b36 100644
--- a/test/test_A4.jl
+++ b/test/test_A4.jl
@@ -38,16 +38,16 @@ end
 end
 
 @testset "$Istr ($i, $j) basic properties" for i in 1:r, j in 1:r
-    Cii_obs = I.(i, i, MTK._get_dual_cache(I)[2][i, i])
-    Cij_obs = I.(i, j, MTK._get_dual_cache(I)[2][i, j])
-    Cji_obs = I.(j, i, MTK._get_dual_cache(I)[2][j, i])
-    Cjj_obs = I.(j, j, MTK._get_dual_cache(I)[2][j, j])
+    Cii_obs = I.(i, i, 1:MTK._numlabels(I, i, i))
+    Cij_obs = I.(i, j, 1:MTK._numlabels(I, i, j))
+    Cji_obs = I.(j, i, 1:MTK._numlabels(I, j, i))
+    Cjj_obs = I.(j, j, 1:MTK._numlabels(I, j, j))
     c, m, mop, d = rand(Cii_obs), rand(Cij_obs), rand(Cji_obs), rand(Cjj_obs)
 
     if i == j
         @testset "Basic fusion properties" begin
             @test isunit(@testinferred(unit(c)))
-            u = I.(i, i, MTK._get_dual_cache(I)[1][i])
+            u = only(filter(isunit, Cii_obs))
             @test u == @testinferred(leftunit(u)) == @testinferred(rightunit(u)) ==
                 @testinferred(unit(u))
         end

From 83a2920a9e823b12d4dc0e1764e3d483a522b18d Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 16:15:16 +0100
Subject: [PATCH 19/23] oopsie

---
 src/bimodulesector.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index a578b10..aa11263 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -264,12 +264,12 @@ function TensorKitSectors.Fsymbol(a::I, b::I, c::I, d::I, e::I, f::I) where {I <
 
     T = sectorscalartype(I)
     Nabe > 0 && Necd > 0 && Nbcf > 0 && Nafd > 0 ||
-        return zeros(sectorscalartype(I), Nabe, Necd, Nbcf, Nafd)
+        return zeros(T, Nabe, Necd, Nbcf, Nafd)
 
     i, j, k, l = a.i, a.j, b.j, c.j
     colordict = _get_Fcache(I)[i, j, k, l]
     return get!(
-        () -> zeros(sectorscalartype(I), Nabe, Necd, Nbcf, Nafd),
+        () -> zeros(T, Nabe, Necd, Nbcf, Nafd),
         colordict, (a.label, b.label, c.label, d.label, e.label, f.label)
     )
 end

From 0efa99eba5f2a7d3e8e3d57b294269f92f4cb27a Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 16:18:51 +0100
Subject: [PATCH 20/23] make random sampling random at least

---
 test/test_A4.jl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/test/test_A4.jl b/test/test_A4.jl
index cc22b36..fd71523 100644
--- a/test/test_A4.jl
+++ b/test/test_A4.jl
@@ -12,6 +12,7 @@ using Test, TestExtras
 using Random
 
 Random.seed!(1234)
+rng = Random.Xoshiro(1234)
 
 const MTK = MultiTensorKit
 
@@ -42,7 +43,7 @@ end
     Cij_obs = I.(i, j, 1:MTK._numlabels(I, i, j))
     Cji_obs = I.(j, i, 1:MTK._numlabels(I, j, i))
     Cjj_obs = I.(j, j, 1:MTK._numlabels(I, j, j))
-    c, m, mop, d = rand(Cii_obs), rand(Cij_obs), rand(Cji_obs), rand(Cjj_obs)
+    c, m, mop, d = rand(rng, Cii_obs), rand(rng, Cij_obs), rand(rng, Cji_obs), rand(rng, Cjj_obs)
 
     if i == j
         @testset "Basic fusion properties" begin
@@ -67,7 +68,7 @@ end
             # forbidden fusions
             for obs in [(c, d), (d, c), (m, m), (mop, mop), (d, m), (m, c), (mop, d), (c, mop)]
                 @test isempty(⊗(obs...))
-                @test_throws argerr Nsymbol(obs..., rand([c, m, mop, d]))
+                @test_throws argerr Nsymbol(obs..., rand(rng, [c, m, mop, d]))
             end
 
             # allowed fusions

From 866a62954d544c3740dd7792cd1fec3f20e86ab2 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 16:19:50 +0100
Subject: [PATCH 21/23] change pkgeval link (doesn't matter for now)

---
 README.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/README.md b/README.md
index 2a8f3a5..405df25 100644
--- a/README.md
+++ b/README.md
@@ -26,8 +26,8 @@
 [ci-img]: https://github.com/QuantumKitHub/MultiTensorKit.jl/actions/workflows/Tests.yml/badge.svg
 [ci-url]: https://github.com/QuantumKitHub/MultiTensorKit.jl/actions/workflows/Tests.yml
 
-[pkgeval-img]: https://JuliaCI.github.io/NanosoldierReports/pkgeval_badges/T/MPSKit.svg
-[pkgeval-url]: https://JuliaCI.github.io/NanosoldierReports/pkgeval_badges/T/MPSKit.html
+[pkgeval-img]: https://JuliaCI.github.io/NanosoldierReports/pkgeval_badges/M/MultiTensorKit.svg
+[pkgeval-url]: https://JuliaCI.github.io/NanosoldierReports/pkgeval_badges/M/MultiTensorKit.html
 
 [aqua-img]: https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg
 [aqua-url]: https://github.com/JuliaTesting/Aqua.jl
\ No newline at end of file

From 49f46ba2593eea1a7fd989c1b95b64c5b3ce6480 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 16:20:53 +0100
Subject: [PATCH 22/23] column check for Fsymbol.txt as well

---
 src/bimodulesector.jl | 1 +
 1 file changed, 1 insertion(+)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index aa11263..8e0c981 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -208,6 +208,7 @@ function extract_Fsymbol(::Type{I}) where {I <: BimoduleSector}
     @assert isfile(filename) "cannot find $filename"
 
     Farray = readdlm(filename)
+    size(Farray, 2) == 16 || throw(ArgumentError("Fsymbol file for $name has wrong number of columns: $(size(Farray, 2)) != 16"))
     for ((i, j, k, l), colordict) in convert_Fs(Farray)
         result[(i, j, k, l)] = Dict{NTuple{6, Int}, Array{ComplexF64, 4}}()
         for ((a, b, c, d, e, f), Fvals) in colordict

From 408eb9ac77b93dd5a460d8c072cb2dfd42b0c2d5 Mon Sep 17 00:00:00 2001
From: Boris De Vos <boris.devos@ugent.be>
Date: Fri, 30 Oct 2026 16:29:58 +0100
Subject: [PATCH 23/23] tiny unit label refactor

---
 src/bimodulesector.jl | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/src/bimodulesector.jl b/src/bimodulesector.jl
index 8e0c981..b6c8551 100644
--- a/src/bimodulesector.jl
+++ b/src/bimodulesector.jl
@@ -74,6 +74,7 @@ end
 function _numlabels(::Type{T}, i, j) where {T <: BimoduleSector}
     return _get_dual_cache(T)[3][i, j]
 end
+_unitlabel(::Type{I}, i::Int) where {I <: BimoduleSector} = _get_dual_cache(I)[1][i]
 
 # User-friendly functions
 # -------------------
@@ -163,7 +164,7 @@ function extract_dual(::Type{I}) where {I <: BimoduleSector}
                 get(Niji, (m, n, Is[i]), 0) == 1 && # leftunit(m) in m x mbar
                     get(Njij, (n, m, Is[j]), 0) == 1 # rightunit(m) in mbar x m
             end
-            isnothing(mbar) && error("no dual found for $I($i, $j, $m)")
+            isnothing(mbar) && throw(ArgumentError("no dual found for $I($i, $j, $m)"))
             return mbar
         end
     end
@@ -172,7 +173,7 @@ end
 
 function TensorKitSectors.unit(a::BimoduleSector)
     a.i == a.j || throw(DomainError("unit of module category ($(a.i), $(a.j)) of $(typeof(a)) is ill-defined"))
-    return typeof(a)(a.i, a.i, _get_dual_cache(typeof(a))[1][a.i])
+    return typeof(a)(a.i, a.i, _unitlabel(typeof(a), a.i))
 end
 
 TensorKitSectors.UnitStyle(::Type{<:BimoduleSector}) = GenericUnit()
@@ -182,7 +183,7 @@ function TensorKitSectors.allunits(::Type{I}) where {I <: BimoduleSector}
 end
 
 function TensorKitSectors.isunit(a::BimoduleSector)
-    return a.i == a.j && a.label == _get_dual_cache(typeof(a))[1][a.i]
+    return a.i == a.j && a.label == _unitlabel(typeof(a), a.i)
 end
 
 function TensorKitSectors.unit(::Type{<:BimoduleSector})
@@ -190,11 +191,11 @@ function TensorKitSectors.unit(::Type{<:BimoduleSector})
 end
 
 function TensorKitSectors.leftunit(a::BimoduleSector)
-    return typeof(a)(a.i, a.i, _get_dual_cache(typeof(a))[1][a.i])
+    return typeof(a)(a.i, a.i, _unitlabel(typeof(a), a.i))
 end
 
 function TensorKitSectors.rightunit(a::BimoduleSector)
-    return typeof(a)(a.j, a.j, _get_dual_cache(typeof(a))[1][a.j])
+    return typeof(a)(a.j, a.j, _unitlabel(typeof(a), a.j))
 end
 
 function TensorKitSectors.dual(a::BimoduleSector)