From f938246e1d490c004ad80d40fce6570a39ec9e48 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Fri, 30 Oct 2026 13:51:53 -0400
Subject: [PATCH 01/10] Give `NormNetwork` checked bra names and layer
 accessors

Default bra names are derived with `derivedname`, and every link name must have one.
`KetView` and `indmap` are removed; `ketnetwork` and `branetwork` return the layers.
Adds `inds`, `axes` and `names` of a vertex and `linknames(tn)` to the network interface.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 Project.toml                                  |   2 +
 src/ITensorNetworkGenerators/ising_network.jl |   4 +-
 src/abstracttensornetwork.jl                  |  37 +++---
 src/beliefpropagation/beliefpropagation.jl    |   6 +-
 src/beliefpropagation/messagecache.jl         |  12 +-
 src/normnetwork.jl                            | 125 +++++++++++++-----
 src/normnetworkview.jl                        |  64 ++++-----
 src/tensornetwork.jl                          |  11 +-
 src/utils.jl                                  |  15 +++
 test/test_basics.jl                           |   3 +
 test/test_normnetwork.jl                      |  88 ++++++++----
 test/test_tensornetwork.jl                    |   6 +-
 12 files changed, 249 insertions(+), 124 deletions(-)

diff --git a/Project.toml b/Project.toml
index 94e3b7e2..df9a94f6 100644
--- a/Project.toml
+++ b/Project.toml
@@ -23,6 +23,7 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SimpleTraits = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
 SplitApplyCombine = "03a91e81-4c3e-53e1-a0a4-9c0c8f19dd66"
 TensorAlgebra = "68bd88dc-f39d-4e12-b2ca-f046b68fcc6a"
+UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
 [weakdeps]
 OMEinsumContractionOrders = "6f22d1fd-8eed-4bb7-9776-e7d684900715"
@@ -48,4 +49,5 @@ Random = "1.10"
 SimpleTraits = "0.9.5"
 SplitApplyCombine = "1.2.3"
 TensorAlgebra = "0.23.1"
+UUIDs = "1.10"
 julia = "1.10"
diff --git a/src/ITensorNetworkGenerators/ising_network.jl b/src/ITensorNetworkGenerators/ising_network.jl
index 702b8787..c1d4b769 100644
--- a/src/ITensorNetworkGenerators/ising_network.jl
+++ b/src/ITensorNetworkGenerators/ising_network.jl
@@ -1,6 +1,6 @@
 using ..ITensorNetworksNext
 using Graphs: degree, dst, edges, src
-using ITensorBase: NamedTensor, name, uniquename
+using ITensorBase: NamedTensor, inds, name, uniquename
 using LinearAlgebra: Diagonal, eigen
 using NamedGraphs: vertextype
 
@@ -33,7 +33,7 @@ function ising_network(
     fp(e) = get(() -> l̃[reverse(e)], l̃, e)
     tn = delta_network(fp, elt, g)
     for v in sz_vertices
-        tn[v] = diagonaltensor(elt[1, -1], axes(tn[v]))
+        tn[v] = diagonaltensor(elt[1, -1], axes(tn, v))
     end
 
     for e in edges(g)
diff --git a/src/abstracttensornetwork.jl b/src/abstracttensornetwork.jl
index eabe39ba..7a6dcd82 100644
--- a/src/abstracttensornetwork.jl
+++ b/src/abstracttensornetwork.jl
@@ -3,8 +3,8 @@ using DataGraphs: DataGraphs, AbstractDataGraph, AbstractVertexDataGraph, edge_d
     set_vertex_data!, underlying_graph, underlying_graph_type, vertex_data
 using Graphs: Graphs, AbstractEdge, AbstractGraph, add_edge!, add_vertex!, dst, edges,
     edgetype, ne, neighbors, nv, rem_edge!, src, vertices
-using ITensorBase: ITensorOperator, NamedUnitRange, inds, inputnames, name, names, nametype,
-    prime, uniquename, unnamedtype
+using ITensorBase: ITensorBase, ITensorOperator, NamedUnitRange, inds, inputnames, name,
+    names, nametype, prime, uniquename, unnamedtype
 using LinearAlgebra: LinearAlgebra
 using MacroTools: @capture
 using NamedGraphs:
@@ -37,13 +37,17 @@ end
 
 # ====================================== interface ======================================= #
 
+ITensorBase.inds(tn::AbstractITensorNetwork, v) = inds(tn[v])
+ITensorBase.axes(tn::AbstractITensorNetwork, v) = axes(tn[v])
+ITensorBase.names(tn::AbstractITensorNetwork, v) = name.(inds(tn, v))
+
 linkinds(tn::AbstractGraph, edge::Pair) = linkinds(tn, edgetype(tn)(edge))
 # Pick the link indices from the `src` side, identified by name match with `dst`.
 # A range-strict intersection (`inds(src) ∩ inds(dst)`) would drop graded links
 # whose two endpoints carry dual-related ranges.
 function linkinds(tn::AbstractGraph, edge::AbstractEdge)
     ln = linknames(tn, edge)
-    return [i for i in inds(tn[src(edge)]) if name(i) in ln]
+    return [i for i in inds(tn, src(edge)) if name(i) in ln]
 end
 
 function linkaxes(tn::AbstractGraph, edge::Pair)
@@ -51,43 +55,46 @@ function linkaxes(tn::AbstractGraph, edge::Pair)
 end
 function linkaxes(tn::AbstractGraph, edge::AbstractEdge)
     ln = linknames(tn, edge)
-    return [ax for ax in axes(tn[src(edge)]) if name(ax) in ln]
+    return [ax for ax in axes(tn, src(edge)) if name(ax) in ln]
 end
 function linknames(tn::AbstractGraph, edge::Pair)
     return linknames(tn, edgetype(tn)(edge))
 end
 function linknames(tn::AbstractGraph, edge::AbstractEdge)
-    return names(tn[src(edge)]) ∩ names(tn[dst(edge)])
+    return names(tn, src(edge)) ∩ names(tn, dst(edge))
+end
+function linknames(tn::AbstractGraph)
+    return unique(Iterators.flatten(linknames(tn, e) for e in edges(tn)))
 end
 
 function siteinds(tn::AbstractGraph, v)
-    s = inds(tn[v])
+    s = inds(tn, v)
     for v′ in neighbors(tn, v)
-        s = setdiff(s, inds(tn[v′]))
+        s = setdiff(s, inds(tn, v′))
     end
     return s
 end
 function siteaxes(tn::AbstractGraph, v)
-    s = axes(tn[v])
+    s = axes(tn, v)
     for v′ in neighbors(tn, v)
-        s = setdiff(s, axes(tn[v′]))
+        s = setdiff(s, axes(tn, v′))
     end
     return s
 end
 function sitenames(tn::AbstractGraph, v)
-    s = names(tn[v])
+    s = names(tn, v)
     for v′ in neighbors(tn, v)
-        s = setdiff(s, names(tn[v′]))
+        s = setdiff(s, names(tn, v′))
     end
     return s
 end
 
 # Return the non-link vertices associated with an dim name
 function dimnamevertices(tn::AbstractGraph, name)
-    sites = vertextype(tn)[]
+    sites = Set{vertextype(tn)}()
 
     for v in vertices(tn)
-        if name ∈ names(tn[v])
+        if name ∈ names(tn, v)
             push!(sites, v)
         end
     end
@@ -97,7 +104,7 @@ end
 
 function has_dimname(tn::AbstractGraph, name)
     for v in vertices(tn)
-        if name ∈ names(tn[v])
+        if name ∈ names(tn, v)
             return true
         end
     end
@@ -107,7 +114,7 @@ end
 has_ind(tn::AbstractGraph, ind) = has_dimname(tn, name(ind))
 
 function insertlink!(tn::AbstractGraph, e)
-    T = eltype(inds(tn[src(e)]))
+    T = eltype(inds(tn, src(e)))
 
     linkind = NamedUnitRange(trivialrange(unnamedtype(T)), uniquename(nametype(T)))
 
diff --git a/src/beliefpropagation/beliefpropagation.jl b/src/beliefpropagation/beliefpropagation.jl
index fa387253..df39650a 100644
--- a/src/beliefpropagation/beliefpropagation.jl
+++ b/src/beliefpropagation/beliefpropagation.jl
@@ -272,9 +272,9 @@ end
 # the message is positive semidefinite and its trace is a positive normalization.
 function message_update!(algorithm::SimpleMessageUpdate, cache, factors::NormNetwork, edge)
     new_tensor = updated_message(algorithm, cache, factors, edge)
-    new_message = operator(
-        new_tensor, linknames(BraView(factors), edge), linknames(KetView(factors), edge)
-    )
+    branames = linknames(branetwork(factors), edge)
+    ketnames = linknames(ketnetwork(factors), edge)
+    new_message = operator(new_tensor, branames, ketnames)
     if algorithm.normalize
         message_norm = tr(new_message)
         iszero(message_norm) || (new_message /= message_norm)
diff --git a/src/beliefpropagation/messagecache.jl b/src/beliefpropagation/messagecache.jl
index ec91cd58..ebbfd759 100644
--- a/src/beliefpropagation/messagecache.jl
+++ b/src/beliefpropagation/messagecache.jl
@@ -191,16 +191,16 @@ bethe_free_energy(factors, messages) = -bethe_free_entropy(factors, messages)
 function similar_message_environment(nn::NormNetwork)
     messages = mapmany(vertices(nn)) do vertex
         return map(in_incident_edges(nn, vertex)) do edge
-            braview = BraView(nn)
-            ketview = KetView(nn)
+            bra = branetwork(nn)
+            ket = ketnetwork(nn)
 
-            ketnames = linknames(ketview, edge)
-            branames = linknames(braview, edge)
-            braaxis = unnamed.(linkaxes(braview, edge))
+            ketnames = linknames(ket, edge)
+            branames = linknames(bra, edge)
+            braaxis = unnamed.(linkaxes(bra, edge))
 
             # Bra leg = operator output, ket leg = input, the bipartition in which the message
             # is positive semidefinite.
-            message = similar_operator(ketview[vertex], braaxis, branames, ketnames)
+            message = similar_operator(ket[vertex], braaxis, branames, ketnames)
 
             return edge => message
         end
diff --git a/src/normnetwork.jl b/src/normnetwork.jl
index d735b22f..6736adcf 100644
--- a/src/normnetwork.jl
+++ b/src/normnetwork.jl
@@ -1,5 +1,5 @@
-using Dictionaries: Dictionary, dictionary
-using ITensorBase: rename, setname, similar_operator, uniquename
+using Dictionaries: Dictionary, Indices, dictionary
+using ITensorBase: ITensorBase, conj, nametype, rename, similar_operator
 using ITensorNetworksNext
 
 """
@@ -16,14 +16,33 @@ struct NormNetwork{T, V, I} <: AbstractITensorNetwork{T, V}
             ket::ITensorNetwork{T, V, I},
             map::Dictionary{I, I}
         ) where {T, V, I}
-        braname = Dictionary{I, I}()
-        for (name, vertices) in pairs(ket.dimname_vertices)
-            if length(vertices) == 2
-                insert!(braname, name, map[name])
-            end
+        check_input(NormNetwork, ket, map)
+        return new{T, V, I}(ket, map)
+    end
+end
+
+function NormNetwork(
+        f::Function, tn::ITensorNetwork, linknames = ITensorNetworksNext.linknames(tn)
+    )
+    return NormNetwork(tn, narrow_map(f, Indices(linknames)))
+end
+function NormNetwork(tn::ITensorNetwork, linknames = ITensorNetworksNext.linknames(tn))
+    return NormNetwork(name -> derivedname(name, "bra"), tn, linknames)
+end
+
+function check_input(::Type{<:NormNetwork}, ket, braname)
+    if !issubset(linknames(ket), keys(braname))
+        error("every link name of the ket layer must have a bra name.")
+    end
+    if !allunique(braname)
+        error("the bra names of a norm network must be distinct.")
+    end
+    for name in braname
+        if has_dimname(ket, name)
+            error("bra name $name is already an index name of the ket layer.")
         end
-        return new{T, V, I}(ket, braname)
     end
+    return nothing
 end
 
 function Base.eltype(::Type{<:NormNetwork})
@@ -32,20 +51,20 @@ function Base.eltype(::Type{<:NormNetwork})
     )
 end
 
-function NormNetwork(tn::ITensorNetwork)
-    return NormNetwork(tn, map(uniquename, keys(tn.dimname_vertices)))
-end
-
 # ====================================== Graphs.jl ======================================= #
 
-Graphs.edges(nn::NormNetwork) = edges(nn.ket)
-Graphs.vertices(nn::NormNetwork) = vertices(nn.ket)
+Graphs.edges(nn::NormNetwork) = edges(ketnetwork(nn))
+Graphs.vertices(nn::NormNetwork) = vertices(ketnetwork(nn))
 
 # ==================================== NamedGraphs.jl ==================================== #
 
-NamedGraphs.encoded_vertex(nn::NormNetwork, vertex) = encoded_vertex(nn.ket, vertex)
-NamedGraphs.decoded_vertex(nn::NormNetwork, code::Integer) = decoded_vertex(nn.ket, code)
-NamedGraphs.encoded_graph(nn::NormNetwork) = encoded_graph(nn.ket)
+function NamedGraphs.encoded_vertex(nn::NormNetwork, vertex)
+    return encoded_vertex(ketnetwork(nn), vertex)
+end
+function NamedGraphs.decoded_vertex(nn::NormNetwork, code::Integer)
+    return decoded_vertex(ketnetwork(nn), code)
+end
+NamedGraphs.encoded_graph(nn::NormNetwork) = encoded_graph(ketnetwork(nn))
 
 # ==================================== DataGraphs.jl ===================================== #
 
@@ -56,8 +75,9 @@ function DataGraphs.get_vertex_data(nn::NormNetwork, vertex)
 end
 
 function DataGraphs.is_vertex_assigned(nn::NormNetwork, vertex)
-    return isassigned(nn.ket, vertex)
+    return isassigned(ketnetwork(nn), vertex)
 end
+
 # =================================== Dictionaries.jl ==================================== #
 
 Dictionaries.issettable(::NormNetwork) = false
@@ -65,22 +85,61 @@ Dictionaries.isinsertable(::NormNetwork) = false
 
 # ====================================== interface ======================================= #
 
+# The name type of the indices, the same as the ket network's.
+ITensorBase.nametype(::Type{<:NormNetwork{T, V, I}}) where {T, V, I} = I
+ITensorBase.nametype(nn::NormNetwork) = nametype(typeof(nn))
+
+"""
+    ketnetwork(nn::NormNetwork)
+
+The ket-layer network of `nn`.
+"""
+ketnetwork(nn::NormNetwork) = nn.ket
+
+"""
+    branetwork(nn::NormNetwork)
+
+The bra-layer network of `nn`, a `BraView` whose tensors are built by [`bratensor`](@ref) when
+accessed.
+"""
+branetwork(nn::NormNetwork) = BraView(nn)
+
+"""
+    branamemap(nn::NormNetwork)
+
+The ket→bra name map, holding a bra name for each ket index name that has a separate bra copy.
+"""
+branamemap(nn::NormNetwork) = nn.braname
+
+"""
+    braname(nn::NormNetwork, name)
+
+The bra-layer index name corresponding to the ket-layer index name `name`.
+"""
 function braname(nn::NormNetwork, name)
-    if !has_dimname(nn.ket, name)
+    if !has_dimname(ketnetwork(nn), name)
         error("index name $name not found underlying tensor network.")
     end
-    # The indices not stored in `nn.braname` are precisely the site indices, which
-    # get mapped to themselves.
-    return get(nn.braname, name, name)
+    # The names absent from the map are the site indices, which map to themselves.
+    return get(branamemap(nn), name, name)
 end
 
-indmap(nn::NormNetwork, ind) = setname(conj(ind), braname(nn, name(ind)))
+"""
+    kettensor(nn::NormNetwork, vertex)
+
+The ket-layer tensor at `vertex`.
+"""
+kettensor(nn::NormNetwork, vertex) = ketnetwork(nn)[vertex]
 
-kettensor(nn::NormNetwork, vertex) = nn.ket[vertex]
 function conj_bratensor(nn::NormNetwork, vertex)
     return rename(n -> braname(nn, n), kettensor(nn, vertex))
 end
 
+"""
+    bratensor(nn::NormNetwork, vertex)
+
+The bra-layer tensor at `vertex`.
+"""
 bratensor(nn::NormNetwork, vertex) = conj(conj_bratensor(nn, vertex))
 
 """
@@ -102,12 +161,14 @@ function flatten_network(nn::NormNetwork)
 end
 
 """
-    normnetwork(tn::ITensorNetwork, [braname]) -> NormNetwork
-
-Build the double-layer norm network `⟨tn|tn⟩`, represented lazily as a `NomnNetwork` object.
-The optional second argument `braname` should implement `braname[ketdimname] = bradimname` for
-every link dimension name `ketdimname` in `tn`. If this is not specified, then a name is
-generated via the `ITensorBase.uniquename` function.
+    normnetwork([f::Function], tn::ITensorNetwork, [linknames]) -> NormNetwork
+    normnetwork(tn::ITensorNetwork, braname::Dictionary) -> NormNetwork
+
+Build the double-layer norm network `⟨tn|tn⟩`, represented lazily as a `NormNetwork` object.
+Each ket index name in `linknames` (by default `linknames(tn)`) gets the bra name `f(name)`,
+where `f` defaults to `name -> derivedname(name, "bra")`. Alternatively pass the ket→bra name
+map `braname` directly. Either way the names mapped must include every link name of `tn` and
+may include others, and an error is thrown if a link name is missing, two bra names coincide
+or a bra name is already an index name of `tn`.
 """
-normnetwork(tn::ITensorNetwork) = NormNetwork(tn)
-normnetwork(tn::ITensorNetwork, braname) = NormNetwork(tn, braname)
+normnetwork(args...) = NormNetwork(args...)
diff --git a/src/normnetworkview.jl b/src/normnetworkview.jl
index 75c57926..8b675089 100644
--- a/src/normnetworkview.jl
+++ b/src/normnetworkview.jl
@@ -1,58 +1,50 @@
 using DataGraphs: DataGraphs, get_vertex_data, is_vertex_assigned
 using Dictionaries: Dictionaries, isinsertable, issettable
 using Graphs: Graphs, edges, vertices
+using ITensorBase: ITensorBase, conj, inds
 using NamedGraphs: NamedGraphs, decoded_vertex, encoded_graph, encoded_vertex
 
-struct KetView{T, V, I} <: AbstractITensorNetwork{T, V}
-    parent::NormNetwork{T, V, I}
-end
+"""
+    struct BraView{T, V, I} <: AbstractITensorNetwork{T, V}
 
+The bra layer of the norm network `parent(view)`, with each vertex tensor built by
+[`bratensor`](@ref) when accessed. Its graph structure and mutability are those of the parent.
+"""
 struct BraView{T, V, I} <: AbstractITensorNetwork{T, V}
     parent::NormNetwork{T, V, I}
 end
 
-# ====================================== Graphs.jl ======================================= #
+Base.parent(nnv::BraView) = nnv.parent
 
-for View in (:KetView, :BraView)
-    @eval begin
-        Graphs.edges(nnv::$View) = edges(nnv.parent)
-        Graphs.vertices(nnv::$View) = vertices(nnv.parent)
-    end
+# ==================================== DataGraphs.jl ===================================== #
+
+DataGraphs.get_vertex_data(nnv::BraView, vertex) = bratensor(parent(nnv), vertex)
+function DataGraphs.is_vertex_assigned(nnv::BraView, vertex)
+    return is_vertex_assigned(parent(nnv), vertex)
 end
 
-# ==================================== NamedGraphs.jl ==================================== #
+# ==================================== ITensorBase.jl ==================================== #
 
-for View in (:KetView, :BraView)
-    @eval begin
-        function NamedGraphs.encoded_vertex(nnv::$View, vertex)
-            return encoded_vertex(nnv.parent, vertex)
-        end
-        function NamedGraphs.decoded_vertex(nnv::$View, code::Integer)
-            return decoded_vertex(nnv.parent, code)
-        end
-
-        NamedGraphs.encoded_graph(nnv::$View) = encoded_graph(nnv.parent)
-    end
+function ITensorBase.inds(nnv::BraView, vertex)
+    return conj.(inds(conj_bratensor(parent(nnv), vertex)))
 end
 
-# ==================================== DataGraphs.jl ===================================== #
+# ====================================== Graphs.jl ======================================= #
+
+Graphs.edges(nnv::BraView) = edges(parent(nnv))
+Graphs.vertices(nnv::BraView) = vertices(parent(nnv))
 
-DataGraphs.get_vertex_data(nn::KetView, vertex) = kettensor(nn.parent, vertex)
-DataGraphs.get_vertex_data(nn::BraView, vertex) = bratensor(nn.parent, vertex)
+# ==================================== NamedGraphs.jl ==================================== #
 
-for View in (:KetView, :BraView)
-    @eval begin
-        function DataGraphs.is_vertex_assigned(nnv::$View, vertex)
-            return isassigned(nnv.parent.ket, vertex)
-        end
-    end
+function NamedGraphs.encoded_vertex(nnv::BraView, vertex)
+    return encoded_vertex(parent(nnv), vertex)
+end
+function NamedGraphs.decoded_vertex(nnv::BraView, code::Integer)
+    return decoded_vertex(parent(nnv), code)
 end
+NamedGraphs.encoded_graph(nnv::BraView) = encoded_graph(parent(nnv))
 
 # =================================== Dictionaries.jl ==================================== #
 
-for View in (:KetView, :BraView)
-    @eval begin
-        Dictionaries.issettable(nnv::$View) = issettable(nnv.parent)
-        Dictionaries.isinsertable(nnv::$View) = isinsertable(nnv.parent)
-    end
-end
+Dictionaries.issettable(nnv::BraView) = issettable(parent(nnv))
+Dictionaries.isinsertable(nnv::BraView) = isinsertable(parent(nnv))
diff --git a/src/tensornetwork.jl b/src/tensornetwork.jl
index 57ad5b2b..1c972cb2 100644
--- a/src/tensornetwork.jl
+++ b/src/tensornetwork.jl
@@ -146,7 +146,7 @@ function DataGraphs.set_vertex_data!(tn::ITensorNetwork, tensor, vertex)
 end
 
 function update_tensornetwork_metadata!(tn, vertex, tensor)
-    oldnames = isassigned(tn, vertex) ? names(tn[vertex]) : Set{nametype(tn)}()
+    oldnames = isassigned(tn, vertex) ? names(tn, vertex) : Set{nametype(tn)}()
     newnames = names(tensor)
 
     update_tensornetwork_metadata!(tn, vertex, oldnames, newnames)
@@ -197,12 +197,19 @@ Graphs.add_edge!(::ITensorNetwork, _edge) = false
 
 # PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
 function dimnamevertices(tn::ITensorNetwork, name)
-    return get(tn.dimname_vertices, name, Set{vertextype(tn)}())
+    return copy(get(tn.dimname_vertices, name, Set{vertextype(tn)}()))
 end
 
 # PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
 has_dimname(tn::ITensorNetwork, name) = haskey(tn.dimname_vertices, name)
 
+# PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
+function linknames(tn::ITensorNetwork)
+    return [
+        name for (name, vertices) in pairs(tn.dimname_vertices) if length(vertices) == 2
+    ]
+end
+
 function NamedGraphs.similar_graph(
         T::Type{<:ITensorNetwork},
         vertices = vertextype(T)[]
diff --git a/src/utils.jl b/src/utils.jl
index abf666e4..5113f317 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -1,6 +1,21 @@
 using Dictionaries: AbstractIndices, Dictionary
+using ITensorBase: ITensorBase, IndexName, settags
+using UUIDs: uuid5
 
 # `map` does something clever to figure out the element type of the output when not
 # inferable, but the `map` overload on `Dictionary` does not, so we fix this here.
 narrow_map(f, v) = map(f, v)
 narrow_map(f, v::AbstractIndices) = Dictionary(v, [f(x) for x in v])
+
+"""
+    derivedname(name::IndexName, key) -> IndexName
+
+Return a name derived deterministically from `name` and `key`: the identifier is replaced by
+the name-based UUID `uuid5(uuid(name), string(key))`, `key` is added as a bare-label tag, and
+the other tags and the prime level are kept. Every process derives the same name from the same
+`name` and `key`, and the result differs from `name` and from any independently minted name.
+"""
+function derivedname(name::IndexName, key)
+    derived = ITensorBase.setuuid(name, uuid5(ITensorBase.uuid(name), string(key)))
+    return settags(derived, string(key))
+end
diff --git a/test/test_basics.jl b/test/test_basics.jl
index a975170c..2c9318bc 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -18,6 +18,7 @@ using Test: @test, @testset
         @test issetequal(vertices(tn), vertices(g))
         for v in vertices(tn)
             @test issetequal(siteinds(tn, v), [s[v]])
+            @test axes(tn, v) == (s[v],)
         end
     end
     @testset "Construct ITensorNetwork partition function" begin
@@ -35,6 +36,8 @@ using Test: @test, @testset
         @test issetequal(arranged_edges(tn), arranged_edges(g))
         for v in vertices(tn)
             @test isempty(siteinds(tn, v))
+            @test axes(tn, v) == axes(tn[v])
+            @test issetequal(axes(tn, v), [l[e] for e in incident_edges(g, v)])
         end
         for v1 in vertices(tn)
             for v2 in vertices(tn)
diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index 4528b220..b5109561 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -1,10 +1,11 @@
 using DataGraphs: is_vertex_assigned
-using Dictionaries: isinsertable, issettable
+using Dictionaries: Indices, isinsertable, issettable
 using Graphs: edges, vertices
-using ITensorBase: ITensor, Index, IndexName, conj, inds, name, setname, uniquename
-using ITensorNetworksNext: BraView, Greedy, ITensorNetwork, KetView, NormNetwork, braname,
-    bratensor, conj_bratensor, contraction_tree, flatten_network, indmap, kettensor,
-    normnetwork, prod_tensors, tensornetwork
+using ITensorBase:
+    ITensor, Index, IndexName, inds, name, nametype, plev, prime, setname, tags, uniquename
+using ITensorNetworksNext: BraView, Greedy, ITensorNetwork, NormNetwork, braname,
+    branetwork, bratensor, conj_bratensor, contraction_tree, derivedname, flatten_network,
+    ketnetwork, kettensor, linknames, normnetwork, prod_tensors, tensornetwork
 using LinearAlgebra: norm
 using NamedGraphs: NamedEdge, incident_edges, named_grid, named_path_graph
 using Test: @test, @test_throws, @testset
@@ -44,6 +45,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         # `eltype` is defined.
         @test_throws ErrorException nn[1]
         @test_throws ErrorException eltype(nn)
+        @test nametype(nn) === nametype(tn) === IndexName
 
         # Vertex data is assigned wherever the underlying network is.
         @test is_vertex_assigned(nn, 1)
@@ -79,11 +81,6 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         # `bra` is the elementwise conjugate of `conj_bratensor` and carries the same indices.
         @test inds(bratensor(nn, 2)) == inds(conj_bratensor(nn, 2))
 
-        # `indmap` conjugates an index and renames it according to the name map.
-        ind = only(i for i in inds(kettensor(nn, 2)) if name(i) == lname)
-        @test name(indmap(nn, ind)) == braname(nn, name(ind))
-        @test indmap(nn, ind) == setname(conj(ind), braname(nn, name(ind)))
-
         # Querying the name map with an index name absent from the network errors.
         @test_throws ErrorException braname(nn, name(Index(2)))
     end
@@ -93,7 +90,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         tn, l, s = random_state(Float64, g)
 
         # A user-supplied map dictates the bra-layer name for each link.
-        custom = map(uniquename, keys(tn.dimname_vertices))
+        custom = map(uniquename, Indices(linknames(tn)))
         nn = normnetwork(tn, custom)
 
         lname = name(l[NamedEdge(1 => 2)])
@@ -101,32 +98,71 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         @test braname(nn, lname) in name.(inds(conj_bratensor(nn, 2)))
     end
 
-    @testset "`KetView` / `BraView`" begin
+    @testset "`derivedname`" begin
+        n = prime(name(Index(2; tags = "Link")))
+
+        # The derived name depends only on the name and key, keeps the decoration and is tagged
+        # with the key.
+        @test derivedname(n, :bra) == derivedname(n, :bra)
+        @test derivedname(n, :bra) != n
+        @test derivedname(n, :bra) != derivedname(n, :other)
+        @test derivedname(n, :bra) != prime(n)
+        @test tags(derivedname(n, :bra)) == merge(tags(n), Dict("bra" => ""))
+        @test plev(derivedname(n, :bra)) == plev(n)
+    end
+
+    @testset "default and function name maps" begin
+        g = named_path_graph(3)
+        tn, l, s = random_state(Float64, g)
+        lname = name(l[NamedEdge(1 => 2)])
+
+        # Two independently constructed norm networks agree on every bra name.
+        @test braname(NormNetwork(tn), lname) == derivedname(lname, :bra)
+        @test braname(normnetwork(tn), lname) == braname(NormNetwork(tn), lname)
+        @test braname(normnetwork(prime, tn), lname) == prime(lname)
+
+        # A bra name that is already an index name of the network is rejected.
+        taken = setname(Index(2), derivedname(lname, :bra))
+        tn[1] = tn[1] * ITensor(ones(2), (taken,))
+        @test_throws ErrorException NormNetwork(tn)
+    end
+
+    @testset "bond to a vertex outside the network" begin
+        g = named_path_graph(3)
+        tn, l, s = random_state(Float64, g)
+
+        # The part of `tn` on vertices 1 and 2, as one rank of a distributed network holds it.
+        part = ITensorNetwork(Dict(v => tn[v] for v in (1, 2)))
+        nn = normnetwork(part, map(uniquename, Indices(linknames(tn))))
+
+        # The bond to vertex 3 is not a link of `part`, but it is in the map, so it gets its
+        # own bra name and the two layers at vertex 2 share only the site index.
+        lname = name(l[NamedEdge(2 => 3)])
+        @test braname(nn, lname) != lname
+        shared =
+            intersect(name.(inds(kettensor(nn, 2))), name.(inds(conj_bratensor(nn, 2))))
+        @test issetequal(shared, [name(s[2])])
+    end
+
+    @testset "`ketnetwork` / `branetwork`" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
         nn = NormNetwork(tn)
 
-        kv = KetView(nn)
-        bv = BraView(nn)
+        # The ket layer is the network the norm network was built from.
+        @test ketnetwork(nn) === tn
 
-        # Views share the graph structure of the underlying network.
-        @test issetequal(vertices(kv), vertices(tn))
+        # The bra layer is not stored, so it is a view sharing the ket layer's graph structure.
+        bv = branetwork(nn)
+        @test bv isa BraView
         @test issetequal(vertices(bv), vertices(tn))
-        @test issetequal(edges(kv), edges(tn))
         @test issetequal(edges(bv), edges(tn))
-
-        # The ket view exposes the bare ket tensors; the bra view exposes the bra tensors.
         for v in vertices(tn)
-            @test kv[v] === kettensor(nn, v)
             @test inds(bv[v]) == inds(bratensor(nn, v))
         end
-
-        @test is_vertex_assigned(kv, 1)
         @test is_vertex_assigned(bv, 1)
 
-        # Views inherit the (non-)mutability of their parent norm network.
-        @test !issettable(kv)
-        @test !isinsertable(kv)
+        # The view inherits the (non-)mutability of its parent norm network.
         @test !issettable(bv)
         @test !isinsertable(bv)
     end
@@ -181,7 +217,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
             @test contract_norm(NormNetwork(tn)) ≈ 1
 
             # The contracted norm does not depend on the chosen bra-layer name map.
-            custom = map(uniquename, keys(tn.dimname_vertices))
+            custom = map(uniquename, Indices(linknames(tn)))
             @test contract_norm(normnetwork(tn, custom)) ≈ contract_norm(NormNetwork(tn))
         end
     end
diff --git a/test/test_tensornetwork.jl b/test/test_tensornetwork.jl
index 0beaad01..7a2bee94 100644
--- a/test/test_tensornetwork.jl
+++ b/test/test_tensornetwork.jl
@@ -1,7 +1,7 @@
 using DataGraphs:
     DataGraph, assigned_edge_data, assigned_vertex_data, underlying_graph, vertex_data
-using Graphs: add_edge!, add_vertex!, dst, edges, edgetype, has_edge, has_vertex,
-    is_directed, ne, nv, rem_edge!, rem_vertex!, src, vertices
+using Graphs: AbstractGraph, add_edge!, add_vertex!, dst, edges, edgetype, has_edge,
+    has_vertex, is_directed, ne, nv, rem_edge!, rem_vertex!, src, vertices
 using ITensorBase: Index, inds, operator
 using ITensorNetworksNext: ITensorNetwork, has_ind, linkaxes, linkinds, linknames,
     operator_support, siteaxes, siteinds, sitenames, tensornetwork
@@ -119,6 +119,8 @@ using Test: @test, @test_throws, @testset
 
         @test linknames(tn, 1 => 2) == [l[E(1 => 2)].name]
         @test linknames(tn, E(1 => 2)) == [l[E(1 => 2)].name]
+        @test issetequal(linknames(tn), [l[e].name for e in edges(g)])
+        @test issetequal(invoke(linknames, Tuple{AbstractGraph}, tn), linknames(tn))
 
         @test siteinds(tn, 1) == [s[1]]
         @test siteaxes(tn, 2) == [s[2]]

From cc83668761ee5951d7b09b9f78404c5c819ee8b7 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Fri, 30 Oct 2026 13:39:16 -0400
Subject: [PATCH 02/10] Bump version to 0.12.0

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 Project.toml          | 2 +-
 docs/Project.toml     | 2 +-
 examples/Project.toml | 2 +-
 test/Project.toml     | 2 +-
 4 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/Project.toml b/Project.toml
index df9a94f6..71015667 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ITensorNetworksNext"
 uuid = "302f2e75-49f0-4526-aef7-d8ba550cb06c"
-version = "0.11.2"
+version = "0.12.0"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
 
 [workspace]
diff --git a/docs/Project.toml b/docs/Project.toml
index eee8bc4e..c8846666 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -10,5 +10,5 @@ path = ".."
 [compat]
 Documenter = "1"
 ITensorFormatter = "0.2.27"
-ITensorNetworksNext = "0.11"
+ITensorNetworksNext = "0.12"
 Literate = "2"
diff --git a/examples/Project.toml b/examples/Project.toml
index 0fa22c56..52c95335 100644
--- a/examples/Project.toml
+++ b/examples/Project.toml
@@ -5,4 +5,4 @@ ITensorNetworksNext = "302f2e75-49f0-4526-aef7-d8ba550cb06c"
 path = ".."
 
 [compat]
-ITensorNetworksNext = "0.11"
+ITensorNetworksNext = "0.12"
diff --git a/test/Project.toml b/test/Project.toml
index 9abc495b..8845e97c 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -32,7 +32,7 @@ Dictionaries = "0.4.5"
 GradedArrays = "0.17"
 Graphs = "1.13.1"
 ITensorBase = "0.16.1"
-ITensorNetworksNext = "0.11"
+ITensorNetworksNext = "0.12"
 ITensorPkgSkeleton = "0.3.42"
 MatrixAlgebraKit = "0.6"
 NamedGraphs = "0.14"

From 9966c90ea084872e72d572eb80040d7e832338d4 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Fri, 30 Oct 2026 14:24:19 -0400
Subject: [PATCH 03/10] Test rejected name maps, `BraView` lookups, vertex
 encoding and the Ising correlator

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 test/test_itensornetworkgenerators.jl | 18 ++++++++
 test/test_normnetwork.jl              | 66 +++++++++++++++++++++++++--
 2 files changed, 79 insertions(+), 5 deletions(-)

diff --git a/test/test_itensornetworkgenerators.jl b/test/test_itensornetworkgenerators.jl
index 0dc9f4b7..1c47b326 100644
--- a/test/test_itensornetworkgenerators.jl
+++ b/test/test_itensornetworkgenerators.jl
@@ -51,6 +51,24 @@ using Test: @test, @testset
             f_analytic = TestUtils.f_1d_ising(β, 4; periodic)
             @test f ≈ f_analytic
         end
+        @testset "1D Ising spin correlator" begin
+            N = 6
+            β = 0.4
+            g = named_grid((N,); periodic = true)
+            ldict = DataGraph(g)
+            for e in edges(g)
+                ldict[e] = Index(2)
+            end
+            l = e -> ldict[e]
+            z = prod_tensors(ising_network(l, β, g), Greedy())[]
+
+            # On a periodic chain ⟨σᵢσᵢ₊d⟩ = (tᵈ + tᴺ⁻ᵈ) / (1 + tᴺ) with t = tanh(β).
+            t = tanh(β)
+            for d in 1:3
+                tn = ising_network(l, β, g; sz_vertices = [(1,), (1 + d,)])
+                @test prod_tensors(tn, Greedy())[] / z ≈ (t^d + t^(N - d)) / (1 + t^N)
+            end
+        end
         @testset "2D Ising" begin
             dims = (4, 4)
             β = TestUtils.βc_2d_ising()
diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index b5109561..d390af7b 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -1,13 +1,15 @@
 using DataGraphs: is_vertex_assigned
-using Dictionaries: Indices, isinsertable, issettable
-using Graphs: edges, vertices
+using Dictionaries: Dictionary, Indices, isinsertable, issettable
+using Graphs: edges, neighbors, vertices
 using ITensorBase:
     ITensor, Index, IndexName, inds, name, nametype, plev, prime, setname, tags, uniquename
 using ITensorNetworksNext: BraView, Greedy, ITensorNetwork, NormNetwork, braname,
-    branetwork, bratensor, conj_bratensor, contraction_tree, derivedname, flatten_network,
-    ketnetwork, kettensor, linknames, normnetwork, prod_tensors, tensornetwork
+    branetwork, bratensor, conj_bratensor, contraction_tree, derivedname, dimnamevertices,
+    flatten_network, has_dimname, ketnetwork, kettensor, linknames, normnetwork,
+    prod_tensors, sitenames, tensornetwork
 using LinearAlgebra: norm
-using NamedGraphs: NamedEdge, incident_edges, named_grid, named_path_graph
+using NamedGraphs: NamedEdge, decoded_vertex, encoded_graph, encoded_vertex, incident_edges,
+    named_grid, named_path_graph
 using Test: @test, @test_throws, @testset
 
 # Build a random `ITensorNetwork` state on the graph `g` with site dimension `d` and
@@ -127,6 +129,23 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         @test_throws ErrorException NormNetwork(tn)
     end
 
+    @testset "rejected name maps" begin
+        g = named_path_graph(3)
+        tn, l, s = random_state(Float64, g)
+        l12 = name(l[NamedEdge(1 => 2)])
+        l23 = name(l[NamedEdge(2 => 3)])
+
+        # A map without a bra name for the link 2 => 3 is rejected.
+        @test_throws ErrorException normnetwork(tn, Dictionary([l12], [uniquename(l12)]))
+
+        # Two links sharing a bra name would join two separate bonds in the bra layer.
+        shared = uniquename(l12)
+        @test_throws ErrorException normnetwork(
+            tn,
+            Dictionary([l12, l23], [shared, shared])
+        )
+    end
+
     @testset "bond to a vertex outside the network" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
@@ -167,6 +186,43 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         @test !isinsertable(bv)
     end
 
+    @testset "`BraView` index lookups" begin
+        g = named_path_graph(3)
+        tn, l, s = random_state(Float64, g)
+        nn = NormNetwork(tn)
+        bv = branetwork(nn)
+        lname = name(l[NamedEdge(1 => 2)])
+        bname = braname(nn, lname)
+
+        # The generic lookups read the bra-layer names through `inds(bv, v)`, so the bra link
+        # name sits on both ends of the bond and the ket link name is absent.
+        @test inds(bv, 2) == inds(bv[2])
+        @test dimnamevertices(bv, bname) == Set([1, 2])
+        @test dimnamevertices(bv, name(s[2])) == Set([2])
+        @test isempty(dimnamevertices(bv, lname))
+        @test has_dimname(bv, bname)
+        @test !has_dimname(bv, lname)
+        @test issetequal(linknames(bv), [braname(nn, name(l[e])) for e in edges(g)])
+        @test sitenames(bv, 2) == [name(s[2])]
+    end
+
+    @testset "vertex encoding" begin
+        g = named_grid((2, 3))
+        tn, l, s = random_state(Float64, g)
+        nn = NormNetwork(tn)
+        bv = branetwork(nn)
+
+        # The norm network and its bra view number the grid vertices as the ket layer does.
+        @test encoded_graph(nn) == encoded_graph(tn)
+        @test encoded_graph(bv) == encoded_graph(tn)
+        for net in (nn, bv), v in vertices(g)
+            code = encoded_vertex(net, v)
+            @test code == encoded_vertex(tn, v)
+            @test decoded_vertex(net, code) == v
+            @test issetequal(neighbors(net, v), neighbors(g, v))
+        end
+    end
+
     @testset "`flatten_network`" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)

From 29029b954cc10338123238c80a9dd01c488fbb03 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Mon, 2 Nov 2026 11:05:15 -0500
Subject: [PATCH 04/10] Simplify the network interface and norm-network tests

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 test/test_normnetwork.jl   | 29 +++++++++++++----------------
 test/test_tensornetwork.jl | 15 +++++++--------
 2 files changed, 20 insertions(+), 24 deletions(-)

diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index d390af7b..812f7e90 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -1,6 +1,6 @@
 using DataGraphs: is_vertex_assigned
 using Dictionaries: Dictionary, Indices, isinsertable, issettable
-using Graphs: edges, neighbors, vertices
+using Graphs: edges, has_edge, neighbors, vertices
 using ITensorBase:
     ITensor, Index, IndexName, inds, name, nametype, plev, prime, setname, tags, uniquename
 using ITensorNetworksNext: BraView, Greedy, ITensorNetwork, NormNetwork, braname,
@@ -8,8 +8,7 @@ using ITensorNetworksNext: BraView, Greedy, ITensorNetwork, NormNetwork, braname
     flatten_network, has_dimname, ketnetwork, kettensor, linknames, normnetwork,
     prod_tensors, sitenames, tensornetwork
 using LinearAlgebra: norm
-using NamedGraphs: NamedEdge, decoded_vertex, encoded_graph, encoded_vertex, incident_edges,
-    named_grid, named_path_graph
+using NamedGraphs: NamedEdge, incident_edges, named_grid, named_path_graph
 using Test: @test, @test_throws, @testset
 
 # Build a random `ITensorNetwork` state on the graph `g` with site dimension `d` and
@@ -135,10 +134,10 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         l12 = name(l[NamedEdge(1 => 2)])
         l23 = name(l[NamedEdge(2 => 3)])
 
-        # A map without a bra name for the link 2 => 3 is rejected.
+        # A map missing the bra name of the link 2 => 3 is rejected.
         @test_throws ErrorException normnetwork(tn, Dictionary([l12], [uniquename(l12)]))
 
-        # Two links sharing a bra name would join two separate bonds in the bra layer.
+        # A map giving two links the same bra name is rejected.
         shared = uniquename(l12)
         @test_throws ErrorException normnetwork(
             tn,
@@ -194,8 +193,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         lname = name(l[NamedEdge(1 => 2)])
         bname = braname(nn, lname)
 
-        # The generic lookups read the bra-layer names through `inds(bv, v)`, so the bra link
-        # name sits on both ends of the bond and the ket link name is absent.
+        # The bra layer has the bra link names and the same site names as the ket layer.
         @test inds(bv, 2) == inds(bv[2])
         @test dimnamevertices(bv, bname) == Set([1, 2])
         @test dimnamevertices(bv, name(s[2])) == Set([2])
@@ -206,21 +204,20 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         @test sitenames(bv, 2) == [name(s[2])]
     end
 
-    @testset "vertex encoding" begin
+    @testset "graph structure on a grid" begin
         g = named_grid((2, 3))
         tn, l, s = random_state(Float64, g)
         nn = NormNetwork(tn)
         bv = branetwork(nn)
 
-        # The norm network and its bra view number the grid vertices as the ket layer does.
-        @test encoded_graph(nn) == encoded_graph(tn)
-        @test encoded_graph(bv) == encoded_graph(tn)
-        for net in (nn, bv), v in vertices(g)
-            code = encoded_vertex(net, v)
-            @test code == encoded_vertex(tn, v)
-            @test decoded_vertex(net, code) == v
-            @test issetequal(neighbors(net, v), neighbors(g, v))
+        # The norm network and its bra layer have the same neighbors and edges as the grid.
+        for v in vertices(g)
+            @test issetequal(neighbors(nn, v), neighbors(g, v))
+            @test issetequal(neighbors(bv, v), neighbors(g, v))
         end
+        @test has_edge(nn, (1, 1) => (1, 2))
+        @test has_edge(bv, (1, 1) => (1, 2))
+        @test !has_edge(nn, (1, 1) => (2, 2))
     end
 
     @testset "`flatten_network`" begin
diff --git a/test/test_tensornetwork.jl b/test/test_tensornetwork.jl
index 7a2bee94..87aa0e7d 100644
--- a/test/test_tensornetwork.jl
+++ b/test/test_tensornetwork.jl
@@ -1,8 +1,8 @@
 using DataGraphs:
     DataGraph, assigned_edge_data, assigned_vertex_data, underlying_graph, vertex_data
-using Graphs: AbstractGraph, add_edge!, add_vertex!, dst, edges, edgetype, has_edge,
-    has_vertex, is_directed, ne, nv, rem_edge!, rem_vertex!, src, vertices
-using ITensorBase: Index, inds, operator
+using Graphs: add_edge!, add_vertex!, dst, edges, edgetype, has_edge, has_vertex,
+    is_directed, ne, nv, rem_edge!, rem_vertex!, src, vertices
+using ITensorBase: Index, inds, name, operator
 using ITensorNetworksNext: ITensorNetwork, has_ind, linkaxes, linkinds, linknames,
     operator_support, siteaxes, siteinds, sitenames, tensornetwork
 using NamedGraphs: convert_vertextype, incident_edges, named_grid, named_path_graph,
@@ -117,14 +117,13 @@ using Test: @test, @test_throws, @testset
         @test linkaxes(tn, 1 => 2) == [l[E(1 => 2)]]
         @test linkaxes(tn, E(1 => 2)) == [l[E(1 => 2)]]
 
-        @test linknames(tn, 1 => 2) == [l[E(1 => 2)].name]
-        @test linknames(tn, E(1 => 2)) == [l[E(1 => 2)].name]
-        @test issetequal(linknames(tn), [l[e].name for e in edges(g)])
-        @test issetequal(invoke(linknames, Tuple{AbstractGraph}, tn), linknames(tn))
+        @test linknames(tn, 1 => 2) == [name(l[E(1 => 2)])]
+        @test linknames(tn, E(1 => 2)) == [name(l[E(1 => 2)])]
+        @test issetequal(linknames(tn), [name(l[e]) for e in edges(g)])
 
         @test siteinds(tn, 1) == [s[1]]
         @test siteaxes(tn, 2) == [s[2]]
-        @test sitenames(tn, 3) == [s[3].name]
+        @test sitenames(tn, 3) == [name(s[3])]
     end
 
     @testset "`operator_support`" begin

From f5928b42bb368bea69bf6b06dfaf89c42ab630ca Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Mon, 2 Nov 2026 13:01:28 -0500
Subject: [PATCH 05/10] `normnetwork` map now includes link indices
 automatically, with dangling as optional arg

Drop some `NormNetwork` constructors.
---
 src/normnetwork.jl             | 31 ++++++++++++++-----------------
 test/test_apply_operator.jl    |  6 +++---
 test/test_beliefpropagation.jl | 12 ++++++------
 test/test_free_fermions.jl     |  6 +++---
 test/test_normnetwork.jl       | 29 +++++++++++++----------------
 5 files changed, 39 insertions(+), 45 deletions(-)

diff --git a/src/normnetwork.jl b/src/normnetwork.jl
index 6736adcf..8d24e235 100644
--- a/src/normnetwork.jl
+++ b/src/normnetwork.jl
@@ -21,15 +21,6 @@ struct NormNetwork{T, V, I} <: AbstractITensorNetwork{T, V}
     end
 end
 
-function NormNetwork(
-        f::Function, tn::ITensorNetwork, linknames = ITensorNetworksNext.linknames(tn)
-    )
-    return NormNetwork(tn, narrow_map(f, Indices(linknames)))
-end
-function NormNetwork(tn::ITensorNetwork, linknames = ITensorNetworksNext.linknames(tn))
-    return NormNetwork(name -> derivedname(name, "bra"), tn, linknames)
-end
-
 function check_input(::Type{<:NormNetwork}, ket, braname)
     if !issubset(linknames(ket), keys(braname))
         error("every link name of the ket layer must have a bra name.")
@@ -161,14 +152,20 @@ function flatten_network(nn::NormNetwork)
 end
 
 """
-    normnetwork([f::Function], tn::ITensorNetwork, [linknames]) -> NormNetwork
+    normnetwork([f::Function], tn::ITensorNetwork, [dangling]) -> NormNetwork
     normnetwork(tn::ITensorNetwork, braname::Dictionary) -> NormNetwork
 
 Build the double-layer norm network `⟨tn|tn⟩`, represented lazily as a `NormNetwork` object.
-Each ket index name in `linknames` (by default `linknames(tn)`) gets the bra name `f(name)`,
-where `f` defaults to `name -> derivedname(name, "bra")`. Alternatively pass the ket→bra name
-map `braname` directly. Either way the names mapped must include every link name of `tn` and
-may include others, and an error is thrown if a link name is missing, two bra names coincide
-or a bra name is already an index name of `tn`.
-"""
-normnetwork(args...) = NormNetwork(args...)
+Each ket index name in `union(dangling, linknames(tn))` gets the bra name `f(name)`,
+where `f` defaults to `name -> derivedname(name, "bra")`, and `dangling` is empty by default.
+Alternatively pass the ket→bra name map `braname` directly, which must include every link
+name of `tn` and may include others. Either way an error is thrown if a link name is missing,
+two bra names coincide or a bra name is already an index name of `tn`.
+"""
+normnetwork(tn::ITensorNetwork, braname::Dictionary) = NormNetwork(tn, braname)
+function normnetwork(f::Function, tn::ITensorNetwork, dangling = nametype(tn)[])
+    return normnetwork(tn, narrow_map(f, Indices(union(linknames(tn), dangling))))
+end
+function normnetwork(tn::ITensorNetwork, dangling = nametype(tn)[])
+    return normnetwork(name -> derivedname(name, "bra"), tn, dangling)
+end
diff --git a/test/test_apply_operator.jl b/test/test_apply_operator.jl
index 8c2048a9..00e4e855 100644
--- a/test/test_apply_operator.jl
+++ b/test/test_apply_operator.jl
@@ -1,8 +1,8 @@
 using GradedArrays: U1, gradedrange
 using Graphs: dst, edges, src, vertices
 using ITensorBase: Index, apply, name, operator, setname, uniquename
-using ITensorNetworksNext: NormNetwork, apply_operator, apply_operators, insertlink!,
-    message_environment, tensornetwork
+using ITensorNetworksNext: apply_operator, apply_operators, insertlink!,
+    message_environment, normnetwork, tensornetwork
 using MatrixAlgebraKit: svd_trunc, truncrank
 using NamedGraphs: named_cycle_graph, named_path_graph
 using Random: AbstractRNG
@@ -35,7 +35,7 @@ function random_state(rng::AbstractRNG, elt::Type, g, site_axes; nlayers, trunc)
         insertlink!(network, edge)
     end
 
-    env = message_environment(one, NormNetwork(network))
+    env = message_environment(one, normnetwork(network))
     for _ in 1:nlayers, e in edges(g)
         gate = randn_operator(rng, elt, (site_axes[src(e)], site_axes[dst(e)]))
         network, env = apply_operator(gate, network, env; trunc)
diff --git a/test/test_beliefpropagation.jl b/test/test_beliefpropagation.jl
index 1591e26f..67ac8555 100644
--- a/test/test_beliefpropagation.jl
+++ b/test/test_beliefpropagation.jl
@@ -6,10 +6,10 @@ using Graphs: AbstractGraph, add_vertex!, dst, edges, has_edge, has_vertex, ne,
     rem_edge!, src, vertices
 using ITensorBase: ITensor, Index, apply, inds, name, noprime, outputnames, prime, state
 using ITensorNetworksNext: ITensorNetworksNext, ContractionTreeAlgorithm, Greedy,
-    ITensorNetwork, MessageCache, NormNetwork, SimpleMessageUpdate, StopWhenConverged,
-    beliefpropagation, bethe_free_energy, bethe_free_entropy, bratensor, contraction_tree,
-    edge_scalar, edge_scalars, factor_tensors, incoming_messages, insertlink!, kettensor,
-    linkaxes, linkinds, message_environment, messagecache, prod_tensors, region_scalar,
+    ITensorNetwork, MessageCache, SimpleMessageUpdate, StopWhenConverged, beliefpropagation,
+    bethe_free_energy, bethe_free_entropy, bratensor, contraction_tree, edge_scalar,
+    edge_scalars, factor_tensors, incoming_messages, insertlink!, kettensor, linkaxes,
+    linkinds, message_environment, messagecache, normnetwork, prod_tensors, region_scalar,
     subgraph, tensornetwork, updated_message, vertex_scalar, vertex_scalars
 using LinearAlgebra: LinearAlgebra, norm, tr
 using NamedGraphs: NamedEdge, all_edges, incident_edges, named_comb_tree, named_grid,
@@ -312,7 +312,7 @@ end
             for edge in edges(g)
                 insertlink!(network, edge)
             end
-            nn = NormNetwork(network)
+            nn = normnetwork(network)
 
             cache = beliefpropagation(
                 nn, message_environment(one, nn);
@@ -364,7 +364,7 @@ end
             for edge in edges(g)
                 insertlink!(network, edge)
             end
-            nn = NormNetwork(network)
+            nn = normnetwork(network)
             v = (2, 2)
 
             # A doubled vertex splits into its two layers.
diff --git a/test/test_free_fermions.jl b/test/test_free_fermions.jl
index c4450b67..686f8060 100644
--- a/test/test_free_fermions.jl
+++ b/test/test_free_fermions.jl
@@ -1,8 +1,8 @@
 using GradedArrays: U1
 using Graphs: dst, edges, src, vertices
 using ITensorBase: Index, apply, inds, operator, prime
-using ITensorNetworksNext: NormNetwork, apply_operator, apply_operators, insertlink!,
-    message_environment, tensornetwork
+using ITensorNetworksNext: apply_operator, apply_operators, insertlink!,
+    message_environment, normnetwork, tensornetwork
 using NamedGraphs: named_comb_tree, named_cycle_graph
 using TensorAlgebra: project, project_aux
 using TensorKitSectors: FermionNumber
@@ -71,7 +71,7 @@ function bp_evolve(sector, g, occupied, bonds)
     for e in edges(g)
         insertlink!(ψ, e)
     end
-    env = message_environment(one, NormNetwork(ψ))
+    env = message_environment(one, normnetwork(ψ))
     for v in occupied
         ψ, env = apply_operator(cdag(sites[v]), ψ, env)
     end
diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index 812f7e90..e3fdec1a 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -32,10 +32,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
     @testset "Basics" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
-        nn = NormNetwork(tn)
-
-        # `normnetwork` is the public constructor and agrees with `NormNetwork`.
-        @test normnetwork(tn) isa NormNetwork
+        nn = normnetwork(tn)
         @test nn isa NormNetwork
 
         # The norm network shares the graph structure of the underlying network.
@@ -59,7 +56,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
     @testset "kettensor / bratensor / conj_bratensor and the name map" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
-        nn = NormNetwork(tn)
+        nn = normnetwork(tn)
 
         # `kettensor` returns the underlying tensor untouched.
         @test kettensor(nn, 2) === tn[2]
@@ -118,14 +115,14 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         lname = name(l[NamedEdge(1 => 2)])
 
         # Two independently constructed norm networks agree on every bra name.
-        @test braname(NormNetwork(tn), lname) == derivedname(lname, :bra)
-        @test braname(normnetwork(tn), lname) == braname(NormNetwork(tn), lname)
+        @test braname(normnetwork(tn), lname) == derivedname(lname, :bra)
+        @test braname(normnetwork(tn), lname) == braname(normnetwork(tn), lname)
         @test braname(normnetwork(prime, tn), lname) == prime(lname)
 
         # A bra name that is already an index name of the network is rejected.
         taken = setname(Index(2), derivedname(lname, :bra))
         tn[1] = tn[1] * ITensor(ones(2), (taken,))
-        @test_throws ErrorException NormNetwork(tn)
+        @test_throws ErrorException normnetwork(tn)
     end
 
     @testset "rejected name maps" begin
@@ -165,7 +162,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
     @testset "`ketnetwork` / `branetwork`" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
-        nn = NormNetwork(tn)
+        nn = normnetwork(tn)
 
         # The ket layer is the network the norm network was built from.
         @test ketnetwork(nn) === tn
@@ -188,7 +185,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
     @testset "`BraView` index lookups" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
-        nn = NormNetwork(tn)
+        nn = normnetwork(tn)
         bv = branetwork(nn)
         lname = name(l[NamedEdge(1 => 2)])
         bname = braname(nn, lname)
@@ -207,7 +204,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
     @testset "graph structure on a grid" begin
         g = named_grid((2, 3))
         tn, l, s = random_state(Float64, g)
-        nn = NormNetwork(tn)
+        nn = normnetwork(tn)
         bv = branetwork(nn)
 
         # The norm network and its bra layer have the same neighbors and edges as the grid.
@@ -223,7 +220,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
     @testset "`flatten_network`" begin
         g = named_path_graph(3)
         tn, l, s = random_state(Float64, g)
-        nn = NormNetwork(tn)
+        nn = normnetwork(tn)
         flat = flatten_network(nn)
 
         # One vertex per layer, so the vertex count doubles and each carries its layer's tensor.
@@ -249,7 +246,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
             v = randn(s)
             v = v / norm(v)
             tn = ITensorNetwork(Dict(1 => v))
-            nn = NormNetwork(tn)
+            nn = normnetwork(tn)
 
             # ⟨ψ|ψ⟩ for a single normalized site tensor is 1.
             @test contract_norm(nn) ≈ 1
@@ -260,18 +257,18 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
             tn, l, s = random_state(T, g)
 
             # The norm network contracts to ⟨tn|tn⟩ = ‖prod(tn)‖², a real nonnegative number.
-            z = contract_norm(NormNetwork(tn))
+            z = contract_norm(normnetwork(tn))
             @test z ≈ norm(prod(tn))^2
             @test imag(z) ≈ 0 atol = 1.0e-12 * abs(z)
             @test real(z) > 0
 
             # Rescaling a single tensor by 1/√z normalizes the state, so ⟨tn|tn⟩ = 1.
             tn[first(vertices(tn))] = tn[first(vertices(tn))] / sqrt(real(z))
-            @test contract_norm(NormNetwork(tn)) ≈ 1
+            @test contract_norm(normnetwork(tn)) ≈ 1
 
             # The contracted norm does not depend on the chosen bra-layer name map.
             custom = map(uniquename, Indices(linknames(tn)))
-            @test contract_norm(normnetwork(tn, custom)) ≈ contract_norm(NormNetwork(tn))
+            @test contract_norm(normnetwork(tn, custom)) ≈ contract_norm(normnetwork(tn))
         end
     end
 end

From 2723695ac1cba9d51e3d1fc0a4b0c7e32013630e Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Mon, 2 Nov 2026 16:21:22 -0500
Subject: [PATCH 06/10] Return `Indices` from `dimnamevertices` and tuples from
 `linkaxes` and `siteaxes`

`dimnamevertices` and the `dimname_vertices` table of `ITensorNetwork` now hold
`Indices` instead of `Set`, so the vertex order is insertion order. `linkaxes` and
`siteaxes` return tuples to match `axes`.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 src/abstracttensornetwork.jl | 14 +++-----------
 src/tensornetwork.jl         | 12 ++++++------
 test/test_normnetwork.jl     |  4 ++--
 test/test_tensornetwork.jl   |  6 +++---
 4 files changed, 14 insertions(+), 22 deletions(-)

diff --git a/src/abstracttensornetwork.jl b/src/abstracttensornetwork.jl
index 7a6dcd82..1b3766c2 100644
--- a/src/abstracttensornetwork.jl
+++ b/src/abstracttensornetwork.jl
@@ -55,7 +55,7 @@ function linkaxes(tn::AbstractGraph, edge::Pair)
 end
 function linkaxes(tn::AbstractGraph, edge::AbstractEdge)
     ln = linknames(tn, edge)
-    return [ax for ax in axes(tn, src(edge)) if name(ax) in ln]
+    return Tuple(ax for ax in axes(tn, src(edge)) if name(ax) in ln)
 end
 function linknames(tn::AbstractGraph, edge::Pair)
     return linknames(tn, edgetype(tn)(edge))
@@ -79,7 +79,7 @@ function siteaxes(tn::AbstractGraph, v)
     for v′ in neighbors(tn, v)
         s = setdiff(s, axes(tn, v′))
     end
-    return s
+    return Tuple(s)
 end
 function sitenames(tn::AbstractGraph, v)
     s = names(tn, v)
@@ -91,15 +91,7 @@ end
 
 # Return the non-link vertices associated with an dim name
 function dimnamevertices(tn::AbstractGraph, name)
-    sites = Set{vertextype(tn)}()
-
-    for v in vertices(tn)
-        if name ∈ names(tn, v)
-            push!(sites, v)
-        end
-    end
-
-    return sites
+    return Indices(filter(v -> name ∈ names(tn, v), vertices(tn)))
 end
 
 function has_dimname(tn::AbstractGraph, name)
diff --git a/src/tensornetwork.jl b/src/tensornetwork.jl
index 1c972cb2..cc6da6fa 100644
--- a/src/tensornetwork.jl
+++ b/src/tensornetwork.jl
@@ -11,11 +11,11 @@ using SplitApplyCombine: mapview
 
 struct ITensorNetwork{T, V, I} <: AbstractITensorNetwork{T, V}
     tensors::Dictionary{V, T}
-    dimname_vertices::Dictionary{I, Set{V}}
+    dimname_vertices::Dictionary{I, Indices{V}}
     underlying_graph::NamedGraph{V}
     function ITensorNetwork{T, V, I}(::UndefInitializer, vertices) where {T, V, I}
         tensors = Dictionary{V, T}()
-        dimname_vertices = Dictionary{I, Set{V}}()
+        dimname_vertices = Dictionary{I, Indices{V}}()
         underlying_graph = NamedGraph(vertices)
         return new{T, V, I}(tensors, dimname_vertices, underlying_graph)
     end
@@ -118,7 +118,7 @@ DataGraphs.get_vertex_data(tn::ITensorNetwork, v) = tn.tensors[v]
 
 function check_input(::typeof(set_vertex_data!), tn, tensor, vertex)
     for name in names(tensor)
-        vertices = get(tn.dimname_vertices, name, Set())
+        vertices = get(tn.dimname_vertices, name, Indices{vertextype(tn)}())
         if length(setdiff(vertices, Set([vertex]))) > 1
             throw(
                 ArgumentError(
@@ -165,7 +165,7 @@ function update_tensornetwork_metadata!(tn, vertex, oldnames, newnames)
 
         # Now `name` must be a new index that's not in `oldinds`
 
-        vertex_list = get!(tn.dimname_vertices, name, Set())
+        vertex_list = get!(tn.dimname_vertices, name, Indices{vertextype(tn)}())
         if length(vertex_list) > 1
             throw(
                 ArgumentError(
@@ -173,7 +173,7 @@ function update_tensornetwork_metadata!(tn, vertex, oldnames, newnames)
                 )
             )
         end
-        push!(vertex_list, vertex)
+        insert!(vertex_list, vertex)
 
         # Add an edge if the index is now shared between two vertices.
         if length(vertex_list) == 2
@@ -197,7 +197,7 @@ Graphs.add_edge!(::ITensorNetwork, _edge) = false
 
 # PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
 function dimnamevertices(tn::ITensorNetwork, name)
-    return copy(get(tn.dimname_vertices, name, Set{vertextype(tn)}()))
+    return copy(get(tn.dimname_vertices, name, Indices{vertextype(tn)}()))
 end
 
 # PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index e3fdec1a..bb916d61 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -192,8 +192,8 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
 
         # The bra layer has the bra link names and the same site names as the ket layer.
         @test inds(bv, 2) == inds(bv[2])
-        @test dimnamevertices(bv, bname) == Set([1, 2])
-        @test dimnamevertices(bv, name(s[2])) == Set([2])
+        @test issetequal(dimnamevertices(bv, bname), [1, 2])
+        @test issetequal(dimnamevertices(bv, name(s[2])), [2])
         @test isempty(dimnamevertices(bv, lname))
         @test has_dimname(bv, bname)
         @test !has_dimname(bv, lname)
diff --git a/test/test_tensornetwork.jl b/test/test_tensornetwork.jl
index 87aa0e7d..405a5b6e 100644
--- a/test/test_tensornetwork.jl
+++ b/test/test_tensornetwork.jl
@@ -114,15 +114,15 @@ using Test: @test, @test_throws, @testset
         @test linkinds(tn, 1 => 2) == [l[E(1 => 2)]]
         @test linkinds(tn, E(1 => 2)) == [l[E(1 => 2)]]
 
-        @test linkaxes(tn, 1 => 2) == [l[E(1 => 2)]]
-        @test linkaxes(tn, E(1 => 2)) == [l[E(1 => 2)]]
+        @test linkaxes(tn, 1 => 2) == (l[E(1 => 2)],)
+        @test linkaxes(tn, E(1 => 2)) == (l[E(1 => 2)],)
 
         @test linknames(tn, 1 => 2) == [name(l[E(1 => 2)])]
         @test linknames(tn, E(1 => 2)) == [name(l[E(1 => 2)])]
         @test issetequal(linknames(tn), [name(l[e]) for e in edges(g)])
 
         @test siteinds(tn, 1) == [s[1]]
-        @test siteaxes(tn, 2) == [s[2]]
+        @test siteaxes(tn, 2) == (s[2],)
         @test sitenames(tn, 3) == [name(s[3])]
     end
 

From 1d5cf747651308a5b22a31fa3b0519415d990f19 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Tue, 3 Nov 2026 11:00:07 -0500
Subject: [PATCH 07/10] Use inferred version of `names` directly in
 `AbstractTensorNetwork` method.

---
 src/abstracttensornetwork.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/abstracttensornetwork.jl b/src/abstracttensornetwork.jl
index 1b3766c2..74ebf770 100644
--- a/src/abstracttensornetwork.jl
+++ b/src/abstracttensornetwork.jl
@@ -39,7 +39,7 @@ end
 
 ITensorBase.inds(tn::AbstractITensorNetwork, v) = inds(tn[v])
 ITensorBase.axes(tn::AbstractITensorNetwork, v) = axes(tn[v])
-ITensorBase.names(tn::AbstractITensorNetwork, v) = name.(inds(tn, v))
+ITensorBase.names(tn::AbstractITensorNetwork, v) = names(tn[v])
 
 linkinds(tn::AbstractGraph, edge::Pair) = linkinds(tn, edgetype(tn)(edge))
 # Pick the link indices from the `src` side, identified by name match with `dst`.

From 5df04b60cad94e30d95fb11f4683bbf1dc9b1aa4 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Tue, 3 Nov 2026 12:22:54 -0500
Subject: [PATCH 08/10] Rename `linknames(tn)` to new function `eachlinkname`;
 make it lazy

---
 src/abstracttensornetwork.jl |  4 +---
 src/normnetwork.jl           |  7 ++++---
 src/tensornetwork.jl         |  8 ++++----
 test/test_normnetwork.jl     | 10 +++++-----
 test/test_tensornetwork.jl   |  6 +++---
 5 files changed, 17 insertions(+), 18 deletions(-)

diff --git a/src/abstracttensornetwork.jl b/src/abstracttensornetwork.jl
index 74ebf770..06f78ef6 100644
--- a/src/abstracttensornetwork.jl
+++ b/src/abstracttensornetwork.jl
@@ -63,9 +63,7 @@ end
 function linknames(tn::AbstractGraph, edge::AbstractEdge)
     return names(tn, src(edge)) ∩ names(tn, dst(edge))
 end
-function linknames(tn::AbstractGraph)
-    return unique(Iterators.flatten(linknames(tn, e) for e in edges(tn)))
-end
+eachlinkname(tn::AbstractGraph) = Iterators.flatten(linknames(tn, e) for e in edges(tn))
 
 function siteinds(tn::AbstractGraph, v)
     s = inds(tn, v)
diff --git a/src/normnetwork.jl b/src/normnetwork.jl
index 8d24e235..7fc6304b 100644
--- a/src/normnetwork.jl
+++ b/src/normnetwork.jl
@@ -22,7 +22,7 @@ struct NormNetwork{T, V, I} <: AbstractITensorNetwork{T, V}
 end
 
 function check_input(::Type{<:NormNetwork}, ket, braname)
-    if !issubset(linknames(ket), keys(braname))
+    if !issubset(eachlinkname(ket), keys(braname))
         error("every link name of the ket layer must have a bra name.")
     end
     if !allunique(braname)
@@ -156,7 +156,7 @@ end
     normnetwork(tn::ITensorNetwork, braname::Dictionary) -> NormNetwork
 
 Build the double-layer norm network `⟨tn|tn⟩`, represented lazily as a `NormNetwork` object.
-Each ket index name in `union(dangling, linknames(tn))` gets the bra name `f(name)`,
+Each ket index name in `union(dangling, eachlinkname(tn))` gets the bra name `f(name)`,
 where `f` defaults to `name -> derivedname(name, "bra")`, and `dangling` is empty by default.
 Alternatively pass the ket→bra name map `braname` directly, which must include every link
 name of `tn` and may include others. Either way an error is thrown if a link name is missing,
@@ -164,7 +164,8 @@ two bra names coincide or a bra name is already an index name of `tn`.
 """
 normnetwork(tn::ITensorNetwork, braname::Dictionary) = NormNetwork(tn, braname)
 function normnetwork(f::Function, tn::ITensorNetwork, dangling = nametype(tn)[])
-    return normnetwork(tn, narrow_map(f, Indices(union(linknames(tn), dangling))))
+    names = Indices{nametype(tn)}(union(eachlinkname(tn), dangling))
+    return normnetwork(tn, narrow_map(f, names))
 end
 function normnetwork(tn::ITensorNetwork, dangling = nametype(tn)[])
     return normnetwork(name -> derivedname(name, "bra"), tn, dangling)
diff --git a/src/tensornetwork.jl b/src/tensornetwork.jl
index cc6da6fa..7f97d97d 100644
--- a/src/tensornetwork.jl
+++ b/src/tensornetwork.jl
@@ -203,11 +203,11 @@ end
 # PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
 has_dimname(tn::ITensorNetwork, name) = haskey(tn.dimname_vertices, name)
 
-# PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
-function linknames(tn::ITensorNetwork)
-    return [
+# PERF: still linear compared to generic method, but in practice order of magnitudes faster.
+function eachlinkname(tn::ITensorNetwork)
+    return (
         name for (name, vertices) in pairs(tn.dimname_vertices) if length(vertices) == 2
-    ]
+    )
 end
 
 function NamedGraphs.similar_graph(
diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index bb916d61..caa28736 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -5,7 +5,7 @@ using ITensorBase:
     ITensor, Index, IndexName, inds, name, nametype, plev, prime, setname, tags, uniquename
 using ITensorNetworksNext: BraView, Greedy, ITensorNetwork, NormNetwork, braname,
     branetwork, bratensor, conj_bratensor, contraction_tree, derivedname, dimnamevertices,
-    flatten_network, has_dimname, ketnetwork, kettensor, linknames, normnetwork,
+    eachlinkname, flatten_network, has_dimname, ketnetwork, kettensor, normnetwork,
     prod_tensors, sitenames, tensornetwork
 using LinearAlgebra: norm
 using NamedGraphs: NamedEdge, incident_edges, named_grid, named_path_graph
@@ -88,7 +88,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         tn, l, s = random_state(Float64, g)
 
         # A user-supplied map dictates the bra-layer name for each link.
-        custom = map(uniquename, Indices(linknames(tn)))
+        custom = map(uniquename, Indices(eachlinkname(tn)))
         nn = normnetwork(tn, custom)
 
         lname = name(l[NamedEdge(1 => 2)])
@@ -148,7 +148,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
 
         # The part of `tn` on vertices 1 and 2, as one rank of a distributed network holds it.
         part = ITensorNetwork(Dict(v => tn[v] for v in (1, 2)))
-        nn = normnetwork(part, map(uniquename, Indices(linknames(tn))))
+        nn = normnetwork(part, map(uniquename, Indices(eachlinkname(tn))))
 
         # The bond to vertex 3 is not a link of `part`, but it is in the map, so it gets its
         # own bra name and the two layers at vertex 2 share only the site index.
@@ -197,7 +197,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         @test isempty(dimnamevertices(bv, lname))
         @test has_dimname(bv, bname)
         @test !has_dimname(bv, lname)
-        @test issetequal(linknames(bv), [braname(nn, name(l[e])) for e in edges(g)])
+        @test issetequal(eachlinkname(bv), [braname(nn, name(l[e])) for e in edges(g)])
         @test sitenames(bv, 2) == [name(s[2])]
     end
 
@@ -267,7 +267,7 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
             @test contract_norm(normnetwork(tn)) ≈ 1
 
             # The contracted norm does not depend on the chosen bra-layer name map.
-            custom = map(uniquename, Indices(linknames(tn)))
+            custom = map(uniquename, Indices(eachlinkname(tn)))
             @test contract_norm(normnetwork(tn, custom)) ≈ contract_norm(normnetwork(tn))
         end
     end
diff --git a/test/test_tensornetwork.jl b/test/test_tensornetwork.jl
index 405a5b6e..77384c9d 100644
--- a/test/test_tensornetwork.jl
+++ b/test/test_tensornetwork.jl
@@ -3,8 +3,8 @@ using DataGraphs:
 using Graphs: add_edge!, add_vertex!, dst, edges, edgetype, has_edge, has_vertex,
     is_directed, ne, nv, rem_edge!, rem_vertex!, src, vertices
 using ITensorBase: Index, inds, name, operator
-using ITensorNetworksNext: ITensorNetwork, has_ind, linkaxes, linkinds, linknames,
-    operator_support, siteaxes, siteinds, sitenames, tensornetwork
+using ITensorNetworksNext: ITensorNetwork, eachlinkname, has_ind, linkaxes, linkinds,
+    linknames, operator_support, siteaxes, siteinds, sitenames, tensornetwork
 using NamedGraphs: convert_vertextype, incident_edges, named_grid, named_path_graph,
     similar_graph, subgraph, vertextype
 using Test: @test, @test_throws, @testset
@@ -119,7 +119,7 @@ using Test: @test, @test_throws, @testset
 
         @test linknames(tn, 1 => 2) == [name(l[E(1 => 2)])]
         @test linknames(tn, E(1 => 2)) == [name(l[E(1 => 2)])]
-        @test issetequal(linknames(tn), [name(l[e]) for e in edges(g)])
+        @test issetequal(eachlinkname(tn), [name(l[e]) for e in edges(g)])
 
         @test siteinds(tn, 1) == [s[1]]
         @test siteaxes(tn, 2) == (s[2],)

From 82aa65d2e9af3db985614dc0194f38e9956697be Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Tue, 3 Nov 2026 12:27:24 -0500
Subject: [PATCH 09/10] Improve performance of `linknames(tn, edge)` using
 comprehension.

---
 src/abstracttensornetwork.jl | 3 ++-
 src/tensornetwork.jl         | 2 +-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/src/abstracttensornetwork.jl b/src/abstracttensornetwork.jl
index 06f78ef6..0fe4148b 100644
--- a/src/abstracttensornetwork.jl
+++ b/src/abstracttensornetwork.jl
@@ -61,7 +61,8 @@ function linknames(tn::AbstractGraph, edge::Pair)
     return linknames(tn, edgetype(tn)(edge))
 end
 function linknames(tn::AbstractGraph, edge::AbstractEdge)
-    return names(tn, src(edge)) ∩ names(tn, dst(edge))
+    dstnames = names(tn, dst(edge))
+    return [n for n in names(tn, src(edge)) if n in dstnames]
 end
 eachlinkname(tn::AbstractGraph) = Iterators.flatten(linknames(tn, e) for e in edges(tn))
 
diff --git a/src/tensornetwork.jl b/src/tensornetwork.jl
index 7f97d97d..5742d749 100644
--- a/src/tensornetwork.jl
+++ b/src/tensornetwork.jl
@@ -203,7 +203,7 @@ end
 # PERF: fast lookup compared to `AbstractITensorNetwork` fallback.
 has_dimname(tn::ITensorNetwork, name) = haskey(tn.dimname_vertices, name)
 
-# PERF: still linear compared to generic method, but in practice order of magnitudes faster.
+# PERF: still linear compared to generic method, but in practice 5x faster
 function eachlinkname(tn::ITensorNetwork)
     return (
         name for (name, vertices) in pairs(tn.dimname_vertices) if length(vertices) == 2

From 9cb685ed00777b016900942cf77c52dee873b7d1 Mon Sep 17 00:00:00 2001
From: Jack Dunham <jdunham@flatironinstitute.org>
Date: Wed, 4 Nov 2026 17:54:56 -0500
Subject: [PATCH 10/10] Use `prime` as default dervived name for bra layer in
 NormNetwork

Calls this via a function `derive_braname`.
---
 src/normnetwork.jl       | 8 ++++++--
 test/test_normnetwork.jl | 7 ++++---
 2 files changed, 10 insertions(+), 5 deletions(-)

diff --git a/src/normnetwork.jl b/src/normnetwork.jl
index 7fc6304b..46308a8f 100644
--- a/src/normnetwork.jl
+++ b/src/normnetwork.jl
@@ -115,6 +115,9 @@ function braname(nn::NormNetwork, name)
     return get(branamemap(nn), name, name)
 end
 
+# The default ket→bra name map
+derive_braname(name) = prime(name)
+
 """
     kettensor(nn::NormNetwork, vertex)
 
@@ -157,7 +160,8 @@ end
 
 Build the double-layer norm network `⟨tn|tn⟩`, represented lazily as a `NormNetwork` object.
 Each ket index name in `union(dangling, eachlinkname(tn))` gets the bra name `f(name)`,
-where `f` defaults to `name -> derivedname(name, "bra")`, and `dangling` is empty by default.
+where `f` defaults to `derive_braname`, which primes the name, and `dangling` is empty by
+default.
 Alternatively pass the ket→bra name map `braname` directly, which must include every link
 name of `tn` and may include others. Either way an error is thrown if a link name is missing,
 two bra names coincide or a bra name is already an index name of `tn`.
@@ -168,5 +172,5 @@ function normnetwork(f::Function, tn::ITensorNetwork, dangling = nametype(tn)[])
     return normnetwork(tn, narrow_map(f, names))
 end
 function normnetwork(tn::ITensorNetwork, dangling = nametype(tn)[])
-    return normnetwork(name -> derivedname(name, "bra"), tn, dangling)
+    return normnetwork(derive_braname, tn, dangling)
 end
diff --git a/test/test_normnetwork.jl b/test/test_normnetwork.jl
index caa28736..7861aec3 100644
--- a/test/test_normnetwork.jl
+++ b/test/test_normnetwork.jl
@@ -115,12 +115,13 @@ contract_norm(nn) = prod_tensors(flatten_network(nn), Greedy())[]
         lname = name(l[NamedEdge(1 => 2)])
 
         # Two independently constructed norm networks agree on every bra name.
-        @test braname(normnetwork(tn), lname) == derivedname(lname, :bra)
+        @test braname(normnetwork(tn), lname) == prime(lname)
         @test braname(normnetwork(tn), lname) == braname(normnetwork(tn), lname)
-        @test braname(normnetwork(prime, tn), lname) == prime(lname)
+        f = n -> derivedname(n, :bra)
+        @test braname(normnetwork(f, tn), lname) == derivedname(lname, :bra)
 
         # A bra name that is already an index name of the network is rejected.
-        taken = setname(Index(2), derivedname(lname, :bra))
+        taken = setname(Index(2), prime(lname))
         tn[1] = tn[1] * ITensor(ones(2), (taken,))
         @test_throws ErrorException normnetwork(tn)
     end