diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
index cef40db6..cd139036 100644
--- a/.github/workflows/publish.yml
+++ b/.github/workflows/publish.yml
@@ -87,16 +87,12 @@ jobs:
           attestations: true
 
   pypi-publish:
-    strategy:
-      matrix:
-        project: ["scipy-openblas32", "scipy-openblas64"]
-    name: Publish ${{ matrix.project }} to PyPI
+    name: Publish scipy-openblas to PyPI
     if: github.event_name == 'workflow_dispatch' && github.event.inputs.environment == 'pypi'
     needs: [call-posix, call-windows, call-windows-arm, check-version]
     runs-on: ubuntu-latest
     environment:
       name: pypi
-      url: https://pypi.org/p/${{ matrix.project }}
     permissions:
       id-token: write  # mandatory for trusted publishing
     steps:
diff --git a/README.md b/README.md
index 813b16a4..92670b12 100644
--- a/README.md
+++ b/README.md
@@ -20,23 +20,27 @@
 
 # OpenBLAS library build process
 
-First, tarballs are built using `build_lib` in `tools/build_steps.sh` (on
+First, OpenBLAS is built using `build_lib` in `tools/build_steps.sh` (on
 posix in a docker and drectly on macos) or `tools/build_steps_windows.sh` on windows.
 
-Then the shared object and header files from the tarball are used to build the
-wheel via `tools/build_prepare_wheel.sh` and `pip build wheel`, and the wheels uploaded to
+Then the shared object and header files are used to build the
+wheel via `tools/build_prepare_wheel.sh` and `pip build wheel`.
+
+If the build is on the `main` branch, the wheels are uploaded to
 https://anaconda.org/scientific=python-nightly-wheels/scipy_openblas32 and
 https://anaconda.org/scientific=python-nightly-wheels/scipy_openblas64 via
-`tools/upload_to_anaconda_staging.sh`. For a release, the wheels are uploaded
-to PyPI by downloading them via tools/dowlnload-wheels.py and uploading via
-[twine](https://twine.readthedocs.io/en/stable/).
-
+`tools/upload_to_anaconda_staging.sh`.
+
+There are workflow triggers for repo admins. They can trigger a testpypi build
+or a pypi build with the publish workflow, which will upload the wheels using
+trusted publishing. In order to publish to PyPI, there must be a tag at the HEAD
+of the branch used to publish. Use annotated tags:
+```
+git tag -a v0.3.31.126.4 -m"fixed something"
+```
 The wheel is self-contained, it includes all needed gfortran support libraries.
 On windows, this is a single DLL. 
 
-The wheel supplies interfaces for building and using OpenBLAS in a python
-project like SciPy or NumPy:
-
 ## Buildtime
 
 - `get_include_dir()`, `get_lib_dir()` and `get_library()` for use in compiler
diff --git a/pyproject.toml b/pyproject.toml
index 0e24297e..46a1584c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -9,7 +9,7 @@ build-backend = "setuptools.build_meta"
 [project]
 name = "scipy-openblas64"
 # v0.3.31-126-g55b16e59
-version = "0.3.31.126.4"
+version = "0.3.31.126.5"
 requires-python = ">=3.7"
 description = "Provides OpenBLAS for python packaging"
 readme = "README.md"