diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index b28dcf5..00a3881 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -21,20 +21,21 @@ jobs:
     strategy:
       matrix:
         julia-version: ['lts', '1', 'pre']
-        julia-arch: [x64, x86]
+        julia-arch: [default]
         os: [ubuntu-latest, windows-latest, macOS-latest]
-        exclude:
-          - os: macOS-latest
+        include:
+          - os: ubuntu-latest
+            julia-version: '1'
             julia-arch: x86
 
     steps:
-      - uses: actions/checkout@v4
-      - uses: julia-actions/setup-julia@v2
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7.0.1
+      - uses: julia-actions/setup-julia@fa02766e078afaaf09b14210362cee14137e6a32 # v3.0.2
         with:
           version: ${{ matrix.julia-version }}
           arch: ${{ matrix.julia-arch }}
-      - uses: julia-actions/cache@v2
-      - uses: julia-actions/julia-buildpkg@v1
-      - uses: julia-actions/julia-runtest@v1
+      - uses: julia-actions/cache@b7788abd52452d5bc033d69796e110d9906af4ab # v3.2.0
+      - uses: julia-actions/julia-buildpkg@e3eb439fad4f9aba7da2667e7510e4a46ebc46e1 # v1.7.0
+      - uses: julia-actions/julia-runtest@6e050c8013b833b1195105ff2fce9cd802f53271 # v1.12.0
         # with:
         #   annotate: true
\ No newline at end of file
diff --git a/README.md b/README.md
index 2c0c445..c827e8a 100644
--- a/README.md
+++ b/README.md
@@ -7,7 +7,7 @@
 Given a Hamiltonian operator $H$ in [MPO](https://tensornetwork.org/mpo/) form, and an initial state $\psi_0$ in [MPS](https://tensornetwork.org/mps/) form, calculate
 
 $$
-\psi(t_k)=e^{-iHk\Delta t}\psi_0~,~~k=0,1,\dots,N 
+\psi(t_k)=e^{-iHk\Delta t}~\psi _0~,~~k\in \lbrace 0,1,\dots,N\rbrace 
 $$
 
 <br/>