diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index c804f15..1e09c59 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -55,12 +55,12 @@ jobs:
       - name: Upload coverage to Codecov
         id: codecov_upload
         uses: codecov/codecov-action@v4
+        continue-on-error: true
         if: matrix.python-version == '3.13'
         with:
           files: ./coverage.xml
+          token: ${{ secrets.CODECOV_TOKEN }}
           fail_ci_if_error: true
-        env:
-          CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
 
       - name: Generate local coverage badge
         if: matrix.python-version == '3.13' && steps.codecov_upload.outcome == 'success'
@@ -77,7 +77,7 @@ jobs:
     name: Update coverage badge
     needs: test-portable
     runs-on: ubuntu-latest
-    if: github.event_name == 'push'
+    if: github.event_name == 'push' && needs.test-portable.result == 'success'
     permissions:
       contents: write
 
@@ -86,11 +86,13 @@ jobs:
 
       - name: Download local coverage badge
         uses: actions/download-artifact@v4
+        continue-on-error: true
         with:
           name: coverage-badge
           path: tmp/coverage-badge
 
       - name: Commit local coverage badge
+        if: hashFiles('tmp/coverage-badge/coverage.svg') != ''
         run: |
           cp tmp/coverage-badge/coverage.svg docs/assets/coverage.svg
           if ! git diff --quiet -- docs/assets/coverage.svg; then
diff --git a/README.md b/README.md
index 4b17ff2..d2338db 100644
--- a/README.md
+++ b/README.md
@@ -60,34 +60,15 @@ data.to_hdf5("modes.h5")
 
 ## Physics
 
-MicroMode solves the source-free frequency-domain Maxwell equations on a
-rasterized Yee mode plane,
-
-$$
-\nabla\times\mathbf{E}=-i\omega\mu\mathbf{H},
-\qquad
-\nabla\times\mathbf{H}=i\omega\epsilon\mathbf{E},
-$$
-
-with modal fields $\mathbf{E},\mathbf{H}\propto e^{i k_0 n_\mathrm{eff} z}.$
+MicroMode solves the source-free frequency-domain Maxwell equations on a rasterized Yee mode plane, $\nabla\times\mathbf{E}=-i\omega\mu\mathbf{H}, \; \nabla\times\mathbf{H}=i\omega\epsilon\mathbf{E},$ with modal fields $\mathbf{E},\mathbf{H}\propto e^{i k_0 n_\mathrm{eff} z}.$
 
 On diagonal material grids this becomes a transverse eigenproblem,
-
-$$
-A_\mathrm{diag}
-\begin{bmatrix}E_x\\E_y\end{bmatrix}
-=
--n_\mathrm{eff}^2
-\begin{bmatrix}E_x\\E_y\end{bmatrix}
-$$
-
 while full tensor or transformed grids use a first-order tensorial form. The
 detailed derivation is in [docs/physics-model.md](docs/physics-model.md), and
-the public solver controls are summarized in
-[docs/mode-solver-methods.md](docs/mode-solver-methods.md).
+the public solver controls are summarized in [docs/mode-solver-methods.md](docs/mode-solver-methods.md).
 
 
-## Performance
+## Solver
 
 MicroMode is designed to make high-performance mode solving available without
 requiring users to install external solver stacks. The production backend is a