diff --git a/.vscode/extensions.json b/.vscode/extensions.json
index f57b991..ee5a6b4 100644
--- a/.vscode/extensions.json
+++ b/.vscode/extensions.json
@@ -4,6 +4,7 @@
     "editorconfig.editorconfig",
     "esbenp.prettier-vscode",
     "executablebookproject.myst-highlight",
+    "github.vscode-github-actions",
     "github.vscode-pull-request-github",
     "mhutchie.git-graph",
     "ms-python.python",
diff --git a/lecture2.ipynb b/lecture2.ipynb
index 474da2f..508a318 100644
--- a/lecture2.ipynb
+++ b/lecture2.ipynb
@@ -111,7 +111,9 @@
    "outputs": [],
    "source": [
     "n_final_state = 3\n",
-    "pa, p1, p2, p3 = (data[i::4].T for i in range(n_final_state + 1))"
+    "pa, p1, p2, p3 = (data[i::4].T for i in range(n_final_state + 1))\n",
+    "p0 = p1 + p2 + p3\n",
+    "pb = p0 - pa"
    ]
   },
   {
@@ -120,6 +122,9 @@
    "id": "a0b70dc7-a087-4b43-a08c-f48840a2c6a3",
    "metadata": {
     "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
     "slideshow": {
      "slide_type": ""
     },
@@ -135,7 +140,6 @@
     "    return p[0] ** 2 - np.sum(p[1:] ** 2, axis=0)\n",
     "\n",
     "\n",
-    "p0 = p1 + p2 + p3\n",
     "m0 = mass(p0)\n",
     "print(f\"{m0.mean():.4g} +/- {m0.std():.4g}\")"
    ]
@@ -160,10 +164,10 @@
    "source": [
     "from IPython.display import Math\n",
     "\n",
+    "display(Math(Rf\"m_a = {mass(pa).mean():.3g}\\text{{ GeV}}\"))\n",
+    "display(Math(Rf\"m_b = {mass(pb).mean():.3g}\\text{{ GeV}}\"))\n",
     "for i, p in enumerate([p0, p1, p2, p3]):\n",
-    "    display(Math(Rf\"m_{i} = {mass(p).mean():.3g}\\text{{ GeV}}\"))\n",
-    "\n",
-    "display(Math(Rf\"m_{{a}} = {mass(pa).mean():.3g}\\text{{ GeV}}\"))"
+    "    display(Math(Rf\"m_{i} = {mass(p).mean():.3g}\\text{{ GeV}}\"))"
    ]
   },
   {
@@ -190,17 +194,35 @@
     "from particle import Particle\n",
     "\n",
     "\n",
-    "def find_candidates(m: float, delta: float = 0.001) -> list[Particle]:\n",
-    "    return Particle.findall(lambda p: (m - delta) < 1e-3 * p.mass < (m + delta))\n",
+    "def find_candidates(\n",
+    "    mass: float, delta: float = 0.001, charge: float | None = None\n",
+    ") -> list[Particle]:\n",
+    "    def identify(p) -> bool:\n",
+    "        if p.pdgid in {21}:\n",
+    "            return\n",
+    "        if charge is not None and p.charge != charge:\n",
+    "            return False\n",
+    "        if (mass - delta) < 1e-3 * p.mass < (mass + delta):\n",
+    "            return True\n",
+    "        return False\n",
     "\n",
+    "    return Particle.findall(identify)\n",
     "\n",
+    "\n",
+    "ma = mass(pa).mean()\n",
+    "mb = mass(pb).mean()\n",
     "m1 = mass(p1).mean()\n",
     "m2 = mass(p2).mean()\n",
     "m3 = mass(p3).mean()\n",
-    "particles = tuple(find_candidates(m.mean())[0] for m in [m1, m2, m3])\n",
-    "\n",
-    "src = R\"\\text{Final state: }\" + \", \".join(f\"{p.latex_name}\" for p in particles)\n",
-    "Math(src)"
+    "initial_state = (\n",
+    "    find_candidates(ma.mean(), delta=1e-4)[0],\n",
+    "    find_candidates(mb.mean())[0],\n",
+    ")\n",
+    "final_state = tuple(find_candidates(m.mean())[0] for m in [m1, m2, m3])\n",
+    "display(\n",
+    "    Math(R\"\\text{Incoming: }\" + \", \".join(f\"{p.latex_name}\" for p in initial_state)),\n",
+    "    Math(R\"\\text{Outgoing: }\" + \", \".join(f\"{p.latex_name}\" for p in final_state)),\n",
+    ")"
    ]
   },
   {
@@ -214,7 +236,7 @@
     "tags": []
    },
    "source": [
-    "So this is probably some photon&nbsp;$\\gamma$ hitting a target that produces a meson&nbsp;$\\eta$, pion&nbsp;$\\pi^0$, and proton&nbsp;$p$."
+    "So this is a photon&nbsp;$\\gamma$ hitting a proton&nbsp;$p$ and producing a meson&nbsp;$\\eta$, pion&nbsp;$\\pi^0$, and proton&nbsp;$p$."
    ]
   },
   {
@@ -457,7 +479,7 @@
    },
    "outputs": [],
    "source": [
-    "find_candidates(m=np.sqrt(R12), delta=0.01)"
+    "find_candidates(mass=np.sqrt(R12), delta=0.01, charge=0)"
    ]
   },
   {
@@ -473,7 +495,7 @@
    },
    "outputs": [],
    "source": [
-    "find_candidates(m=np.sqrt(R23), delta=0.01)"
+    "find_candidates(mass=np.sqrt(R23), delta=0.01, charge=+1)"
    ]
   },
   {
@@ -489,7 +511,7 @@
    },
    "outputs": [],
    "source": [
-    "find_candidates(m=np.sqrt(R31), delta=0.01)"
+    "find_candidates(mass=np.sqrt(R31), delta=0.01, charge=+1)"
    ]
   },
   {