docs: more descriptive comments on set-membership witness fixing (#526)

examples/notebooks/set_membership.ipynb

@@ -314,6 +314,17 @@
         "assert os.path.isfile(witness_path_truthy)"
       ]
     },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "id": "41fd15a8",
+      "metadata": {},
+      "outputs": [],
+      "source": [
+        "witness = json.load(open(witness_path, \"r\"))\n",
+        "witness"
+      ]
+    },
     {
       "cell_type": "code",
       "execution_count": null,
@@ -329,7 +340,14 @@
         "# WE GOT CIRCUIT PARAMETERS\n",
         "# EVERYTHING ANYONE HAS EVER NEEDED FOR ZK\n",
         "\n",
+        "# we force the output to be 0 this corresponds to the set membership test being true -- and we set this to a fixed vis output\n",
+        "# this means that the output is fixed and the verifier can see it but that if the input is not in the set the output will not be 0 and the verifier will reject\n",
+        "witness = json.load(open(witness_path, \"r\"))\n",
+        "witness[\"outputs\"][0] = [[0, 0, 0, 0]]\n",
+        "json.dump(witness, open(witness_path, \"w\"))\n",
         "\n",
+        "witness = json.load(open(witness_path, \"r\"))\n",
+        "print(witness[\"outputs\"][0])\n",
         "\n",
         "res = ezkl.setup(\n",
         "        compiled_model_path,\n",
@@ -497,7 +515,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.9.15"
+      "version": "3.9.13"
     }
   },
   "nbformat": 4,