diff --git a/docs/package-lock.json b/docs/package-lock.json
index 23558fb..3750ffc 100644
--- a/docs/package-lock.json
+++ b/docs/package-lock.json
@@ -11,7 +11,7 @@
         "@astrojs/markdown-remark": "^7.3.1",
         "@astrojs/starlight": "^0.42.5",
         "astro": "^7.3.5",
-        "katex": "^0.16.22",
+        "katex": "^0.19.0",
         "rehype-katex": "^7.0.1",
         "remark-math": "^6.0.0",
         "sharp": "^0.35.3",
@@ -2637,12 +2637,12 @@
       }
     },
     "node_modules/commander": {
-      "version": "8.3.0",
-      "resolved": "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz",
-      "integrity": "sha512-OkTL9umf+He2DZkUq8f8J9of7yL6RJKI24dVITBmNfZBmri9zYZQrKkuXiKhyfPSu8tUhnVBB1iKXevvnlR4Ww==",
+      "version": "15.0.0",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-15.0.0.tgz",
+      "integrity": "sha512-z67u4ZhzCL/Tydu1lJARtEZYWbWaN7oYLHbsuzocr6y4N6WZAagG3RQ4FW61V1/0+jImpj293XfrcYnd1qxtPg==",
       "license": "MIT",
       "engines": {
-        "node": ">= 12"
+        "node": ">=22.12.0"
       }
     },
     "node_modules/common-ancestor-path": {
@@ -3918,16 +3918,16 @@
       "license": "MIT"
     },
     "node_modules/katex": {
-      "version": "0.16.47",
-      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
-      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "version": "0.19.0",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.19.0.tgz",
+      "integrity": "sha512-v6Tznz3zJ7u3niRCoDTsumM2+HA2XXcCu+WAacCeHD2z3p9A9Ks987o5FzfTGBN0e8A0vjEgIDvLbICrXpdw/Q==",
       "funding": [
         "https://opencollective.com/katex",
         "https://github.com/sponsors/katex"
       ],
       "license": "MIT",
       "dependencies": {
-        "commander": "^8.3.0"
+        "commander": "^15.0.0"
       },
       "bin": {
         "katex": "cli.js"
@@ -4833,6 +4833,31 @@
         "url": "https://opencollective.com/unified"
       }
     },
+    "node_modules/micromark-extension-math/node_modules/commander": {
+      "version": "8.3.0",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz",
+      "integrity": "sha512-OkTL9umf+He2DZkUq8f8J9of7yL6RJKI24dVITBmNfZBmri9zYZQrKkuXiKhyfPSu8tUhnVBB1iKXevvnlR4Ww==",
+      "license": "MIT",
+      "engines": {
+        "node": ">= 12"
+      }
+    },
+    "node_modules/micromark-extension-math/node_modules/katex": {
+      "version": "0.16.47",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
+      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "funding": [
+        "https://opencollective.com/katex",
+        "https://github.com/sponsors/katex"
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "commander": "^8.3.0"
+      },
+      "bin": {
+        "katex": "cli.js"
+      }
+    },
     "node_modules/micromark-extension-mdx-expression": {
       "version": "3.0.1",
       "resolved": "https://registry.npmjs.org/micromark-extension-mdx-expression/-/micromark-extension-mdx-expression-3.0.1.tgz",
@@ -5892,6 +5917,31 @@
         "url": "https://opencollective.com/unified"
       }
     },
+    "node_modules/rehype-katex/node_modules/commander": {
+      "version": "8.3.0",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-8.3.0.tgz",
+      "integrity": "sha512-OkTL9umf+He2DZkUq8f8J9of7yL6RJKI24dVITBmNfZBmri9zYZQrKkuXiKhyfPSu8tUhnVBB1iKXevvnlR4Ww==",
+      "license": "MIT",
+      "engines": {
+        "node": ">= 12"
+      }
+    },
+    "node_modules/rehype-katex/node_modules/katex": {
+      "version": "0.16.47",
+      "resolved": "https://registry.npmjs.org/katex/-/katex-0.16.47.tgz",
+      "integrity": "sha512-Eeo8Ys1doU1z+x8AZsPpQu+p/QcZBI5PeOo7QGQdy2x2m0MU/hYagBbGOmXwr5KVbEfVuWv9LpnQWeehogurjg==",
+      "funding": [
+        "https://opencollective.com/katex",
+        "https://github.com/sponsors/katex"
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "commander": "^8.3.0"
+      },
+      "bin": {
+        "katex": "cli.js"
+      }
+    },
     "node_modules/rehype-raw": {
       "version": "7.0.0",
       "resolved": "https://registry.npmjs.org/rehype-raw/-/rehype-raw-7.0.0.tgz",
diff --git a/docs/package.json b/docs/package.json
index 81aad0f..c4be530 100644
--- a/docs/package.json
+++ b/docs/package.json
@@ -18,7 +18,7 @@
     "@astrojs/markdown-remark": "^7.3.1",
     "@astrojs/starlight": "^0.42.5",
     "astro": "^7.3.5",
-    "katex": "^0.16.22",
+    "katex": "^0.19.0",
     "rehype-katex": "^7.0.1",
     "remark-math": "^6.0.0",
     "sharp": "^0.35.3",