From 4c496774695841f3cb61709086ec060734fd0292 Mon Sep 17 00:00:00 2001
From: lintianle <lintianle@deepseek.com>
Date: Thu, 16 Jul 2026 18:57:44 +0800
Subject: [PATCH] website: render the design essays' TeX (math: true, mathjax3
 pinned to v4)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

design/revertible-effects and design/context-model carry real TeX that was
showing as literal $$ source. markdown: { math: true } enables
markdown-it-mathjax3; pinned ^4.3.2 deliberately — v5 injects a <style> tag
per formula (31 on one page), which Vue's template compiler rejects, so v5
cannot work under VitePress; v4 emits pure SVG (probed: 0 style tags).
---
 pnpm-lock.yaml                     | 304 ++++++++++++++++++++++++++++-
 website/.vitepress/config/index.ts |   7 +
 website/package.json               |   1 +
 3 files changed, 310 insertions(+), 2 deletions(-)

diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml
index 52575ae3de..f682c5e3f2 100644
--- a/pnpm-lock.yaml
+++ b/pnpm-lock.yaml
@@ -1488,9 +1488,12 @@ importers:
 
   website:
     devDependencies:
+      markdown-it-mathjax3:
+        specifier: ^4.3.2
+        version: 4.3.2
       vitepress:
         specifier: ^1.6.3
-        version: 1.6.4(@algolia/client-search@5.55.2)(@types/node@25.9.3)(lightningcss@1.32.0)(postcss@8.5.15)(search-insights@2.17.3)(typescript@6.0.3)
+        version: 1.6.4(@algolia/client-search@5.55.2)(@types/node@25.9.3)(lightningcss@1.32.0)(markdown-it-mathjax3@4.3.2)(postcss@8.5.15)(search-insights@2.17.3)(typescript@6.0.3)
       vue:
         specifier: ^3.5.13
         version: 3.5.39(typescript@6.0.3)
@@ -3306,6 +3309,10 @@ packages:
   '@vueuse/shared@12.8.2':
     resolution: {integrity: sha512-dznP38YzxZoNloI0qpEfpkms8knDtaoQ6Y/sfS0L7Yki4zh40LFHEhur0odJC6xTHG5dxWVPiUWBXn+wCG2s5w==}
 
+  '@xmldom/xmldom@0.9.10':
+    resolution: {integrity: sha512-A9gOqLdi6cV4ibazAjcQufGj0B1y/vDqYrcuP6d/6x8P27gRS8643Dj9o1dEKtB6O7fwxb2FgBmJS2mX7gpvdw==}
+    engines: {node: '>=14.6'}
+
   acorn-jsx@5.3.2:
     resolution: {integrity: sha512-rq9s+JNhf0IChjtDXxllJ7g41oZk5SlXtp0LHwyA5cejwn7vKmKp4pPri6YEePv2PU65sAsegbXtIinmDFDXgQ==}
     peerDependencies:
@@ -3327,6 +3334,10 @@ packages:
     resolution: {integrity: sha512-OyacJsaeuLUvGWOynNqYc6sx88XvyoG39wMT8SYqL3l9wwaorDW/LPRbUPfhzw0bWsUWzNCZTnFYOrWFBKsUaw==}
     engines: {node: '>= 14.0.0'}
 
+  ansi-colors@4.1.3:
+    resolution: {integrity: sha512-/6w/C21Pm1A7aZitlI5Ni/2J6FFQN8i1Cvz3kHABAAbw93v/NlvKdVOqz7CCWz/3iv/JplRSEEZ83XION15ovw==}
+    engines: {node: '>=6'}
+
   ansis@4.3.1:
     resolution: {integrity: sha512-BJ8/l4R5LRE7hW9WdSuGYrLSHi2ynxeFpDFbH0K/CgNeY/tyhk+vO6TYxXC5r5CpUhNVX310xzPsN/H9lCdfOA==}
     engines: {node: '>=14'}
@@ -3367,6 +3378,9 @@ packages:
   birpc@4.0.0:
     resolution: {integrity: sha512-LShSxJP0KTmd101b6DRyGBj57LZxSDYWKitQNW/mi8GRMvZb078Uf9+pveax1DrVL89vm7mWe+TovdI/UDOuPw==}
 
+  boolbase@1.0.0:
+    resolution: {integrity: sha512-JZOSA7Mo9sNGB8+UjSgzdLtokWAky1zbztM3WRLCbZ70/3cTANmQmOdR7y2g+J0e2WXywy1yS468tY+IruqEww==}
+
   bowser@2.14.1:
     resolution: {integrity: sha512-tzPjzCxygAKWFOJP011oxFHs57HzIhOEracIgAePE4pqB3LikALKnSzUyU4MGs9/iCEUuHlAJTjTc5M+u7YEGg==}
 
@@ -3397,6 +3411,13 @@ packages:
   character-entities@2.0.2:
     resolution: {integrity: sha512-shx7oQ0Awen/BRIdkjkvz54PnEEI/EjwXDSIZp86/KKdbafHh1Df/RYGBhn4hbe2+uKC9FnT5UCEdyPz3ai9hQ==}
 
+  cheerio-select@1.6.0:
+    resolution: {integrity: sha512-eq0GdBvxVFbqWgmCm7M3XGs1I8oLy/nExUnh6oLqmBditPO9AqQJrkslDpMun/hZ0yyTs8L0m85OHp4ho6Qm9g==}
+
+  cheerio@1.0.0-rc.10:
+    resolution: {integrity: sha512-g0J0q/O6mW8z5zxQ3A8E8J1hUgp4SMOvEoW/x84OwyHKe/Zccz83PVT4y5Crcr530FV6NgmKI1qvGTKVl9XXVw==}
+    engines: {node: '>= 6'}
+
   chokidar@4.0.3:
     resolution: {integrity: sha512-Qgzu8kfBvo+cA4962jnP1KkS6Dop5NS6g7R5LFYJr4b8Ub94PPQXUksCw9PvXoeXPRRddRNC5C1JQUR2SMGtnA==}
     engines: {node: '>= 14.16.0'}
@@ -3404,6 +3425,14 @@ packages:
   comma-separated-tokens@2.0.3:
     resolution: {integrity: sha512-Fu4hJdvzeylCfQPp9SGWidpzrMs7tTrlu6Vb8XGaRGck8QSNZJJp538Wrb60Lax4fPwR64ViY468OIUTbRlGZg==}
 
+  commander@13.1.0:
+    resolution: {integrity: sha512-/rFeCpNJQbhSZjGVwO9RFV3xPqbnERS8MmIQzCtD/zl6gpJuV/bMLuN92oG3F7d8oDEHHRrujSXNUr8fpjntKw==}
+    engines: {node: '>=18'}
+
+  commander@6.2.1:
+    resolution: {integrity: sha512-U7VdrJFnJgo4xjrHpTzu0yrHPGImdsmD95ZlgYSEajAn2JKzDhDTPG9kBTefmObL2w/ngeZnilk+OV9CG3d7UA==}
+    engines: {node: '>= 6'}
+
   commander@7.2.0:
     resolution: {integrity: sha512-QrWXB+ZQSVPmIWIhtEO9H+gwHaMGYiF5ChvoJ+K9ZGHG/sVsa6yiesAD1GC/x46sET00Xlwo1u49RVVVzvcSkw==}
     engines: {node: '>= 10'}
@@ -3444,10 +3473,17 @@ packages:
     resolution: {integrity: sha512-uV2QOWP2nWzsy2aMp8aRibhi9dlzF5Hgh5SHaB9OiTGEyDTiJJyx0uy51QXdyWbtAHNua4XJzUKca3OzKUd3vA==}
     engines: {node: '>= 8'}
 
+  css-select@4.3.0:
+    resolution: {integrity: sha512-wPpOYtnsVontu2mODhA19JrqWxNsfdatRKd64kmpRbQgh1KtItko5sTnEpPdpSaJszTOhEMlF/RPz28qj4HqhQ==}
+
   css-tree@3.2.1:
     resolution: {integrity: sha512-X7sjQzceUhu1u7Y/ylrRZFU2FS6LRiFVp6rKLPg23y3x3c3DOKAwuXGDp+PAGjh6CSnCjYeAul8pcT8bAl+lSA==}
     engines: {node: ^10 || ^12.20.0 || ^14.13.0 || >=15.0.0}
 
+  css-what@6.2.2:
+    resolution: {integrity: sha512-u/O3vwbptzhMs3L1fQE82ZSLHQQfto5gyZzwteVIEyeaY5Fc7R4dapF/BvRoSYFeqfBk4m0V1Vafq5Pjv25wvA==}
+    engines: {node: '>= 6'}
+
   csstype@3.2.3:
     resolution: {integrity: sha512-z1HGKcYy2xA8AGQfwrn0PAy+PB7X/GSj3UVJW9qKyn43xWa+gl5nXmU4qqLMRzWVLFC8KusUX8T/0kCiOYpAIQ==}
 
@@ -3657,9 +3693,26 @@ packages:
     resolution: {integrity: sha512-svtcdpS8CgJyqAjEQIXdb3OjhFVVYjzGAPO8WGCmRbrml64SPw/jJD4GoE98aR7r25A0XcgrK3F02yw9R/vhQw==}
     engines: {node: '>=0.3.1'}
 
+  dom-serializer@1.4.1:
+    resolution: {integrity: sha512-VHwB3KfrcOOkelEG2ZOfxqLZdfkil8PtJi4P8N2MMXucZq2yLp75ClViUlOVwyoHEDjYU433Aq+5zWP61+RGag==}
+
+  domelementtype@2.3.0:
+    resolution: {integrity: sha512-OLETBj6w0OsagBwdXnPdN0cnMfF9opN69co+7ZrbfPGrdpPVNBUj02spi6B1N7wChLQiPn4CSH/zJvXw56gmHw==}
+
+  domhandler@3.3.0:
+    resolution: {integrity: sha512-J1C5rIANUbuYK+FuFL98650rihynUOEzRLxW+90bKZRWB6A1X1Tf82GxR1qAWLyfNPRvjqfip3Q5tdYlmAa9lA==}
+    engines: {node: '>= 4'}
+
+  domhandler@4.3.1:
+    resolution: {integrity: sha512-GrwoxYN+uWlzO8uhUXRl0P+kHE4GtVPfYzVLcUxPL7KNdHKj66vvlhiweIHqYYXWlw+T8iLMp42Lm67ghw4WMQ==}
+    engines: {node: '>= 4'}
+
   dompurify@3.4.11:
     resolution: {integrity: sha512-zhlUV12GsaRzMsf9q5M254YhA4+VuF0fG+QFqu6aYpoGlKtz+w8//jBcGVYBgQkR5GHjUomejY84AV+/uPbWdw==}
 
+  domutils@2.8.0:
+    resolution: {integrity: sha512-w96Cjofp72M5IIhpjgobBimYEfoPjx1Vx0BSX9P30WBdZW2WIKU0T1Bd0kz2eNZ9ikjKgHbEyKx8BB6H1L3h3A==}
+
   dts-resolver@3.0.0:
     resolution: {integrity: sha512-1T1f+z+4tl9XD+m+0HBgWoL/nm0bOIffyWaUuUSBlFg/86IWvfx+wjNaO/ybU0AJzG9/Mi5hBUgGV6zCmWEN7Q==}
     engines: {node: ^22.18.0 || >=24.0.0}
@@ -3679,6 +3732,9 @@ packages:
     resolution: {integrity: sha512-YGRs8knHhKHVShLkFET/rWAU8kmHbOV5LwN938RHI0pljAJ1Gf6SzXsSmRaEzcXTtOOmVqJ5+WtQPL5uigY50Q==}
     engines: {node: '>=14'}
 
+  entities@2.2.0:
+    resolution: {integrity: sha512-p92if5Nz619I0w+akJrLZH0MX0Pb5DX39XOwQTtXSdQQOaYH03S1uIQp4mhOZtAXrxq4ViO67YTiLBo2638o9A==}
+
   entities@7.0.1:
     resolution: {integrity: sha512-TWrgLOFUQTH994YUyl1yT4uyavY5nNB5muff+RtWaqNVCAK408b5ZnnbNAUEWLTCpum9w6arT70i1XdQ4UeOPA==}
     engines: {node: '>=0.12'}
@@ -3703,6 +3759,10 @@ packages:
     engines: {node: '>=18'}
     hasBin: true
 
+  escape-goat@3.0.0:
+    resolution: {integrity: sha512-w3PwNZJwRxlp47QGzhuEBldEqVHHhh8/tIPcl6ecf2Bou99cdAt0knihBV0Ecc7CGxYduXVBDheH1K2oADRlvw==}
+    engines: {node: '>=10'}
+
   escape-string-regexp@4.0.0:
     resolution: {integrity: sha512-TtpcNJ3XAzx3Gq8sWRzJaVajRs0uVxA2YAkdb1jm2YkPz4G6egUFAyA3n5vtEIZefPk5Wa4UXbKuS5fKkJWdgA==}
     engines: {node: '>=10'}
@@ -3737,6 +3797,10 @@ packages:
       jiti:
         optional: true
 
+  esm@3.2.25:
+    resolution: {integrity: sha512-U1suiZ2oDVWv4zPO56S0NcR5QriEahGtdN2OR6FiOG4WJvcjBVFB0qI4+eKoWFH483PKGuLuu6V8Z4T5g63UVA==}
+    engines: {node: '>=6'}
+
   espree@10.4.0:
     resolution: {integrity: sha512-j6PAQ2uUr79PZhBjP5C5fhl8e39FmRnOjsD5lGnWrFU8i2G776tBK7+nP8KuQUTTyAZUwfQqXAgrVH5MbH9CYQ==}
     engines: {node: ^18.18.0 || ^20.9.0 || >=21.1.0}
@@ -3901,6 +3965,12 @@ packages:
   html-void-elements@3.0.0:
     resolution: {integrity: sha512-bEqo66MRXsUGxWHV5IP0PUiAWwoEjba4VCzg0LjFJBpchPaTfyfCKTG6bc5F8ucKec3q5y6qOdGyYTSBEvhCrg==}
 
+  htmlparser2@5.0.1:
+    resolution: {integrity: sha512-vKZZra6CSe9qsJzh0BjBGXo8dvzNsq/oGvsjfRdOrrryfeD9UOBEEQdeoqCRmKZchF5h2zOBMQ6YuQ0uRUmdbQ==}
+
+  htmlparser2@6.1.0:
+    resolution: {integrity: sha512-gyyPk6rgonLFEDGoeRgQNaEUvdJ4ktTmmUh/h2t7s+M8oPpIPxgNACWa+6ESR57kXstwqPiCut0V8NRpcwgU7A==}
+
   http-proxy-agent@7.0.2:
     resolution: {integrity: sha512-T1gkAiYYDWYx3V5Bmyu7HcfcvL7mUrTWiM6yOfa3PIphViJ/gFPbvidQ+veqSOHci/PxBcDabeUNCzpOODJZig==}
     engines: {node: '>= 14'}
@@ -4013,6 +4083,11 @@ packages:
   json-stable-stringify-without-jsonify@1.0.1:
     resolution: {integrity: sha512-Bdboy+l7tA3OGW6FjyFHWkP5LuByj1Tk33Ljyq0axyzdk9//JSi2u3fP1QSmd1KNwq6VOKYGlAu87CisVir6Pw==}
 
+  juice@8.1.0:
+    resolution: {integrity: sha512-FLzurJrx5Iv1e7CfBSZH68dC04EEvXvvVvPYB7Vx1WAuhCp1ZPIMtqxc+WTWxVkpTIC2Ach/GAv0rQbtGf6YMA==}
+    engines: {node: '>=10.0.0'}
+    hasBin: true
+
   jwa@2.0.1:
     resolution: {integrity: sha512-hRF04fqJIP8Abbkq5NKGN0Bbr3JxlQ+qhZufXVr0DvujKy93ZCbXZMHDL4EOtodSbCWxOqR8MS1tXA5hwqCXDg==}
 
@@ -4202,6 +4277,9 @@ packages:
   mark.js@8.11.1:
     resolution: {integrity: sha512-1I+1qpDt4idfgLQG+BNWmrqku+7/2bi5nLf4YwF8y8zXvmfiTBY3PV3ZibfrjBueCByROpuBjLLFCajqkgYoLQ==}
 
+  markdown-it-mathjax3@4.3.2:
+    resolution: {integrity: sha512-TX3GW5NjmupgFtMJGRauioMbbkGsOXAAt1DZ/rzzYmTHqzkO1rNAdiMD4NiruurToPApn2kYy76x02QN26qr2w==}
+
   markdown-table@3.0.4:
     resolution: {integrity: sha512-wiYz4+JrLyb/DqW2hkFJxP7Vd7JuTDm77fvbM8VfEQdmSMqcImWeeRbHwZjBjIFki/VaMK2BhFi7oUUZeM5bqw==}
 
@@ -4210,6 +4288,10 @@ packages:
     engines: {node: '>= 20'}
     hasBin: true
 
+  mathjax-full@3.2.2:
+    resolution: {integrity: sha512-+LfG9Fik+OuI8SLwsiR02IVdjcnRCy5MufYLi0C3TdMT56L/pjB0alMVGgoWJF8pN9Rc7FESycZB9BMNWIid5w==}
+    deprecated: Version 4 replaces this package with the scoped package @mathjax/src
+
   mdast-util-find-and-replace@3.0.2:
     resolution: {integrity: sha512-Tmd1Vg/m3Xz43afeNxDIhWRtFZgM2VLyaf4vSTYwudTyeuTneoL3qtWMA5jeLyz/O1vDJmmV4QuScFCA2tBPwg==}
 
@@ -4249,9 +4331,15 @@ packages:
   mdn-data@2.27.1:
     resolution: {integrity: sha512-9Yubnt3e8A0OKwxYSXyhLymGW4sCufcLG6VdiDdUGVkPhpqLxlvP5vl1983gQjJl3tqbrM731mjaZaP68AgosQ==}
 
+  mensch@0.3.4:
+    resolution: {integrity: sha512-IAeFvcOnV9V0Yk+bFhYR07O3yNina9ANIN5MoXBKYJ/RLYPurd2d0yw14MDhpr9/momp0WofT1bPUh3hkzdi/g==}
+
   mermaid@11.16.0:
     resolution: {integrity: sha512-Zvm3kbstgdpvIJPPItlL7fppIZ3kibvc1oZIGxdvk9t6UFz6flv+Jw7FtRGKwfcI8OckmH04LqG6LlS6X4B1pA==}
 
+  mhchemparser@4.2.1:
+    resolution: {integrity: sha512-kYmyrCirqJf3zZ9t/0wGgRZ4/ZJw//VwaRVGA75C4nhE60vtnIzhl9J9ndkX/h6hxSN7pjg/cE0VxbnNM+bnDQ==}
+
   micromark-core-commonmark@2.0.3:
     resolution: {integrity: sha512-RDBrHEMSxVFLg6xvnXmb1Ayr2WzLAWjeSATAoxwKYJV94TeNavgoIdA0a9ytzDSVzBy2YKFK+emCPOEibLeCrg==}
 
@@ -4336,6 +4424,11 @@ packages:
   micromark@4.0.2:
     resolution: {integrity: sha512-zpe98Q6kvavpCr1NPVSCMebCKfD7CA2NqZ+rykeNhONIJBpc1tFKt9hucLGwha3jNTNI8lHpctWJWoimVF4PfA==}
 
+  mime@2.6.0:
+    resolution: {integrity: sha512-USPkMeET31rOMiarsBNIHZKLGgvKc/LrjofAnBlOttf5ajRvqiRA8QsenbcooctK6d6Ts6aqZXBA+XbkKthiQg==}
+    engines: {node: '>=4.0.0'}
+    hasBin: true
+
   minimatch@10.2.5:
     resolution: {integrity: sha512-MULkVLfKGYDFYejP07QOurDLLQpcjk7Fw+7jXS2R2czRQzR56yHRveU5NDJEOviH+hETZKSkIk5c+T23GjFUMg==}
     engines: {node: 18 || 20 || >=22}
@@ -4346,6 +4439,9 @@ packages:
   mitt@3.0.1:
     resolution: {integrity: sha512-vKivATfr97l2/QBCYAkXYDbrIWPM2IIKEl7YPhjCvKlG3kE2gm+uBo6nEXK3M5/Ffh/FLpKExzOQ3JJoJGFKBw==}
 
+  mj-context-menu@0.6.1:
+    resolution: {integrity: sha512-7NO5s6n10TIV96d4g2uDpG7ZDpIhMh0QNfGdJw/W47JswFcosz457wqz/b5sAKvl12sxINGFCn80NZHKwxQEXA==}
+
   mri@1.2.0:
     resolution: {integrity: sha512-tzzskb3bG8LvYGFF/mDTpq3jpI6Q9wc3LEmBaghu+DdCssd1FakN7Bc0hVNmEyGq1bq3RgfkCb3cmQLpNPOroA==}
     engines: {node: '>=4'}
@@ -4366,10 +4462,22 @@ packages:
     engines: {node: '>=10.5.0'}
     deprecated: Use your platform's native DOMException instead
 
+  node-fetch@2.7.0:
+    resolution: {integrity: sha512-c4FRfUm/dbcWZ7U+1Wq0AwCyFL+3nt2bEw05wfxSz+DWpWsitgmSgYmy2dQdWyKC1694ELPqMs/YzUSNozLt8A==}
+    engines: {node: 4.x || >=6.0.0}
+    peerDependencies:
+      encoding: ^0.1.0
+    peerDependenciesMeta:
+      encoding:
+        optional: true
+
   node-fetch@3.3.2:
     resolution: {integrity: sha512-dRB78srN/l6gqWulah9SrxeYnxeddIG30+GOqK/9OlLVyLg3HPnr6SqOWTWOXKRwC2eGYCkZ59NNuSgvSrpgOA==}
     engines: {node: ^12.20.0 || ^14.13.1 || >=16.0.0}
 
+  nth-check@2.1.1:
+    resolution: {integrity: sha512-lqjrjmaOoAnWfMmBPL+XNnynZh2+swxiX3WUE0s4yEHI6m+AwrK2UZOimIRl3X/4QctVqS8AiZjFqyOGrMXb/w==}
+
   obug@2.1.3:
     resolution: {integrity: sha512-9miFgM2OFba7hB+pRgvtV84pYTBaoTHohvmIgiRt6dRIzbwEOIaNaP+dIlGs2fNFoB0SeISs0Jz5WFVRid6Xyg==}
     engines: {node: '>=12.20.0'}
@@ -4415,6 +4523,12 @@ packages:
   package-manager-detector@1.6.0:
     resolution: {integrity: sha512-61A5ThoTiDG/C8s8UMZwSorAGwMJ0ERVGj2OjoW5pAalsNOg15+iQiPzrLJ4jhZ1HJzmC2PIHT2oEiH3R5fzNA==}
 
+  parse5-htmlparser2-tree-adapter@6.0.1:
+    resolution: {integrity: sha512-qPuWvbLgvDGilKc5BoicRovlT4MtYT6JfJyBOMDsKoiT+GiuP5qyrPCnR9HcPECIJJmZh5jRndyNThnhhb/vlA==}
+
+  parse5@6.0.1:
+    resolution: {integrity: sha512-Ofn/CTFzRGTTxwpNEs9PP93gXShHcTq255nzRYSKe8AkVpZY7e1fpmTfOyoIvjP5HG7Z2ZM7VS9PPhQGW2pOpw==}
+
   parse5@8.0.1:
     resolution: {integrity: sha512-z1e/HMG90obSGeidlli3hj7cbocou0/wa5HacvI3ASx34PecNjNQeaHNo5WIZpWofN9kgkqV1q5YvXe3F0FoPw==}
 
@@ -4602,6 +4716,9 @@ packages:
   siginfo@2.0.0:
     resolution: {integrity: sha512-ybx0WO1/8bSBLEWXZvEd7gMW3Sn3JFlW3TvX1nREbDLRNQNaeNN8WK0meBwPdAaOI7TtRRRJn/Es1zhrrCHu7g==}
 
+  slick@1.12.2:
+    resolution: {integrity: sha512-4qdtOGcBjral6YIBCWJ0ljFSKNLz9KkhbWtuGvUyRowl1kxfuE1x/Z/aJcaiilpb3do9bl5K7/1h9XC5wWpY/A==}
+
   smol-toml@1.6.1:
     resolution: {integrity: sha512-dWUG8F5sIIARXih1DTaQAX4SsiTXhInKf1buxdY9DIg4ZYPZK5nGM1VRIYmEbDbsHt7USo99xSLFu5Q1IqTmsg==}
     engines: {node: '>= 18'}
@@ -4617,6 +4734,10 @@ packages:
     resolution: {integrity: sha512-1POYv7uv2gXoyGFpBCmpDVSNV74IfsWlDW216UPjbWufNf+bSU6GdbDsxdcxtfwb4xlI3yxzOTKClUosxARYrQ==}
     engines: {node: '>=0.10.0'}
 
+  speech-rule-engine@4.1.4:
+    resolution: {integrity: sha512-i/VCLG1fvRc95pMHRqG4aQNscv+9aIsqA2oI7ZQS51sTdUcDHYX6cpT8/tqZ+enjs1tKVwbRBWgxut9SWn+f9g==}
+    hasBin: true
+
   stackback@0.0.2:
     resolution: {integrity: sha512-1XMJE5fQo1jGH6Y/7ebnwPOBEkIEnT4QF32d5R1+VXdXveM0IBMJt8zfaxX1P3QhVwrYe+576+jkANtSS2mBbw==}
 
@@ -4680,6 +4801,9 @@ packages:
     resolution: {integrity: sha512-LktZQb3IeoUWB9lqR5EWTHgW/VTITCXg4D21M+lvybRVdylLrRMnqaIONLVb5mav8vM19m44HIcGq4qASeu2Qw==}
     engines: {node: '>=16'}
 
+  tr46@0.0.3:
+    resolution: {integrity: sha512-N3WMsuqV66lT30CrXNbEjx4GEwlow3v6rr4mCcv6prnfwhS01rkgyFdjPNBYd9br7LpXV1+Emh01fHnq2Gdgrw==}
+
   tr46@6.0.0:
     resolution: {integrity: sha512-bLVMLPtstlZ4iMQHpFHTR7GAGj2jxi8Dg0s2h2MafAE4uSWF98FC/3MomU51iQAMf8/qDUbKWf5GxuvvVcXEhw==}
     engines: {node: '>=20'}
@@ -4815,6 +4939,10 @@ packages:
     resolution: {integrity: sha512-6ZxzVpzDXDa3bJWaHilVayA+BH/1zmxCJoVgvmqJnid/gPoKHxUrS/aC/T6LGQtNHT+XHG9fXPJB4d+IrU30Ew==}
     hasBin: true
 
+  valid-data-url@3.0.1:
+    resolution: {integrity: sha512-jOWVmzVceKlVVdwjNSenT4PbGghU0SBIizAev8ofZVgivk/TVHXSbNL8LP6M3spZvkR9/QolkyJavGSX5Cs0UA==}
+    engines: {node: '>=10'}
+
   vfile-message@4.0.3:
     resolution: {integrity: sha512-QTHzsGd1EhbZs4AsQ20JX1rC3cOlt/IWJruk893DfLRr57lcnOeMaWG4K0JrRta4mIJZKth2Au3mM3u03/JWKw==}
 
@@ -4969,10 +5097,17 @@ packages:
     resolution: {integrity: sha512-3hu+tD8YzSLGuFYtPRb48vdhKMi0KQV5sn+uWr8+7dMEq/2G/dtLrdDinkLjqq5TIbIBjYJ4Ax/n3YiaW7QM8A==}
     engines: {node: 20 || >=22}
 
+  web-resource-inliner@6.0.1:
+    resolution: {integrity: sha512-kfqDxt5dTB1JhqsCUQVFDj0rmY+4HLwGQIsLPbyrsN9y9WV/1oFDSx3BQ4GfCv9X+jVeQ7rouTqwK53rA/7t8A==}
+    engines: {node: '>=10.0.0'}
+
   web-streams-polyfill@3.3.3:
     resolution: {integrity: sha512-d2JWLCivmZYTSIoge9MsgFCZrt571BikcWGYkjC1khllbTeDlGqZ2D8vD8E/lJa8WGWbb7Plm8/XJYV7IJHZZw==}
     engines: {node: '>= 8'}
 
+  webidl-conversions@3.0.1:
+    resolution: {integrity: sha512-2JAn3z8AR6rjK8Sm8orRC0h/bcl/DqL7tRPdGZ4I1CjdF+EaMLmYxBHyXuKL849eucPFhvBoxMsflfOb8kxaeQ==}
+
   webidl-conversions@8.0.1:
     resolution: {integrity: sha512-BMhLD/Sw+GbJC21C/UgyaZX41nPt8bUTg+jWyDeg7e7YN4xOM05YPSIXceACnXVtqyEw/LMClUQMtMZ+PGGpqQ==}
     engines: {node: '>=20'}
@@ -4985,6 +5120,9 @@ packages:
     resolution: {integrity: sha512-1to4zXBxmXHV3IiSSEInrreIlu02vUOvrhxJJH5vcxYTBDAx51cqZiKdyTxlecdKNSjj8EcxGBxNf6Vg+945gw==}
     engines: {node: ^20.19.0 || ^22.12.0 || >=24.0.0}
 
+  whatwg-url@5.0.0:
+    resolution: {integrity: sha512-saE57nupxk6v3HY35+jzBwYa0rKSy0XR8JSxZPwgLr7ys0IBzhGviA1/TUGJLmSVqs8pb9AnvICXEuOHLprYTw==}
+
   which@2.0.2:
     resolution: {integrity: sha512-BLI3Tl1TW3Pvl70l3yq3Y64i+awpwXqsGBYWkkqMtnbXgrMD+yj7rhW0kuEDxzJaYXGjEW5ogapKNMEKNMjibA==}
     engines: {node: '>= 8'}
@@ -4995,6 +5133,9 @@ packages:
     engines: {node: '>=8'}
     hasBin: true
 
+  wicked-good-xpath@1.3.0:
+    resolution: {integrity: sha512-Gd9+TUn5nXdwj/hFsPVx5cuHHiF5Bwuc30jZ4+ronF1qHK5O7HD0sgmXWSEgwKquT3ClLoKPVbO6qGwVwLzvAw==}
+
   word-wrap@1.2.5:
     resolution: {integrity: sha512-BN22B5eaMMI9UMtjrGd5g5eCYPpCPDUy0FJXbYsaT5zYxjFOckS53SQDE3pWkVoWpHXVb3BrYcEN4Twa55B5cA==}
     engines: {node: '>=0.10.0'}
@@ -6741,6 +6882,8 @@ snapshots:
     transitivePeerDependencies:
       - typescript
 
+  '@xmldom/xmldom@0.9.10': {}
+
   acorn-jsx@5.3.2(acorn@8.17.0):
     dependencies:
       acorn: 8.17.0
@@ -6773,6 +6916,8 @@ snapshots:
       '@algolia/requester-fetch': 5.55.2
       '@algolia/requester-node-http': 5.55.2
 
+  ansi-colors@4.1.3: {}
+
   ansis@4.3.1: {}
 
   anynum@1.0.0: {}
@@ -6807,6 +6952,8 @@ snapshots:
 
   birpc@4.0.0: {}
 
+  boolbase@1.0.0: {}
+
   bowser@2.14.1: {}
 
   brace-expansion@5.0.6:
@@ -6827,12 +6974,34 @@ snapshots:
 
   character-entities@2.0.2: {}
 
+  cheerio-select@1.6.0:
+    dependencies:
+      css-select: 4.3.0
+      css-what: 6.2.2
+      domelementtype: 2.3.0
+      domhandler: 4.3.1
+      domutils: 2.8.0
+
+  cheerio@1.0.0-rc.10:
+    dependencies:
+      cheerio-select: 1.6.0
+      dom-serializer: 1.4.1
+      domhandler: 4.3.1
+      htmlparser2: 6.1.0
+      parse5: 6.0.1
+      parse5-htmlparser2-tree-adapter: 6.0.1
+      tslib: 2.8.1
+
   chokidar@4.0.3:
     dependencies:
       readdirp: 4.1.2
 
   comma-separated-tokens@2.0.3: {}
 
+  commander@13.1.0: {}
+
+  commander@6.2.1: {}
+
   commander@7.2.0: {}
 
   commander@8.3.0: {}
@@ -6875,11 +7044,21 @@ snapshots:
       shebang-command: 2.0.0
       which: 2.0.2
 
+  css-select@4.3.0:
+    dependencies:
+      boolbase: 1.0.0
+      css-what: 6.2.2
+      domhandler: 4.3.1
+      domutils: 2.8.0
+      nth-check: 2.1.1
+
   css-tree@3.2.1:
     dependencies:
       mdn-data: 2.27.1
       source-map-js: 1.2.1
 
+  css-what@6.2.2: {}
+
   csstype@3.2.3: {}
 
   cytoscape-cose-bilkent@4.1.0(cytoscape@3.34.0):
@@ -7105,10 +7284,32 @@ snapshots:
 
   diff@9.0.0: {}
 
+  dom-serializer@1.4.1:
+    dependencies:
+      domelementtype: 2.3.0
+      domhandler: 4.3.1
+      entities: 2.2.0
+
+  domelementtype@2.3.0: {}
+
+  domhandler@3.3.0:
+    dependencies:
+      domelementtype: 2.3.0
+
+  domhandler@4.3.1:
+    dependencies:
+      domelementtype: 2.3.0
+
   dompurify@3.4.11:
     optionalDependencies:
       '@types/trusted-types': 2.0.7
 
+  domutils@2.8.0:
+    dependencies:
+      dom-serializer: 1.4.1
+      domelementtype: 2.3.0
+      domhandler: 4.3.1
+
   dts-resolver@3.0.0(oxc-resolver@11.20.0):
     optionalDependencies:
       oxc-resolver: 11.20.0
@@ -7121,6 +7322,8 @@ snapshots:
 
   empathic@2.0.1: {}
 
+  entities@2.2.0: {}
+
   entities@7.0.1: {}
 
   entities@8.0.0: {}
@@ -7184,6 +7387,8 @@ snapshots:
       '@esbuild/win32-ia32': 0.28.1
       '@esbuild/win32-x64': 0.28.1
 
+  escape-goat@3.0.0: {}
+
   escape-string-regexp@4.0.0: {}
 
   escape-string-regexp@5.0.0: {}
@@ -7238,6 +7443,8 @@ snapshots:
     transitivePeerDependencies:
       - supports-color
 
+  esm@3.2.25: {}
+
   espree@10.4.0:
     dependencies:
       acorn: 8.17.0
@@ -7417,6 +7624,20 @@ snapshots:
 
   html-void-elements@3.0.0: {}
 
+  htmlparser2@5.0.1:
+    dependencies:
+      domelementtype: 2.3.0
+      domhandler: 3.3.0
+      domutils: 2.8.0
+      entities: 2.2.0
+
+  htmlparser2@6.1.0:
+    dependencies:
+      domelementtype: 2.3.0
+      domhandler: 4.3.1
+      domutils: 2.8.0
+      entities: 2.2.0
+
   http-proxy-agent@7.0.2:
     dependencies:
       agent-base: 7.1.4
@@ -7527,6 +7748,16 @@ snapshots:
 
   json-stable-stringify-without-jsonify@1.0.1: {}
 
+  juice@8.1.0:
+    dependencies:
+      cheerio: 1.0.0-rc.10
+      commander: 6.2.1
+      mensch: 0.3.4
+      slick: 1.12.2
+      web-resource-inliner: 6.0.1
+    transitivePeerDependencies:
+      - encoding
+
   jwa@2.0.1:
     dependencies:
       buffer-equal-constant-time: 1.0.1
@@ -7693,10 +7924,24 @@ snapshots:
 
   mark.js@8.11.1: {}
 
+  markdown-it-mathjax3@4.3.2:
+    dependencies:
+      juice: 8.1.0
+      mathjax-full: 3.2.2
+    transitivePeerDependencies:
+      - encoding
+
   markdown-table@3.0.4: {}
 
   marked@16.4.2: {}
 
+  mathjax-full@3.2.2:
+    dependencies:
+      esm: 3.2.25
+      mhchemparser: 4.2.1
+      mj-context-menu: 0.6.1
+      speech-rule-engine: 4.1.4
+
   mdast-util-find-and-replace@3.0.2:
     dependencies:
       '@types/mdast': 4.0.4
@@ -7813,6 +8058,8 @@ snapshots:
 
   mdn-data@2.27.1: {}
 
+  mensch@0.3.4: {}
+
   mermaid@11.16.0:
     dependencies:
       '@braintree/sanitize-url': 7.1.2
@@ -7837,6 +8084,8 @@ snapshots:
       ts-dedent: 2.3.0
       uuid: 14.0.1
 
+  mhchemparser@4.2.1: {}
+
   micromark-core-commonmark@2.0.3:
     dependencies:
       decode-named-character-reference: 1.3.0
@@ -8028,6 +8277,8 @@ snapshots:
     transitivePeerDependencies:
       - supports-color
 
+  mime@2.6.0: {}
+
   minimatch@10.2.5:
     dependencies:
       brace-expansion: 5.0.6
@@ -8036,6 +8287,8 @@ snapshots:
 
   mitt@3.0.1: {}
 
+  mj-context-menu@0.6.1: {}
+
   mri@1.2.0: {}
 
   ms@2.1.3: {}
@@ -8046,12 +8299,20 @@ snapshots:
 
   node-domexception@1.0.0: {}
 
+  node-fetch@2.7.0:
+    dependencies:
+      whatwg-url: 5.0.0
+
   node-fetch@3.3.2:
     dependencies:
       data-uri-to-buffer: 4.0.1
       fetch-blob: 3.2.0
       formdata-polyfill: 4.0.10
 
+  nth-check@2.1.1:
+    dependencies:
+      boolbase: 1.0.0
+
   obug@2.1.3: {}
 
   oniguruma-to-es@3.1.1:
@@ -8136,6 +8397,12 @@ snapshots:
 
   package-manager-detector@1.6.0: {}
 
+  parse5-htmlparser2-tree-adapter@6.0.1:
+    dependencies:
+      parse5: 6.0.1
+
+  parse5@6.0.1: {}
+
   parse5@8.0.1:
     dependencies:
       entities: 8.0.0
@@ -8364,6 +8631,8 @@ snapshots:
 
   siginfo@2.0.0: {}
 
+  slick@1.12.2: {}
+
   smol-toml@1.6.1: {}
 
   source-map-js@1.2.1: {}
@@ -8372,6 +8641,12 @@ snapshots:
 
   speakingurl@14.0.1: {}
 
+  speech-rule-engine@4.1.4:
+    dependencies:
+      '@xmldom/xmldom': 0.9.10
+      commander: 13.1.0
+      wicked-good-xpath: 1.3.0
+
   stackback@0.0.2: {}
 
   std-env@4.1.0: {}
@@ -8424,6 +8699,8 @@ snapshots:
     dependencies:
       tldts: 7.4.5
 
+  tr46@0.0.3: {}
+
   tr46@6.0.0:
     dependencies:
       punycode: 2.3.1
@@ -8540,6 +8817,8 @@ snapshots:
 
   uuid@14.0.1: {}
 
+  valid-data-url@3.0.1: {}
+
   vfile-message@4.0.3:
     dependencies:
       '@types/unist': 3.0.3
@@ -8600,7 +8879,7 @@ snapshots:
       tsx: 4.22.4
       yaml: 2.9.0
 
-  vitepress@1.6.4(@algolia/client-search@5.55.2)(@types/node@25.9.3)(lightningcss@1.32.0)(postcss@8.5.15)(search-insights@2.17.3)(typescript@6.0.3):
+  vitepress@1.6.4(@algolia/client-search@5.55.2)(@types/node@25.9.3)(lightningcss@1.32.0)(markdown-it-mathjax3@4.3.2)(postcss@8.5.15)(search-insights@2.17.3)(typescript@6.0.3):
     dependencies:
       '@docsearch/css': 3.8.2
       '@docsearch/js': 3.8.2(@algolia/client-search@5.55.2)(search-insights@2.17.3)
@@ -8621,6 +8900,7 @@ snapshots:
       vite: 5.4.21(@types/node@25.9.3)(lightningcss@1.32.0)
       vue: 3.5.39(typescript@6.0.3)
     optionalDependencies:
+      markdown-it-mathjax3: 4.3.2
       postcss: 8.5.15
     transitivePeerDependencies:
       - '@algolia/client-search'
@@ -8724,8 +9004,21 @@ snapshots:
 
   walk-up-path@4.0.0: {}
 
+  web-resource-inliner@6.0.1:
+    dependencies:
+      ansi-colors: 4.1.3
+      escape-goat: 3.0.0
+      htmlparser2: 5.0.1
+      mime: 2.6.0
+      node-fetch: 2.7.0
+      valid-data-url: 3.0.1
+    transitivePeerDependencies:
+      - encoding
+
   web-streams-polyfill@3.3.3: {}
 
+  webidl-conversions@3.0.1: {}
+
   webidl-conversions@8.0.1: {}
 
   whatwg-mimetype@5.0.0: {}
@@ -8738,6 +9031,11 @@ snapshots:
     transitivePeerDependencies:
       - '@noble/hashes'
 
+  whatwg-url@5.0.0:
+    dependencies:
+      tr46: 0.0.3
+      webidl-conversions: 3.0.1
+
   which@2.0.2:
     dependencies:
       isexe: 2.0.0
@@ -8747,6 +9045,8 @@ snapshots:
       siginfo: 2.0.0
       stackback: 0.0.2
 
+  wicked-good-xpath@1.3.0: {}
+
   word-wrap@1.2.5: {}
 
   ws@8.21.0: {}
diff --git a/website/.vitepress/config/index.ts b/website/.vitepress/config/index.ts
index b4978ca4aa..764d8619a9 100644
--- a/website/.vitepress/config/index.ts
+++ b/website/.vitepress/config/index.ts
@@ -5,6 +5,13 @@ export default defineConfig({
   title: 'DeepSeek Harness',
   description: '插件化 Agent 开发框架',
 
+  // The design essays (design/revertible-effects, design/context-model) carry
+  // real TeX; math: true wires markdown-it-mathjax3 into the pipeline.
+  // markdown-it-mathjax3 is pinned to ^4 (NOT 5.x): v5 injects a <style> tag
+  // per formula, which Vue's template compiler rejects ("Tags with side
+  // effect … are ignored in client component templates"); v4 emits pure SVG.
+  markdown: { math: true },
+
   locales: {
     'zh-CN': zhCN,
   },
diff --git a/website/package.json b/website/package.json
index 33c32fae4c..3c582ed0a9 100644
--- a/website/package.json
+++ b/website/package.json
@@ -9,6 +9,7 @@
     "preview": "vitepress preview ."
   },
   "devDependencies": {
+    "markdown-it-mathjax3": "^4.3.2",
     "vitepress": "^1.6.3",
     "vue": "^3.5.13"
   }