feat: page interactive, démos Play/Step et simulateur Carnot

Ajoute le pipeline PageSpec (validation, rendu, publication /p/{slug}),
les démos TipTap /demo, et le simulateur Carnot (modes frigo/PAC/moteur,
énergie kJ vs puissance W, unités K/°C/°F) avec correctifs d’équations KaTeX.

Co-authored-by: Cursor <cursoragent@cursor.com>

memento-note/components/interactive-demo/demo-speak.tsx

@@ -0,0 +1,62 @@
+'use client'
+
+import { useEffect, useMemo, useState } from 'react'
+import katex from 'katex'
+import { marked } from 'marked'
+import { sanitizeRichHtml } from '@/lib/sanitize-content'
+import 'katex/dist/katex.min.css'
+
+/**
+ * Render demo `speak`: light markdown + inline $KaTeX$ via the note pipeline pieces.
+ */
+export function DemoSpeak({ speak, className }: { speak: string; className?: string }) {
+  const html = useMemo(() => {
+    const placeholders: string[] = []
+    const withSlots = speak.replace(/\$([^$]+)\$/g, (_, tex: string) => {
+      const i = placeholders.length
+      try {
+        placeholders.push(
+          katex.renderToString(tex, { displayMode: false, throwOnError: false })
+        )
+      } catch {
+        placeholders.push(tex)
+      }
+      return `%%KATEX${i}%%`
+    })
+
+    let md = marked.parse(withSlots, { gfm: true, breaks: true }) as string
+    placeholders.forEach((frag, i) => {
+      md = md.replace(`%%KATEX${i}%%`, frag)
+    })
+    return sanitizeRichHtml(md)
+  }, [speak])
+
+  return (
+    <div
+      className={className}
+      dangerouslySetInnerHTML={{ __html: html }}
+    />
+  )
+}
+
+export function useDarkMode(): boolean {
+  const [isDark, setIsDark] = useState(() =>
+    typeof document !== 'undefined'
+      ? document.documentElement.classList.contains('dark')
+      : false
+  )
+
+  useEffect(() => {
+    const check = () =>
+      setIsDark(document.documentElement.classList.contains('dark'))
+    check()
+    const obs = new MutationObserver(check)
+    obs.observe(document.documentElement, {
+      attributes: true,
+      attributeFilter: ['class'],
+    })
+    return () => obs.disconnect()
+  }, [])
+
+  return isDark
+}