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/app/(public)/p/[slug]/page.tsx

@@ -8,6 +8,8 @@ import { processNoteHtmlForPublish } from '@/lib/publish/process-note-html'
 import { REWRITE_SHARED_CSS, KATEX_PUBLISH_CSS } from '@/lib/publish/shared-css'
 import { ReadingProgress } from '@/components/publish/reading-progress'
 import { CopyLinkButton } from '@/components/publish/copy-link-button'
+import { InteractivePublishedPage } from '@/components/interactive-page/interactive-published-page'
+import { isInteractivePageTemplate } from '@/lib/publish/types'
 
 export async function generateMetadata({ params }: { params: Promise<{ slug: string }> }) {
   const { slug } = await params
@@ -1075,16 +1077,29 @@ export default async function PublishedNotePage({ params }: { params: Promise<{
   const note = await getPublishedNote(slug)
   if (!note) notFound()
 
+  const isStale = Boolean(
+    note.publishedSourceHash
+    && computePublishedSourceHash(note.content || '') !== note.publishedSourceHash
+  )
+
+  if (
+    isInteractivePageTemplate(note.publishedTemplate) &&
+    note.publishedContent
+  ) {
+    return (
+      <InteractivePublishedPage
+        publishedContent={note.publishedContent}
+        isStale={isStale}
+      />
+    )
+  }
+
   const usesAiLayout = Boolean(note.publishedContent)
   const rawHtml = usesAiLayout ? note.publishedContent! : (note.content || '')
   const bodyHtml = processNoteHtmlForPublish(rawHtml)
 
   const readingSource = usesAiLayout ? note.publishedContent! : (note.content || '')
   const readingTime = estimateReadingTime(readingSource)
-  const isStale = Boolean(
-    note.publishedSourceHash
-    && computePublishedSourceHash(note.content || '') !== note.publishedSourceHash
-  )
 
   const props: PageProps = { note, bodyHtml, readingTime, slug, isStale }