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/lib/simulators/index.ts

@@ -0,0 +1,65 @@
+import type { IntentId } from '@/lib/interactive-demo/types'
+import { carnotCycleSimulator } from './carnot-cycle'
+import { carnotCycleAnim } from './carnot-cycle-anim'
+import { tsDiagramAnim } from './ts-diagram'
+import type { AnimPlugin, AnyPlugin, SimulatorPlugin } from './types'
+
+export const GENERIC_SIM_ID = 'generic-formula' as const
+
+const REGISTRY: Record<string, AnyPlugin> = {
+  [carnotCycleSimulator.id]: carnotCycleSimulator,
+  [carnotCycleAnim.id]: carnotCycleAnim,
+  [tsDiagramAnim.id]: tsDiagramAnim,
+}
+
+export function getPlugin(id: string): AnyPlugin | null {
+  return REGISTRY[id] ?? null
+}
+
+export function getSimulator(id: string): SimulatorPlugin | null {
+  const p = REGISTRY[id]
+  return p?.family === 'sim' ? p : null
+}
+
+export function getAnimPlugin(id: string): AnimPlugin | null {
+  const p = REGISTRY[id]
+  return p?.family === 'anim' ? p : null
+}
+
+export function isCatalogSimId(id: string): boolean {
+  return id !== GENERIC_SIM_ID && id in REGISTRY
+}
+
+export function listSimulators(): AnyPlugin[] {
+  return Object.values(REGISTRY)
+}
+
+/**
+ * Compact catalog injected into the section-generation prompt so the LLM
+ * can pick a curated plugin (sim or anim) and bind note values into a preset.
+ */
+export function catalogForPrompt(lang: string): string {
+  const fr = lang.startsWith('fr')
+  const catalog = listSimulators().map((plugin) => ({
+    simId: plugin.id,
+    family: plugin.family,
+    summary: fr ? plugin.summary.fr : plugin.summary.en,
+    keywords: plugin.keywords.slice(0, 10),
+    ...(plugin.family === 'sim'
+      ? {
+          params: plugin.params.map((p) => ({
+            id: p.id,
+            symbol: p.symbol,
+            range: [p.min, p.max],
+            default: p.defaultValue,
+            unit: p.unit,
+          })),
+          outputs: plugin.outputs.map((o) => o.symbol),
+        }
+      : {}),
+  }))
+  return JSON.stringify(catalog, null, 1)
+}
+
+export type { SimulatorPlugin, AnimPlugin, AnyPlugin, AnimBeat, SimI18n, SimParamDef, SimOutputDef } from './types'
+export type { IntentId }