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/interactive-demo/intent-colors.ts

@@ -0,0 +1,62 @@
+import type { IntentId } from '@/lib/interactive-demo/types'
+
+/**
+ * Desaturated palette — one set for light, one for dark (P11).
+ * No free hex in demo JSON; app maps intents here.
+ */
+export const INTENT_PALETTE_LIGHT: Record<IntentId | 'neutral', string> = {
+  neutral: '#5c5c5c',
+  highlight: '#5a7a9a', // prune / slate-blue
+  flow: '#4a7d68',
+  cache: '#7a6a8a',
+  compute: '#8a6b4a',
+  output: '#4a7a8a',
+  warning: '#9a6548',
+}
+
+export const INTENT_PALETTE_DARK: Record<IntentId | 'neutral', string> = {
+  neutral: '#a8a8a8',
+  highlight: '#8aabca',
+  flow: '#7ab89a',
+  cache: '#a898b8',
+  compute: '#c0a080',
+  output: '#7ab0c0',
+  warning: '#d09070',
+}
+
+/** Light: ~35% readable on white; dark: ~20% as spec. */
+export const DIM_OPACITY_LIGHT = 0.35
+export const DIM_OPACITY_DARK = 0.2
+
+export function intentColor(
+  intent: IntentId | null | undefined,
+  dark: boolean
+): string {
+  const palette = dark ? INTENT_PALETTE_DARK : INTENT_PALETTE_LIGHT
+  if (!intent) return palette.neutral
+  return palette[intent] ?? palette.neutral
+}
+
+export function spotlightColor(dark: boolean): string {
+  return intentColor('highlight', dark)
+}
+
+export function dimOpacity(dark: boolean): number {
+  return dark ? DIM_OPACITY_DARK : DIM_OPACITY_LIGHT
+}
+
+export const CIRCLED_NUMBERS = ['①', '②', '③', '④', '⑤', '⑥', '⑦', '⑧', '⑨', '⑩'] as const
+
+export function badgeGlyph(index: number): string {
+  if (index >= 1 && index <= CIRCLED_NUMBERS.length) {
+    return CIRCLED_NUMBERS[index - 1]!
+  }
+  return String(index)
+}
+
+/** Writing rule for generation prompts (not enforced in renderer). */
+export const SPEAK_WRITING_GUIDE = {
+  maxWordsApprox: 25,
+  sentences: '1–2',
+  note: 'Demo tempo is decided at writing time, not at render.',
+} as const