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/schema.ts

@@ -0,0 +1,136 @@
+import { z } from 'zod'
+import {
+  ANNOTATION_KINDS,
+  CHART_TYPES,
+  INTENT_IDS,
+  INTERACTIVE_DEMO_CAPS,
+  INTERACTIVE_DEMO_SCHEMA_VERSION,
+  PANEL_TYPES,
+  PATTERN_IDS,
+  SCOPE_IDS,
+  TRANSITIONS,
+} from './constants'
+
+const intentSchema = z.enum(INTENT_IDS).optional()
+const patternSchema = z.enum(PATTERN_IDS)
+const scopeSchema = z.enum(SCOPE_IDS)
+
+const revealSchema = z.object({
+  ids: z.array(z.string().min(1)).min(1),
+  scope: scopeSchema,
+})
+
+const annotationSchema = z.object({
+  kind: z.enum(ANNOTATION_KINDS),
+  targetIds: z.array(z.string().min(1)).min(1),
+  scope: scopeSchema,
+  text: z.string().optional(),
+  intent: intentSchema,
+})
+
+const stepSchema = z.object({
+  id: z.string().min(1),
+  speak: z.string().min(1),
+  pattern: patternSchema.optional(),
+  pointTo: z.array(z.string().min(1)).optional(),
+  reveal: z.array(revealSchema).optional(),
+  annotate: z
+    .array(annotationSchema)
+    .max(INTERACTIVE_DEMO_CAPS.maxAnnotationsPerStep)
+    .optional(),
+})
+
+const svgNodeSchema = z.object({
+  id: z.string().min(1),
+  label: z.string().optional(),
+  intent: intentSchema,
+})
+
+const svgEdgeSchema = z.object({
+  id: z.string().min(1),
+  from: z.string().min(1),
+  to: z.string().min(1),
+  style: z.enum(['solid', 'dashed']).optional(),
+  weight: z.number().optional(),
+  intent: intentSchema,
+})
+
+const svgScenePayloadSchema = z.object({
+  nodes: z.array(svgNodeSchema).min(1),
+  edges: z.array(svgEdgeSchema).optional(),
+})
+
+const chartSeriesSchema = z.object({
+  id: z.string().min(1),
+  label: z.string().optional(),
+  values: z.array(z.number()),
+  intent: intentSchema,
+})
+
+const chartPayloadSchema = z.object({
+  chartType: z.enum(CHART_TYPES),
+  series: z.array(chartSeriesSchema).min(1),
+})
+
+const heatmapPayloadSchema = z.object({
+  rows: z.number().int().positive(),
+  cols: z.number().int().positive(),
+  values: z.array(z.array(z.number())),
+  triangular: z.enum(['lower', 'upper', 'none']).optional(),
+  rowLabels: z.array(z.string()).optional(),
+  colLabels: z.array(z.string()).optional(),
+})
+
+const panelSchema = z.discriminatedUnion('type', [
+  z.object({
+    id: z.string().min(1),
+    type: z.literal('svg-scene'),
+    payload: svgScenePayloadSchema,
+  }),
+  z.object({
+    id: z.string().min(1),
+    type: z.literal('chart'),
+    payload: chartPayloadSchema,
+  }),
+  z.object({
+    id: z.string().min(1),
+    type: z.literal('heatmap-matrix'),
+    payload: heatmapPayloadSchema,
+  }),
+])
+
+const sceneSchema = z.object({
+  id: z.string().min(1).optional(),
+  panels: z
+    .array(panelSchema)
+    .min(1)
+    .max(INTERACTIVE_DEMO_CAPS.maxPanelsPerScene),
+})
+
+const actSchema = z.object({
+  id: z.string().min(1),
+  title: z.string().min(1),
+  scene: sceneSchema.optional(),
+  transition: z.enum(TRANSITIONS).optional(),
+  pattern: patternSchema.optional(),
+  steps: z.array(stepSchema).min(1).max(INTERACTIVE_DEMO_CAPS.maxStepsPerAct),
+})
+
+/** Loose BCP-47: primary tag + optional subtags (fr, en, zh-Hans, pt-BR). */
+const langSchema = z
+  .string()
+  .regex(/^[a-zA-Z]{2,3}(-[a-zA-Z0-9]{2,8})*$/, 'Invalid BCP-47 language tag')
+
+export const interactiveDemoV1Schema = z.object({
+  schemaVersion: z.literal(INTERACTIVE_DEMO_SCHEMA_VERSION),
+  id: z.string().min(1),
+  lang: langSchema,
+  disclaimer: z.string().optional(),
+  scene: sceneSchema,
+  acts: z.array(actSchema).min(1).max(INTERACTIVE_DEMO_CAPS.maxActs),
+})
+
+export type InteractiveDemoV1Parsed = z.infer<typeof interactiveDemoV1Schema>
+
+/** Re-export allowlists for callers that need them at runtime. */
+export { PANEL_TYPES, PATTERN_IDS }