feat: dashboard Second Brain, essai 7 jours et vérification e-mail

Rendre le dashboard actionnable (inbox, peek, carte mentale), aligner la facturation sur l’essai 7 jours, et bloquer le login e-mail tant que l’adresse n’est pas confirmée.

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

memento-note/lib/ai/services/slide-source-assets.ts

@@ -4,24 +4,55 @@
  * Critical for STEM notes: formulas must be harvested, not hoped for from the model.
  */
 
+import { extractPublishImageUrls } from '@/lib/publish/process-note-html'
+
 export interface SourceAssets {
   formulas: string[]
   numbers: Array<{ label: string; value: number; raw: string }>
   keySentences: string[]
   hasMath: boolean
   hasNumbers: boolean
+  hasImages: boolean
   wordCount: number
+  images: string[]
 }
 
 /** Extract LaTeX / equation-like fragments from note plain text or HTML. */
 export function extractFormulas(raw: string): string[] {
   if (!raw) return []
   const found: string[] = []
+  // 3+ consecutive plain words at brace depth 0 = prose tail captured after a
+  // formula (KaTeX eats spaces in math mode → must never reach $…$).
+  const PROSE_TAIL_RE =
+    /(?:[.!?]?\s+)[A-ZÀ-ÖØ-Þ]?[a-zA-ZÀ-ÿ'’]{2,}\s+[a-zA-ZÀ-ÿ'’]{2,}\s+[a-zA-ZÀ-ÿ'’]{2,}[\s\S]*$/g
+  const braceDepth = (s: string): number => {
+    let d = 0
+    for (const ch of s) {
+      if (ch === '{') d++
+      else if (ch === '}') d = Math.max(0, d - 1)
+    }
+    return d
+  }
   const push = (s: string) => {
-    const t = s.replace(/\s+/g, ' ').trim()
+    let t = s.replace(/\s+/g, ' ').trim()
+    t = t.replace(/^\$+|\$+$/g, '').trim()
+    PROSE_TAIL_RE.lastIndex = 0
+    let m: RegExpExecArray | null
+    while ((m = PROSE_TAIL_RE.exec(t)) !== null) {
+      if (braceDepth(t.slice(0, m.index)) === 0) {
+        t = t.slice(0, m.index).trim()
+        break
+      }
+    }
+    t = t.replace(/^\$+|\$+$/g, '').trim()
     if (t.length >= 2 && t.length <= 280 && !found.includes(t)) found.push(t)
   }
 
+  // TipTap / published HTML: data-latex="..."
+  for (const m of raw.matchAll(/data-latex=["']([^"']+)["']/gi)) {
+    push(decodeHtmlEntities(m[1] || ''))
+  }
+
   // $$ ... $$
   for (const m of raw.matchAll(/\$\$([\s\S]+?)\$\$/g)) push(m[1] || '')
   // \[ ... \]
@@ -47,20 +78,34 @@ export function extractFormulas(raw: string): string[] {
   return found.slice(0, 24)
 }
 
+function decodeHtmlEntities(s: string): string {
+  return s
+    .replace(/&quot;/g, '"')
+    .replace(/&#39;/g, "'")
+    .replace(/&lt;/g, '<')
+    .replace(/&gt;/g, '>')
+    .replace(/&amp;/g, '&')
+}
+
 export function extractNumbers(raw: string): Array<{ label: string; value: number; raw: string }> {
   if (!raw) return []
+  // Normalize Persian (۰-۹) and Arabic (٠-٩) numerals to Western (0-9)
+  const text = raw
+    .replace(/[\u06F0-\u06F9]/g, (c) => String.fromCharCode(c.charCodeAt(0) - 0x06f0 + 0x30))
+    .replace(/[\u0660-\u0669]/g, (c) => String.fromCharCode(c.charCodeAt(0) - 0x0660 + 0x30))
+
   const out: Array<{ label: string; value: number; raw: string }> = []
   const re =
     /(?:^|[^\d])((?:≈|~)?\s*-?\d+(?:[.,]\d+)?)\s*(%|€|\$|k|m|bn|ms|s|°C)?\b/gi
   let m: RegExpExecArray | null
-  while ((m = re.exec(raw)) !== null && out.length < 20) {
+  while ((m = re.exec(text)) !== null && out.length < 20) {
     const numStr = (m[1] || '').replace(/[≈~\s]/g, '').replace(',', '.')
     const value = parseFloat(numStr)
     if (!Number.isFinite(value)) continue
     const unit = m[2] || ''
     // crude label: 40 chars before
     const start = Math.max(0, m.index - 40)
-    const ctx = raw.slice(start, m.index).replace(/\s+/g, ' ').trim()
+    const ctx = text.slice(start, m.index).replace(/\s+/g, ' ').trim()
     const label = ctx.split(/[.;:!?\n]/).pop()?.trim().slice(-32) || `n${out.length + 1}`
     out.push({ label, value: unit === '%' ? value : value, raw: `${numStr}${unit}` })
   }
@@ -88,16 +133,20 @@ export function extractKeySentences(raw: string, max = 16): string[] {
 }
 
 export function extractSourceAssets(raw: string): SourceAssets {
-  const formulas = extractFormulas(raw)
-  const numbers = extractNumbers(raw)
+  const plain = raw.replace(/<[^>]+>/g, ' ')
+  const formulas = extractFormulas(plain)
+  const numbers = extractNumbers(plain)
   const keySentences = extractKeySentences(raw)
-  const wordCount = raw.replace(/<[^>]+>/g, ' ').split(/\s+/).filter(Boolean).length
+  const images = extractPublishImageUrls(raw).slice(0, 8)
+  const wordCount = plain.split(/\s+/).filter(Boolean).length
   return {
     formulas,
     numbers,
     keySentences,
-    hasMath: formulas.length > 0 || /équat|equat|différen|differen|dériv|deriv|intégr|integr|EDO|ODE|PDE|latex/i.test(raw),
+    hasMath: formulas.length > 0 || /équat|equat|différen|differen|dériv|deriv|intégr|integr|EDO|ODE|PDE|latex/i.test(plain),
     hasNumbers: numbers.length >= 2,
+    hasImages: images.length > 0,
     wordCount,
+    images,
   }
 }