feat(credits): solde IA unique (option M), packs Stripe et polish billing

Un pot de crédits global (BASIC 100 / PRO 1 000 / BUSINESS 4 000) remplace
les seaux par fonction côté débit. Packs one-shot S/M/L, admin sans seaux
legacy, usage multi-features, hints de coût, anti-flash thème et hydratation
admin. Inclut aussi le pipeline slides renforcé et la page publique polishée.

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

@@ -0,0 +1,103 @@
+/**
+ * Server-side extraction of usable assets from a note BEFORE any slide LLM call.
+ * Inspired by PPTAgent (retrieve relevant content per slide) and DeckForge (data_needs).
+ * Critical for STEM notes: formulas must be harvested, not hoped for from the model.
+ */
+
+export interface SourceAssets {
+  formulas: string[]
+  numbers: Array<{ label: string; value: number; raw: string }>
+  keySentences: string[]
+  hasMath: boolean
+  hasNumbers: boolean
+  wordCount: number
+}
+
+/** Extract LaTeX / equation-like fragments from note plain text or HTML. */
+export function extractFormulas(raw: string): string[] {
+  if (!raw) return []
+  const found: string[] = []
+  const push = (s: string) => {
+    const t = s.replace(/\s+/g, ' ').trim()
+    if (t.length >= 2 && t.length <= 280 && !found.includes(t)) found.push(t)
+  }
+
+  // $$ ... $$
+  for (const m of raw.matchAll(/\$\$([\s\S]+?)\$\$/g)) push(m[1] || '')
+  // \[ ... \]
+  for (const m of raw.matchAll(/\\\[([\s\S]+?)\\\]/g)) push(m[1] || '')
+  // \( ... \)
+  for (const m of raw.matchAll(/\\\(([\s\S]+?)\\\)/g)) push(m[1] || '')
+  // $ ... $ (single line)
+  for (const m of raw.matchAll(/(?<![\\$])\$([^$\n]{2,120})\$(?!\$)/g)) push(m[1] || '')
+  // Common latex commands in free text
+  for (const m of raw.matchAll(
+    /(?:^|[\s(])((?:\\frac\{[^}]+\}\{[^}]+\}|\\partial|\\nabla|\\sum|\\int|\\frac|\\cdot|\\times|\\left|\\right|y'|y''|d[xy]\/d[xy]|∂)[^\n]{0,100})/g,
+  )) {
+    push(m[1] || '')
+  }
+  // Equation-like: f(x) = ..., dy/dx = ...
+  for (const m of raw.matchAll(
+    /(?:^|\n)\s*([A-Za-zΑ-ω∂∇][A-Za-z0-9_'"′]*\s*(?:\([^)]*\))?\s*[=≈≡]\s*[^\n]{3,100})/g,
+  )) {
+    const line = (m[1] || '').trim()
+    if (/[=≈]/.test(line) && /[a-zA-Z0-9]/.test(line)) push(line)
+  }
+
+  return found.slice(0, 24)
+}
+
+export function extractNumbers(raw: string): Array<{ label: string; value: number; raw: string }> {
+  if (!raw) return []
+  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) {
+    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 label = ctx.split(/[.;:!?\n]/).pop()?.trim().slice(-32) || `n${out.length + 1}`
+    out.push({ label, value: unit === '%' ? value : value, raw: `${numStr}${unit}` })
+  }
+  return out
+}
+
+export function extractKeySentences(raw: string, max = 16): string[] {
+  if (!raw) return []
+  const plain = raw
+    .replace(/<[^>]+>/g, ' ')
+    .replace(/\$\$[\s\S]+?\$\$/g, ' ')
+    .replace(/\\\[[\s\S]+?\\\]/g, ' ')
+    .replace(/\s+/g, ' ')
+    .trim()
+  const parts = plain
+    .split(/(?<=[.!?])\s+/)
+    .map((s) => s.trim())
+    .filter((s) => s.length >= 40 && s.length <= 220)
+  const out: string[] = []
+  for (const p of parts) {
+    if (out.length >= max) break
+    if (!out.some((x) => x.slice(0, 40) === p.slice(0, 40))) out.push(p)
+  }
+  return out
+}
+
+export function extractSourceAssets(raw: string): SourceAssets {
+  const formulas = extractFormulas(raw)
+  const numbers = extractNumbers(raw)
+  const keySentences = extractKeySentences(raw)
+  const wordCount = raw.replace(/<[^>]+>/g, ' ').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),
+    hasNumbers: numbers.length >= 2,
+    wordCount,
+  }
+}