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/tests/unit/slide-source-assets.test.ts

@@ -0,0 +1,133 @@
+import { describe, expect, it } from 'vitest'
+import { extractFormulas, extractSourceAssets } from '@/lib/ai/services/slide-source-assets'
+import {
+  assertDeckHasSubstance,
+  injectEquationSlidesFromFormulas,
+  normalizeSlideDeck,
+} from '@/lib/ai/services/slide-content-quality'
+import { buildPresentationHTML } from '@/lib/ai/tools/slides-html-builder'
+import { encodeSlideIntentDescription, decodeSlideIntentDescription } from '@/lib/ai/services/slide-intent'
+
+describe('extractFormulas for STEM notes', () => {
+  it('extracts display math $$...$$', () => {
+    const text = 'On étudie $$\\frac{dy}{dx} + P(x)y = Q(x)$$ et la solution.'
+    const f = extractFormulas(text)
+    expect(f.some((x) => x.includes('dy') || x.includes('frac'))).toBe(true)
+  })
+
+  it('extracts equation-like lines', () => {
+    const text = 'La dérivée:\ny\' + 2y = e^x\nPuis on intègre.'
+    const f = extractFormulas(text)
+    expect(f.length).toBeGreaterThan(0)
+  })
+
+  it('flags math domain for differential equations notes', () => {
+    const assets = extractSourceAssets(
+      'Cours sur les équations différentielles. $$y\' + P(x)y = Q(x)$$. Méthode du facteur intégrant.',
+    )
+    expect(assets.hasMath).toBe(true)
+    expect(assets.formulas.length).toBeGreaterThan(0)
+  })
+})
+
+describe('equation slides render with katex hooks', () => {
+  it('emits data-latex and katex CDN for equation slides', () => {
+    const deck = normalizeSlideDeck({
+      title: 'EDO',
+      theme: 'clinical-precision',
+      slides: [
+        { type: 'title', title: 'Équations différentielles', subtitle: 'Cours' },
+        {
+          type: 'equation',
+          title: 'Forme générale',
+          equations: [{ latex: "y' + P(x)y = Q(x)", label: 'Linéaire 1er ordre' }],
+          explanation: 'Forme standard',
+        },
+        {
+          type: 'bullets',
+          title: 'Méthode',
+          items: ['Identifier P et Q', 'Calculer le facteur intégrant', 'Intégrer les deux membres'],
+        },
+        {
+          type: 'summary',
+          title: 'À retenir',
+          items: ['Forme standard', 'Facteur intégrant', 'Condition initiale'],
+        },
+      ],
+    })
+    expect(assertDeckHasSubstance(deck).ok).toBe(true)
+    const html = buildPresentationHTML({
+      title: deck.title,
+      theme: deck.theme,
+      slides: deck.slides as any,
+    })
+    expect(html).toContain('katex')
+    expect(html).toContain('data-latex')
+    expect(html).toContain("y' + P(x)y = Q(x)")
+    // cards grid must not force 2 empty columns for 1 card
+    const oneCard = buildPresentationHTML({
+      title: 't',
+      theme: 'architectural-saas',
+      slides: [
+        { type: 'title', title: 'T' },
+        {
+          type: 'cards',
+          title: 'One',
+          cards: [{ title: 'Seul', description: 'Plein largeur' }],
+        },
+        { type: 'summary', title: 'S', items: ['a', 'b'] },
+      ] as any,
+    })
+    expect(oneCard).toContain('repeat(1,minmax(0,1fr))')
+  })
+})
+
+describe('STEM gate + model + intent', () => {
+  it('fails substance when formulas required but no equation latex', () => {
+    const deck = normalizeSlideDeck({
+      title: 'EDO',
+      slides: [
+        { type: 'title', title: 'EDO' },
+        { type: 'bullets', title: 'Intro', items: ['a', 'b', 'c'] },
+        { type: 'summary', title: 'Fin', items: ['x', 'y'] },
+      ],
+    })
+    const gate = assertDeckHasSubstance(deck, {
+      requireFormulas: ["y' + P y = Q"],
+    })
+    expect(gate.ok).toBe(false)
+  })
+
+  it('injects equation slides from formulas', () => {
+    const thin = normalizeSlideDeck({
+      title: 'EDO',
+      theme: 'clinical-precision',
+      slides: [
+        { type: 'title', title: 'EDO', subtitle: 'Cours' },
+        { type: 'bullets', title: 'Méthode', items: ['A', 'B', 'C'] },
+        { type: 'summary', title: 'Fin', items: ['1', '2'] },
+      ],
+    })
+    const filled = injectEquationSlidesFromFormulas(thin, ["y' + P(x)y = Q(x)", '\\mu(x) = e^{\\int P}'], {
+      lang: 'fr',
+    })
+    expect(filled.slides.some((s) => s.type === 'equation')).toBe(true)
+    const gate = assertDeckHasSubstance(filled, {
+      requireFormulas: ["y' + P(x)y = Q(x)"],
+    })
+    expect(gate.ok).toBe(true)
+  })
+
+  it('encodes and decodes slide intent', () => {
+    const enc = encodeSlideIntentDescription({
+      purpose: 'course',
+      audience: 'student',
+      slideCount: 6,
+      template: 'auto',
+    })
+    const dec = decodeSlideIntentDescription(enc)
+    expect(dec.purpose).toBe('course')
+    expect(dec.audience).toBe('student')
+    expect(dec.slideCount).toBe(6)
+  })
+})