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/interactive-page/constants.ts

@@ -8,7 +8,7 @@ export const INTERACTIVE_PAGE_CAPS = {
   maxDemosPerPage: 5,
   maxSimsPerPage: 3,
   maxOverviewCards: 4,
-  minOverviewCards: 2,
+  minOverviewCards: 3,
   maxStatsItems: 5,
   minStatsItems: 2,
   maxJsonBytes: 128 * 1024,
@@ -30,8 +30,14 @@ export const PAGE_BLOCK_TYPES = [
   'table',
   'image',
   'sim',
+  'steps',
 ] as const
 
+export const STEPS_CAPS = {
+  minSteps: 2,
+  maxSteps: 12,
+} as const
+
 export const CALLOUT_KINDS = [
   'definition',
   'warning',
@@ -69,6 +75,8 @@ export const PAGE_HUMAN_STRING_KEYS = [
   'intro',
   'xLabel',
   'yLabel',
+  // steps blocks
+  'rule',
   // inherited from demos (speak etc. scanned via demo validator)
   'speak',
   'text',

memento-note/lib/interactive-page/fixtures/thermo-page.json

@@ -63,6 +63,33 @@
             "simId": "ts-diagram"
           },
           "caption": "Le même cycle sur le diagramme T–s : les aires sont les chaleurs échangées."
+        },
+        {
+          "type": "steps",
+          "title": "Le COP frigorifique, dérivé pas à pas",
+          "steps": [
+            {
+              "tex": "\\eta_{\\text{Carnot}} = 1 - \\frac{T_c}{T_h}",
+              "rule": "Point de départ — rendement de Carnot",
+              "speak": "Le rendement maximal d'un moteur entre $T_h$ et $T_c$ ne dépend que des températures."
+            },
+            {
+              "tex": "\\mathrm{COP}_{\\text{PAC}} = \\frac{1}{\\eta_{\\text{Carnot}}} = \\frac{T_h}{T_h - T_c}",
+              "rule": "Inversion — pompe à chaleur",
+              "speak": "La pompe à chaleur est l'inverse du moteur : son COP est l'inverse du rendement."
+            },
+            {
+              "tex": "\\mathrm{COP}_{\\text{frigo}} = \\mathrm{COP}_{\\text{PAC}} - 1 = \\frac{T_c}{T_h - T_c}",
+              "rule": "Soustraction de 1 — réfrigérateur",
+              "speak": "Le frigo ne compte que la chaleur utile $Q_c$ : on retire 1 au COP de la PAC."
+            },
+            {
+              "tex": "\\mathrm{COP}_{\\text{frigo}} = \\frac{260}{300 - 260} = 6{,}5",
+              "rule": "Application numérique",
+              "speak": "Avec $T_c = 260$ K et $T_h = 300$ K : le COP maximal vaut 6,5."
+            }
+          ],
+          "caption": "Chaque ligne découle de la précédente — la règle appliquée est en marge."
         }
       ]
     },

memento-note/lib/interactive-page/index.ts

@@ -4,6 +4,7 @@ export {
   PAGE_BLOCK_TYPES,
   CALLOUT_KINDS,
   PAGE_HUMAN_STRING_KEYS,
+  STEPS_CAPS,
   isPageHumanStringKey,
 } from './constants'
 export { pageSpecV1Schema, pageBlockSchema } from './schema'
@@ -22,4 +23,6 @@ export type {
   CatalogSimRef,
   GenericFormulaSim,
   SimBlock,
+  StepsBlock,
+  DerivationStep,
 } from './types'

memento-note/lib/interactive-page/normalize.ts

@@ -189,6 +189,31 @@ function normalizeBlock(
     return out
   }
 
+  if (type === 'steps' || type === 'derivation' || type === 'walkthrough' || type === 'solution' || type === 'proof') {
+    const rawSteps = Array.isArray(obj.steps) ? obj.steps : []
+    const steps = rawSteps
+      .map((st) => {
+        const r = asRecord(st)
+        if (!r) return null
+        const tex = asString(r.tex) || asString(r.latex) || asString(r.equation) || asString(r.math)
+        if (!tex) return null
+        const out: Record<string, unknown> = { tex }
+        const rule = asString(r.rule) || asString(r.transform) || asString(r.action) || asString(r.operation)
+        const speak = asString(r.speak) || asString(r.note) || asString(r.comment)
+        if (rule) out.rule = rule
+        if (speak) out.speak = speak
+        return out
+      })
+      .filter(Boolean)
+    if (steps.length < 2) return null
+    const out: Record<string, unknown> = { type: 'steps', steps }
+    const title = asString(obj.title)
+    if (title) out.title = title
+    const caption = asString(obj.caption)
+    if (caption) out.caption = caption
+    return out
+  }
+
   return null
 }
 

memento-note/lib/interactive-page/schema.ts

@@ -7,7 +7,9 @@ import {
   INTERACTIVE_PAGE_SCHEMA_VERSION,
   PAGE_BLOCK_TYPES,
   SIM_CAPS,
+  STEPS_CAPS,
 } from './constants'
+import { isValidSimParamId } from './sim-eval'
 
 const intentSchema = z.enum(INTENT_IDS).optional()
 
@@ -90,6 +92,9 @@ const imageBlock = z.object({
 const simParamIdSchema = z
   .string()
   .regex(/^[A-Za-z_][A-Za-z0-9_]*$/, 'Invalid sim identifier')
+  .refine(isValidSimParamId, {
+    message: 'Identifier collides with a reserved constant/function',
+  })
 
 const genericSimParamSchema = z.object({
   id: simParamIdSchema,
@@ -150,6 +155,22 @@ const simBlock = z.object({
   caption: z.string().optional(),
 })
 
+const stepsBlock = z.object({
+  type: z.literal('steps'),
+  title: z.string().optional(),
+  steps: z
+    .array(
+      z.object({
+        tex: z.string().min(1),
+        rule: z.string().optional(),
+        speak: z.string().optional(),
+      })
+    )
+    .min(STEPS_CAPS.minSteps)
+    .max(STEPS_CAPS.maxSteps),
+  caption: z.string().optional(),
+})
+
 export const pageBlockSchema = z.discriminatedUnion('type', [
   proseBlock,
   formulaBlock,
@@ -160,6 +181,7 @@ export const pageBlockSchema = z.discriminatedUnion('type', [
   tableBlock,
   imageBlock,
   simBlock,
+  stepsBlock,
 ])
 
 const sectionSchema = z.object({
@@ -199,7 +221,7 @@ export const pageSpecV1Schema = z.object({
   overview: overviewSchema.optional(),
   sections: z
     .array(sectionSchema)
-    .min(1)
+    .min(2)
     .max(INTERACTIVE_PAGE_CAPS.maxSections),
   footer: z.string().optional(),
 })

memento-note/lib/interactive-page/types.ts

@@ -115,6 +115,27 @@ export type SimBlock = {
   caption?: string
 }
 
+/**
+ * Step-by-step derivation (Symbolab/Khan style): equation states revealed
+ * line by line with the transformation rule used at each step. Fully
+ * generic — the LLM writes KaTeX + rules, the app renders; no drawing.
+ */
+export type DerivationStep = {
+  /** KaTeX of the equation state at this step. */
+  tex: string
+  /** Transformation rule applied to reach this state (e.g. "on sépare les variables"). */
+  rule?: string
+  /** Narration for the Play/Step player (falls back to rule). */
+  speak?: string
+}
+
+export type StepsBlock = {
+  type: 'steps'
+  title?: string
+  steps: DerivationStep[]
+  caption?: string
+}
+
 export type PageBlock =
   | ProseBlock
   | FormulaBlock
@@ -125,6 +146,7 @@ export type PageBlock =
   | TableBlock
   | ImageBlock
   | SimBlock
+  | StepsBlock
 
 export type PageSection = {
   id: string

memento-note/lib/interactive-page/validate.ts

@@ -6,7 +6,7 @@ import {
   isPageHumanStringKey,
 } from './constants'
 import { pageSpecV1Schema } from './schema'
-import { validateSimExprRefs } from './sim-eval'
+import { validateSimExprRefs, isValidSimParamId } from './sim-eval'
 import type {
   PageBlock,
   PageSpecV1,
@@ -79,6 +79,13 @@ function validateSim(
   if (sim.simId === 'generic-formula') {
     const generic = sim as Extract<typeof sim, { simId: 'generic-formula' }>
     const paramIds = new Set(generic.params.map((p) => p.id))
+    if (paramIds.size !== generic.params.length) {
+      out.push(issue('sim_duplicate_id', `${path}.params`, 'Duplicate param id'))
+    }
+    const computedIds = new Set(generic.computed.map((c) => c.id))
+    if (computedIds.size !== generic.computed.length) {
+      out.push(issue('sim_duplicate_id', `${path}.computed`, 'Duplicate computed id'))
+    }
     for (const p of generic.params) {
       if (p.min >= p.max) {
         out.push(issue('sim_param_range', `${path}.params`, `Param "${p.id}": min >= max`))