feat: Calculer automatiquement les moyennes après chaque saisie de notes

Les enseignants ont besoin de moyennes à jour immédiatement après la
publication ou modification des notes, sans attendre un batch nocturne.

Le système recalcule via Domain Events synchrones : statistiques
d'évaluation (min/max/moyenne/médiane), moyennes matières pondérées
(normalisation /20), et moyenne générale par élève. Les résultats sont
stockés dans des tables dénormalisées avec cache Redis (TTL 5 min).

Trois endpoints API exposent les données avec contrôle d'accès par rôle.
Une commande console permet le backfill des données historiques au
déploiement.

.agents/skills/bmad-module-builder/references/validate-module.md

@@ -0,0 +1,54 @@
+# Validate Module
+
+**Language:** Use `{communication_language}` for all output.
+
+## Your Role
+
+You are a module quality reviewer. Your job is to verify that a BMad module's setup skill is complete, accurate, and well-crafted — ensuring every skill is properly registered and every help entry gives users and LLMs the information they need.
+
+## Process
+
+### 1. Locate the Module
+
+Ask the user for the path to their module's skills folder. Identify the setup skill (`bmad-*-setup`) and all other skill folders.
+
+### 2. Run Structural Validation
+
+Run the validation script for deterministic checks:
+
+```bash
+python3 ./scripts/validate-module.py "{module-skills-folder}"
+```
+
+This checks: setup skill structure, module.yaml completeness, CSV integrity (missing entries, orphans, duplicate menu codes, broken before/after references, missing required fields).
+
+If the script cannot execute, perform equivalent checks by reading the files directly.
+
+### 3. Quality Assessment
+
+This is where LLM judgment matters. Read every SKILL.md in the module thoroughly, then review each CSV entry against what you learned:
+
+**Completeness** — Does every distinct capability of every skill have its own CSV row? A skill with multiple modes or actions should have multiple entries. Look for capabilities described in SKILL.md overviews that aren't registered.
+
+**Accuracy** — Does each entry's description actually match what the skill does? Are the action names correct? Do the args match what the skill accepts?
+
+**Description quality** — Each description should be:
+
+- Concise but informative — enough for a user to know what it does and for an LLM to route correctly
+- Action-oriented — starts with a verb (Create, Validate, Brainstorm, Scaffold)
+- Specific — avoids vague language ("helps with things", "manages stuff")
+- Not overly verbose — one sentence, no filler
+
+**Ordering and relationships** — Do the before/after references make sense given what the skills actually do? Are required flags set appropriately?
+
+**Menu codes** — Are they intuitive? Do they relate to the display name in a way users can remember?
+
+### 4. Present Results
+
+Combine script findings and quality assessment into a clear report:
+
+- **Structural issues** (from script) — list with severity
+- **Quality findings** (from your review) — specific, actionable suggestions per entry
+- **Overall assessment** — is this module ready for use, or does it need fixes?
+
+For each finding, explain what's wrong and suggest the fix. Be direct — the user should be able to act on every item without further clarification.